Finite Group Databasebeta

← C2×C31×#2554 #21491582

Subgroups — C2×C31×#2554 #21491582

Order 7936.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#126C211yesmaximal, characteristic, complemented
2C22×C31×#123C211yesmaximal, characteristic, complemented
3C31×#2554C2116yesmaximal, direct product factor
4C2×C31×#398C211yesmaximal, characteristic, complemented
5C2×C31×#396C211yesmaximal, characteristic, complemented
6C2×C31×#394C211yesmaximal, characteristic, complemented
7C2×C31×#392C211yesmaximal, characteristic
8C2×C31×#390C211yesmaximal, characteristic, complemented
9C2×C31×#390C211yesmaximal, characteristic, complemented
10C2×C31×#390C211yesmaximal, characteristic, complemented
11C2×C31×#388C211yesmaximal, characteristic, complemented
12C2×C31×#388C211yesmaximal, characteristic, complemented
13C2×C31×#388C211yesmaximal, characteristic, complemented
14C2×C31×#386C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C23×D4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C2×C31×#126—28no—
22C2×C31×#126C2218yescomplemented
23C2×C31×#123—28no—
24C2×C31×#123C2218yescomplemented
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
43C22×C22⋊C4×C31C2211yescharacteristic
44C22×C22⋊C4×C31C2211yescharacteristic
45C22×C22⋊C4×C31C2211yescharacteristic
46C22×C42×C31C2211yescharacteristic
47C22×C42×C31C2211yescharacteristic
48C22×C42×C31C2211yescharacteristic
49C22×C42×C31C2211yescharacteristic
50C31×#398C2218yescomplemented
51C31×#396C2218yescomplemented
52C31×#394C2218yescomplemented
53C31×#392C2218yes—
54C31×#390C2218yescomplemented
55C31×#390C2218yescomplemented
56C31×#390C2218yescomplemented
57C31×#388C2218yescomplemented
58C31×#388C2218yescomplemented
59C31×#388C2218yescomplemented
60C31×#386C2218yescomplemented
61C4×C4⋊C4×C31C2218yescomplemented
62C4×C22⋊C4×C31C2218yescomplemented
63C2×C31×#95C2211yescharacteristic
64C2×C31×#95C2211yescharacteristic
65C2×C31×#95C2211yescharacteristic
66C2×C31×#95C2211yescharacteristic
67C2×C31×#95C2211yescharacteristic
68C2×C31×#95C2211yescharacteristic
69C25×C31C2311yescharacteristic
70C25×C31C2311yescharacteristic
71C25×C31C2311yescharacteristic
72C22×D4×C31—24no—
73C22×D4×C31—24no—
74C22×D4×C31—24no—
75C22×D4×C31—24no—
76C22×D4×C31—24no—
77C22×D4×C31—42no—
78C22×D4×C31—42no—
79C22×D4×C31—42no—
80C22×D4×C31—42no—
81C22×D4×C31C2314yes—
82C22×D4×C31C2314yes—
83C22×D4×C31C2314yes—
84C23×C4×C31—24no—
85C23×C4×C31—24no—
86C23×C4×C31—42no—
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2314yes—
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C31×#126—232no—
101C31×#123—232no—
102C2×C4⋊C4×C31—24no—
103C2×C4⋊C4×C31—24no—
104C2×C4⋊C4×C31—24no—
105C2×C4⋊C4×C31—24no—
106C2×C4⋊C4×C31—42no—
107C2×C4⋊C4×C31—42no—
