Finite Group Databasebeta

← C31×#14114 #21470873

Subgroups — C31×#14114 #21470873

Order 7936.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C211yesmaximal, characteristic
2C2×C31×#388C211yesmaximal, characteristic
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
4C31×#1442C211yesmaximal, characteristic, complemented
5C31×#1441C211yesmaximal, characteristic, complemented
6C31×#1439C211yesmaximal, characteristic
7C31×#1439C211yesmaximal, characteristic
8C31×#1436C211yesmaximal, characteristic, complemented
9C31×#1436C211yesmaximal, characteristic, complemented
10C31×#1436C211yesmaximal, characteristic, complemented
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C31×#1434C211yesmaximal, characteristic, complemented
13C31×C22⋊#95C211yesmaximal, characteristic
14C31×C22⋊#95C211yesmaximal, characteristic
15C4×C31×#95C211yesmaximal, characteristic, complemented
16C24×C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C22×C42×C31C2211yescharacteristic
29C22×C42×C31C2211yescharacteristic
30C22×C42×C31C2211yescharacteristic
31C31×#388—24no—
32C31×#388C418yescomplemented
33C4×C22⋊C4×C31—24no—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C25×C31C2311yescharacteristic
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—41no—
61C23×C4×C31—41no—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—41no—
82C2×C4⋊C4×C31—41no—
83C2×C4⋊C4×C31—41no—
84C2×C4⋊C4×C31—41no—
85C2×C4⋊C4×C31—41no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31C2×C414yescomplemented
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—41no—
96C2×C22⋊C4×C31—41no—
97C2×C22⋊C4×C31—41no—
98C2×C22⋊C4×C31—41no—
99C2×C22⋊C4×C31—41no—
100C2×C22⋊C4×C31—41no—
101C2×C22⋊C4×C31C2×C414yes—
102C2×C22⋊C4×C31C2×C414yes—
103C2×C22⋊C4×C31C2×C414yes—
104C2×C22⋊C4×C31D414yes—
105C2×C22⋊C4×C31Q814yes—
106C2×C42×C31—22no—
107C2×C42×C31—22no—
108C2×C42×C31—22no—
109C2×C42×C31—22no—
110C2×C42×C31—22no—
111C2×C42×C31—22no—
112C2×C42×C31—41no—
113C2×C42×C31—41no—
114C2×C42×C31—41no—
115C2×C42×C31—41no—
116C2×C42×C31—41no—
117C2×C42×C31C2×C414yescomplemented
118C31×#95—22no—
119C31×#95—22no—
120C31×#95—22no—
121C31×#95—22no—
122C31×#95—22no—
123C31×#95—22no—
124C31×#95—22no—
125C31×#95—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—22no—
131C31×#95—41no—
132C31×#95—41no—
133C31×#95—41no—
134C31×#95—41no—
135C31×#95—41no—
136C31×#95C2×C414yescomplemented
137C31×#95C2×C414yescomplemented
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31—21no—
143C24×C31—21no—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31C22×C412yes—
151C24×C31C2×D412yes—
152C24×C31C2×Q812yes—
153C24×C31C2411yescharacteristic
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—28no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—44no—
236C22×C4×C31—44no—
237C22×C4×C31—44no—
238C22×C4×C31—44no—
239C22×C4×C31—44no—
240C22×C4×C31—44no—
241C22×C4×C31C22×C412yes—
242C22×C4×C31C22×C412yes—
243C22×C4×C31C22×C412yes—
244C22×C4×C31C22×C412yes—
245C22×C4×C31C22×C412yes—
246C22×C4×C31C22×C412yes—
