Finite Group Databasebeta

← C31×#18464 #21475223

Subgroups — C31×#18464 #21475223

Order 7936.

970 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3564C211yesmaximal, characteristic, complemented
2C31×#3217C211yesmaximal, characteristic, complemented
3C31×#3208C211yesmaximal, characteristic, complemented
4C31×#2818C211yesmaximal, characteristic, complemented
5C31×#1600C212yesmaximal, complemented
6C31×#1599C212yesmaximal, complemented
7C31×#1597C212yesmaximal, complemented
8C31×#1596C212yesmaximal, complemented
9C31×#1521C211yesmaximal, characteristic, complemented
10C31×#1515C211yesmaximal, characteristic, complemented
11C31×#1473C211yesmaximal, characteristic, complemented
12C31×#563—21no—
13C31×#563—21no—
14C31×#556—21no—
15C31×#554—21no—
16C31×#552—21no—
17C31×#552—21no—
18C31×#551—21no—
19C31×#551—21no—
20C31×#544C2211yescharacteristic
21C31×#543C2211yescharacteristic
22C31×#542—21no—
23C31×#541—21no—
24C31×#541—21no—
25C31×#539—21no—
26C31×#539C2211yescharacteristic
27C31×#538C2211yescharacteristic
28C31×#533C2211yescharacteristic
29C2×C31×#127C2211yescharacteristic
30C31×#529C2211yescharacteristic
31C2×C31×#126C2211yescharacteristic
32C31×#496—21no—
33C31×#492—21no—
34C31×#490—21no—
35C31×#486—21no—
36C31×#460—21no—
37C31×#460—21no—
38C31×#460—21no—
39C31×#459—21no—
40C31×#450C2212yes—
41C31×#450C2212yes—
42C31×#450C2212yes—
43C31×#447C2212yes—
44C31×#432C2211yescharacteristic
45C31×#431C2211yescharacteristic
46C31×#394—21no—
47C31×#394—21no—
48C31×#394C2212yes—
49C31×#392—21no—
50C31×#392—21no—
51C31×#392C2212yes—
52C31×#383C2211yescharacteristic
53C31×#328C2212yes—
54C31×#328C2212yes—
55C31×#328C2212yes—
56C31×#327C2212yes—
57C31×#324C2212yes—
58C31×#323C2212yes—
59C22×D4×C31—22no—
60C22×D4×C31—21no—
61C22×D4×C31—21no—
62C22×D4×C31C2312yes—
63C2×SD16×C31—22no—
64C2×SD16×C31—22no—
65C2×SD16×C31—22no—
66C2×D8×C31—22no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—21no—
70C31×C4⋊Q8D411yescharacteristic, complemented
71C31×C4⋊Q8D411yescharacteristic, complemented
72C31×#127—21no—
73C31×#127—21no—
74C31×#127—21no—
75C31×#127—21no—
76C31×#126—21no—
77C31×#126—21no—
78C31×#126—21no—
79C31×#126—21no—
80C31×#126—21no—
81C31×#126—21no—
82C31×#126—21no—
83C31×#126—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#125—21no—
90C31×#125—21no—
91C31×#125—21no—
92C31×#125—21no—
93C31×#125—21no—
94C31×#125—21no—
95C31×#125—21no—
96C31×#125—21no—
97C31×#125—21no—
98C31×#125D411yescharacteristic, complemented
99C31×#124—21no—
100C31×#124—21no—
101C31×#124—21no—
102C31×#124D411yescharacteristic, complemented
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×#123—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8—21no—
116C31×C22⋊Q8—21no—
117C31×C22⋊Q8—21no—
118C31×C22⋊Q8—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8C2311yescharacteristic
126C31×C22⋊Q8C2311yescharacteristic
127C31×C22⋊Q8C2311yescharacteristic
128C31×#121—21no—
129C31×#121C2311yescharacteristic
130C31×#120—21no—
131C4×Q8×C31—21no—
132C4×Q8×C31—21no—
133C4×Q8×C31—21no—
134C4×Q8×C31D411yescharacteristic, complemented
135C4×Q8×C31D411yescharacteristic, complemented
136C4×Q8×C31D411yescharacteristic, complemented
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31—21no—
140C4×D4×C31—21no—
141C4×D4×C31—21no—
142C4×D4×C31D411yescharacteristic, complemented
143C31×#117—21no—
144C31×#117—21no—
145C31×#117—21no—
146C31×#117—21no—
147C31×#117—21no—
148C31×#117—21no—
149C2×C4⋊C4×C31—21no—
150C2×C4⋊C4×C31D411yescharacteristic
151C2×C4⋊C4×C31D411yescharacteristic
152C2×C4⋊C4×C31C2311yescharacteristic
