Finite Group Databasebeta

← C31×#18463 #21475222

Subgroups — C31×#18463 #21475222

Order 7936.

930 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3560C211yesmaximal, characteristic
2C31×#3218C211yesmaximal, characteristic, complemented
3C31×#3206C211yesmaximal, characteristic, complemented
4C31×#2821C211yesmaximal, characteristic, complemented
5C31×#1606C212yesmaximal, complemented
6C31×#1604C212yesmaximal, complemented
7C31×#1603C212yesmaximal, complemented
8C31×#1601C212yesmaximal, complemented
9C31×#1521C211yesmaximal, characteristic, complemented
10C31×#1514C211yesmaximal, characteristic, complemented
11C31×#1473C211yesmaximal, characteristic, complemented
12C31×#563—21no—
13C31×#560—21no—
14C31×#553—21no—
15C31×#553—21no—
16C31×#551—21no—
17C31×#547—21no—
18C31×#546—21no—
19C31×#546—21no—
20C31×#542—21no—
21C31×#539—21no—
22C31×#539C2211yescharacteristic
23C31×#538—21no—
24C31×#538—21no—
25C31×#538C2211yescharacteristic
26C31×#537C2211yescharacteristic
27C31×#534C2211yescharacteristic
28C31×#532C2211yescharacteristic
29C2×C31×C4⋊Q8C2211yescharacteristic, complemented
30C31×#529C2211yescharacteristic
31C2×C31×#126C2211yescharacteristic
32C31×#497—21no—
33C31×#492—21no—
34C31×#491—21no—
35C31×#487—21no—
36C31×#462—21no—
37C31×#461—21no—
38C31×#461—21no—
39C31×#461—21no—
40C31×#451C2212yescomplemented
41C31×#448C2212yes—
42C31×#448C2212yes—
43C31×#448C2212yescomplemented
44C31×#432C2211yescharacteristic, complemented
45C31×#431C2211yescharacteristic, complemented
46C31×#400—21no—
47C31×#399—21no—
48C31×#398—21no—
49C31×#397—21no—
50C31×#395C2212yescomplemented
51C31×#393C2212yes—
52C31×#383C2211yescharacteristic, complemented
53C31×#328C2212yescomplemented
54C31×#327C2212yes—
55C31×#327C2212yes—
56C31×#327C2212yescomplemented
57C31×#324C2212yescomplemented
58C31×#323C2212yes—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C22×Q8×C31C2312yes—
62C22×D4×C31—21no—
63C2×Q16×C31—22no—
64C2×SD16×C31—22no—
65C2×SD16×C31—22no—
66C2×SD16×C31—22no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—21no—
70C31×C4⋊Q8—21no—
71C31×C4⋊Q8—21no—
72C31×C4⋊Q8D411yescharacteristic
73C31×#127D411yescharacteristic
74C31×#126—21no—
75C31×#126—21no—
76C31×#126—21no—
77C31×#126—21no—
78C31×#126—21no—
79C31×#126—21no—
80C31×#126—21no—
81C31×#126—21no—
82C31×#126—21no—
83C31×#125—21no—
84C31×#125—21no—
85C31×#125D411yescharacteristic
86C31×#124—21no—
87C31×#124—21no—
88C31×#124—21no—
89C31×#124—21no—
90C31×#124D411yescharacteristic
91C31×#123—21no—
92C31×#123—21no—
93C31×#123—21no—
94C31×#123—21no—
95C31×#123—21no—
96C31×#123—21no—
97C31×#123—21no—
98C31×#123—21no—
99C31×#123—21no—
100C31×#123—21no—
101C31×#123—21no—
102C31×#123—21no—
103C31×C22⋊Q8—21no—
104C31×C22⋊Q8—21no—
105C31×C22⋊Q8—21no—
106C31×C22⋊Q8—21no—
107C31×C22⋊Q8—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8C2311yescharacteristic
111C31×#121—21no—
112C31×#121—21no—
113C31×#121—21no—
114C31×#121—21no—
115C31×#121—21no—
116C31×#121—21no—
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121C2311yescharacteristic
124C31×#121C2311yescharacteristic
125C31×#121C2311yescharacteristic
126C31×#120—21no—
127C31×#120—21no—
128C31×#120—21no—
129C31×#120—21no—
130C31×#120—21no—
131C4×Q8×C31D411yescharacteristic
132C4×D4×C31—21no—
133C4×D4×C31—21no—
134C4×D4×C31—21no—
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31—21no—
140C4×D4×C31D411yescharacteristic
141C4×D4×C31D411yescharacteristic
142C4×D4×C31D411yescharacteristic
143C31×#117—21no—
144C31×#117—21no—
145C2×C4⋊C4×C31—21no—
146C2×C4⋊C4×C31—21no—
147C2×C4⋊C4×C31—21no—
148C2×C4⋊C4×C31—22no—
149C2×C4⋊C4×C31D411yescharacteristic
150C2×C4⋊C4×C31D411yescharacteristic