108C2×C4⋊C4×C31D418yescomplemented
109C2×C4⋊C4×C31C2314yes—
110C2×C4⋊C4×C31C2314yes—
111C2×C4⋊C4×C31C2314yes—
112C2×C4⋊C4×C31C2314yes—
113C2×C4⋊C4×C31C2314yes—
114C2×C4⋊C4×C31C2314yes—
115C2×C4⋊C4×C31C2314yes—
116C2×C22⋊C4×C31—24no—
117C2×C22⋊C4×C31—24no—
118C2×C22⋊C4×C31—24no—
119C2×C22⋊C4×C31—24no—
120C2×C22⋊C4×C31—24no—
121C2×C22⋊C4×C31—24no—
122C2×C22⋊C4×C31—24no—
123C2×C22⋊C4×C31—24no—
124C2×C22⋊C4×C31—24no—
125C2×C22⋊C4×C31—24no—
126C2×C22⋊C4×C31—24no—
127C2×C22⋊C4×C31—42no—
128C2×C22⋊C4×C31—42no—
129C2×C22⋊C4×C31—42no—
130C2×C22⋊C4×C31C2314yes—
131C2×C22⋊C4×C31C2314yes—
132C2×C22⋊C4×C31C2314yes—
133C2×C22⋊C4×C31C2314yes—
134C2×C22⋊C4×C31C2314yes—
135C2×C22⋊C4×C31C2314yes—
136C2×C22⋊C4×C31C2314yes—
137C2×C22⋊C4×C31C2314yes—
138C2×C22⋊C4×C31C2314yes—
139C2×C22⋊C4×C31C2314yes—
140C2×C22⋊C4×C31C2314yes—
141C2×C22⋊C4×C31C2314yes—
142C2×C22⋊C4×C31C2314yes—
143C2×C22⋊C4×C31C2314yes—
144C2×C42×C31—24no—
145C2×C42×C31—24no—
146C2×C42×C31—42no—
147C2×C42×C31—42no—
148C2×C42×C31C2314yes—
149C2×C42×C31C2314yes—
150C2×C42×C31C2314yes—
151C2×C42×C31C2314yes—
152C31×#95C2314yes—
153C31×#95C2314yes—
154C31×#95C2314yes—
155C31×#95C2314yes—
156C31×#95C2314yes—
157C31×#95C2314yes—
158C24×C31—22no—
159C24×C31—22no—
160C24×C31—22no—
161C24×C31—22no—
162C24×C31—22no—
163C24×C31—22no—
164C24×C31—22no—
165C24×C31—22no—
166C24×C31—22no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—22no—
171C24×C31—22no—
172C24×C31—22no—
173C24×C31—22no—
174C24×C31—22no—
175C24×C31—22no—
176C24×C31—22no—
177C24×C31—22no—
178C24×C31#4114yes—
179C24×C31C2412yes—
180C24×C31C2412yes—
181C24×C31C2412yes—
182C24×C31C2411yescharacteristic
183C2×D4×C31—28no—
184C2×D4×C31—28no—
185C2×D4×C31—28no—
186C2×D4×C31—28no—
187C2×D4×C31—28no—
188C2×D4×C31—44no—
189C2×D4×C31—44no—
190C2×D4×C31—44no—
191C2×D4×C31—44no—
192C2×D4×C31—416no—
193C2×D4×C31—416no—
194C2×D4×C31—416no—
195C22×C4×C31—22no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—22no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—22no—
217C22×C4×C31—22no—
218C22×C4×C31—28no—
219C22×C4×C31—22no—
220C22×C4×C31—22no—
221C22×C4×C31—22no—
222C22×C4×C31—22no—
223C22×C4×C31—22no—
224C22×C4×C31—22no—
225C22×C4×C31—22no—
226C22×C4×C31—28no—
227C22×C4×C31—44no—
228C22×C4×C31—416no—
229C22×C4×C31C2×D414yes—
230C22×C4×C31C2×D414yes—
231C22×C4×C31C2×D414yes—
232C22×C4×C31#4114yes—
233C22×C4×C31#4114yes—
234C22×C4×C31#4114yes—
235C22×C4×C31C2412yes—
236C22×C4×C31C2412yes—
237C22×C4×C31C2412yes—
238C22×C4×C31C2412yes—
239C22×C4×C31C2412yes—
240C22×C4×C31C2412yes—
241C22×C4×C31C2412yes—
242C22×C4×C31C2412yes—
243C22×C4×C31C2412yes—
244C22×C4×C31C2412yes—
245C22×C4×C31C2412yes—
246C22×C4×C31C2412yes—
247C4⋊C4×C31—28no—
248C4⋊C4×C31—28no—
249C4⋊C4×C31—28no—
