Finite Group Databasebeta

← C31×#36856 #21493615

Subgroups — C31×#36856 #21493615

Order 7936.

2112 conjugacy classes of subgroups.

The subgroup lattice has 1674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2849C211yesmaximal, characteristic, complemented
2C31×#2847C211yesmaximal, characteristic, complemented
3C31×#2797C211yesmaximal, characteristic, complemented
4C31×#2782C211yesmaximal, characteristic, complemented
5C31×#2780C211yesmaximal, characteristic, complemented
6C31×#2750C211yesmaximal, characteristic, complemented
7C31×#2744C211yesmaximal, characteristic, complemented
8C31×#2708C211yesmaximal, characteristic, complemented
9C31×#2697C211yesmaximal, characteristic, complemented
10C31×#2693C211yesmaximal, characteristic, complemented
11C31×#2693C211yesmaximal, characteristic, complemented
12C31×#2688C211yesmaximal, characteristic, complemented
13C31×#2688C211yesmaximal, characteristic, complemented
14C31×#2682C211yesmaximal, characteristic, complemented
15C31×#2678C211yesmaximal, characteristic, complemented
16C31×#2673C211yesmaximal, characteristic, complemented
17C31×#2669C211yesmaximal, characteristic, complemented
18C31×#2668C211yesmaximal, characteristic, complemented
19C31×#2649C211yesmaximal, characteristic, complemented
20C31×#2648C211yesmaximal, characteristic, complemented
21C31×#2530C211yesmaximal, characteristic, complemented
22C31×#2526C211yesmaximal, characteristic, complemented
23C31×#2464C211yesmaximal, characteristic, complemented
24C31×#2457C211yesmaximal, characteristic, complemented
25C31×#2456C211yesmaximal, characteristic, complemented
26C31×#2456C211yesmaximal, characteristic, complemented
27C31×#2444C211yesmaximal, characteristic, complemented
28C31×#2425C211yesmaximal, characteristic, complemented
29C31×#2328C211yesmaximal, characteristic, complemented
30C31×#2325C211yesmaximal, characteristic, complemented
31C4×C31×#120C211yesmaximal, characteristic, complemented
32C24×C4×C31C2211yescharacteristic
33C2×C31×#127C2211yescharacteristic
34C2×C31×#123C2211yescharacteristic
35C2×C31×#123C2211yescharacteristic
36C2×C31×#123C2211yescharacteristic
37C2×C31×#123C2211yescharacteristic
38C2×C31×#123C2211yescharacteristic, complemented
39C2×C31×#123C2211yescharacteristic, complemented
40C2×C31×#121C2211yescharacteristic
41C2×C31×#121C2211yescharacteristic
42C2×C31×#121C2211yescharacteristic
43C2×C31×#121C2211yescharacteristic
44C2×C31×#121C2211yescharacteristic
45C2×C31×#121C2211yescharacteristic
46C2×C31×#121C2211yescharacteristic
47C2×C31×#121C2211yescharacteristic
48C2×C31×#120C2211yescharacteristic
49C2×C31×#120C2211yescharacteristic
50C2×C31×#120C2211yescharacteristic
51C2×C31×#120C2211yescharacteristic
52C2×C4×D4×C31C2211yescharacteristic
53C2×C4×D4×C31C2211yescharacteristic
54C2×C4×D4×C31C2211yescharacteristic
55C2×C4×D4×C31C2211yescharacteristic, complemented
56C2×C4×D4×C31C2211yescharacteristic, complemented
57C31×#400C2211yescharacteristic, complemented
58C31×#400C2211yescharacteristic, complemented
59C31×#400C2211yescharacteristic, complemented
60C31×#400C2211yescharacteristic, complemented
61C31×#400C2211yescharacteristic, complemented
62C31×#400C2211yescharacteristic, complemented
63C31×#400C2211yescharacteristic, complemented
64C31×#400C2211yescharacteristic, complemented
65C31×#399C2211yescharacteristic
66C31×#398C2211yescharacteristic, complemented
67C31×#398C2211yescharacteristic, complemented
68C31×#397C2211yescharacteristic
69C31×#397C2211yescharacteristic
70C31×#397C2211yescharacteristic
71C31×#397C2211yescharacteristic
72C31×#397C2211yescharacteristic
73C31×#397C2211yescharacteristic, complemented
74C31×#397C2211yescharacteristic, complemented
75C31×#397C2211yescharacteristic, complemented
76C31×#397C2211yescharacteristic, complemented
77C31×#397C2211yescharacteristic, complemented
78C31×#396C2211yescharacteristic
79C31×#396C2211yescharacteristic
80C31×#396C2211yescharacteristic
81C31×#396C2211yescharacteristic, complemented
82C31×#396C2211yescharacteristic, complemented
83C31×#396C2211yescharacteristic, complemented
84C31×#396C2211yescharacteristic, complemented
85C31×#394C2211yescharacteristic
86C31×#394C2211yescharacteristic
87C31×#394C2211yescharacteristic
88C31×#394C2211yescharacteristic
89C31×#394C2211yescharacteristic
90C31×#394C2211yescharacteristic
91C31×#394C2211yescharacteristic
92C31×#394C2211yescharacteristic
93C31×#394C2211yescharacteristic, complemented
94C31×#394C2211yescharacteristic, complemented
95C31×#392C2211yescharacteristic
96C31×#392C2211yescharacteristic
97C31×#392C2211yescharacteristic
98C31×#392C2211yescharacteristic
99C31×#392C2211yescharacteristic
100C31×#392C2211yescharacteristic
101C31×#392C2211yescharacteristic
102C31×#392C2211yescharacteristic, complemented
103C31×#392C2211yescharacteristic, complemented
104C31×#392C2211yescharacteristic, complemented
105C31×#390C2211yescharacteristic
106C31×#390C2211yescharacteristic
107C31×#390C2211yescharacteristic
108C31×#390C2211yescharacteristic, complemented
109C31×#390C2211yescharacteristic, complemented
110C31×#389C2211yescharacteristic, complemented
111C31×#389C2211yescharacteristic, complemented
112C31×#388C2211yescharacteristic
113C31×#388C2211yescharacteristic
114C31×#388C2211yescharacteristic
115C31×#388C2211yescharacteristic
116C31×#388C2211yescharacteristic
117C31×#388C2211yescharacteristic, complemented
118C31×#388C2211yescharacteristic, complemented
119C31×#388C2211yescharacteristic, complemented
120C31×#388C2211yescharacteristic, complemented
121C31×#388C2211yescharacteristic, complemented
122C31×#388C2211yescharacteristic, complemented
123C31×#388C2211yescharacteristic, complemented
124C31×#387C2211yescharacteristic, complemented
125C31×#387C2211yescharacteristic, complemented
126C31×#387C2211yescharacteristic, complemented
127C31×#387C2211yescharacteristic, complemented
128C31×#387C2211yescharacteristic, complemented
129C31×#387C2211yescharacteristic, complemented
130C31×#387C2211yescharacteristic, complemented
131C31×#386C2211yescharacteristic
132C31×#386C2211yescharacteristic
133C31×#386C2211yescharacteristic