247C22×C4×C31C2×D412yes—
248C22×C4×C31C2×D412yes—
249C22×C4×C31C2×Q812yes—
250C22×C4×C31C2×Q812yes—
251C22×C4×C31#4112yes—
252C22×C4×C31#4112yes—
253C22×C4×C31#4112yes—
254C22×C4×C31#4112yes—
255C22×C4×C31#4112yes—
256C22×C4×C31#4112yes—
257C22×C4×C31#4112yes—
258C22×C4×C31#4112yes—
259C4⋊C4×C31—44no—
260C4⋊C4×C31—44no—
261C4⋊C4×C31—44no—
262C4⋊C4×C31—44no—
263C22⋊C4×C31—28no—
264C22⋊C4×C31—44no—
265C22⋊C4×C31—44no—
266C22⋊C4×C31—44no—
267C22⋊C4×C31—44no—
268C22⋊C4×C31C4⋊C4116yescomplemented
269C42×C31—44no—
270C42×C31—44no—
271C42×C31—44no—
272C42×C31—44no—
273#14114C3111yesmaximal, characteristic, direct product factor, Sylow
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—22no—
277C23×C31—22no—
278C23×C31—22no—
279C23×C31—22no—
280C23×C31—22no—
281C23×C31—22no—
282C23×C31—22no—
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—22no—
286C23×C31—22no—
287C23×C31—22no—
288C23×C31—22no—
289C23×C31—22no—
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31—41no—
296C23×C31—41no—
297C23×C31—41no—
298C23×C31—41no—
299C23×C31—41no—
300C23×C31—41no—
301C23×C31—41no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31C2×C4⋊C414yes—
309C23×C31C23×C411yescharacteristic
310C23×C31C22×D411yescharacteristic
311C23×C31C22×Q811yescharacteristic
312C23×C31C2×#4111yescharacteristic
313C23×C31C2×#4111yescharacteristic
314C23×C31C2×#4111yescharacteristic
315C23×C31C2×#4111yescharacteristic
316C23×C31C2×#4111yescharacteristic
317C23×C31C2×#4111yescharacteristic
318C23×C31C2×#4111yescharacteristic
319C23×C31C2×#4111yescharacteristic
320C23×C31H(5,𝔽2)11yescharacteristic
321C23×C31H(5,𝔽2)11yescharacteristic
322C23×C31H(5,𝔽2)11yescharacteristic
323C23×C31H(5,𝔽2)11yescharacteristic
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
339C2×C4×C31—22no—
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—416no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31C2×C4⋊C414yes—
421C2×C4×C31C2×C4⋊C414yes—
422C2×C4×C31#12614yes—
423C2×#388C2×C3111yescharacteristic
424C2×#388C2×C3111yescharacteristic
425C2×C4×C22⋊C4C2×C3111yescharacteristic
426#1442C2×C3111yescharacteristic, complemented
427#1441C2×C3111yescharacteristic, complemented
428#1439C2×C3111yescharacteristic
429#1439C2×C3111yescharacteristic
430#1436C2×C3111yescharacteristic, complemented
431#1436C2×C3111yescharacteristic, complemented
432#1436C2×C3111yescharacteristic, complemented
433C4⋊#95C2×C3111yescharacteristic, complemented
434#1434C2×C3111yescharacteristic, complemented
435C22⋊#95C2×C3111yescharacteristic
436C22⋊#95C2×C3111yescharacteristic
437C4×#95C2×C3111yescharacteristic, complemented
438C22×C31—24no—
439C22×C31—24no—
440C22×C31—24no—
441C22×C31—42no—
442C22×C31—42no—
443C22×C31—42no—
444C22×C31—42no—
445C22×C31—42no—
446C22×C31—42no—
447C22×C31—42no—
448C22×C31—42no—
449C22×C31—42no—
450C22×C31—42no—
451C22×C31—42no—
452C22×C31—42no—
453C22×C31C22×C4⋊C411yescharacteristic
454C22×C31C4×#4111yescharacteristic
455C22×C31C4×#4111yescharacteristic
456C22×C31C4×#4111yescharacteristic