250C4⋊C4×C31—28no—
251C4⋊C4×C31—44no—
252C4⋊C4×C31—44no—
253C4⋊C4×C31C2×D4116yescomplemented
254C22⋊C4×C31—28no—
255C22⋊C4×C31—28no—
256C22⋊C4×C31—28no—
257C22⋊C4×C31—28no—
258C22⋊C4×C31—28no—
259C22⋊C4×C31—28no—
260C22⋊C4×C31—28no—
261C22⋊C4×C31—28no—
262C22⋊C4×C31—28no—
263C22⋊C4×C31—28no—
264C22⋊C4×C31—28no—
265C22⋊C4×C31—44no—
266C22⋊C4×C31—44no—
267C22⋊C4×C31—44no—
268C42×C31—28no—
269C42×C31—28no—
270C42×C31—44no—
271C42×C31—44no—
272C2×#2554C3111yesmaximal, characteristic, direct product factor, Sylow
273C23×C31—28no—
274C23×C31—28no—
275C23×C31—28no—
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—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—44no—
297C23×C31—44no—
298C23×C31—44no—
299C23×C31—44no—
300C23×C31—44no—
301C23×C31—44no—
302C23×C31—44no—
303C23×C31—44no—
304C23×C31—44no—
305C23×C31—44no—
306C23×C31—44no—
307C23×C31—44no—
308C23×C31—44no—
309C23×C31—44no—
310C23×C31—44no—
311C23×C31—44no—
312C23×C31—44no—
313C23×C31—44no—
314C23×C31C22×D412yes—
315C23×C31C2×#4114yes—
316C23×C31C2×#4112yes—
317C23×C31C2×#4112yes—
318C23×C31C2×#4112yes—
319C23×C31C2×#4112yes—
320C23×C31H(5,𝔽2)12yes—
321C23×C31H(5,𝔽2)12yes—
322C23×C31C2511yescharacteristic
323D4×C31—416no—
324D4×C31—416no—
325D4×C31—416no—
326C2×C4×C31—28no—
327C2×C4×C31—28no—
328C2×C4×C31—28no—
329C2×C4×C31—28no—
330C2×C4×C31—28no—
331C2×C4×C31—28no—
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—416no—
363C2×C4×C31—44no—
364C2×C4×C31—44no—
365C2×C4×C31—44no—
366C2×C4×C31—44no—
367C2×C4×C31—44no—
368C2×C4×C31—44no—
369C2×C4×C31C22×D414yes—
370C2×C4×C31C22×D414yes—
371C2×C4×C31C22×D414yes—
372C2×C4×C31C2×#4114yes—
373C2×C4×C31C2×#4114yes—
374C2×C4×C31C2×#4114yes—
375C22×#126C2×C3111yescharacteristic, complemented
376C22×#123C2×C3111yescharacteristic, complemented
377#2554C2×C31116yesdirect product factor
378C2×#398C2×C3111yescharacteristic, complemented
379C2×#396C2×C3111yescharacteristic, complemented
380C2×#394C2×C3111yescharacteristic, complemented
381C2×#392C2×C3111yescharacteristic
382C2×#390C2×C3111yescharacteristic, complemented
383C2×#390C2×C3111yescharacteristic, complemented
384C2×#390C2×C3111yescharacteristic, complemented
385C2×#388C2×C3111yescharacteristic, complemented
386C2×#388C2×C3111yescharacteristic, complemented
387C2×#388C2×C3111yescharacteristic, complemented
388C2×#386C2×C3111yescharacteristic, complemented
389C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
390C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
391C22×C31—24no—
392C22×C31—24no—
393C22×C31—24no—
394C22×C31—42no—
395C22×C31—42no—
396C22×C31—42no—
397C22×C31—42no—
398C22×C31—416no—
399C22×C31—42no—
400C22×C31—42no—
401C22×C31—42no—
402C22×C31—42no—
403C22×C31—42no—
