Finite Group Databasebeta

← C31×#18705 #21475464

Subgroups — C31×#18705 #21475464

Order 7936.

938 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3546C211yesmaximal, characteristic
2C31×#3252C211yesmaximal, characteristic, complemented
3C31×#3235C211yesmaximal, characteristic, complemented
4C31×#3167C211yesmaximal, characteristic, complemented
5C31×#1654C211yesmaximal, characteristic, complemented
6C31×#1652C211yesmaximal, characteristic, complemented
7C31×#1641C211yesmaximal, characteristic, complemented
8C31×#1639C211yesmaximal, characteristic, complemented
9C31×#1638C211yesmaximal, characteristic, complemented
10C31×#1635C211yesmaximal, characteristic, complemented
11C31×#1631C211yesmaximal, characteristic, complemented
12C31×#1629C211yesmaximal, characteristic, complemented
13C31×#1557C211yesmaximal, characteristic, complemented
14C31×#1494C211yesmaximal, characteristic, complemented
15C31×#1492C211yesmaximal, characteristic, complemented
16C31×#560—22no—
17C31×#556C2211yescharacteristic
18C31×#553—21no—
19C31×#550—21no—
20C31×#550C2211yescharacteristic
21C31×#547C2211yescharacteristic
22C31×#546—21no—
23C31×#546—21no—
24D42×C31C2211yescharacteristic
25C31×#542—21no—
26C31×#538—22no—
27C31×#537—21no—
28C31×#535—21no—
29C31×#535—21no—
30C31×#533C2211yescharacteristic, complemented
31C31×#532C2211yescharacteristic
32C31×#532C2211yescharacteristic
33C31×#529C2211yescharacteristic
34C31×#501—21no—
35C31×#498C2211yescharacteristic, complemented
36C31×#492C2211yescharacteristic
37C31×#490—21no—
38C31×#487C2211yescharacteristic, complemented
39C31×#486C2211yescharacteristic
40C31×#482—21no—
41C31×#482—21no—
42C31×#479—21no—
43C31×#477C2211yescharacteristic, complemented
44C31×#476C2211yescharacteristic
45C31×#476C2211yescharacteristic
46C31×#476C2211yescharacteristic, complemented
47C31×#474C2211yescharacteristic
48C31×#474C2211yescharacteristic, complemented
49C31×#470—21no—
50C31×#468—21no—
51C31×#465—22no—
52C31×#464—21no—
53C31×#462C2211yescharacteristic, complemented
54C31×#461C2211yescharacteristic
55C4×SD16×C31—22no—
56C31×#432C2211yescharacteristic, complemented
57C31×#423C2211yescharacteristic, complemented
58C2×C4×C8×C31C2211yescharacteristic, complemented
59C31×#332C2211yescharacteristic, complemented
60C31×#332C2211yescharacteristic, complemented
61C31×#331C2211yescharacteristic
62C31×#331C2211yescharacteristic
63C31×Q8⋊C8C2211yescharacteristic, complemented
64C31×Q8⋊C8C2211yescharacteristic, complemented
65C31×D4⋊C8C2211yescharacteristic
66C31×D4⋊C8C2211yescharacteristic
67C31×D4⋊C8C2211yescharacteristic
68C31×D4⋊C8C2211yescharacteristic
69C31×D4⋊C8C2211yescharacteristic, complemented
70C31×D4⋊C8C2211yescharacteristic, complemented
71C2×#41×C31—21no—
72C2×#41×C31—21no—
73C2×#41×C31—21no—
74C2×#41×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C2×Q16×C31—21no—
78C2×SD16×C31—22no—
79C2×SD16×C31—21no—
80C2×M16×C31—21no—
81C22×C8×C31—21no—
82C31×C4⋊Q8D411yescharacteristic
83C31×C4⋊Q8C2311yescharacteristic
84C31×C4⋊Q8C2311yescharacteristic
85C31×C4⋊Q8C2311yescharacteristic
86C31×#127—22no—
87C31×#127—21no—
88C31×#127D411yescharacteristic
89C31×#127C2311yescharacteristic
90C31×#126—22no—
91C31×#126—22no—
92C31×#126—21no—
93C31×#125—21no—
94C31×#125D411yescharacteristic
95C31×#124—22no—
96C31×#124—21no—
97C31×#124—21no—
98C31×#124—21no—
99C31×#124D411yescharacteristic
100C31×#123—22no—
101C31×#123—22no—
102C31×#123—21no—
103C31×#123—22no—
104C31×C22⋊Q8—22no—
105C31×C22⋊Q8—21no—