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31—22no—
156C2×C22⋊C4×C31—22no—
157C2×C22⋊C4×C31D411yescharacteristic
158C2×C22⋊C4×C31D411yescharacteristic
159C2×C22⋊C4×C31C2311yescharacteristic
160C2×C42×C31C2311yescharacteristic
161C31×C4⋊C8—21no—
162C31×C4⋊C8—21no—
163C31×#102—22no—
164C31×#102—22no—
165C31×#102—22no—
166C31×#102—22no—
167C31×C22⋊C8C2312yes—
168C31×C22⋊C8C2312yes—
169C31×#97—21no—
170C4×C8×C31—21no—
171C31×#95—21no—
172C31×#95—21no—
173C31×#95C2312yes—
174C24×C31—22no—
175C24×C31C2×D411yescharacteristic
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31C2×D411yescharacteristic
180C2×Q8×C31C2×D411yescharacteristic
181C2×Q8×C31C2×D411yescharacteristic
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—22no—
186C2×D4×C31—22no—
187C2×D4×C31—41no—
188C2×D4×C31—41no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—82no—
192C2×D4×C31—82no—
193C2×D4×C31—82no—
194C2×D4×C31—82no—
195C2×D4×C31—82no—
196C2×D4×C31—82no—
197C2×D4×C31C2×D411yescharacteristic
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2411yescharacteristic
210SD16×C31—82no—
211SD16×C31—82no—
212SD16×C31—82no—
213D8×C31—82no—
214C2×C8×C31—22no—
215C2×C8×C31—22no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
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—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—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31C2×D411yescharacteristic
246C4⋊C4×C31C2×D411yescharacteristic
247C4⋊C4×C31C2×D411yescharacteristic
248C4⋊C4×C31C2×D411yescharacteristic
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—82no—
271C22⋊C4×C31—82no—
272C22⋊C4×C31—82no—
273C42×C31—21no—
274C42×C31—21no—
275C42×C31—21no—
276C42×C31—21no—
277C42×C31—21no—
278C42×C31—21no—
279C42×C31—21no—
280C42×C31C2×D411yescharacteristic
281C42×C31C2×D411yescharacteristic
282C42×C31C2×D411yescharacteristic
283C42×C31C2×D411yescharacteristic
284#18464C3111yesmaximal, characteristic, direct product factor, Sylow
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—22no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—42no—
291C23×C31—42no—
292C23×C31—42no—
293C23×C31—42no—
294C23×C31—42no—
295C23×C31—42no—
296C23×C31—42no—
297C23×C31C22×D411yescharacteristic
298Q8×C31—41no—
299Q8×C31—41no—
300Q8×C31—41no—
301Q8×C31—81no—
302Q8×C31—81no—
303Q8×C31—81no—
304D4×C31—41no—
305D4×C31—42no—
306D4×C31—42no—
307D4×C31—42no—
308D4×C31—42no—
309D4×C31—42no—
310D4×C31—82no—
311D4×C31—82no—
312D4×C31—82no—
313D4×C31—82no—
314D4×C31—81no—
315D4×C31—81no—
316D4×C31—88no—
317C2×C4×C31—22no—
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—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—22no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—81no—
337C2×C4×C31—81no—
338C2×C4×C31—81no—
339C2×C4×C31—81no—
340C2×C4×C31—81no—
341C2×C4×C31#12011yescharacteristic
342C2×C4×C31#12011yescharacteristic
343C2×C4×C31#12011yescharacteristic
344C2×C4×C31#12011yescharacteristic
345C2×C4×C31C22×D411yescharacteristic
346C2×C4×C31C22×D411yescharacteristic
347C8×C31—42no—
348C8×C31—42no—
349#3564C2×C3111yescharacteristic, complemented
350#3217C2×C3111yescharacteristic, complemented
351#3208C2×C3111yescharacteristic, complemented
352#2818C2×C3111yescharacteristic, complemented
353#1600C2×C3112yescomplemented
354#1599C2×C3112yescomplemented
355#1597C2×C3112yescomplemented
356#1596C2×C3112yescomplemented
357#1521C2×C3111yescharacteristic, complemented
358#1515C2×C3111yescharacteristic, complemented
359#1473C2×C3111yescharacteristic, complemented
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—41no—
363C22×C31—41no—
364C22×C31—41no—