404C22×C31—42no—
405C22×C31—42no—
406C22×C31—42no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—42no—
410C22×C31—42no—
411C22×C31—42no—
412C22×C31—42no—
413C22×C31—88no—
414C22×C31—88no—
415C22×C31#52914yes—
416C22×C31#53214yes—
417C22×C31#53814yes—
418C22×C31#54614yes—
419C22×C31#55014yes—
420C22×C31#55114yes—
421C22×C31#55314yes—
422C22×C31C23×D411yescharacteristic
423C22×C31C22×#4111yescharacteristic
424C22×C31C22×#4111yescharacteristic
425C22×C31C22×#4111yescharacteristic
426C22×C31C22×#4111yescharacteristic
427C22×C31C2×H(5,𝔽2)11yescharacteristic
428C22×C31C2×H(5,𝔽2)11yescharacteristic
429C4×C31—24no—
430C4×C31—24no—
431C4×C31—24no—
432C4×C31—24no—
433C4×C31—24no—
434C4×C31—24no—
435C4×C31—42no—
436C4×C31—42no—
437C4×C31—42no—
438C4×C31—42no—
439C4×C31—42no—
440C4×C31—42no—
441C23×D4C22×C3111yescharacteristic
442C23×D4C22×C3111yescharacteristic
443C23×D4C22×C3111yescharacteristic
444C24×C4C22×C3111yescharacteristic
445C2×#126—28no—
446C2×#126C22×C3118yescomplemented
447C2×#123—28no—
448C2×#123C22×C3118yescomplemented
449C22×C4⋊C4C22×C3111yescharacteristic
450C22×C4⋊C4C22×C3111yescharacteristic
451C22×C4⋊C4C22×C3111yescharacteristic
452C22×C4⋊C4C22×C3111yescharacteristic
453C22×C4⋊C4C22×C3111yescharacteristic
454C22×C4⋊C4C22×C3111yescharacteristic
455C22×C4⋊C4C22×C3111yescharacteristic
456C22×C22⋊C4C22×C3111yescharacteristic
457C22×C22⋊C4C22×C3111yescharacteristic
458C22×C22⋊C4C22×C3111yescharacteristic
459C22×C22⋊C4C22×C3111yescharacteristic
460C22×C22⋊C4C22×C3111yescharacteristic
461C22×C22⋊C4C22×C3111yescharacteristic
462C22×C22⋊C4C22×C3111yescharacteristic
463C22×C22⋊C4C22×C3111yescharacteristic
464C22×C22⋊C4C22×C3111yescharacteristic
465C22×C22⋊C4C22×C3111yescharacteristic
466C22×C22⋊C4C22×C3111yescharacteristic
467C22×C22⋊C4C22×C3111yescharacteristic
468C22×C22⋊C4C22×C3111yescharacteristic
469C22×C22⋊C4C22×C3111yescharacteristic
470C22×C42C22×C3111yescharacteristic
471C22×C42C22×C3111yescharacteristic
472C22×C42C22×C3111yescharacteristic
473C22×C42C22×C3111yescharacteristic
474#398C22×C3118yescomplemented
475#396C22×C3118yescomplemented
476#394C22×C3118yescomplemented
477#392C22×C3118yes—
478#390C22×C3118yescomplemented
479#390C22×C3118yescomplemented
480#390C22×C3118yescomplemented
481#388C22×C3118yescomplemented
482#388C22×C3118yescomplemented
483#388C22×C3118yescomplemented
484#386C22×C3118yescomplemented
485C4×C4⋊C4C22×C3118yescomplemented
486C4×C22⋊C4C22×C3118yescomplemented
487C2×#95C22×C3111yescharacteristic
488C2×#95C22×C3111yescharacteristic
489C2×#95C22×C3111yescharacteristic
490C2×#95C22×C3111yescharacteristic
491C2×#95C22×C3111yescharacteristic
492C2×#95C22×C3111yescharacteristic
493C2×C31—44no—
494C2×C31—82no—
495C2×C31—82no—