106C31×C22⋊Q8—21no—
107C31×C22⋊Q8—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8D411yescharacteristic
110C31×#121—22no—
111C31×#121—22no—
112C31×#121—22no—
113C31×#121—22no—
114C31×#121—22no—
115C31×#121—21no—
116C31×#121—22no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121D412yes—
123C31×#121D411yescharacteristic
124C31×#121D411yescharacteristic
125C31×#121D411yescharacteristic
126C31×#120—22no—
127C31×#120—22no—
128C31×#120—22no—
129C31×#120—22no—
130C4×Q8×C31—21no—
131C4×Q8×C31—21no—
132C4×Q8×C31—21no—
133C4×Q8×C31C2311yescharacteristic
134C4×D4×C31—22no—
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31D412yes—
140C4×D4×C31C2311yescharacteristic
141C4×D4×C31C2311yescharacteristic
142C4×D4×C31C2311yescharacteristic
143C31×#117—21no—
144C31×#117—21no—
145C31×#117—21no—
146C2×C4⋊C4×C31—21no—
147C2×C22⋊C4×C31—22no—
148C2×C42×C31C2311yescharacteristic
149C31×#107—21no—
150C31×#107—21no—
151C31×#107—21no—
152C31×#106—22no—
153C31×#106—21no—
154C31×#106—21no—
155C31×#106—21no—
156C31×C4⋊C8—21no—
157C31×C4⋊C8C2311yescharacteristic
158C31×C4⋊C8C2311yescharacteristic
159C31×C4⋊C8C2311yescharacteristic
160C31×C4⋊C8C2311yescharacteristic
161C31×#103—21no—
162C31×#103—22no—
163C31×#103—21no—
164C31×#103—21no—
165C31×#102—22no—
166C31×#102—21no—
167C31×#102—21no—
168C31×#102—21no—
169C31×#102—21no—
170C31×#102—21no—
171C31×C22⋊C8—21no—
172C31×#97—21no—
173C4×C8×C31—21no—
174C4×C8×C31C2311yescharacteristic
175C4×C8×C31C2311yescharacteristic
176C24×C31—22no—
177#41×C31—81no—
178#41×C31—81no—
179#41×C31—81no—
180#41×C31—81no—
181#41×C31—81no—
182#41×C31—81no—
183#41×C31—81no—
184#41×C31—81no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31C2×D411yescharacteristic
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—22no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—81no—
204C2×D4×C31—81no—
205C2×D4×C31—81no—
206C2×D4×C31—81no—
207C2×D4×C31C2×D411yescharacteristic
208C2×D4×C31C2×D411yescharacteristic
209C2×D4×C31C2×D411yescharacteristic
210C2×D4×C31C2×D412yes—
211C22×C4×C31—22no—
212C22×C4×C31—22no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—22no—
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220Q16×C31—81no—
221SD16×C31—44no—
222SD16×C31—81no—
223M16×C31—81no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—42no—
231C4⋊C4×C31—22no—
232C4⋊C4×C31—22no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—41no—
244C4⋊C4×C31—41no—
245C4⋊C4×C31C2×D411yescharacteristic
246C4⋊C4×C31C2×D412yes—
247C4⋊C4×C31C2×D411yescharacteristic
248C4⋊C4×C31C2×D411yescharacteristic
249C4⋊C4×C31C2×D411yescharacteristic
250C22⋊C4×C31—22no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—21no—
256C22⋊C4×C31—21no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—21no—
259C22⋊C4×C31—21no—
260C22⋊C4×C31—21no—
261C22⋊C4×C31—22no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—21no—
265C22⋊C4×C31—21no—
266C22⋊C4×C31—41no—
267C42×C31—22no—
268C42×C31—21no—
269C42×C31—41no—
270C42×C31C2×D411yescharacteristic
271C42×C31C2×D411yescharacteristic
272C42×C31C2×D411yescharacteristic
273C42×C31C2411yescharacteristic
274#18705C3111yesmaximal, characteristic, direct product factor, Sylow
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—22no—
278C23×C31—21no—
279C23×C31—82no—
280C23×C31—82no—
281C23×C31—82no—
282C23×C31#12011yescharacteristic
283Q8×C31—21no—
284Q8×C31—21no—
285Q8×C31—42no—
286Q8×C31—41no—
287Q8×C31—41no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—81no—