365C22×C31—41no—
366C22×C31—41no—
367C22×C31—41no—
368C22×C31—82no—
369C22×C31—82no—
370C22×C31—82no—
371C22×C31—82no—
372C22×C31—82no—
373C22×C31—82no—
374C22×C31—82no—
375C22×C31—82no—
376C22×C31C2×#12011yescharacteristic
377C22×C31#57712yes—
378C4×C31—21no—
379C4×C31—21no—
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—21no—
383C4×C31—21no—
384C4×C31—41no—
385C4×C31—41no—
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—
395#563—21no—
396#563—21no—
397#556—21no—
398#554—21no—
399#552—21no—
400#552—21no—
401#551—21no—
402#551—21no—
403#544C22×C3111yescharacteristic
404#543C22×C3111yescharacteristic
405#542—21no—
406#541—21no—
407#541—21no—
408#539—21no—
409#539C22×C3111yescharacteristic
410#538C22×C3111yescharacteristic
411#533C22×C3111yescharacteristic
412C2×#127C22×C3111yescharacteristic
413#529C22×C3111yescharacteristic
414C2×#126C22×C3111yescharacteristic
415#496—21no—
416#492—21no—
417#490—21no—
418#486—21no—
419#460—21no—
420#460—21no—
421#460—21no—
422#459—21no—
423#450C22×C3112yes—
424#450C22×C3112yes—
425#450C22×C3112yes—
426#447C22×C3112yes—
427#432C22×C3111yescharacteristic
428#431C22×C3111yescharacteristic
429#394—21no—
430#394—21no—
431#394C22×C3112yes—
432#392—21no—
433#392—21no—
434#392C22×C3112yes—
435#383C22×C3111yescharacteristic
436#328C22×C3112yes—
437#328C22×C3112yes—
438#328C22×C3112yes—
439#327C22×C3112yes—
440#324C22×C3112yes—
441#323C22×C3112yes—
442C2×C31—22no—
443C2×C31—81no—
444C2×C31—81no—
445C2×C31—162no—
446C2×C31#301011yescharacteristic
447C2×C31#302111yescharacteristic
448C2×C31#302711yescharacteristic
449C22×D4—22no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4C23×C3112yes—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×D8—22no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459C4⋊Q8—21no—
460C4⋊Q8D4×C3111yescharacteristic, complemented
461C4⋊Q8D4×C3111yescharacteristic, complemented
462#127—21no—
463#127—21no—
464#127—21no—
465#127—21no—
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#126—21no—
476#126—21no—
477#126—21no—
478#126—21no—
479#125—21no—
480#125—21no—
481#125—21no—
482#125—21no—
483#125—21no—
484#125—21no—
485#125—21no—
486#125—21no—
487#125—21no—
488#125D4×C3111yescharacteristic, complemented
489#124—21no—
490#124—21no—
491#124—21no—
492#124D4×C3111yescharacteristic, complemented
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123—21no—
499#123—21no—
500#123—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503C22⋊Q8—21no—
504C22⋊Q8—21no—
505C22⋊Q8—21no—
506C22⋊Q8—21no—
507C22⋊Q8—21no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512C22⋊Q8—21no—
513C22⋊Q8—21no—
514C22⋊Q8—21no—
515C22⋊Q8C23×C3111yescharacteristic
516C22⋊Q8C23×C3111yescharacteristic
517C22⋊Q8C23×C3111yescharacteristic
518#121—21no—
519#121C23×C3111yescharacteristic
520#120—21no—
521C4×Q8—21no—
522C4×Q8—21no—
523C4×Q8—21no—
524C4×Q8D4×C3111yescharacteristic, complemented
525C4×Q8D4×C3111yescharacteristic, complemented
526C4×Q8D4×C3111yescharacteristic, complemented
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4D4×C3111yescharacteristic, complemented
533#117—21no—
534#117—21no—
535#117—21no—
536#117—21no—
537#117—21no—
538#117—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4D4×C3111yescharacteristic
541C2×C4⋊C4D4×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—22no—
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#102—22no—
554#102—22no—
555#102—22no—
556#102—22no—
557C22⋊C8C23×C3112yes—
558C22⋊C8C23×C3112yes—
559#97—21no—
560C4×C8—21no—
561#95—21no—
562#95—21no—
563#95C23×C3112yes—
564C31#1846411yescharacteristic, direct product factor, Sylow