457C22×C31C4×#4111yescharacteristic
458C22×C31#51811yescharacteristic
459C22×C31#51811yescharacteristic
460C22×C31#52511yescharacteristic
461C22×C31#52511yescharacteristic
462C22×C31C2×#12611yescharacteristic
463C22×C31#52911yescharacteristic
464C22×C31#52911yescharacteristic
465C22×C31#52911yescharacteristic
466C22×C31#53311yescharacteristic
467C22×C31#53311yescharacteristic
468C22×C31#53811yescharacteristic
469C22×C31#53811yescharacteristic
470C22×C31#54011yescharacteristic
471C22×C31#54011yescharacteristic
472C22×C31#54611yescharacteristic
473C22×C31#54611yescharacteristic
474C22×C31#54611yescharacteristic
475C22×C31#54611yescharacteristic
476C22×C31#55111yescharacteristic
477C22×C31#55111yescharacteristic
478C22×C31#55111yescharacteristic
479C22×C31#55311yescharacteristic
480C22×C31#55311yescharacteristic
481C22×C31#55411yescharacteristic
482C22×C31#55411yescharacteristic
483C22×C31#55411yescharacteristic
484C22×C31#55411yescharacteristic
485C22×C31#55511yescharacteristic
486C22×C31#55511yescharacteristic
487C22×C31#55911yescharacteristic
488C4×C31—24no—
489C4×C31—24no—
490C4×C31—24no—
491C4×C31—42no—
492C4×C31—42no—
493C4×C31—42no—
494C4×C31—42no—
495C4×C31—42no—
496C4×C31—42no—
497C4×C31—42no—
498C4×C31—42no—
499C4×C31—42no—
500C4×C31—81no—
501C4×C31—81no—
502C24×C4C22×C3111yescharacteristic
503C22×C4⋊C4C22×C3111yescharacteristic
504C22×C4⋊C4C22×C3111yescharacteristic
505C22×C4⋊C4C22×C3111yescharacteristic
506C22×C4⋊C4C22×C3111yescharacteristic
507C22×C22⋊C4C22×C3111yescharacteristic
508C22×C22⋊C4C22×C3111yescharacteristic
509C22×C22⋊C4C22×C3111yescharacteristic
510C22×C22⋊C4C22×C3111yescharacteristic
511C22×C22⋊C4C22×C3111yescharacteristic
512C22×C22⋊C4C22×C3111yescharacteristic
513C22×C42C22×C3111yescharacteristic
514C22×C42C22×C3111yescharacteristic
515C22×C42C22×C3111yescharacteristic
516C22×C42C22×C3111yescharacteristic
517#388—24no—
518#388C4×C3118yescomplemented
519C4×C22⋊C4—24no—
520C2×#95C22×C3111yescharacteristic
521C2×#95C22×C3111yescharacteristic
522C2×#95C22×C3111yescharacteristic
523C2×#95C22×C3111yescharacteristic
524C2×#95C22×C3111yescharacteristic
525C2×#95C22×C3111yescharacteristic
526C2×#95C22×C3111yescharacteristic
527C2×#95C22×C3111yescharacteristic
528C2×#95C22×C3111yescharacteristic
529C2×#95C22×C3111yescharacteristic
530C2×#95C22×C3111yescharacteristic
531C2×#95C22×C3111yescharacteristic
532C2×#95C22×C3111yescharacteristic
533C2×#95C22×C3111yescharacteristic
534C2×#95C22×C3111yescharacteristic
535C2×#95C22×C3111yescharacteristic
536C2×#95C22×C3111yescharacteristic
537C2×#95C22×C3111yescharacteristic
538C2×#95C22×C3111yescharacteristic
539C2×#95C22×C3111yescharacteristic
540C2×C31—44no—
541C2×C31#229611yescharacteristic
542C2×C31C4×#12611yescharacteristic
543C2×C31#233311yescharacteristic
544C2×C31#234911yescharacteristic
545C2×C31#234911yescharacteristic
546C2×C31#237211yescharacteristic
547C2×C31#237411yescharacteristic
548C2×C31#245711yescharacteristic
549C2×C31#245911yescharacteristic
550C2×C31#247611yescharacteristic
551C2×C31#248011yescharacteristic