291D4×C31—21no—
292D4×C31—21no—
293D4×C31—21no—
294D4×C31—21no—
295D4×C31—21no—
296D4×C31—21no—
297D4×C31—42no—
298D4×C31—41no—
299D4×C31—41no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—81no—
303D4×C31—81no—
304D4×C31—81no—
305D4×C31—82no—
306D4×C31—81no—
307D4×C31—81no—
308D4×C31—82no—
309D4×C31—82no—
310D4×C31—82no—
311D4×C31—82no—
312D4×C31—82no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—82no—
333C2×C4×C31—82no—
334C2×C4×C31—82no—
335C2×C4×C31#12011yescharacteristic
336C2×C4×C31#12011yescharacteristic
337C2×C4×C31#12011yescharacteristic
338C2×C4×C31C22×D411yescharacteristic
339C2×C4×C31C22×D411yescharacteristic
340C2×C4×C31C22×D411yescharacteristic
341C8×C31—22no—
342C8×C31—41no—
343C8×C31—41no—
344C8×C31—41no—
345C8×C31—41no—
346C8×C31—41no—
347#3546C2×C3111yescharacteristic
348#3252C2×C3111yescharacteristic, complemented
349#3235C2×C3111yescharacteristic, complemented
350#3167C2×C3111yescharacteristic, complemented
351#1654C2×C3111yescharacteristic, complemented
352#1652C2×C3111yescharacteristic, complemented
353#1641C2×C3111yescharacteristic, complemented
354#1639C2×C3111yescharacteristic, complemented
355#1638C2×C3111yescharacteristic, complemented
356#1635C2×C3111yescharacteristic, complemented
357#1631C2×C3111yescharacteristic, complemented
358#1629C2×C3111yescharacteristic, complemented
359#1557C2×C3111yescharacteristic, complemented
360#1494C2×C3111yescharacteristic, complemented
361#1492C2×C3111yescharacteristic, complemented
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—21no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—42no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—42no—
372C22×C31—41no—
373C22×C31—42no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—41no—
377C22×C31—164no—
378C22×C31C2×#12011yescharacteristic
379C4×C31—21no—
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—21no—
383C4×C31—41no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—41no—
388C4×C31—41no—
389C4×C31—81no—
390C4×C31—81no—
391C4×C31#57611yescharacteristic
392C4×C31#57711yescharacteristic
393C4×C31#57711yescharacteristic
394C4×C31#57711yescharacteristic
395#560—22no—
396#556C22×C3111yescharacteristic
397#553—21no—
398#550—21no—
399#550C22×C3111yescharacteristic
400#547C22×C3111yescharacteristic
401#546—21no—
402#546—21no—
403D42C22×C3111yescharacteristic
404#542—21no—
405#538—22no—
406#537—21no—
407#535—21no—
408#535—21no—
409#533C22×C3111yescharacteristic, complemented
410#532C22×C3111yescharacteristic
411#532C22×C3111yescharacteristic
412#529C22×C3111yescharacteristic
413#501—21no—
414#498C22×C3111yescharacteristic, complemented
415#492C22×C3111yescharacteristic
416#490—21no—
417#487C22×C3111yescharacteristic, complemented
418#486C22×C3111yescharacteristic
419#482—21no—
420#482—21no—
421#479—21no—
422#477C22×C3111yescharacteristic, complemented
423#476C22×C3111yescharacteristic
424#476C22×C3111yescharacteristic
425#476C22×C3111yescharacteristic, complemented
426#474C22×C3111yescharacteristic
427#474C22×C3111yescharacteristic, complemented
428#470—21no—
429#468—21no—
430#465—22no—
431#464—21no—
432#462C22×C3111yescharacteristic, complemented
433#461C22×C3111yescharacteristic
434C4×SD16—22no—
435#432C22×C3111yescharacteristic, complemented
436#423C22×C3111yescharacteristic, complemented
437C2×C4×C8C22×C3111yescharacteristic, complemented
438#332C22×C3111yescharacteristic, complemented
439#332C22×C3111yescharacteristic, complemented
440#331C22×C3111yescharacteristic