134C31×#386C2211yescharacteristic
135C31×#386C2211yescharacteristic
136C31×#386C2211yescharacteristic
137C31×#386C2211yescharacteristic
138C31×#386C2211yescharacteristic
139C31×#386C2211yescharacteristic
140C31×#386C2211yescharacteristic
141C31×#386C2211yescharacteristic
142C31×#386C2211yescharacteristic
143C31×#386C2211yescharacteristic
144C31×#386C2211yescharacteristic
145C31×#386C2211yescharacteristic
146C31×#386C2211yescharacteristic
147C31×#386C2211yescharacteristic
148C31×#386C2211yescharacteristic
149C31×#386C2211yescharacteristic
150C31×#386C2211yescharacteristic
151C31×#386C2211yescharacteristic
152C31×#386C2211yescharacteristic, complemented
153C31×#386C2211yescharacteristic, complemented
154C31×#386C2211yescharacteristic, complemented
155C31×#386C2211yescharacteristic, complemented
156C31×#386C2211yescharacteristic, complemented
157C31×#386C2211yescharacteristic, complemented
158C31×#386C2211yescharacteristic, complemented
159C31×#385C2211yescharacteristic
160C31×#385C2211yescharacteristic
161C31×#385C2211yescharacteristic
162C31×#385C2211yescharacteristic
163C31×#385C2211yescharacteristic
164C31×#385C2211yescharacteristic
165C31×#385C2211yescharacteristic
166C31×#385C2211yescharacteristic, complemented
167C31×#385C2211yescharacteristic, complemented
168C31×#385C2211yescharacteristic, complemented
169C31×#385C2211yescharacteristic, complemented
170C31×#385C2211yescharacteristic, complemented
171C31×#382C2211yescharacteristic, complemented
172C31×#381C2211yescharacteristic
173C31×#381C2211yescharacteristic
174C31×#381C2211yescharacteristic, complemented
175C31×#380C2211yescharacteristic
176C31×#380C2211yescharacteristic
177C31×#380C2211yescharacteristic
178C31×#380C2211yescharacteristic, complemented
179C31×#380C2211yescharacteristic, complemented
180C31×#379C2211yescharacteristic
181C31×#379C2211yescharacteristic
182C4×C22⋊C4×C31C2211yescharacteristic
183C4×C22⋊C4×C31C2211yescharacteristic
184C4×C22⋊C4×C31C2211yescharacteristic
185C31×#376C2211yescharacteristic, complemented
186C2×C31×#95C2211yescharacteristic, complemented
187C25×C31C2311yescharacteristic
188C22×D4×C31C2311yescharacteristic
189C22×D4×C31C2311yescharacteristic
190C22×D4×C31C2311yescharacteristic
191C22×D4×C31C2311yescharacteristic
192C22×D4×C31C2311yescharacteristic
193C22×D4×C31C2311yescharacteristic
194C22×D4×C31C2311yescharacteristic
195C22×D4×C31C2311yescharacteristic
196C22×D4×C31C2311yescharacteristic
197C22×D4×C31C2311yescharacteristic
198C22×D4×C31C2311yescharacteristic
199C22×D4×C31C2311yescharacteristic
200C22×D4×C31C2311yescharacteristic
201C22×D4×C31C2311yescharacteristic
202C22×D4×C31C2311yescharacteristic
203C22×D4×C31C2311yescharacteristic
204C22×D4×C31C2311yescharacteristic
205C22×D4×C31C2311yescharacteristic
206C23×C4×C31—42no—
207C23×C4×C31—42no—
208C23×C4×C31—42no—
209C23×C4×C31C2311yescharacteristic
210C23×C4×C31C2311yescharacteristic
211C23×C4×C31C2311yescharacteristic
212C23×C4×C31C2311yescharacteristic
213C23×C4×C31C2311yescharacteristic
214C23×C4×C31C2311yescharacteristic
215C23×C4×C31C2311yescharacteristic
216C23×C4×C31C2311yescharacteristic
217C23×C4×C31C2311yescharacteristic
218C23×C4×C31C2311yescharacteristic
219C23×C4×C31C2311yescharacteristic
220C23×C4×C31C2311yescharacteristic
221C31×#127—24no—
222C31×#123—42no—
223C31×#123—42no—
224C31×#123—42no—
225C31×#123—42no—
226C31×#123—42no—
227C31×#123—42no—
228C31×#121—24no—
229C31×#121—42no—
230C31×#121—42no—
231C31×#121—42no—
232C31×#121—42no—
233C31×#121—42no—
234C31×#121—42no—
235C31×#121—42no—
236C31×#120—24no—
237C31×#120—42no—
238C31×#120—42no—
239C31×#120—42no—
240C4×D4×C31—42no—
241C4×D4×C31—42no—
242C4×D4×C31—42no—
243C4×D4×C31—42no—
244C4×D4×C31—42no—
245C2×C4⋊C4×C31C2311yescharacteristic
246C2×C4⋊C4×C31C2311yescharacteristic
247C2×C4⋊C4×C31C2311yescharacteristic
248C2×C4⋊C4×C31C2311yescharacteristic
249C2×C4⋊C4×C31C2311yescharacteristic
250C2×C4⋊C4×C31C2311yescharacteristic
251C2×C4⋊C4×C31C2311yescharacteristic
252C2×C4⋊C4×C31C2311yescharacteristic
253C2×C4⋊C4×C31C2311yescharacteristic
254C2×C4⋊C4×C31C2311yescharacteristic
255C2×C4⋊C4×C31C2311yescharacteristic
256C2×C4⋊C4×C31C2311yescharacteristic
257C2×C4⋊C4×C31C2311yescharacteristic
258C2×C4⋊C4×C31C2311yescharacteristic
259C2×C4⋊C4×C31C2311yescharacteristic
260C2×C4⋊C4×C31C2311yescharacteristic
261C2×C4⋊C4×C31C2311yescharacteristic
262C2×C4⋊C4×C31C2311yescharacteristic
263C2×C4⋊C4×C31C2311yescharacteristic
264C2×C4⋊C4×C31C2311yescharacteristic
265C2×C4⋊C4×C31C2311yescharacteristic
266C2×C4⋊C4×C31C2311yescharacteristic
267C2×C4⋊C4×C31C2311yescharacteristic
268C2×C4⋊C4×C31C2311yescharacteristic
269C2×C22⋊C4×C31C2311yescharacteristic
270C2×C22⋊C4×C31C2311yescharacteristic
271C2×C22⋊C4×C31C2311yescharacteristic
272C2×C22⋊C4×C31C2311yescharacteristic
273C2×C22⋊C4×C31C2311yescharacteristic
274C2×C22⋊C4×C31C2311yescharacteristic
275C2×C22⋊C4×C31C2311yescharacteristic
276C2×C22⋊C4×C31C2311yescharacteristic
277C2×C22⋊C4×C31C2311yescharacteristic
278C2×C22⋊C4×C31C2311yescharacteristic
279C2×C22⋊C4×C31C2311yescharacteristic
280C2×C22⋊C4×C31C2311yescharacteristic
281C2×C22⋊C4×C31C2311yescharacteristic
282C2×C22⋊C4×C31C2311yescharacteristic
283C2×C22⋊C4×C31C2311yescharacteristic
284C2×C22⋊C4×C31C2311yescharacteristic
285C2×C22⋊C4×C31C2311yescharacteristic
286C2×C22⋊C4×C31C2311yescharacteristic
287C2×C22⋊C4×C31C2311yescharacteristic
288C2×C22⋊C4×C31C2311yescharacteristic
289C2×C22⋊C4×C31C2311yescharacteristic
290C2×C22⋊C4×C31C2311yescharacteristic
291C2×C22⋊C4×C31C2311yescharacteristic
292C2×C22⋊C4×C31C2311yescharacteristic
293C2×C22⋊C4×C31C2311yescharacteristic
294C2×C22⋊C4×C31C2311yescharacteristic
295C2×C22⋊C4×C31C2311yescharacteristic
296C2×C22⋊C4×C31C2311yescharacteristic
297C2×C22⋊C4×C31C2311yescharacteristic
298C2×C22⋊C4×C31C2311yescharacteristic
299C2×C22⋊C4×C31C2311yescharacteristic
300C2×C22⋊C4×C31C2311yescharacteristic
301C2×C22⋊C4×C31C2311yescharacteristic
302C2×C22⋊C4×C31C2311yescharacteristic
303C2×C22⋊C4×C31C2311yescharacteristic
304C2×C22⋊C4×C31C2311yescharacteristic
305C2×C22⋊C4×C31C2311yescharacteristic