496C2×C31#255418yesdirect product factor
497C2×C31C2×#52911yescharacteristic
498C2×C31C2×#53211yescharacteristic
499C2×C31C2×#53811yescharacteristic
500C2×C31C2×#54611yescharacteristic
501C2×C31C2×#55011yescharacteristic
502C2×C31C2×#55111yescharacteristic
503C2×C31C2×#55311yescharacteristic
504C25C23×C3111yescharacteristic
505C25C23×C3111yescharacteristic
506C25C23×C3111yescharacteristic
507C22×D4—24no—
508C22×D4—24no—
509C22×D4—24no—
510C22×D4—24no—
511C22×D4—24no—
512C22×D4—42no—
513C22×D4—42no—
514C22×D4—42no—
515C22×D4—42no—
516C22×D4C23×C3114yes—
517C22×D4C23×C3114yes—
518C22×D4C23×C3114yes—
519C23×C4—24no—
520C23×C4—24no—
521C23×C4—42no—
522C23×C4C23×C3111yescharacteristic
523C23×C4C23×C3111yescharacteristic
524C23×C4C23×C3111yescharacteristic
525C23×C4C23×C3111yescharacteristic
526C23×C4C23×C3111yescharacteristic
527C23×C4C23×C3111yescharacteristic
528C23×C4C23×C3114yes—
529C23×C4C23×C3111yescharacteristic
530C23×C4C23×C3111yescharacteristic
531C23×C4C23×C3111yescharacteristic
532C23×C4C23×C3111yescharacteristic
533C23×C4C23×C3111yescharacteristic
534C23×C4C23×C3111yescharacteristic
535#126—232no—
536#123—232no—
537C2×C4⋊C4—24no—
538C2×C4⋊C4—24no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—42no—
542C2×C4⋊C4—42no—
543C2×C4⋊C4D4×C3118yescomplemented
544C2×C4⋊C4C23×C3114yes—
545C2×C4⋊C4C23×C3114yes—
546C2×C4⋊C4C23×C3114yes—
547C2×C4⋊C4C23×C3114yes—
548C2×C4⋊C4C23×C3114yes—
549C2×C4⋊C4C23×C3114yes—
550C2×C4⋊C4C23×C3114yes—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—24no—
554C2×C22⋊C4—24no—
555C2×C22⋊C4—24no—
556C2×C22⋊C4—24no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—24no—
562C2×C22⋊C4—42no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4—42no—
565C2×C22⋊C4C23×C3114yes—
566C2×C22⋊C4C23×C3114yes—
567C2×C22⋊C4C23×C3114yes—
568C2×C22⋊C4C23×C3114yes—
569C2×C22⋊C4C23×C3114yes—
570C2×C22⋊C4C23×C3114yes—
571C2×C22⋊C4C23×C3114yes—
572C2×C22⋊C4C23×C3114yes—
573C2×C22⋊C4C23×C3114yes—
574C2×C22⋊C4C23×C3114yes—
575C2×C22⋊C4C23×C3114yes—
576C2×C22⋊C4C23×C3114yes—
577C2×C22⋊C4C23×C3114yes—
578C2×C22⋊C4C23×C3114yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582C2×C42—42no—
583C2×C42C23×C3114yes—
584C2×C42C23×C3114yes—
585C2×C42C23×C3114yes—
586C2×C42C23×C3114yes—
587#95C23×C3114yes—
588#95C23×C3114yes—
589#95C23×C3114yes—
590#95C23×C3114yes—
591#95C23×C3114yes—
592#95C23×C3114yes—
593C31C2×#255411yescharacteristic, direct product factor, Sylow
594C24—22no—
595C24—22no—
596C24—22no—
597C24—22no—
598C24—22no—
599C24—22no—
600C24—22no—
601C24—22no—
602C24—22no—
603C24—22no—
604C24—22no—
605C24—22no—
606C24—22no—
607C24—22no—
608C24—22no—
609C24—22no—
610C24—22no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24#41×C3114yes—