552C2×C31#249711yescharacteristic
553C2×C31#252211yescharacteristic
554C2×C31#257411yescharacteristic
555C2×C31#258911yescharacteristic
556C25C23×C3111yescharacteristic
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4C23×C3111yescharacteristic
565C23×C4C23×C3111yescharacteristic
566C23×C4C23×C3111yescharacteristic
567C23×C4C23×C3111yescharacteristic
568C23×C4C23×C3111yescharacteristic
569C23×C4C23×C3111yescharacteristic
570C23×C4C23×C3111yescharacteristic
571C23×C4C23×C3111yescharacteristic
572C23×C4C23×C3111yescharacteristic
573C23×C4C23×C3111yescharacteristic
574C23×C4C23×C3111yescharacteristic
575C23×C4C23×C3111yescharacteristic
576C23×C4C23×C3111yescharacteristic
577C23×C4C23×C3111yescharacteristic
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4C2×C4×C3114yescomplemented
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4C2×C4×C3114yes—
604C2×C22⋊C4C2×C4×C3114yes—
605C2×C22⋊C4C2×C4×C3114yes—
606C2×C22⋊C4D4×C3114yes—
607C2×C22⋊C4Q8×C3114yes—
608C2×C42—22no—
609C2×C42—22no—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—41no—
615C2×C42—41no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—41no—
619C2×C42C2×C4×C3114yescomplemented
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—41no—
634#95—41no—
635#95—41no—
636#95—41no—
637#95—41no—
638#95C2×C4×C3114yescomplemented
639#95C2×C4×C3114yescomplemented
640C31#1411411yescharacteristic, direct product factor, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×C4×C3112yes—
654C24C2×D4×C3112yes—
655C24C2×Q8×C3112yes—
656C24C24×C3111yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—28no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—44no—
739C22×C4—44no—
740C22×C4—44no—
741C22×C4—44no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4C22×C4×C3112yes—
745C22×C4C22×C4×C3112yes—
746C22×C4C22×C4×C3112yes—
747C22×C4C22×C4×C3112yes—
748C22×C4C22×C4×C3112yes—
749C22×C4C22×C4×C3112yes—
750C22×C4C2×D4×C3112yes—
751C22×C4C2×D4×C3112yes—
752C22×C4C2×Q8×C3112yes—
753C22×C4C2×Q8×C3112yes—
754C22×C4#41×C3112yes—
755C22×C4#41×C3112yes—
756C22×C4#41×C3112yes—
757C22×C4#41×C3112yes—
758C22×C4#41×C3112yes—
759C22×C4#41×C3112yes—
760C22×C4#41×C3112yes—
761C22×C4#41×C3112yes—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4C4⋊C4×C31116yescomplemented
772C42—44no—
773C42—44no—
774C42—44no—
775C42—44no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C2×C4⋊C4×C3114yes—
811C23C23×C4×C3111yescharacteristic
812C23C22×D4×C3111yescharacteristic
813C23C22×Q8×C3111yescharacteristic
814C23C2×#41×C3111yescharacteristic
815C23C2×#41×C3111yescharacteristic
816C23C2×#41×C3111yescharacteristic
817C23C2×#41×C3111yescharacteristic
818C23C2×#41×C3111yescharacteristic
819C23C2×#41×C3111yescharacteristic
820C23C2×#41×C3111yescharacteristic
821C23C2×#41×C3111yescharacteristic
822C23C31×H(5,𝔽2)11yescharacteristic
823C23C31×H(5,𝔽2)11yescharacteristic
824C23C31×H(5,𝔽2)11yescharacteristic
825C23C31×H(5,𝔽2)11yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—416no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4C2×C4⋊C4×C3114yes—