306C2×C22⋊C4×C31C2311yescharacteristic
307C2×C22⋊C4×C31C2311yescharacteristic
308C2×C22⋊C4×C31C2311yescharacteristic
309C2×C22⋊C4×C31C2311yescharacteristic
310C2×C22⋊C4×C31C2311yescharacteristic
311C2×C22⋊C4×C31C2311yescharacteristic
312C2×C22⋊C4×C31C2311yescharacteristic
313C2×C22⋊C4×C31C2311yescharacteristic
314C2×C22⋊C4×C31C2311yescharacteristic
315C2×C22⋊C4×C31C2311yescharacteristic
316C2×C22⋊C4×C31C2311yescharacteristic
317C2×C22⋊C4×C31C2311yescharacteristic
318C2×C22⋊C4×C31C2311yescharacteristic
319C2×C22⋊C4×C31C2311yescharacteristic
320C2×C22⋊C4×C31C2311yescharacteristic
321C2×C22⋊C4×C31C2311yescharacteristic
322C2×C22⋊C4×C31C2311yescharacteristic
323C2×C42×C31C2311yescharacteristic
324C2×C42×C31C2311yescharacteristic
325C2×C42×C31C2311yescharacteristic
326C2×C42×C31C2311yescharacteristic
327C2×C42×C31C2311yescharacteristic
328C2×C42×C31C2311yescharacteristic
329C31×#95C2311yescharacteristic
330C31×#95C2311yescharacteristic
331C31×#95C2311yescharacteristic
332C31×#95C2311yescharacteristic
333C31×#95C2311yescharacteristic
334C31×#95C2311yescharacteristic
335C31×#95C2311yescharacteristic
336C31×#95C2311yescharacteristic
337C31×#95C2311yescharacteristic
338C31×#95C2311yescharacteristic
339C31×#95C2311yescharacteristic
340C31×#95C2311yescharacteristic
341C31×#95C2311yescharacteristic
342C31×#95C2311yescharacteristic
343C31×#95C2311yescharacteristic
344C31×#95C2311yescharacteristic
345C31×#95C2311yescharacteristic
346C31×#95C2311yescharacteristic
347C31×#95C2311yescharacteristic
348C31×#95C2311yescharacteristic
349C31×#95C2311yescharacteristic
350C31×#95C2311yescharacteristic
351C31×#95C2311yescharacteristic
352C31×#95C2311yescharacteristic
353C31×#95C2311yescharacteristic
354C31×#95C2311yescharacteristic
355C31×#95C2311yescharacteristic
356C31×#95C2311yescharacteristic
357C31×#95C2311yescharacteristic
358C31×#95C2311yescharacteristic
359C31×#95C2311yescharacteristic
360C31×#95C2311yescharacteristic
361C31×#95C2311yescharacteristic
362C31×#95C2311yescharacteristic
363C31×#95C2311yescharacteristic
364C31×#95C2311yescharacteristic
365C31×#95C2311yescharacteristic
366C31×#95C2311yescharacteristic
367C31×#95C2311yescharacteristic
368C31×#95C2311yescharacteristic
369C24×C31—22no—
370C24×C31—22no—
371C24×C31—22no—
372C24×C31—41no—
373C24×C31—41no—
374C24×C31—41no—
375C24×C31—41no—
376C24×C31C2411yescharacteristic
377C24×C31C2411yescharacteristic
378C24×C31C2411yescharacteristic
379C24×C31C2411yescharacteristic
380C24×C31C2411yescharacteristic
381C24×C31C2411yescharacteristic
382C24×C31C2411yescharacteristic
383C2×D4×C31—22no—
384C2×D4×C31—22no—
385C2×D4×C31—22no—
386C2×D4×C31—22no—
387C2×D4×C31—22no—
388C2×D4×C31—22no—
389C2×D4×C31—22no—
390C2×D4×C31—22no—
391C2×D4×C31—22no—
392C2×D4×C31—22no—
393C2×D4×C31—22no—
394C2×D4×C31—22no—
395C2×D4×C31—22no—
396C2×D4×C31—22no—
397C2×D4×C31—22no—
398C2×D4×C31—22no—
399C2×D4×C31—22no—
400C2×D4×C31—22no—
401C2×D4×C31—41no—
402C2×D4×C31—41no—
403C2×D4×C31—41no—
404C2×D4×C31—41no—
405C2×D4×C31—41no—
406C2×D4×C31—41no—
407C2×D4×C31—41no—
408C2×D4×C31—41no—
409C2×D4×C31—41no—
410C2×D4×C31—41no—
411C2×D4×C31—41no—
412C2×D4×C31—41no—
413C2×D4×C31—41no—
414C2×D4×C31—41no—
415C2×D4×C31—41no—
416C2×D4×C31—41no—
417C2×D4×C31—41no—
418C2×D4×C31—41no—
419C2×D4×C31—41no—
420C2×D4×C31—41no—
421C2×D4×C31—41no—
422C2×D4×C31—41no—
423C2×D4×C31—41no—
424C2×D4×C31—41no—
425C2×D4×C31—41no—
426C2×D4×C31—41no—
427C2×D4×C31—41no—
428C2×D4×C31—41no—
429C2×D4×C31—41no—
430C2×D4×C31—41no—
431C2×D4×C31—41no—
432C2×D4×C31—41no—
433C2×D4×C31—41no—
434C2×D4×C31—41no—
435C2×D4×C31—41no—
436C2×D4×C31#4114yes—
437C22×C4×C31—22no—
438C22×C4×C31—22no—
439C22×C4×C31—22no—
440C22×C4×C31—22no—
441C22×C4×C31—22no—
442C22×C4×C31—22no—
443C22×C4×C31—22no—
444C22×C4×C31—22no—
445C22×C4×C31—22no—
446C22×C4×C31—22no—
447C22×C4×C31—41no—
448C22×C4×C31—41no—
449C22×C4×C31—41no—
450C22×C4×C31—41no—
451C22×C4×C31—41no—
452C22×C4×C31—41no—
453C22×C4×C31—41no—
454C22×C4×C31—41no—
455C22×C4×C31—41no—
456C22×C4×C31—41no—
457C22×C4×C31—41no—
458C22×C4×C31—41no—
459C22×C4×C31—41no—
460C22×C4×C31—41no—
461C22×C4×C31—41no—
462C22×C4×C31—41no—
463C22×C4×C31—41no—
464C22×C4×C31—41no—
465C22×C4×C31—41no—
466C22×C4×C31—41no—
467C22×C4×C31—41no—
468C22×C4×C31—41no—
469C22×C4×C31—41no—
470C22×C4×C31—41no—
471C22×C4×C31—41no—
472C22×C4×C31—41no—
473C22×C4×C31—416no—
474C22×C4×C31C2411yescharacteristic
475C22×C4×C31C2411yescharacteristic
476C22×C4×C31C2411yescharacteristic
477C22×C4×C31C2411yescharacteristic
478C22×C4×C31C2411yescharacteristic
479C22×C4×C31C2411yescharacteristic
480C22×C4×C31C2411yescharacteristic
481C22×C4×C31C2411yescharacteristic
482C22×C4×C31C2411yescharacteristic
483C22×C4×C31C2411yescharacteristic
484C22×C4×C31C2411yescharacteristic
485C22×C4×C31C2411yescharacteristic
486C22×C4×C31C2411yescharacteristic
487C22×C4×C31C2411yescharacteristic
488C22×C4×C31C2411yescharacteristic
489C22×C4×C31C2411yescharacteristic
490C22×C4×C31C2411yescharacteristic
491C22×C4×C31C2411yescharacteristic
492C22×C4×C31C2411yescharacteristic
493C22×C4×C31C2411yescharacteristic
494C22×C4×C31C2411yescharacteristic
495C22×C4×C31C2411yescharacteristic
496C22×C4×C31C2411yescharacteristic
497C22×C4×C31C2411yescharacteristic
498C4⋊C4×C31—22no—
499C4⋊C4×C31—22no—
500C4⋊C4×C31—22no—
501C4⋊C4×C31—22no—
502C4⋊C4×C31—22no—
503C4⋊C4×C31—41no—
504C4⋊C4×C31—41no—
505C4⋊C4×C31—41no—
506C4⋊C4×C31—41no—
507C4⋊C4×C31—41no—
508C4⋊C4×C31—41no—
509C4⋊C4×C31—41no—
510C4⋊C4×C31—41no—
511C4⋊C4×C31—41no—
512C4⋊C4×C31—41no—
513C4⋊C4×C31—41no—
514C4⋊C4×C31—41no—
515C4⋊C4×C31—41no—
516C4⋊C4×C31—41no—
517C4⋊C4×C31—41no—
518C4⋊C4×C31—41no—
519C4⋊C4×C31—41no—
520C4⋊C4×C31—41no—
521C4⋊C4×C31—41no—
522C22⋊C4×C31—22no—
523C22⋊C4×C31—22no—
524C22⋊C4×C31—22no—
525C22⋊C4×C31—22no—
526C22⋊C4×C31—22no—
527C22⋊C4×C31—22no—
528C22⋊C4×C31—22no—
529C22⋊C4×C31—22no—
530C22⋊C4×C31—22no—
531C22⋊C4×C31—22no—
532C22⋊C4×C31—22no—
533C22⋊C4×C31—22no—
534C22⋊C4×C31—22no—
535C22⋊C4×C31—22no—
536C22⋊C4×C31—22no—
537C22⋊C4×C31—22no—
538C22⋊C4×C31—41no—
539C22⋊C4×C31—41no—
540C22⋊C4×C31—41no—
541C22⋊C4×C31—41no—