151C2×C4⋊C4×C31C2311yescharacteristic
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31D411yescharacteristic
156C2×C22⋊C4×C31D411yescharacteristic
157C2×C22⋊C4×C31C2311yescharacteristic
158C2×C42×C31C2311yescharacteristic
159C31×C4⋊C8—21no—
160C31×C4⋊C8—21no—
161C31×#103—22no—
162C31×#103—22no—
163C31×#103—22no—
164C31×#103—22no—
165C31×C22⋊C8C2312yes—
166C31×C22⋊C8C2312yes—
167C31×#97—21no—
168C4×C8×C31—21no—
169C31×#95—22no—
170C31×#95—21no—
171C31×#95—22no—
172C31×#95—21no—
173C31×#95C2312yes—
174C24×C31—21no—
175C24×C31C2×D411yescharacteristic
176#41×C31—82no—
177#41×C31—82no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—22no—
181C2×Q8×C31—22no—
182C2×Q8×C31—82no—
183C2×Q8×C31C2×D411yescharacteristic
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—82no—
197C2×D4×C31C2×D411yescharacteristic
198C2×D4×C31C2×D411yescharacteristic
199C2×D4×C31C2×D411yescharacteristic
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—22no—
209C22×C4×C31—22no—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2411yescharacteristic
216Q16×C31—82no—
217SD16×C31—82no—
218SD16×C31—82no—
219SD16×C31—82no—
220C2×C8×C31—22no—
221C2×C8×C31—22no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
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—41no—
240C4⋊C4×C31—41no—
241C4⋊C4×C31—41no—
242C4⋊C4×C31—41no—
243C4⋊C4×C31—82no—
244C4⋊C4×C31C2×D411yescharacteristic
245C4⋊C4×C31C2×D411yescharacteristic
246C4⋊C4×C31C2×D411yescharacteristic
247C4⋊C4×C31C2×D411yescharacteristic
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—21no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—21no—
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—21no—
262C22⋊C4×C31—21no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—21no—
265C22⋊C4×C31—21no—
266C22⋊C4×C31—21no—
267C22⋊C4×C31—21no—
268C22⋊C4×C31—21no—
269C22⋊C4×C31—21no—
270C22⋊C4×C31—21no—
271C22⋊C4×C31—21no—
272C22⋊C4×C31—21no—
273C22⋊C4×C31—82no—
274C42×C31—21no—
275C42×C31—21no—
276C42×C31—21no—
277C42×C31C2×D411yescharacteristic
278C42×C31C2×D411yescharacteristic
279C42×C31C2×D411yescharacteristic
280C42×C31C2×D411yescharacteristic
281#18463C3111yesmaximal, characteristic, direct product factor, Sylow
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—22no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—81no—
290C23×C31—81no—
291C23×C31—81no—
292C23×C31C22×D411yescharacteristic
293Q8×C31—41no—
294Q8×C31—42no—
295Q8×C31—42no—
296Q8×C31—42no—
297Q8×C31—42no—
298Q8×C31—81no—
299Q8×C31—81no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—42no—
304D4×C31—42no—
305D4×C31—42no—
306D4×C31—81no—
307D4×C31—81no—
308D4×C31—81no—
309D4×C31—81no—
310D4×C31—81no—
311D4×C31—81no—
312D4×C31—81no—
313D4×C31—81no—
314D4×C31—81no—
315C2×C4×C31—22no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—22no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—81no—
336C2×C4×C31—81no—
337C2×C4×C31—81no—
338C2×C4×C31—81no—
339C2×C4×C31—81no—
340C2×C4×C31—81no—
341C2×C4×C31—81no—
342C2×C4×C31—81no—
343C2×C4×C31#12011yescharacteristic
344C2×C4×C31#12011yescharacteristic
345C2×C4×C31#12011yescharacteristic
346C2×C4×C31#12011yescharacteristic
347C2×C4×C31C22×D411yescharacteristic
348C2×C4×C31C22×D411yescharacteristic
349C8×C31—42no—
350C8×C31—42no—
351#3560C2×C3111yescharacteristic
352#3218C2×C3111yescharacteristic, complemented
353#3206C2×C3111yescharacteristic, complemented
354#2821C2×C3111yescharacteristic, complemented
355#1606C2×C3112yescomplemented
356#1604C2×C3112yescomplemented
357#1603C2×C3112yescomplemented
358#1601C2×C3112yescomplemented
359#1521C2×C3111yescharacteristic, complemented
360#1514C2×C3111yescharacteristic, complemented