923C2×C4C2×C4⋊C4×C3114yes—
924C2×C4C31×#12614yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C22×C4⋊C4×C3111yescharacteristic
941C22C4×#41×C3111yescharacteristic
942C22C4×#41×C3111yescharacteristic
943C22C4×#41×C3111yescharacteristic
944C22C4×#41×C3111yescharacteristic
945C22C31×#51811yescharacteristic
946C22C31×#51811yescharacteristic
947C22C31×#52511yescharacteristic
948C22C31×#52511yescharacteristic
949C22C2×C31×#12611yescharacteristic
950C22C31×#52911yescharacteristic
951C22C31×#52911yescharacteristic
952C22C31×#52911yescharacteristic
953C22C31×#53311yescharacteristic
954C22C31×#53311yescharacteristic
955C22C31×#53811yescharacteristic
956C22C31×#53811yescharacteristic
957C22C31×#54011yescharacteristic
958C22C31×#54011yescharacteristic
959C22C31×#54611yescharacteristic
960C22C31×#54611yescharacteristic
961C22C31×#54611yescharacteristic
962C22C31×#54611yescharacteristic
963C22C31×#55111yescharacteristic
964C22C31×#55111yescharacteristic
965C22C31×#55111yescharacteristic
966C22C31×#55311yescharacteristic
967C22C31×#55311yescharacteristic
968C22C31×#55411yescharacteristic
969C22C31×#55411yescharacteristic
970C22C31×#55411yescharacteristic
971C22C31×#55411yescharacteristic
972C22C31×#55511yescharacteristic
973C22C31×#55511yescharacteristic
974C22C31×#55911yescharacteristic
975C4—24no—
976C4—24no—
977C4—24no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—81no—
988C4—81no—
989C2—44no—
990C2C31×#229611yescharacteristic
991C2C4×C31×#12611yescharacteristic
992C2C31×#233311yescharacteristic
993C2C31×#234911yescharacteristic
994C2C31×#234911yescharacteristic
995C2C31×#237211yescharacteristic
996C2C31×#237411yescharacteristic
997C2C31×#245711yescharacteristic
998C2C31×#245911yescharacteristic
999C2C31×#247611yescharacteristic
1000C2C31×#248011yescharacteristic
1001C2C31×#249711yescharacteristic
1002C2C31×#252211yescharacteristic
1003C2C31×#257411yescharacteristic
1004C2C31×#258911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C31×#1442C2semidirect
5. C31×#1441C2semidirect
8. C31×#1436C2semidirect
9. C31×#1436C2semidirect
10. C31×#1436C2semidirect
11. C31×C4⋊#95C2semidirect
12. C31×#1434C2semidirect
15. C4×C31×#95C2semidirect
32. C31×#388C4semidirect
87. C2×C4⋊C4×C31C2×C4semidirect
117. C2×C42×C31C2×C4semidirect
136. C31×#95C2×C4semidirect
137. C31×#95C2×C4semidirect
268. C22⋊C4×C31C4⋊C4semidirect
273. #14114C31direct (N × H)
426. #1442C2×C31semidirect
427. #1441C2×C31semidirect
430. #1436C2×C31semidirect
431. #1436C2×C31semidirect
432. #1436C2×C31semidirect
433. C4⋊#95C2×C31semidirect
434. #1434C2×C31semidirect
437. C4×#95C2×C31semidirect
518. #388C4×C31semidirect
589. C2×C4⋊C4C2×C4×C31semidirect
619. C2×C42C2×C4×C31semidirect
638. #95C2×C4×C31semidirect
639. #95C2×C4×C31semidirect
640. C31#14114direct (N × H)
771. C22⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C2×C4×C22⋊C4×C312
C31×#14422
C31×#14412
C31×#14392
C31×#14362
C31×C4⋊#952
C31×#14342
C31×C22⋊#952
C4×C31×#952
#1411431