542C22⋊C4×C31—41no—
543C22⋊C4×C31—41no—
544C22⋊C4×C31—41no—
545C22⋊C4×C31—41no—
546C22⋊C4×C31—41no—
547C22⋊C4×C31—41no—
548C22⋊C4×C31—41no—
549C22⋊C4×C31—41no—
550C22⋊C4×C31—41no—
551C22⋊C4×C31—41no—
552C22⋊C4×C31—41no—
553C22⋊C4×C31—41no—
554C22⋊C4×C31—41no—
555C22⋊C4×C31—41no—
556C22⋊C4×C31—41no—
557C22⋊C4×C31—41no—
558C22⋊C4×C31—41no—
559C22⋊C4×C31—41no—
560C22⋊C4×C31—41no—
561C22⋊C4×C31—41no—
562C22⋊C4×C31—41no—
563C22⋊C4×C31—41no—
564C22⋊C4×C31—41no—
565C22⋊C4×C31—41no—
566C22⋊C4×C31—41no—
567C22⋊C4×C31—41no—
568C22⋊C4×C31—41no—
569C22⋊C4×C31—41no—
570C22⋊C4×C31—41no—
571C22⋊C4×C31—41no—
572C22⋊C4×C31—41no—
573C22⋊C4×C31—41no—
574C22⋊C4×C31—41no—
575C22⋊C4×C31—41no—
576C42×C31—22no—
577C42×C31—22no—
578C42×C31—41no—
579C42×C31—41no—
580C42×C31—41no—
581C42×C31—41no—
582#36856C3111yesmaximal, characteristic, direct product factor, Sylow
583C23×C31—21no—
584C23×C31—21no—
585C23×C31—21no—
586C23×C31—21no—
587C23×C31—21no—
588C23×C31—21no—
589C23×C31—21no—
590C23×C31—21no—
591C23×C31—21no—
592C23×C31—21no—
593C23×C31—21no—
594C23×C31—21no—
595C23×C31—21no—
596C23×C31—21no—
597C23×C31—21no—
598C23×C31—21no—
599C23×C31—21no—
600C23×C31—21no—
601C23×C31—21no—
602C23×C31—21no—
603C23×C31—21no—
604C23×C31—21no—
605C23×C31—21no—
606C23×C31—21no—
607C23×C31—21no—
608C23×C31—21no—
609C23×C31—21no—
610C23×C31—21no—
611C23×C31—21no—
612C23×C31—21no—
613C23×C31—21no—
614C23×C31—21no—
615C23×C31—21no—
616C23×C31—21no—
617C23×C31—21no—
618C23×C31—21no—
619C23×C31—21no—
620C23×C31—21no—
621C23×C31—21no—
622C23×C31—21no—
623C23×C31—21no—
624C23×C31—21no—
625C23×C31—21no—
626C23×C31—21no—
627C23×C31—21no—
628C23×C31—44no—
629C23×C31—44no—
630C23×C31—44no—
631C23×C31—44no—
632C23×C31—44no—
633C23×C31—44no—
634C23×C31—44no—
635C23×C31C2×#4112yes—
636C23×C31C2×#4112yes—
637C23×C31H(5,𝔽2)12yes—
638C23×C31H(5,𝔽2)12yes—
639C23×C31C2511yescharacteristic
640D4×C31—44no—
641D4×C31—44no—
642D4×C31—44no—
643D4×C31—44no—
644D4×C31—44no—
645D4×C31—82no—
646D4×C31—82no—
647D4×C31—82no—
648D4×C31—82no—
649D4×C31—82no—
650D4×C31—82no—
651D4×C31—82no—
652D4×C31—82no—
653D4×C31—82no—
654D4×C31—82no—
655D4×C31—82no—
656D4×C31—82no—
657D4×C31—82no—
658C2×C4×C31—21no—
659C2×C4×C31—21no—
660C2×C4×C31—21no—
661C2×C4×C31—21no—
662C2×C4×C31—21no—
663C2×C4×C31—21no—
664C2×C4×C31—21no—
665C2×C4×C31—21no—
666C2×C4×C31—21no—
667C2×C4×C31—21no—
668C2×C4×C31—21no—
669C2×C4×C31—21no—
670C2×C4×C31—21no—
671C2×C4×C31—21no—
672C2×C4×C31—21no—
673C2×C4×C31—21no—
674C2×C4×C31—21no—
675C2×C4×C31—21no—
676C2×C4×C31—21no—
677C2×C4×C31—21no—
678C2×C4×C31—21no—
679C2×C4×C31—21no—
680C2×C4×C31—21no—
681C2×C4×C31—21no—
682C2×C4×C31—21no—
683C2×C4×C31—21no—
684C2×C4×C31—21no—
685C2×C4×C31—21no—
686C2×C4×C31—21no—
687C2×C4×C31—21no—
688C2×C4×C31—21no—
689C2×C4×C31—21no—
690C2×C4×C31—21no—
691C2×C4×C31—21no—
692C2×C4×C31—21no—
693C2×C4×C31—21no—
694C2×C4×C31—21no—
695C2×C4×C31—21no—
696C2×C4×C31—21no—
697C2×C4×C31—21no—
698C2×C4×C31—21no—
699C2×C4×C31—21no—
700C2×C4×C31—21no—
701C2×C4×C31—21no—
702C2×C4×C31—21no—
703C2×C4×C31—21no—
704C2×C4×C31—21no—
705C2×C4×C31—21no—
706C2×C4×C31—21no—
707C2×C4×C31—21no—
708C2×C4×C31—21no—
709C2×C4×C31—21no—
710C2×C4×C31—21no—
711C2×C4×C31—21no—
712C2×C4×C31—21no—
713C2×C4×C31—21no—
714C2×C4×C31—21no—
715C2×C4×C31—21no—
716C2×C4×C31—21no—
717C2×C4×C31—21no—
718C2×C4×C31—21no—
719C2×C4×C31—21no—
720C2×C4×C31—21no—
721C2×C4×C31—21no—
722C2×C4×C31—21no—
723C2×C4×C31—21no—
724C2×C4×C31—21no—
725C2×C4×C31—21no—
726C2×C4×C31—21no—
727C2×C4×C31—44no—
728C2×C4×C31—44no—
729C2×C4×C31—44no—
730C2×C4×C31—44no—
731C2×C4×C31—44no—
732C2×C4×C31—44no—
733C2×C4×C31—82no—
734C2×C4×C31—82no—
735C2×C4×C31—82no—
736C2×C4×C31—82no—
737C2×C4×C31—82no—
738C2×C4×C31—82no—
739C2×C4×C31C2×#4112yes—
740C2×C4×C31H(5,𝔽2)12yes—
741C2×C4×C31H(5,𝔽2)12yes—
742#2849C2×C3111yescharacteristic, complemented
743#2847C2×C3111yescharacteristic, complemented
744#2797C2×C3111yescharacteristic, complemented
745#2782C2×C3111yescharacteristic, complemented
746#2780C2×C3111yescharacteristic, complemented
747#2750C2×C3111yescharacteristic, complemented
748#2744C2×C3111yescharacteristic, complemented
749#2708C2×C3111yescharacteristic, complemented
750#2697C2×C3111yescharacteristic, complemented
751#2693C2×C3111yescharacteristic, complemented
752#2693C2×C3111yescharacteristic, complemented
753#2688C2×C3111yescharacteristic, complemented
754#2688C2×C3111yescharacteristic, complemented
755#2682C2×C3111yescharacteristic, complemented
756#2678C2×C3111yescharacteristic, complemented
757#2673C2×C3111yescharacteristic, complemented
758#2669C2×C3111yescharacteristic, complemented
759#2668C2×C3111yescharacteristic, complemented
760#2649C2×C3111yescharacteristic, complemented
761#2648C2×C3111yescharacteristic, complemented
762#2530C2×C3111yescharacteristic, complemented
763#2526C2×C3111yescharacteristic, complemented
764#2464C2×C3111yescharacteristic, complemented
765#2457C2×C3111yescharacteristic, complemented
766#2456C2×C3111yescharacteristic, complemented
767#2456C2×C3111yescharacteristic, complemented
768#2444C2×C3111yescharacteristic, complemented
769#2425C2×C3111yescharacteristic, complemented
770#2328C2×C3111yescharacteristic, complemented
771#2325C2×C3111yescharacteristic, complemented
772C4×#120C2×C3111yescharacteristic, complemented
773C22×C31—22no—
774C22×C31—22no—
775C22×C31—22no—
776C22×C31—22no—
777C22×C31—22no—
778C22×C31—22no—
779C22×C31—22no—
780C22×C31—22no—
781C22×C31—22no—
782C22×C31—22no—
783C22×C31—22no—
784C22×C31—22no—
785C22×C31—416no—
786C22×C31—41no—
787C22×C31—41no—
788C22×C31—41no—
789C22×C31—41no—
790C22×C31—41no—
791C22×C31—41no—
792C22×C31—41no—
793C22×C31—41no—
794C22×C31—41no—
795C22×C31—41no—
796C22×C31—41no—
797C22×C31—41no—
798C22×C31—41no—
799C22×C31—41no—
800C22×C31—41no—
801C22×C31—41no—
802C22×C31—41no—
803C22×C31—41no—
804C22×C31—41no—
805C22×C31—41no—
806C22×C31—41no—
807C22×C31—41no—
808C22×C31—41no—
809C22×C31—41no—
810C22×C31—41no—
811C22×C31—41no—
812C22×C31—41no—
813C22×C31—41no—
814C22×C31—41no—
815C22×C31—41no—
816C22×C31—41no—
817C22×C31—41no—
818C22×C31—41no—
819C22×C31—41no—