361#1473C2×C3111yescharacteristic, complemented
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—41no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—41no—
374C22×C31—41no—
375C22×C31—41no—
376C22×C31—82no—
377C22×C31—162no—
378C22×C31C2×#12011yescharacteristic
379C22×C31#57712yes—
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—21no—
383C4×C31—21no—
384C4×C31—21no—
385C4×C31—21no—
386C4×C31—41no—
387C4×C31—41no—
388C4×C31—41no—
389C4×C31—41no—
390C4×C31—41no—
391C4×C31—41no—
392C4×C31—41no—
393C4×C31—41no—
394C4×C31—82no—
395C4×C31—82no—
396#563—21no—
397#560—21no—
398#553—21no—
399#553—21no—
400#551—21no—
401#547—21no—
402#546—21no—
403#546—21no—
404#542—21no—
405#539—21no—
406#539C22×C3111yescharacteristic
407#538—21no—
408#538—21no—
409#538C22×C3111yescharacteristic
410#537C22×C3111yescharacteristic
411#534C22×C3111yescharacteristic
412#532C22×C3111yescharacteristic
413C2×C4⋊Q8C22×C3111yescharacteristic, complemented
414#529C22×C3111yescharacteristic
415C2×#126C22×C3111yescharacteristic
416#497—21no—
417#492—21no—
418#491—21no—
419#487—21no—
420#462—21no—
421#461—21no—
422#461—21no—
423#461—21no—
424#451C22×C3112yescomplemented
425#448C22×C3112yes—
426#448C22×C3112yes—
427#448C22×C3112yescomplemented
428#432C22×C3111yescharacteristic, complemented
429#431C22×C3111yescharacteristic, complemented
430#400—21no—
431#399—21no—
432#398—21no—
433#397—21no—
434#395C22×C3112yescomplemented
435#393C22×C3112yes—
436#383C22×C3111yescharacteristic, complemented
437#328C22×C3112yescomplemented
438#327C22×C3112yes—
439#327C22×C3112yes—
440#327C22×C3112yescomplemented
441#324C22×C3112yescomplemented
442#323C22×C3112yes—
443C2×C31—22no—
444C2×C31—81no—
445C2×C31—81no—
446C2×C31—81no—
447C2×C31—81no—
448C2×C31#300911yescharacteristic
449C2×C31#302211yescharacteristic
450C2×C31#302711yescharacteristic
451C2×#41—21no—
452C2×#41—21no—
453C22×Q8C23×C3112yes—
454C22×D4—21no—
455C2×Q16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—22no—
459C4⋊Q8—21no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8—21no—
463C4⋊Q8—21no—
464C4⋊Q8D4×C3111yescharacteristic
465#127D4×C3111yescharacteristic
466#126—21no—
467#126—21no—
468#126—21no—
469#126—21no—
470#126—21no—
471#126—21no—
472#126—21no—
473#126—21no—
474#126—21no—
475#125—21no—
476#125—21no—
477#125D4×C3111yescharacteristic
478#124—21no—
479#124—21no—
480#124—21no—
481#124—21no—
482#124D4×C3111yescharacteristic
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8C23×C3111yescharacteristic
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121C23×C3111yescharacteristic
516#121C23×C3111yescharacteristic
517#121C23×C3111yescharacteristic
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523C4×Q8D4×C3111yescharacteristic
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4D4×C3111yescharacteristic
533C4×D4D4×C3111yescharacteristic
534C4×D4D4×C3111yescharacteristic
535#117—21no—
536#117—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4D4×C3111yescharacteristic
542C2×C4⋊C4D4×C3111yescharacteristic
543C2×C4⋊C4C23×C3111yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4D4×C3111yescharacteristic
548C2×C22⋊C4D4×C3111yescharacteristic
549C2×C22⋊C4C23×C3111yescharacteristic
550C2×C42C23×C3111yescharacteristic
551C4⋊C8—21no—
552C4⋊C8—21no—
553#103—22no—
554#103—22no—
555#103—22no—
556#103—22no—
557C22⋊C8C23×C3112yes—
558C22⋊C8C23×C3112yes—
559#97—21no—
560C4×C8—21no—
561#95—21no—
562#95—21no—
563#95—22no—
564#95—22no—
565#95C23×C3112yes—
566C31#1846311yescharacteristic, direct product factor, Sylow
567C24—21no—
568C24C2×D4×C3111yescharacteristic
569#41—82no—
570#41—82no—