565C24—22no—
566C24C2×D4×C3111yescharacteristic
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8C2×D4×C3111yescharacteristic
571C2×Q8C2×D4×C3111yescharacteristic
572C2×Q8C2×D4×C3111yescharacteristic
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—82no—
583C2×D4—82no—
584C2×D4—82no—
585C2×D4—82no—
586C2×D4—82no—
587C2×D4—82no—
588C2×D4C2×D4×C3111yescharacteristic
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C24×C3111yescharacteristic
601SD16—82no—
602SD16—82no—
603SD16—82no—
604D8—82no—
605C2×C8—22no—
606C2×C8—22no—
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—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—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4C2×D4×C3111yescharacteristic
637C4⋊C4C2×D4×C3111yescharacteristic
638C4⋊C4C2×D4×C3111yescharacteristic
639C4⋊C4C2×D4×C3111yescharacteristic
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—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—82no—
662C22⋊C4—82no—
663C22⋊C4—82no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42C2×D4×C3111yescharacteristic
672C42C2×D4×C3111yescharacteristic
673C42C2×D4×C3111yescharacteristic
674C42C2×D4×C3111yescharacteristic
675C23—21no—
676C23—21no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23C22×D4×C3111yescharacteristic
688Q8—41no—
689Q8—41no—
690Q8—41no—
691Q8—81no—
692Q8—81no—
693Q8—81no—
694D4—41no—
695D4—42no—
696D4—42no—
697D4—42no—
698D4—42no—
699D4—42no—
700D4—82no—
701D4—82no—
702D4—82no—
703D4—82no—
704D4—81no—
705D4—81no—
706D4—88no—
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—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4C31×#12011yescharacteristic
732C2×C4C31×#12011yescharacteristic
733C2×C4C31×#12011yescharacteristic
734C2×C4C31×#12011yescharacteristic
735C2×C4C22×D4×C3111yescharacteristic
736C2×C4C22×D4×C3111yescharacteristic
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—82no—
748C22—82no—
749C22—82no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22C2×C31×#12011yescharacteristic
756C22C31×#57712yes—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—41no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—82no—
774C2—22no—
775C2—81no—
776C2—81no—
777C2—162no—
778C2C31×#301011yescharacteristic
779C2C31×#302111yescharacteristic
780C2C31×#302711yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C31×#3564C2semidirect
2. C31×#3217C2semidirect
3. C31×#3208C2semidirect
4. C31×#2818C2semidirect
5. C31×#1600C2semidirect
6. C31×#1599C2semidirect
7. C31×#1597C2semidirect
8. C31×#1596C2semidirect
9. C31×#1521C2semidirect
10. C31×#1515C2semidirect
11. C31×#1473C2semidirect
70. C31×C4⋊Q8D4semidirect
71. C31×C4⋊Q8D4semidirect
98. C31×#125D4semidirect
102. C31×#124D4semidirect
134. C4×Q8×C31D4semidirect
135. C4×Q8×C31D4semidirect
136. C4×Q8×C31D4semidirect
142. C4×D4×C31D4semidirect
284. #18464C31direct (N × H)
349. #3564C2×C31semidirect
350. #3217C2×C31semidirect
351. #3208C2×C31semidirect
352. #2818C2×C31semidirect
353. #1600C2×C31semidirect
354. #1599C2×C31semidirect
355. #1597C2×C31semidirect
356. #1596C2×C31semidirect
357. #1521C2×C31semidirect
358. #1515C2×C31semidirect
359. #1473C2×C31semidirect
460. C4⋊Q8D4×C31semidirect
461. C4⋊Q8D4×C31semidirect
488. #125D4×C31semidirect
492. #124D4×C31semidirect
524. C4×Q8D4×C31semidirect
525. C4×Q8D4×C31semidirect
526. C4×Q8D4×C31semidirect
532. C4×D4D4×C31semidirect
564. C31#18464direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35642
C31×#32172
C31×#32082
C31×#28182
C31×#16002
C31×#15992
C31×#15972
C31×#15962
C31×#15212
C31×#15152
C31×#14732
#1846431