820C22×C31—41no—
821C22×C31—41no—
822C22×C31—41no—
823C22×C31C22×#4111yescharacteristic
824C22×C31C2×H(5,𝔽2)11yescharacteristic
825C22×C31C2×H(5,𝔽2)11yescharacteristic
826C22×C31C2×H(5,𝔽2)11yescharacteristic
827C22×C31C2×H(5,𝔽2)11yescharacteristic
828C22×C31#58511yescharacteristic
829C22×C31#58511yescharacteristic
830C4×C31—22no—
831C4×C31—22no—
832C4×C31—22no—
833C4×C31—41no—
834C4×C31—41no—
835C4×C31—41no—
836C4×C31—41no—
837C4×C31—41no—
838C4×C31—41no—
839C4×C31—41no—
840C4×C31—41no—
841C4×C31—41no—
842C4×C31—41no—
843C4×C31—41no—
844C4×C31—41no—
845C4×C31—41no—
846C4×C31—41no—
847C4×C31—41no—
848C4×C31—41no—
849C4×C31—41no—
850C4×C31—41no—
851C4×C31—41no—
852C4×C31—41no—
853C4×C31—41no—
854C24×C4C22×C3111yescharacteristic
855C2×#127C22×C3111yescharacteristic
856C2×#123C22×C3111yescharacteristic
857C2×#123C22×C3111yescharacteristic
858C2×#123C22×C3111yescharacteristic
859C2×#123C22×C3111yescharacteristic
860C2×#123C22×C3111yescharacteristic, complemented
861C2×#123C22×C3111yescharacteristic, complemented
862C2×#121C22×C3111yescharacteristic
863C2×#121C22×C3111yescharacteristic
864C2×#121C22×C3111yescharacteristic
865C2×#121C22×C3111yescharacteristic
866C2×#121C22×C3111yescharacteristic
867C2×#121C22×C3111yescharacteristic
868C2×#121C22×C3111yescharacteristic
869C2×#121C22×C3111yescharacteristic
870C2×#120C22×C3111yescharacteristic
871C2×#120C22×C3111yescharacteristic
872C2×#120C22×C3111yescharacteristic
873C2×#120C22×C3111yescharacteristic
874C2×C4×D4C22×C3111yescharacteristic
875C2×C4×D4C22×C3111yescharacteristic
876C2×C4×D4C22×C3111yescharacteristic
877C2×C4×D4C22×C3111yescharacteristic, complemented
878C2×C4×D4C22×C3111yescharacteristic, complemented
879#400C22×C3111yescharacteristic, complemented
880#400C22×C3111yescharacteristic, complemented
881#400C22×C3111yescharacteristic, complemented
882#400C22×C3111yescharacteristic, complemented
883#400C22×C3111yescharacteristic, complemented
884#400C22×C3111yescharacteristic, complemented
885#400C22×C3111yescharacteristic, complemented
886#400C22×C3111yescharacteristic, complemented
887#399C22×C3111yescharacteristic
888#398C22×C3111yescharacteristic, complemented
889#398C22×C3111yescharacteristic, complemented
890#397C22×C3111yescharacteristic
891#397C22×C3111yescharacteristic
892#397C22×C3111yescharacteristic
893#397C22×C3111yescharacteristic
894#397C22×C3111yescharacteristic
895#397C22×C3111yescharacteristic, complemented
896#397C22×C3111yescharacteristic, complemented
897#397C22×C3111yescharacteristic, complemented
898#397C22×C3111yescharacteristic, complemented
899#397C22×C3111yescharacteristic, complemented
900#396C22×C3111yescharacteristic
901#396C22×C3111yescharacteristic
902#396C22×C3111yescharacteristic
903#396C22×C3111yescharacteristic, complemented
904#396C22×C3111yescharacteristic, complemented
905#396C22×C3111yescharacteristic, complemented
906#396C22×C3111yescharacteristic, complemented
907#394C22×C3111yescharacteristic
908#394C22×C3111yescharacteristic
909#394C22×C3111yescharacteristic
910#394C22×C3111yescharacteristic
911#394C22×C3111yescharacteristic
912#394C22×C3111yescharacteristic
913#394C22×C3111yescharacteristic
914#394C22×C3111yescharacteristic
915#394C22×C3111yescharacteristic, complemented
916#394C22×C3111yescharacteristic, complemented
917#392C22×C3111yescharacteristic
918#392C22×C3111yescharacteristic
919#392C22×C3111yescharacteristic
920#392C22×C3111yescharacteristic
921#392C22×C3111yescharacteristic
922#392C22×C3111yescharacteristic
923#392C22×C3111yescharacteristic
924#392C22×C3111yescharacteristic, complemented
925#392C22×C3111yescharacteristic, complemented
926#392C22×C3111yescharacteristic, complemented
927#390C22×C3111yescharacteristic
928#390C22×C3111yescharacteristic
929#390C22×C3111yescharacteristic
930#390C22×C3111yescharacteristic, complemented
931#390C22×C3111yescharacteristic, complemented
932#389C22×C3111yescharacteristic, complemented
933#389C22×C3111yescharacteristic, complemented
934#388C22×C3111yescharacteristic
935#388C22×C3111yescharacteristic
936#388C22×C3111yescharacteristic
937#388C22×C3111yescharacteristic
938#388C22×C3111yescharacteristic
939#388C22×C3111yescharacteristic, complemented
940#388C22×C3111yescharacteristic, complemented
941#388C22×C3111yescharacteristic, complemented
942#388C22×C3111yescharacteristic, complemented
943#388C22×C3111yescharacteristic, complemented
944#388C22×C3111yescharacteristic, complemented
945#388C22×C3111yescharacteristic, complemented
946#387C22×C3111yescharacteristic, complemented
947#387C22×C3111yescharacteristic, complemented
948#387C22×C3111yescharacteristic, complemented
949#387C22×C3111yescharacteristic, complemented
950#387C22×C3111yescharacteristic, complemented
951#387C22×C3111yescharacteristic, complemented
952#387C22×C3111yescharacteristic, complemented
953#386C22×C3111yescharacteristic
954#386C22×C3111yescharacteristic
955#386C22×C3111yescharacteristic
956#386C22×C3111yescharacteristic
957#386C22×C3111yescharacteristic
958#386C22×C3111yescharacteristic
959#386C22×C3111yescharacteristic
960#386C22×C3111yescharacteristic
961#386C22×C3111yescharacteristic
962#386C22×C3111yescharacteristic
963#386C22×C3111yescharacteristic
964#386C22×C3111yescharacteristic
965#386C22×C3111yescharacteristic
966#386C22×C3111yescharacteristic
967#386C22×C3111yescharacteristic
968#386C22×C3111yescharacteristic
969#386C22×C3111yescharacteristic
970#386C22×C3111yescharacteristic
971#386C22×C3111yescharacteristic
972#386C22×C3111yescharacteristic
973#386C22×C3111yescharacteristic
974#386C22×C3111yescharacteristic, complemented
975#386C22×C3111yescharacteristic, complemented
976#386C22×C3111yescharacteristic, complemented
977#386C22×C3111yescharacteristic, complemented
978#386C22×C3111yescharacteristic, complemented
979#386C22×C3111yescharacteristic, complemented
980#386C22×C3111yescharacteristic, complemented
981#385C22×C3111yescharacteristic
982#385C22×C3111yescharacteristic
983#385C22×C3111yescharacteristic
984#385C22×C3111yescharacteristic
985#385C22×C3111yescharacteristic
986#385C22×C3111yescharacteristic
