Finite Group Databasebeta

← C31×#19055 #21475814

Subgroups — C31×#19055 #21475814

Order 7936.

898 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3545C211yesmaximal, characteristic
2C31×#3239C211yesmaximal, characteristic, complemented
3C31×#3218C211yesmaximal, characteristic, complemented
4C2×C31×#489C211yesmaximal, characteristic, complemented
5C31×#1664C212yesmaximal, complemented
6C31×#1662C212yesmaximal, complemented
7C31×#1661C212yesmaximal, complemented
8C31×#1659C212yesmaximal, complemented
9C31×#1533C211yesmaximal, characteristic, complemented
10C31×#1532C211yesmaximal, characteristic, complemented
11C31×#1532C211yesmaximal, characteristic, complemented
12C31×#563C2211yescharacteristic
13C31×#562C2211yescharacteristic
14C31×#562C2211yescharacteristic
15C31×H(3,𝔽4)C2211yescharacteristic
16C31×#555—21no—
17C31×#551—21no—
18C31×#551—21no—
19C31×#551—21no—
20C31×#546—21no—
21C31×#546—21no—
22C31×#542—21no—
23C31×#542—21no—
24C31×#538—21no—
25C31×#538—21no—
26C31×#536—21no—
27C31×#534—21no—
28C2×C31×C4⋊Q8C2211yescharacteristic, complemented
29C31×#529C2211yescharacteristic
30C31×#529C2211yescharacteristic
31C2×C31×#124C2211yescharacteristic
32C31×#501C2212yescomplemented
33C31×#497C2212yescomplemented
34C31×#491C2212yescomplemented
35C31×#489—21no—
36C31×#489—21no—
37C31×#489C2212yes—
38C31×#489C2212yescomplemented
39C31×#489C2212yescomplemented
40C31×#484—21no—
41C31×#481—21no—
42C31×#475—21no—
43C31×#474—21no—
44C31×#462—21no—
45C31×#461—21no—
46C31×#451—21no—
47C31×#448—21no—
48C31×#432C2211yescharacteristic, complemented
49C31×#432C2211yescharacteristic, complemented
50C2×C31×#103—21no—
51C2×C31×#102—21no—
52C2×C31×#97C2211yescharacteristic, complemented
53C31×#330C2212yescomplemented
54C31×#330C2212yescomplemented
55C31×#329C2212yes—
56C31×#329C2212yescomplemented
57C31×#329C2212yescomplemented
58C31×#329C2212yescomplemented
59C2×#41×C31—21no—
60C22×Q8×C31—21no—
61C22×Q8×C31D411yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31D411yescharacteristic
64C2×Q16×C31—22no—
65C2×SD16×C31—22no—
66C22×C8×C31—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—21no—
70C31×C4⋊Q8—21no—
71C31×C4⋊Q8—21no—
72C31×C4⋊Q8C2312yes—
73C31×#126—21no—
74C31×#126—21no—
75C31×#126—21no—
76C31×#126—21no—
77C31×#126—21no—
78C31×#126—21no—
79C31×#125C2311yescharacteristic
80C31×#125C2311yescharacteristic
81C31×#124—21no—
82C31×#124—21no—
83C31×#124—21no—
84C31×#124—21no—
85C31×#124—21no—
86C31×#124—21no—
87C31×#124—21no—
88C31×#124—21no—
89C31×#124D411yescharacteristic
90C31×#124D411yescharacteristic
91C31×#124C2311yescharacteristic
92C31×#124C2311yescharacteristic
93C31×#124C2311yescharacteristic
94C31×#124C2311yescharacteristic
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×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×C22⋊Q8—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8D411yescharacteristic
116C31×C22⋊Q8D411yescharacteristic
117C31×#121—21no—
118C31×#121—21no—
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121—21no—
124C31×#121—21no—
125C31×#121D411yescharacteristic
126C31×#121D411yescharacteristic
127C31×#120—21no—
128C31×#120—21no—
129C31×#120—21no—
130C31×#120—21no—
131C31×#120—21no—
132C31×#120—21no—
133C4×Q8×C31D411yescharacteristic
134C4×Q8×C31D411yescharacteristic
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31—21no—
140C4×D4×C31—21no—
141C4×D4×C31D411yescharacteristic
142C4×D4×C31D411yescharacteristic
143C31×#117—21no—
144C31×#117—21no—
145C31×#117—21no—
146C31×#117—21no—
147C31×#117—21no—
148C2×C4⋊C4×C31—21no—
149C2×C4⋊C4×C31—21no—
150C2×C22⋊C4×C31—21no—
151C2×C22⋊C4×C31—21no—
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—21no—
155C2×C42×C31C2311yescharacteristic
156C31×#107—22no—
157C31×#106—22no—
158C31×C4⋊C8—21no—
159C31×C4⋊C8—21no—
160C31×#103—22no—
161C31×#103—22no—
162C31×#103—22no—
163C31×#103—22no—
164C31×#103—22no—
165C31×#102—22no—
166C31×#102—22no—
167C31×#102—22no—
168C31×C22⋊C8—21no—
169C31×C22⋊C8—21no—
170C31×#97—21no—
171C31×#97C2312yes—
172C31×#97C2312yes—
173C31×#97C2312yes—
174C24×C31—21no—
175C24×C31—21no—
176#41×C31—82no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—22no—
180C2×Q8×C31—42no—
181C2×Q8×C31—41no—
182C2×Q8×C31—82no—
183C2×Q8×C31C2×D411yescharacteristic
184C2×Q8×C31C2×D411yescharacteristic
185C2×Q8×C31C2×D411yescharacteristic
186C2×Q8×C31C2×D411yescharacteristic