441#331C22×C3111yescharacteristic
442Q8⋊C8C22×C3111yescharacteristic, complemented
443Q8⋊C8C22×C3111yescharacteristic, complemented
444D4⋊C8C22×C3111yescharacteristic
445D4⋊C8C22×C3111yescharacteristic
446D4⋊C8C22×C3111yescharacteristic
447D4⋊C8C22×C3111yescharacteristic
448D4⋊C8C22×C3111yescharacteristic, complemented
449D4⋊C8C22×C3111yescharacteristic, complemented
450C2×C31—41no—
451C2×C31—81no—
452C2×C31—82no—
453C2×C31—81no—
454C2×C31—81no—
455C2×C31#300911yescharacteristic
456C2×C31#301211yescharacteristic
457C2×C31#301811yescharacteristic
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C22×D4—21no—
463C22×D4—21no—
464C2×Q16—21no—
465C2×SD16—22no—
466C2×SD16—21no—
467C2×M16—21no—
468C22×C8—21no—
469C4⋊Q8D4×C3111yescharacteristic
470C4⋊Q8C23×C3111yescharacteristic
471C4⋊Q8C23×C3111yescharacteristic
472C4⋊Q8C23×C3111yescharacteristic
473#127—22no—
474#127—21no—
475#127D4×C3111yescharacteristic
476#127C23×C3111yescharacteristic
477#126—22no—
478#126—22no—
479#126—21no—
480#125—21no—
481#125D4×C3111yescharacteristic
482#124—22no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124D4×C3111yescharacteristic
487#123—22no—
488#123—22no—
489#123—21no—
490#123—22no—
491C22⋊Q8—22no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8D4×C3111yescharacteristic
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—22no—
502#121—21no—
503#121—22no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121D4×C3111yescharacteristic
510#121D4×C3111yescharacteristic
511#121D4×C3111yescharacteristic
512#121D4×C3112yes—
513#120—22no—
514#120—22no—
515#120—22no—
516#120—22no—
517C4×Q8—21no—
518C4×Q8—21no—
519C4×Q8—21no—
520C4×Q8C23×C3111yescharacteristic
521C4×D4—22no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4D4×C3112yes—
527C4×D4C23×C3111yescharacteristic
528C4×D4C23×C3111yescharacteristic
529C4×D4C23×C3111yescharacteristic
530#117—21no—
531#117—21no—
532#117—21no—
533C2×C4⋊C4—21no—
534C2×C22⋊C4—22no—
535C2×C42C23×C3111yescharacteristic
536#107—21no—
537#107—21no—
538#107—21no—
539#106—22no—
540#106—21no—
541#106—21no—
542#106—21no—
543C4⋊C8—21no—
544C4⋊C8C23×C3111yescharacteristic
545C4⋊C8C23×C3111yescharacteristic
546C4⋊C8C23×C3111yescharacteristic
547C4⋊C8C23×C3111yescharacteristic
548#103—21no—
549#103—22no—
550#103—21no—
551#103—21no—
552#102—22no—
553#102—21no—
554#102—21no—
555#102—21no—
556#102—21no—
557#102—21no—
558C22⋊C8—21no—
559#97—21no—
560C4×C8—21no—
561C4×C8C23×C3111yescharacteristic
562C4×C8C23×C3111yescharacteristic
563C31#1870511yescharacteristic, direct product factor, Sylow
564C24—22no—
565#41—81no—
566#41—81no—
567#41—81no—
568#41—81no—
569#41—81no—
570#41—81no—
571#41—81no—
572#41—81no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8C2×D4×C3111yescharacteristic
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4—81no—
594C2×D4—81no—
595C2×D4C2×D4×C3111yescharacteristic
596C2×D4C2×D4×C3111yescharacteristic
597C2×D4C2×D4×C3111yescharacteristic
598C2×D4C2×D4×C3112yes—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608Q16—81no—
609SD16—44no—
610SD16—81no—
611M16—81no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—42no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—41no—
632C4⋊C4—41no—
633C4⋊C4C2×D4×C3111yescharacteristic
634C4⋊C4C2×D4×C3112yes—
635C4⋊C4C2×D4×C3111yescharacteristic
636C4⋊C4C2×D4×C3111yescharacteristic
637C4⋊C4C2×D4×C3111yescharacteristic
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—41no—
655C42—22no—
656C42—21no—
657C42—41no—