987#385C22×C3111yescharacteristic
988#385C22×C3111yescharacteristic, complemented
989#385C22×C3111yescharacteristic, complemented
990#385C22×C3111yescharacteristic, complemented
991#385C22×C3111yescharacteristic, complemented
992#385C22×C3111yescharacteristic, complemented
993#382C22×C3111yescharacteristic, complemented
994#381C22×C3111yescharacteristic
995#381C22×C3111yescharacteristic
996#381C22×C3111yescharacteristic, complemented
997#380C22×C3111yescharacteristic
998#380C22×C3111yescharacteristic
999#380C22×C3111yescharacteristic
1000#380C22×C3111yescharacteristic, complemented
1001#380C22×C3111yescharacteristic, complemented
1002#379C22×C3111yescharacteristic
1003#379C22×C3111yescharacteristic
1004C4×C22⋊C4C22×C3111yescharacteristic
1005C4×C22⋊C4C22×C3111yescharacteristic
1006C4×C22⋊C4C22×C3111yescharacteristic
1007#376C22×C3111yescharacteristic, complemented
1008C2×#95C22×C3111yescharacteristic, complemented
1009C2×C31—42no—
1010C2×C31—42no—
1011C2×C31—42no—
1012C2×C31—42no—
1013C2×C31—81no—
1014C2×C31—81no—
1015C2×C31—81no—
1016C2×C31#345911yescharacteristic
1017C2×C31#351311yescharacteristic
1018C2×C31#351911yescharacteristic
1019C2×C31#353211yescharacteristic
1020C2×C31#353411yescharacteristic
1021C2×C31#353911yescharacteristic
1022C2×C31#354211yescharacteristic
1023C25C23×C3111yescharacteristic
1024C22×D4C23×C3111yescharacteristic
1025C22×D4C23×C3111yescharacteristic
1026C22×D4C23×C3111yescharacteristic
1027C22×D4C23×C3111yescharacteristic
1028C22×D4C23×C3111yescharacteristic
1029C22×D4C23×C3111yescharacteristic
1030C22×D4C23×C3111yescharacteristic
1031C22×D4C23×C3111yescharacteristic
1032C22×D4C23×C3111yescharacteristic
1033C22×D4C23×C3111yescharacteristic
1034C22×D4C23×C3111yescharacteristic
1035C22×D4C23×C3111yescharacteristic
1036C22×D4C23×C3111yescharacteristic
1037C22×D4C23×C3111yescharacteristic
1038C22×D4C23×C3111yescharacteristic
1039C22×D4C23×C3111yescharacteristic
1040C22×D4C23×C3111yescharacteristic
1041C22×D4C23×C3111yescharacteristic
1042C23×C4—42no—
1043C23×C4—42no—
1044C23×C4—42no—
1045C23×C4C23×C3111yescharacteristic
1046C23×C4C23×C3111yescharacteristic
1047C23×C4C23×C3111yescharacteristic
1048C23×C4C23×C3111yescharacteristic
1049C23×C4C23×C3111yescharacteristic
1050C23×C4C23×C3111yescharacteristic
1051C23×C4C23×C3111yescharacteristic
1052C23×C4C23×C3111yescharacteristic
1053C23×C4C23×C3111yescharacteristic
1054C23×C4C23×C3111yescharacteristic
1055C23×C4C23×C3111yescharacteristic
1056C23×C4C23×C3111yescharacteristic
1057#127—24no—
1058#123—42no—
1059#123—42no—
1060#123—42no—
1061#123—42no—
1062#123—42no—
1063#123—42no—
1064#121—24no—
1065#121—42no—
1066#121—42no—
1067#121—42no—
1068#121—42no—
1069#121—42no—
1070#121—42no—
1071#121—42no—
1072#120—24no—
1073#120—42no—
1074#120—42no—
1075#120—42no—
1076C4×D4—42no—
1077C4×D4—42no—
1078C4×D4—42no—
1079C4×D4—42no—
1080C4×D4—42no—
1081C2×C4⋊C4C23×C3111yescharacteristic
1082C2×C4⋊C4C23×C3111yescharacteristic
1083C2×C4⋊C4C23×C3111yescharacteristic
1084C2×C4⋊C4C23×C3111yescharacteristic
1085C2×C4⋊C4C23×C3111yescharacteristic
1086C2×C4⋊C4C23×C3111yescharacteristic
1087C2×C4⋊C4C23×C3111yescharacteristic
1088C2×C4⋊C4C23×C3111yescharacteristic
1089C2×C4⋊C4C23×C3111yescharacteristic
1090C2×C4⋊C4C23×C3111yescharacteristic
1091C2×C4⋊C4C23×C3111yescharacteristic
1092C2×C4⋊C4C23×C3111yescharacteristic
1093C2×C4⋊C4C23×C3111yescharacteristic
1094C2×C4⋊C4C23×C3111yescharacteristic
1095C2×C4⋊C4C23×C3111yescharacteristic
1096C2×C4⋊C4C23×C3111yescharacteristic
1097C2×C4⋊C4C23×C3111yescharacteristic
1098C2×C4⋊C4C23×C3111yescharacteristic
1099C2×C4⋊C4C23×C3111yescharacteristic
1100C2×C4⋊C4C23×C3111yescharacteristic
1101C2×C4⋊C4C23×C3111yescharacteristic
1102C2×C4⋊C4C23×C3111yescharacteristic
1103C2×C4⋊C4C23×C3111yescharacteristic
1104C2×C4⋊C4C23×C3111yescharacteristic
1105C2×C22⋊C4C23×C3111yescharacteristic
1106C2×C22⋊C4C23×C3111yescharacteristic
1107C2×C22⋊C4C23×C3111yescharacteristic
1108C2×C22⋊C4C23×C3111yescharacteristic
1109C2×C22⋊C4C23×C3111yescharacteristic
1110C2×C22⋊C4C23×C3111yescharacteristic
1111C2×C22⋊C4C23×C3111yescharacteristic
1112C2×C22⋊C4C23×C3111yescharacteristic
1113C2×C22⋊C4C23×C3111yescharacteristic
1114C2×C22⋊C4C23×C3111yescharacteristic
1115C2×C22⋊C4C23×C3111yescharacteristic
1116C2×C22⋊C4C23×C3111yescharacteristic
1117C2×C22⋊C4C23×C3111yescharacteristic
1118C2×C22⋊C4C23×C3111yescharacteristic
1119C2×C22⋊C4C23×C3111yescharacteristic
1120C2×C22⋊C4C23×C3111yescharacteristic
1121C2×C22⋊C4C23×C3111yescharacteristic
1122C2×C22⋊C4C23×C3111yescharacteristic
1123C2×C22⋊C4C23×C3111yescharacteristic
1124C2×C22⋊C4C23×C3111yescharacteristic
1125C2×C22⋊C4C23×C3111yescharacteristic
1126C2×C22⋊C4C23×C3111yescharacteristic
1127C2×C22⋊C4C23×C3111yescharacteristic
1128C2×C22⋊C4C23×C3111yescharacteristic
1129C2×C22⋊C4C23×C3111yescharacteristic
1130C2×C22⋊C4C23×C3111yescharacteristic
1131C2×C22⋊C4C23×C3111yescharacteristic
1132C2×C22⋊C4C23×C3111yescharacteristic
1133C2×C22⋊C4C23×C3111yescharacteristic
1134C2×C22⋊C4C23×C3111yescharacteristic
1135C2×C22⋊C4C23×C3111yescharacteristic
1136C2×C22⋊C4C23×C3111yescharacteristic
1137C2×C22⋊C4C23×C3111yescharacteristic
1138C2×C22⋊C4C23×C3111yescharacteristic
1139C2×C22⋊C4C23×C3111yescharacteristic
1140C2×C22⋊C4C23×C3111yescharacteristic
1141C2×C22⋊C4C23×C3111yescharacteristic
1142C2×C22⋊C4C23×C3111yescharacteristic
1143C2×C22⋊C4C23×C3111yescharacteristic
1144C2×C22⋊C4C23×C3111yescharacteristic
1145C2×C22⋊C4C23×C3111yescharacteristic
1146C2×C22⋊C4C23×C3111yescharacteristic
1147C2×C22⋊C4C23×C3111yescharacteristic
1148C2×C22⋊C4C23×C3111yescharacteristic
1149C2×C22⋊C4C23×C3111yescharacteristic
1150C2×C22⋊C4C23×C3111yescharacteristic
1151C2×C22⋊C4C23×C3111yescharacteristic
1152C2×C22⋊C4C23×C3111yescharacteristic
1153C2×C22⋊C4C23×C3111yescharacteristic
1154C2×C22⋊C4C23×C3111yescharacteristic
1155C2×C22⋊C4C23×C3111yescharacteristic
1156C2×C22⋊C4C23×C3111yescharacteristic
1157C2×C22⋊C4C23×C3111yescharacteristic
1158C2×C22⋊C4C23×C3111yescharacteristic
1159C2×C42C23×C3111yescharacteristic
1160C2×C42C23×C3111yescharacteristic
1161C2×C42C23×C3111yescharacteristic
