Finite Group Databasebeta

← C31×#18470 #21475229

Subgroups — C31×#18470 #21475229

Order 7936.

906 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3560C211yesmaximal, characteristic
2C31×#3238C211yesmaximal, characteristic, complemented
3C31×#3226C211yesmaximal, characteristic, complemented
4C31×#2821C211yesmaximal, characteristic, complemented
5C31×#1612C212yesmaximal, complemented
6C31×#1610C212yesmaximal, complemented
7C31×#1609C212yesmaximal, complemented
8C31×#1607C212yesmaximal, 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×#501—21no—
33C31×#500—21no—
34C31×#489—21no—
35C31×#486—21no—
36C31×#483C2212yescomplemented
37C31×#480C2212yes—
38C31×#480C2212yes—
39C31×#480C2212yescomplemented
40C31×#477—21no—
41C31×#476—21no—
42C31×#474—21no—
43C31×#474—21no—
44C31×#432C2211yescharacteristic, complemented
45C31×#431C2211yescharacteristic, complemented
46C31×#400—21no—
47C31×#399—21no—
48C31×#398C2212yescomplemented
49C31×#397C2212yes—
50C31×#395—21no—
51C31×#393—21no—
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×C31—21no—
62C22×D4×C31—21no—
63C31×C4⋊Q8—21no—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8D411yescharacteristic
69C31×#127D411yescharacteristic
70C31×#126—21no—
71C31×#126—21no—
72C31×#126—21no—
73C31×#126—21no—
74C31×#126—21no—
75C31×#126—21no—
76C31×#126—21no—
77C31×#126—21no—
78C31×#126—21no—
79C31×#125—21no—
80C31×#125—21no—
81C31×#125D411yescharacteristic
82C31×#124—21no—
83C31×#124—21no—
84C31×#124—21no—
85C31×#124—21no—
86C31×#124D411yescharacteristic
87C31×#123—21no—
88C31×#123—21no—
89C31×#123—21no—
90C31×#123—21no—
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×C22⋊Q8—21no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—21no—
102C31×C22⋊Q8—21no—
103C31×C22⋊Q8—21no—
104C31×C22⋊Q8—21no—
105C31×C22⋊Q8—21no—
106C31×C22⋊Q8C2311yescharacteristic
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#121—21no—
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×#121C2311yescharacteristic
120C31×#121C2311yescharacteristic
121C31×#121C2311yescharacteristic
122C31×#120—21no—
123C31×#120—21no—
124C31×#120—21no—
125C31×#120—21no—
126C31×#120—21no—
127C4×Q8×C31D411yescharacteristic
128C4×D4×C31—21no—
129C4×D4×C31—21no—
130C4×D4×C31—21no—
131C4×D4×C31—21no—
132C4×D4×C31—21no—
133C4×D4×C31—21no—
134C4×D4×C31—21no—
135C4×D4×C31—21no—
136C4×D4×C31D411yescharacteristic
137C4×D4×C31D411yescharacteristic
138C4×D4×C31D411yescharacteristic
139C31×#117—21no—
140C31×#117—21no—
141C2×C4⋊C4×C31—21no—
142C2×C4⋊C4×C31—21no—
143C2×C4⋊C4×C31—22no—
144C2×C4⋊C4×C31D411yescharacteristic
145C2×C4⋊C4×C31D411yescharacteristic
146C2×C4⋊C4×C31C2312yes—
147C2×C4⋊C4×C31C2311yescharacteristic
148C2×C22⋊C4×C31—21no—
149C2×C22⋊C4×C31—21no—
150C2×C22⋊C4×C31—22no—
151C2×C22⋊C4×C31D411yescharacteristic
152C2×C22⋊C4×C31D411yescharacteristic
153C2×C22⋊C4×C31C2311yescharacteristic
154C2×C42×C31C2311yescharacteristic
155C31×#107—22no—
156C31×#107—22no—
157C31×#107—22no—
158C31×#106—22no—
159C31×C4⋊C8—21no—
160C31×C4⋊C8—21no—
161C31×#103—22no—
162C31×#102—22no—
163C31×#102—22no—
164C31×#102—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—41no—
181C2×Q8×C31—41no—
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
216C2×C8×C31—22no—
217C2×C8×C31—22no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
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—22no—
236C4⋊C4×C31—22no—
237C4⋊C4×C31—41no—
238C4⋊C4×C31—41no—
239C4⋊C4×C31—82no—
240C4⋊C4×C31C2×D411yescharacteristic
241C4⋊C4×C31C2×D411yescharacteristic
242C4⋊C4×C31C2×D411yescharacteristic
243C4⋊C4×C31C2×D411yescharacteristic
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
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—82no—
270C42×C31—21no—
271C42×C31—21no—
272C42×C31—21no—
273C42×C31C2×D411yescharacteristic
274C42×C31C2×D411yescharacteristic
275C42×C31C2×D411yescharacteristic
276C42×C31C2×D411yescharacteristic
277#18470C3111yesmaximal, characteristic, direct product factor, Sylow
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—22no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—81no—
286C23×C31—81no—
287C23×C31—81no—