658C42C2×D4×C3111yescharacteristic
659C42C2×D4×C3111yescharacteristic
660C42C2×D4×C3111yescharacteristic
661C42C24×C3111yescharacteristic
662C23—21no—
663C23—21no—
664C23—22no—
665C23—21no—
666C23—82no—
667C23—82no—
668C23—82no—
669C23C31×#12011yescharacteristic
670Q8—21no—
671Q8—21no—
672Q8—42no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—41no—
677Q8—81no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—21no—
682D4—21no—
683D4—21no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—82no—
693D4—81no—
694D4—81no—
695D4—82no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—82no—
720C2×C4—82no—
721C2×C4—82no—
722C2×C4C31×#12011yescharacteristic
723C2×C4C31×#12011yescharacteristic
724C2×C4C31×#12011yescharacteristic
725C2×C4C22×D4×C3111yescharacteristic
726C2×C4C22×D4×C3111yescharacteristic
727C2×C4C22×D4×C3111yescharacteristic
728C8—22no—
729C8—41no—
730C8—41no—
731C8—41no—
732C8—41no—
733C8—41no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—41no—
738C22—41no—
739C22—42no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—164no—
750C22C2×C31×#12011yescharacteristic
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—42no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4C31×#57611yescharacteristic
764C4C31×#57711yescharacteristic
765C4C31×#57711yescharacteristic
766C4C31×#57711yescharacteristic
767C2—41no—
768C2—81no—
769C2—81no—
770C2—82no—
771C2—81no—
772C2C31×#300911yescharacteristic
773C2C31×#301211yescharacteristic
774C2C31×#301811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3546C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3252C2semidirect
3. C31×#3235C2semidirect
4. C31×#3167C2semidirect
5. C31×#1654C2semidirect
6. C31×#1652C2semidirect
7. C31×#1641C2semidirect
8. C31×#1639C2semidirect
9. C31×#1638C2semidirect
10. C31×#1635C2semidirect
11. C31×#1631C2semidirect
12. C31×#1629C2semidirect
13. C31×#1557C2semidirect
14. C31×#1494C2semidirect
15. C31×#1492C2semidirect
30. C31×#533C22semidirect
35. C31×#498C22semidirect
38. C31×#487C22semidirect
43. C31×#477C22semidirect
46. C31×#476C22semidirect
48. C31×#474C22semidirect
53. C31×#462C22semidirect
56. C31×#432C22semidirect
57. C31×#423C22semidirect
58. C2×C4×C8×C31C22semidirect
59. C31×#332C22semidirect
60. C31×#332C22semidirect
63. C31×Q8⋊C8C22semidirect
64. C31×Q8⋊C8C22semidirect
69. C31×D4⋊C8C22semidirect
70. C31×D4⋊C8C22semidirect
274. #18705C31direct (N × H)
348. #3252C2×C31semidirect
349. #3235C2×C31semidirect
350. #3167C2×C31semidirect
351. #1654C2×C31semidirect
352. #1652C2×C31semidirect
353. #1641C2×C31semidirect
354. #1639C2×C31semidirect
355. #1638C2×C31semidirect
356. #1635C2×C31semidirect
357. #1631C2×C31semidirect
358. #1629C2×C31semidirect
359. #1557C2×C31semidirect
360. #1494C2×C31semidirect
361. #1492C2×C31semidirect
409. #533C22×C31semidirect
414. #498C22×C31semidirect
417. #487C22×C31semidirect
422. #477C22×C31semidirect
425. #476C22×C31semidirect
427. #474C22×C31semidirect
432. #462C22×C31semidirect
435. #432C22×C31semidirect
436. #423C22×C31semidirect
437. C2×C4×C8C22×C31semidirect
438. #332C22×C31semidirect
439. #332C22×C31semidirect
442. Q8⋊C8C22×C31semidirect
443. Q8⋊C8C22×C31semidirect
448. D4⋊C8C22×C31semidirect
449. D4⋊C8C22×C31semidirect
563. C31#18705direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35462
C31×#32522
C31×#32352
C31×#31672
C31×#16542
C31×#16522
C31×#16412
C31×#16392
C31×#16382
C31×#16352
C31×#16312
C31×#16292
C31×#15572
C31×#14942
C31×#14922
#1870531