1162C2×C42C23×C3111yescharacteristic
1163C2×C42C23×C3111yescharacteristic
1164C2×C42C23×C3111yescharacteristic
1165#95C23×C3111yescharacteristic
1166#95C23×C3111yescharacteristic
1167#95C23×C3111yescharacteristic
1168#95C23×C3111yescharacteristic
1169#95C23×C3111yescharacteristic
1170#95C23×C3111yescharacteristic
1171#95C23×C3111yescharacteristic
1172#95C23×C3111yescharacteristic
1173#95C23×C3111yescharacteristic
1174#95C23×C3111yescharacteristic
1175#95C23×C3111yescharacteristic
1176#95C23×C3111yescharacteristic
1177#95C23×C3111yescharacteristic
1178#95C23×C3111yescharacteristic
1179#95C23×C3111yescharacteristic
1180#95C23×C3111yescharacteristic
1181#95C23×C3111yescharacteristic
1182#95C23×C3111yescharacteristic
1183#95C23×C3111yescharacteristic
1184#95C23×C3111yescharacteristic
1185#95C23×C3111yescharacteristic
1186#95C23×C3111yescharacteristic
1187#95C23×C3111yescharacteristic
1188#95C23×C3111yescharacteristic
1189#95C23×C3111yescharacteristic
1190#95C23×C3111yescharacteristic
1191#95C23×C3111yescharacteristic
1192#95C23×C3111yescharacteristic
1193#95C23×C3111yescharacteristic
1194#95C23×C3111yescharacteristic
1195#95C23×C3111yescharacteristic
1196#95C23×C3111yescharacteristic
1197#95C23×C3111yescharacteristic
1198#95C23×C3111yescharacteristic
1199#95C23×C3111yescharacteristic
1200#95C23×C3111yescharacteristic
1201#95C23×C3111yescharacteristic
1202#95C23×C3111yescharacteristic
1203#95C23×C3111yescharacteristic
1204#95C23×C3111yescharacteristic
1205C31#3685611yescharacteristic, direct product factor, Sylow
1206C24—22no—
1207C24—22no—
1208C24—22no—
1209C24—41no—
1210C24—41no—
1211C24—41no—
1212C24—41no—
1213C24C24×C3111yescharacteristic
1214C24C24×C3111yescharacteristic
1215C24C24×C3111yescharacteristic
1216C24C24×C3111yescharacteristic
1217C24C24×C3111yescharacteristic
1218C24C24×C3111yescharacteristic
1219C24C24×C3111yescharacteristic
1220C2×D4—22no—
1221C2×D4—22no—
1222C2×D4—22no—
1223C2×D4—22no—
1224C2×D4—22no—
1225C2×D4—22no—
1226C2×D4—22no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—41no—
1262C2×D4—41no—
1263C2×D4—41no—
1264C2×D4—41no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—41no—
1270C2×D4—41no—
1271C2×D4—41no—
1272C2×D4—41no—
1273C2×D4#41×C3114yes—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—41no—
1285C22×C4—41no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—41no—
1304C22×C4—41no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4—41no—
1308C22×C4—41no—
1309C22×C4—41no—
1310C22×C4—416no—
1311C22×C4C24×C3111yescharacteristic
1312C22×C4C24×C3111yescharacteristic
1313C22×C4C24×C3111yescharacteristic
1314C22×C4C24×C3111yescharacteristic
1315C22×C4C24×C3111yescharacteristic
1316C22×C4C24×C3111yescharacteristic
1317C22×C4C24×C3111yescharacteristic
1318C22×C4C24×C3111yescharacteristic
1319C22×C4C24×C3111yescharacteristic
1320C22×C4C24×C3111yescharacteristic
1321C22×C4C24×C3111yescharacteristic
1322C22×C4C24×C3111yescharacteristic
1323C22×C4C24×C3111yescharacteristic
1324C22×C4C24×C3111yescharacteristic
1325C22×C4C24×C3111yescharacteristic
1326C22×C4C24×C3111yescharacteristic
1327C22×C4C24×C3111yescharacteristic
1328C22×C4C24×C3111yescharacteristic
1329C22×C4C24×C3111yescharacteristic
1330C22×C4C24×C3111yescharacteristic
1331C22×C4C24×C3111yescharacteristic
1332C22×C4C24×C3111yescharacteristic
1333C22×C4C24×C3111yescharacteristic
1334C22×C4C24×C3111yescharacteristic
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—41no—
1347C4⋊C4—41no—
1348C4⋊C4—41no—
1349C4⋊C4—41no—
1350C4⋊C4—41no—
1351C4⋊C4—41no—
1352C4⋊C4—41no—
1353C4⋊C4—41no—
1354C4⋊C4—41no—
1355C4⋊C4—41no—
1356C4⋊C4—41no—
1357C4⋊C4—41no—
1358C4⋊C4—41no—
1359C22⋊C4—22no—
1360C22⋊C4—22no—
1361C22⋊C4—22no—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—22no—
1369C22⋊C4—22no—
1370C22⋊C4—22no—
1371C22⋊C4—22no—
1372C22⋊C4—22no—
1373C22⋊C4—22no—
1374C22⋊C4—22no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—41no—
1386C22⋊C4—41no—
1387C22⋊C4—41no—
1388C22⋊C4—41no—
1389C22⋊C4—41no—
1390C22⋊C4—41no—
1391C22⋊C4—41no—
1392C22⋊C4—41no—
1393C22⋊C4—41no—
1394C22⋊C4—41no—
1395C22⋊C4—41no—
1396C22⋊C4—41no—
1397C22⋊C4—41no—
1398C22⋊C4—41no—
1399C22⋊C4—41no—
1400C22⋊C4—41no—
1401C22⋊C4—41no—
1402C22⋊C4—41no—
1403C22⋊C4—41no—
1404C22⋊C4—41no—
1405C22⋊C4—41no—
1406C22⋊C4—41no—
1407C22⋊C4—41no—
1408C22⋊C4—41no—
1409C22⋊C4—41no—
1410C22⋊C4—41no—
1411C22⋊C4—41no—
1412C22⋊C4—41no—
1413C42—22no—
1414C42—22no—
1415C42—41no—
1416C42—41no—
1417C42—41no—
1418C42—41no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23—44no—
1465C23—44no—
1466C23—44no—
1467C23—44no—
1468C23—44no—
1469C23—44no—
1470C23—44no—
1471C23C2×#41×C3112yes—
1472C23C2×#41×C3112yes—
1473C23C31×H(5,𝔽2)12yes—
1474C23C31×H(5,𝔽2)12yes—
1475C23C25×C3111yescharacteristic
1476D4—44no—
1477D4—44no—
1478D4—44no—
1479D4—44no—
1480D4—44no—
1481D4—82no—
1482D4—82no—
1483D4—82no—
1484D4—82no—
1485D4—82no—
1486D4—82no—
1487D4—82no—
1488D4—82no—
1489D4—82no—
1490D4—82no—
1491D4—82no—
1492D4—82no—
1493D4—82no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—44no—
1564C2×C4—44no—
1565C2×C4—44no—
1566C2×C4—44no—
1567C2×C4—44no—
1568C2×C4—44no—
1569C2×C4—82no—
1570C2×C4—82no—
1571C2×C4—82no—
1572C2×C4—82no—
1573C2×C4—82no—
1574C2×C4—82no—
1575C2×C4C2×#41×C3112yes—
1576C2×C4C31×H(5,𝔽2)12yes—
1577C2×C4C31×H(5,𝔽2)12yes—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—22no—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—416no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—41no—
1617C22—41no—
1618C22—41no—
1619C22—41no—
1620C22—41no—
1621C22—41no—
1622C22—41no—
1623C22—41no—
1624C22—41no—
1625C22—41no—
1626C22—41no—
1627C22—41no—
1628C22C22×#41×C3111yescharacteristic
1629C22C2×C31×H(5,𝔽2)11yescharacteristic
1630C22C2×C31×H(5,𝔽2)11yescharacteristic
1631C22C2×C31×H(5,𝔽2)11yescharacteristic
1632C22C2×C31×H(5,𝔽2)11yescharacteristic
1633C22C31×#58511yescharacteristic
1634C22C31×#58511yescharacteristic
1635C4—22no—
1636C4—22no—
1637C4—22no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—41no—
1647C4—41no—
1648C4—41no—
1649C4—41no—
1650C4—41no—
1651C4—41no—
1652C4—41no—
1653C4—41no—