288C23×C31C22×D411yescharacteristic
289Q8×C31—41no—
290Q8×C31—81no—
291Q8×C31—82no—
292Q8×C31—82no—
293Q8×C31—81no—
294D4×C31—41no—
295D4×C31—41no—
296D4×C31—41no—
297D4×C31—42no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—81no—
301D4×C31—81no—
302D4×C31—81no—
303D4×C31—81no—
304D4×C31—81no—
305D4×C31—81no—
306D4×C31—81no—
307D4×C31—81no—
308D4×C31—81no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—22no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—81no—
330C2×C4×C31—81no—
331C2×C4×C31—81no—
332C2×C4×C31—81no—
333C2×C4×C31—81no—
334C2×C4×C31—81no—
335C2×C4×C31—81no—
336C2×C4×C31—81no—
337C2×C4×C31#12011yescharacteristic
338C2×C4×C31#12011yescharacteristic
339C2×C4×C31#12011yescharacteristic
340C2×C4×C31#12011yescharacteristic
341C2×C4×C31C22×D411yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C8×C31—42no—
344C8×C31—42no—
345#3560C2×C3111yescharacteristic
346#3238C2×C3111yescharacteristic, complemented
347#3226C2×C3111yescharacteristic, complemented
348#2821C2×C3111yescharacteristic, complemented
349#1612C2×C3112yescomplemented
350#1610C2×C3112yescomplemented
351#1609C2×C3112yescomplemented
352#1607C2×C3112yescomplemented
353#1521C2×C3111yescharacteristic, complemented
354#1514C2×C3111yescharacteristic, complemented
355#1473C2×C3111yescharacteristic, complemented
356C22×C31—21no—
357C22×C31—21no—
358C22×C31—41no—
359C22×C31—41no—
360C22×C31—41no—
361C22×C31—41no—
362C22×C31—41no—
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—82no—
371C22×C31—162no—
372C22×C31C2×#12011yescharacteristic
373C22×C31#57612yes—
374C4×C31—21no—
375C4×C31—21no—
376C4×C31—21no—
377C4×C31—21no—
378C4×C31—21no—
379C4×C31—21no—
380C4×C31—41no—
381C4×C31—41no—
382C4×C31—41no—
383C4×C31—41no—
384C4×C31—41no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—41no—
388C4×C31—82no—
389C4×C31—82no—
390#563—21no—
391#560—21no—
392#553—21no—
393#553—21no—
394#551—21no—
395#547—21no—
396#546—21no—
397#546—21no—
398#542—21no—
399#539—21no—
400#539C22×C3111yescharacteristic
401#538—21no—
402#538—21no—
403#538C22×C3111yescharacteristic
404#537C22×C3111yescharacteristic
405#534C22×C3111yescharacteristic
406#532C22×C3111yescharacteristic
407C2×C4⋊Q8C22×C3111yescharacteristic, complemented
408#529C22×C3111yescharacteristic
409C2×#126C22×C3111yescharacteristic
410#501—21no—
411#500—21no—
412#489—21no—
413#486—21no—
414#483C22×C3112yescomplemented
415#480C22×C3112yes—
416#480C22×C3112yes—
417#480C22×C3112yescomplemented
418#477—21no—
419#476—21no—
420#474—21no—
421#474—21no—
422#432C22×C3111yescharacteristic, complemented
423#431C22×C3111yescharacteristic, complemented
424#400—21no—
425#399—21no—
426#398C22×C3112yescomplemented
427#397C22×C3112yes—
428#395—21no—
429#393—21no—
430#383C22×C3111yescharacteristic, complemented
431#328C22×C3112yescomplemented
432#327C22×C3112yes—
433#327C22×C3112yes—
434#327C22×C3112yescomplemented
435#324C22×C3112yescomplemented
436#323C22×C3112yes—
437C2×C31—22no—
438C2×C31—81no—
439C2×C31—81no—
440C2×C31—81no—
441C2×C31—81no—
442C2×C31#300811yescharacteristic
443C2×C31#302211yescharacteristic
444C2×C31#302811yescharacteristic
445C2×#41—21no—
446C2×#41—21no—
447C22×Q8—21no—
448C22×D4—21no—
449C4⋊Q8—21no—
450C4⋊Q8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8D4×C3111yescharacteristic
455#127D4×C3111yescharacteristic
456#126—21no—
457#126—21no—
458#126—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#126—21no—
465#125—21no—
466#125—21no—
467#125D4×C3111yescharacteristic
468#124—21no—
469#124—21no—
470#124—21no—
471#124—21no—
472#124D4×C3111yescharacteristic
473#123—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8C23×C3111yescharacteristic
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121C23×C3111yescharacteristic
506#121C23×C3111yescharacteristic
507#121C23×C3111yescharacteristic
508#120—21no—
509#120—21no—
510#120—21no—
511#120—21no—
512#120—21no—
513C4×Q8D4×C3111yescharacteristic
514C4×D4—21no—
515C4×D4—21no—
516C4×D4—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4D4×C3111yescharacteristic
523C4×D4D4×C3111yescharacteristic
524C4×D4D4×C3111yescharacteristic
525#117—21no—