615C24C24×C3112yes—
616C24C24×C3112yes—
617C24C24×C3112yes—
618C24C24×C3111yescharacteristic
619C2×D4—28no—
620C2×D4—28no—
621C2×D4—28no—
622C2×D4—28no—
623C2×D4—28no—
624C2×D4—44no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—416no—
629C2×D4—416no—
630C2×D4—416no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—28no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—28no—
663C22×C4—44no—
664C22×C4—416no—
665C22×C4C2×D4×C3114yes—
666C22×C4C2×D4×C3114yes—
667C22×C4C2×D4×C3114yes—
668C22×C4#41×C3114yes—
669C22×C4#41×C3114yes—
670C22×C4#41×C3114yes—
671C22×C4C24×C3112yes—
672C22×C4C24×C3112yes—
673C22×C4C24×C3112yes—
674C22×C4C24×C3112yes—
675C22×C4C24×C3112yes—
676C22×C4C24×C3112yes—
677C22×C4C24×C3112yes—
678C22×C4C24×C3112yes—
679C22×C4C24×C3112yes—
680C22×C4C24×C3112yes—
681C22×C4C24×C3112yes—
682C22×C4C24×C3112yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—28no—
686C4⋊C4—28no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4C2×D4×C31116yescomplemented
690C22⋊C4—28no—
691C22⋊C4—28no—
692C22⋊C4—28no—
693C22⋊C4—28no—
694C22⋊C4—28no—
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—28no—
698C22⋊C4—28no—
699C22⋊C4—28no—
700C22⋊C4—28no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—44no—
704C42—28no—
705C42—28no—
706C42—44no—
707C42—44no—
708C23—28no—
709C23—28no—
710C23—28no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—22no—
730C23—22no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—44no—
735C23—44no—
736C23—44no—
737C23—44no—
738C23—44no—
739C23—44no—
740C23—44no—
741C23—44no—
742C23—44no—
743C23—44no—
744C23—44no—
745C23—44no—
746C23—44no—
747C23—44no—
748C23—44no—
749C23C22×D4×C3112yes—
750C23C2×#41×C3114yes—
751C23C2×#41×C3112yes—
752C23C2×#41×C3112yes—
753C23C2×#41×C3112yes—
754C23C2×#41×C3112yes—
755C23C31×H(5,𝔽2)12yes—
756C23C31×H(5,𝔽2)12yes—
757C23C25×C3111yescharacteristic
758D4—416no—
759D4—416no—
760D4—416no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—28no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—416no—
798C2×C4—44no—
799C2×C4—44no—
800C2×C4—44no—
801C2×C4—44no—
802C2×C4—44no—
803C2×C4—44no—
804C2×C4C22×D4×C3114yes—
805C2×C4C22×D4×C3114yes—
806C2×C4C22×D4×C3114yes—
807C2×C4C2×#41×C3114yes—
808C2×C4C2×#41×C3114yes—
809C2×C4C2×#41×C3114yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—88no—
833C22—88no—
834C22C31×#52914yes—
835C22C31×#53214yes—
836C22C31×#53814yes—
837C22C31×#54614yes—
838C22C31×#55014yes—
839C22C31×#55114yes—
840C22C31×#55314yes—
841C22C23×D4×C3111yescharacteristic
842C22C22×#41×C3111yescharacteristic
843C22C22×#41×C3111yescharacteristic
844C22C22×#41×C3111yescharacteristic
845C22C22×#41×C3111yescharacteristic
846C22C2×C31×H(5,𝔽2)11yescharacteristic