1654C4—41no—
1655C4—41no—
1656C4—41no—
1657C4—41no—
1658C4—41no—
1659C2—42no—
1660C2—42no—
1661C2—42no—
1662C2—42no—
1663C2—81no—
1664C2—81no—
1665C2—81no—
1666C2C31×#345911yescharacteristic
1667C2C31×#351311yescharacteristic
1668C2C31×#351911yescharacteristic
1669C2C31×#353211yescharacteristic
1670C2C31×#353411yescharacteristic
1671C2C31×#353911yescharacteristic
1672C2C31×#354211yescharacteristic
subgroupG/H
center, socleC23×C31C25
commutator, Frattini, cosocleC23C25×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C31×#2849C2semidirect
2. C31×#2847C2semidirect
3. C31×#2797C2semidirect
4. C31×#2782C2semidirect
5. C31×#2780C2semidirect
6. C31×#2750C2semidirect
7. C31×#2744C2semidirect
8. C31×#2708C2semidirect
9. C31×#2697C2semidirect
10. C31×#2693C2semidirect
11. C31×#2693C2semidirect
12. C31×#2688C2semidirect
13. C31×#2688C2semidirect
14. C31×#2682C2semidirect
15. C31×#2678C2semidirect
16. C31×#2673C2semidirect
17. C31×#2669C2semidirect
18. C31×#2668C2semidirect
19. C31×#2649C2semidirect
20. C31×#2648C2semidirect
21. C31×#2530C2semidirect
22. C31×#2526C2semidirect
23. C31×#2464C2semidirect
24. C31×#2457C2semidirect
25. C31×#2456C2semidirect
26. C31×#2456C2semidirect
27. C31×#2444C2semidirect
28. C31×#2425C2semidirect
29. C31×#2328C2semidirect
30. C31×#2325C2semidirect
31. C4×C31×#120C2semidirect
38. C2×C31×#123C22semidirect
39. C2×C31×#123C22semidirect
55. C2×C4×D4×C31C22semidirect
56. C2×C4×D4×C31C22semidirect
57. C31×#400C22semidirect
58. C31×#400C22semidirect
59. C31×#400C22semidirect
60. C31×#400C22semidirect
61. C31×#400C22semidirect
62. C31×#400C22semidirect
63. C31×#400C22semidirect
64. C31×#400C22semidirect
66. C31×#398C22semidirect
67. C31×#398C22semidirect
73. C31×#397C22semidirect
74. C31×#397C22semidirect
75. C31×#397C22semidirect
76. C31×#397C22semidirect
77. C31×#397C22semidirect
81. C31×#396C22semidirect
82. C31×#396C22semidirect
83. C31×#396C22semidirect
84. C31×#396C22semidirect
93. C31×#394C22semidirect
94. C31×#394C22semidirect
102. C31×#392C22semidirect
103. C31×#392C22semidirect
104. C31×#392C22semidirect
108. C31×#390C22semidirect
109. C31×#390C22semidirect
110. C31×#389C22semidirect
111. C31×#389C22semidirect
117. C31×#388C22semidirect
118. C31×#388C22semidirect
119. C31×#388C22semidirect
120. C31×#388C22semidirect
121. C31×#388C22semidirect
122. C31×#388C22semidirect
123. C31×#388C22semidirect
124. C31×#387C22semidirect
125. C31×#387C22semidirect
126. C31×#387C22semidirect
127. C31×#387C22semidirect
128. C31×#387C22semidirect
129. C31×#387C22semidirect
130. C31×#387C22semidirect
152. C31×#386C22semidirect
153. C31×#386C22semidirect
154. C31×#386C22semidirect
155. C31×#386C22semidirect
156. C31×#386C22semidirect
157. C31×#386C22semidirect
158. C31×#386C22semidirect
166. C31×#385C22semidirect
167. C31×#385C22semidirect
168. C31×#385C22semidirect
169. C31×#385C22semidirect
170. C31×#385C22semidirect
171. C31×#382C22semidirect
174. C31×#381C22semidirect
178. C31×#380C22semidirect
179. C31×#380C22semidirect
185. C31×#376C22semidirect
186. C2×C31×#95C22semidirect
582. #36856C31direct (N × H)
742. #2849C2×C31semidirect
743. #2847C2×C31semidirect
744. #2797C2×C31semidirect
745. #2782C2×C31semidirect
746. #2780C2×C31semidirect
747. #2750C2×C31semidirect
748. #2744C2×C31semidirect
749. #2708C2×C31semidirect
750. #2697C2×C31semidirect
751. #2693C2×C31semidirect
752. #2693C2×C31semidirect
753. #2688C2×C31semidirect
754. #2688C2×C31semidirect
755. #2682C2×C31semidirect
756. #2678C2×C31semidirect
757. #2673C2×C31semidirect
758. #2669C2×C31semidirect
759. #2668C2×C31semidirect
760. #2649C2×C31semidirect
761. #2648C2×C31semidirect
762. #2530C2×C31semidirect
763. #2526C2×C31semidirect
764. #2464C2×C31semidirect
765. #2457C2×C31semidirect
766. #2456C2×C31semidirect
767. #2456C2×C31semidirect
768. #2444C2×C31semidirect
769. #2425C2×C31semidirect
770. #2328C2×C31semidirect
771. #2325C2×C31semidirect
772. C4×#120C2×C31semidirect
860. C2×#123C22×C31semidirect
861. C2×#123C22×C31semidirect
877. C2×C4×D4C22×C31semidirect
878. C2×C4×D4C22×C31semidirect
879. #400C22×C31semidirect
880. #400C22×C31semidirect
881. #400C22×C31semidirect
882. #400C22×C31semidirect
883. #400C22×C31semidirect
884. #400C22×C31semidirect
885. #400C22×C31semidirect
886. #400C22×C31semidirect
888. #398C22×C31semidirect
889. #398C22×C31semidirect
895. #397C22×C31semidirect
896. #397C22×C31semidirect
897. #397C22×C31semidirect
898. #397C22×C31semidirect
899. #397C22×C31semidirect
903. #396C22×C31semidirect
904. #396C22×C31semidirect
905. #396C22×C31semidirect
906. #396C22×C31semidirect
915. #394C22×C31semidirect
916. #394C22×C31semidirect
924. #392C22×C31semidirect
925. #392C22×C31semidirect
926. #392C22×C31semidirect
930. #390C22×C31semidirect
931. #390C22×C31semidirect
932. #389C22×C31semidirect
933. #389C22×C31semidirect
939. #388C22×C31semidirect
940. #388C22×C31semidirect
941. #388C22×C31semidirect
942. #388C22×C31semidirect
943. #388C22×C31semidirect
944. #388C22×C31semidirect
945. #388C22×C31semidirect
946. #387C22×C31semidirect
947. #387C22×C31semidirect
948. #387C22×C31semidirect
949. #387C22×C31semidirect
950. #387C22×C31semidirect
951. #387C22×C31semidirect
952. #387C22×C31semidirect
974. #386C22×C31semidirect
975. #386C22×C31semidirect
976. #386C22×C31semidirect
977. #386C22×C31semidirect
978. #386C22×C31semidirect
979. #386C22×C31semidirect
980. #386C22×C31semidirect
988. #385C22×C31semidirect
989. #385C22×C31semidirect
990. #385C22×C31semidirect
991. #385C22×C31semidirect
992. #385C22×C31semidirect
993. #382C22×C31semidirect
996. #381C22×C31semidirect
1000. #380C22×C31semidirect
1001. #380C22×C31semidirect
1007. #376C22×C31semidirect
1008. C2×#95C22×C31semidirect
1205. C31#36856direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C31×#28492
C31×#28472
C31×#27972
C31×#27822
C31×#27802
C31×#27502
C31×#27442
C31×#27082
C31×#26972
C31×#26932
C31×#26882
C31×#26822
C31×#26782
C31×#26732
C31×#26692
C31×#26682
C31×#26492
C31×#26482
C31×#25302
C31×#25262
C31×#24642
C31×#24572
C31×#24562
C31×#24442
C31×#24252
C31×#23282
C31×#23252
C4×C31×#1202
#3685631