526#117—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4D4×C3111yescharacteristic
531C2×C4⋊C4D4×C3111yescharacteristic
532C2×C4⋊C4C23×C3112yes—
533C2×C4⋊C4C23×C3111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—22no—
537C2×C22⋊C4D4×C3111yescharacteristic
538C2×C22⋊C4D4×C3111yescharacteristic
539C2×C22⋊C4C23×C3111yescharacteristic
540C2×C42C23×C3111yescharacteristic
541#107—22no—
542#107—22no—
543#107—22no—
544#106—22no—
545C4⋊C8—21no—
546C4⋊C8—21no—
547#103—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8C23×C3112yes—
552C22⋊C8C23×C3112yes—
553#97—21no—
554C4×C8—21no—
555#95—21no—
556#95—21no—
557#95—22no—
558#95—22no—
559#95C23×C3112yes—
560C31#1847011yescharacteristic, direct product factor, Sylow
561C24—21no—
562C24C2×D4×C3111yescharacteristic
563#41—82no—
564#41—82no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—41no—
568C2×Q8—41no—
569C2×Q8—82no—
570C2×Q8C2×D4×C3111yescharacteristic
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—82no—
584C2×D4C2×D4×C3111yescharacteristic
585C2×D4C2×D4×C3111yescharacteristic
586C2×D4C2×D4×C3111yescharacteristic
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C24×C3111yescharacteristic
603C2×C8—22no—
604C2×C8—22no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—41no—
625C4⋊C4—41no—
626C4⋊C4—82no—
627C4⋊C4C2×D4×C3111yescharacteristic
628C4⋊C4C2×D4×C3111yescharacteristic
629C4⋊C4C2×D4×C3111yescharacteristic
630C4⋊C4C2×D4×C3111yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—21no—
637C22⋊C4—21no—
638C22⋊C4—21no—
639C22⋊C4—21no—
640C22⋊C4—21no—
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—82no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×D4×C3111yescharacteristic
661C42C2×D4×C3111yescharacteristic
662C42C2×D4×C3111yescharacteristic
663C42C2×D4×C3111yescharacteristic
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23C22×D4×C3111yescharacteristic
675Q8—41no—
676Q8—81no—
677Q8—82no—
678Q8—82no—
679Q8—81no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—81no—
687D4—81no—
688D4—81no—
689D4—81no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—81no—
719C2×C4—81no—
720C2×C4—81no—
721C2×C4—81no—
722C2×C4—81no—
723C2×C4C31×#12011yescharacteristic
724C2×C4C31×#12011yescharacteristic
725C2×C4C31×#12011yescharacteristic
726C2×C4C31×#12011yescharacteristic
727C2×C4C22×D4×C3111yescharacteristic
728C2×C4C22×D4×C3111yescharacteristic
729C8—42no—
730C8—42no—
731C22—21no—
732C22—21no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—82no—
746C22—162no—
747C22C2×C31×#12011yescharacteristic
748C22C31×#57612yes—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—82no—
764C4—82no—
765C2—22no—
766C2—81no—
767C2—81no—
768C2—81no—
769C2—81no—
770C2C31×#300811yescharacteristic
771C2C31×#302211yescharacteristic
772C2C31×#302811yescharacteristic
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×#3238C2semidirect
3. C31×#3226C2semidirect
4. C31×#2821C2semidirect
5. C31×#1612C2semidirect
6. C31×#1610C2semidirect
7. C31×#1609C2semidirect
8. C31×#1607C2semidirect
9. C31×#1521C2semidirect
10. C31×#1514C2semidirect
11. C31×#1473C2semidirect
29. C2×C31×C4⋊Q8C22semidirect
36. C31×#483C22semidirect
39. C31×#480C22semidirect
44. C31×#432C22semidirect
45. C31×#431C22semidirect
48. C31×#398C22semidirect
52. C31×#383C22semidirect
53. C31×#328C22semidirect
56. C31×#327C22semidirect
57. C31×#324C22semidirect
277. #18470C31direct (N × H)
346. #3238C2×C31semidirect
347. #3226C2×C31semidirect
348. #2821C2×C31semidirect
349. #1612C2×C31semidirect
350. #1610C2×C31semidirect
351. #1609C2×C31semidirect
352. #1607C2×C31semidirect
353. #1521C2×C31semidirect
354. #1514C2×C31semidirect
355. #1473C2×C31semidirect
407. C2×C4⋊Q8C22×C31semidirect
414. #483C22×C31semidirect
417. #480C22×C31semidirect
422. #432C22×C31semidirect
423. #431C22×C31semidirect
426. #398C22×C31semidirect
430. #383C22×C31semidirect
431. #328C22×C31semidirect
434. #327C22×C31semidirect
435. #324C22×C31semidirect
560. C31#18470direct (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×#32382
C31×#32262
C31×#28212
C31×#16122
C31×#16102
C31×#16092
C31×#16072
C31×#15212
C31×#15142
C31×#14732
#1847031