571C2×Q8—21no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—22no—
575C2×Q8—82no—
576C2×Q8C2×D4×C3111yescharacteristic
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—82no—
590C2×D4C2×D4×C3111yescharacteristic
591C2×D4C2×D4×C3111yescharacteristic
592C2×D4C2×D4×C3111yescharacteristic
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C2×D4×C3111yescharacteristic
607C22×C4C2×D4×C3111yescharacteristic
608C22×C4C24×C3111yescharacteristic
609Q16—82no—
610SD16—82no—
611SD16—82no—
612SD16—82no—
613C2×C8—22no—
614C2×C8—22no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
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—21no—
632C4⋊C4—41no—
633C4⋊C4—41no—
634C4⋊C4—41no—
635C4⋊C4—41no—
636C4⋊C4—82no—
637C4⋊C4C2×D4×C3111yescharacteristic
638C4⋊C4C2×D4×C3111yescharacteristic
639C4⋊C4C2×D4×C3111yescharacteristic
640C4⋊C4C2×D4×C3111yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
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—82no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42C2×D4×C3111yescharacteristic
671C42C2×D4×C3111yescharacteristic
672C42C2×D4×C3111yescharacteristic
673C42C2×D4×C3111yescharacteristic
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—41no—
680C23—41no—
681C23—81no—
682C23—81no—
683C23—81no—
684C23C22×D4×C3111yescharacteristic
685Q8—41no—
686Q8—42no—
687Q8—42no—
688Q8—42no—
689Q8—42no—
690Q8—81no—
691Q8—81no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—81no—
699D4—81no—
700D4—81no—
701D4—81no—
702D4—81no—
703D4—81no—
704D4—81no—
705D4—81no—
706D4—81no—
707C2×C4—22no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—81no—
732C2×C4—81no—
733C2×C4—81no—
734C2×C4—81no—
735C2×C4C31×#12011yescharacteristic
736C2×C4C31×#12011yescharacteristic
737C2×C4C31×#12011yescharacteristic
738C2×C4C31×#12011yescharacteristic
739C2×C4C22×D4×C3111yescharacteristic
740C2×C4C22×D4×C3111yescharacteristic
741C8—42no—
742C8—42no—
743C22—21no—
744C22—21no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—82no—
758C22—162no—
759C22C2×C31×#12011yescharacteristic
760C22C31×#57712yes—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—82no—
776C4—82no—
777C2—22no—
778C2—81no—
779C2—81no—
780C2—81no—
781C2—81no—
782C2C31×#300911yescharacteristic
783C2C31×#302211yescharacteristic
784C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3560C2
LCSG ▷ C22×C4 ▷ 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×#3218C2semidirect
3. C31×#3206C2semidirect
4. C31×#2821C2semidirect
5. C31×#1606C2semidirect
6. C31×#1604C2semidirect
7. C31×#1603C2semidirect
8. C31×#1601C2semidirect
9. C31×#1521C2semidirect
10. C31×#1514C2semidirect
11. C31×#1473C2semidirect
29. C2×C31×C4⋊Q8C22semidirect
40. C31×#451C22semidirect
43. C31×#448C22semidirect
44. C31×#432C22semidirect
45. C31×#431C22semidirect
50. C31×#395C22semidirect
52. C31×#383C22semidirect
53. C31×#328C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
281. #18463C31direct (N × H)
352. #3218C2×C31semidirect
353. #3206C2×C31semidirect
354. #2821C2×C31semidirect
355. #1606C2×C31semidirect
356. #1604C2×C31semidirect
357. #1603C2×C31semidirect
358. #1601C2×C31semidirect
359. #1521C2×C31semidirect
360. #1514C2×C31semidirect
361. #1473C2×C31semidirect
413. C2×C4⋊Q8C22×C31semidirect
424. #451C22×C31semidirect
427. #448C22×C31semidirect
428. #432C22×C31semidirect
429. #431C22×C31semidirect
434. #395C22×C31semidirect
436. #383C22×C31semidirect
437. #328C22×C31semidirect
440. #327C22×C31semidirect
441. #324C22×C31semidirect
566. C31#18463direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35602
C31×#32182
C31×#32062
C31×#28212
C31×#16062
C31×#16042
C31×#16032
C31×#16012
C31×#15212
C31×#15142
C31×#14732
#1846331