847C22C2×C31×H(5,𝔽2)11yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—24no—
852C4—24no—
853C4—24no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C2—44no—
861C2—82no—
862C2—82no—
863C2C31×#255418yesdirect product factor
864C2C2×C31×#52911yescharacteristic
865C2C2×C31×#53211yescharacteristic
866C2C2×C31×#53811yescharacteristic
867C2C2×C31×#54611yescharacteristic
868C2C2×C31×#55011yescharacteristic
869C2C2×C31×#55111yescharacteristic
870C2C2×C31×#55311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC23C25×C31
prime radicalC2×C31×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#126C2semidirect
2. C22×C31×#123C2semidirect
3. C31×#2554C2direct (N × H)
4. C2×C31×#398C2semidirect
5. C2×C31×#396C2semidirect
6. C2×C31×#394C2semidirect
8. C2×C31×#390C2semidirect
9. C2×C31×#390C2semidirect
10. C2×C31×#390C2semidirect
11. C2×C31×#388C2semidirect
12. C2×C31×#388C2semidirect
13. C2×C31×#388C2semidirect
14. C2×C31×#386C2semidirect
15. C2×C4×C4⋊C4×C31C2semidirect
16. C2×C4×C22⋊C4×C31C2semidirect
22. C2×C31×#126C22semidirect
24. C2×C31×#123C22semidirect
50. C31×#398C22semidirect
51. C31×#396C22semidirect
52. C31×#394C22semidirect
54. C31×#390C22semidirect
55. C31×#390C22semidirect
56. C31×#390C22semidirect
57. C31×#388C22semidirect
58. C31×#388C22semidirect
59. C31×#388C22semidirect
60. C31×#386C22semidirect
61. C4×C4⋊C4×C31C22semidirect
62. C4×C22⋊C4×C31C22semidirect
108. C2×C4⋊C4×C31D4semidirect
253. C4⋊C4×C31C2×D4semidirect
272. C2×#2554C31direct (N × H)
375. C22×#126C2×C31semidirect
376. C22×#123C2×C31semidirect
377. #2554C2×C31direct (N × H)
378. C2×#398C2×C31semidirect
379. C2×#396C2×C31semidirect
380. C2×#394C2×C31semidirect
382. C2×#390C2×C31semidirect
383. C2×#390C2×C31semidirect
384. C2×#390C2×C31semidirect
385. C2×#388C2×C31semidirect
386. C2×#388C2×C31semidirect
387. C2×#388C2×C31semidirect
388. C2×#386C2×C31semidirect
389. C2×C4×C4⋊C4C2×C31semidirect
390. C2×C4×C22⋊C4C2×C31semidirect
446. C2×#126C22×C31semidirect
448. C2×#123C22×C31semidirect
474. #398C22×C31semidirect
475. #396C22×C31semidirect
476. #394C22×C31semidirect
478. #390C22×C31semidirect
479. #390C22×C31semidirect
480. #390C22×C31semidirect
481. #388C22×C31semidirect
482. #388C22×C31semidirect
483. #388C22×C31semidirect
484. #386C22×C31semidirect
485. C4×C4⋊C4C22×C31semidirect
486. C4×C22⋊C4C22×C31semidirect
496. C2×C31#2554direct (N × H)
543. C2×C4⋊C4D4×C31semidirect
593. C31C2×#2554direct (N × H)
689. C4⋊C4C2×D4×C31semidirect
863. C2C31×#2554direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×#1262
C22×C31×#1232
C31×#25542
C2×C31×#3982
C2×C31×#3962
C2×C31×#3942
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C4×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C2×#255431