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—21no—
197C2×D4×C31—42no—
198C2×D4×C31—82no—
199C2×D4×C31C2×D411yescharacteristic
200C2×D4×C31C2×D411yescharacteristic
201C2×D4×C31C2×D411yescharacteristic
202C2×D4×C31C2×D411yescharacteristic
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—41no—
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215Q16×C31—82no—
216SD16×C31—82no—
217C2×C8×C31—22no—
218C2×C8×C31—22no—
219C2×C8×C31—22no—
220C2×C8×C31—42no—
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×C31C2×D411yescharacteristic
240C4⋊C4×C31C2×D411yescharacteristic
241C4⋊C4×C31C2×D411yescharacteristic
242C4⋊C4×C31C2×D411yescharacteristic
243C22⋊C4×C31—21no—
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—21no—
270C22⋊C4×C31—21no—
271C42×C31—21no—
272C42×C31—21no—
273C42×C31—21no—
274C42×C31—21no—
275C42×C31C2×D411yescharacteristic
276C42×C31C2×D411yescharacteristic
277C42×C31C2×D411yescharacteristic
278C42×C31C2411yescharacteristic
279#19055C3111yesmaximal, characteristic, direct product factor, Sylow
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—42no—
285C23×C31—81no—
286C23×C31—81no—
287C23×C31—81no—
288C23×C31—81no—
289C23×C31—81no—
290C23×C31#12011yescharacteristic
291Q8×C31—41no—
292Q8×C31—41no—
293Q8×C31—41no—
294Q8×C31—41no—
295Q8×C31—42no—
296Q8×C31—42no—
297Q8×C31—81no—
298Q8×C31—82no—
299Q8×C31—81no—
300D4×C31—41no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
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—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
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—41no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—42no—
327C2×C4×C31—81no—
328C2×C4×C31—81no—
329C2×C4×C31—81no—
330C2×C4×C31—81no—
331C2×C4×C31—81no—
332C2×C4×C31—81no—
333C2×C4×C31—81no—
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—42no—
342C8×C31—42no—
343C8×C31—42no—
344#3545C2×C3111yescharacteristic
345#3239C2×C3111yescharacteristic, complemented
346#3218C2×C3111yescharacteristic, complemented
347C2×#489C2×C3111yescharacteristic, complemented
348#1664C2×C3112yescomplemented
349#1662C2×C3112yescomplemented
350#1661C2×C3112yescomplemented
351#1659C2×C3112yescomplemented
352#1533C2×C3111yescharacteristic, complemented
353#1532C2×C3111yescharacteristic, complemented
354#1532C2×C3111yescharacteristic, complemented
355C22×C31—21no—
356C22×C31—21no—
357C22×C31—41no—
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—162no—
370C22×C31—162no—
371C22×C31#45512yes—
372C22×C31C2×#12011yescharacteristic
373C4×C31—21no—
374C4×C31—21no—
375C4×C31—21no—
376C4×C31—21no—
377C4×C31—21no—
378C4×C31—21no—
379C4×C31—41no—
380C4×C31—41no—
381C4×C31—41no—
382C4×C31—41no—
383C4×C31—41no—
384C4×C31—41no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—82no—
388#563C22×C3111yescharacteristic
389#562C22×C3111yescharacteristic
390#562C22×C3111yescharacteristic
391H(3,𝔽4)C22×C3111yescharacteristic
392#555—21no—
393#551—21no—
394#551—21no—
395#551—21no—
396#546—21no—
397#546—21no—
398#542—21no—
399#542—21no—
400#538—21no—
401#538—21no—
402#536—21no—
403#534—21no—
404C2×C4⋊Q8C22×C3111yescharacteristic, complemented
405#529C22×C3111yescharacteristic
406#529C22×C3111yescharacteristic
407C2×#124C22×C3111yescharacteristic
408#501C22×C3112yescomplemented
409#497C22×C3112yescomplemented
410#491C22×C3112yescomplemented
411#489—21no—
412#489—21no—
413#489C22×C3112yes—
414#489C22×C3112yescomplemented
415#489C22×C3112yescomplemented
416#484—21no—
417#481—21no—
418#475—21no—
419#474—21no—
420#462—21no—
421#461—21no—
422#451—21no—
423#448—21no—
424#432C22×C3111yescharacteristic, complemented
425#432C22×C3111yescharacteristic, complemented
426C2×#103—21no—
427C2×#102—21no—
428C2×#97C22×C3111yescharacteristic, complemented
429#330C22×C3112yescomplemented
430#330C22×C3112yescomplemented
431#329C22×C3112yes—
432#329C22×C3112yescomplemented
433#329C22×C3112yescomplemented
434#329C22×C3112yescomplemented
435C2×C31—22no—
436C2×C31—81no—
437C2×C31—81no—
438C2×C31—81no—
439C2×C31—81no—
440C2×C31C2×#45511yescharacteristic
441C2×C31#302111yescharacteristic
442C2×C31#302211yescharacteristic
443C2×#41—21no—
444C22×Q8—21no—
445C22×Q8D4×C3111yescharacteristic
446C22×D4—21no—
447C22×D4D4×C3111yescharacteristic
448C2×Q16—22no—
449C2×SD16—22no—
450C22×C8—21no—
451C4⋊Q8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—21no—
454C4⋊Q8—21no—
455C4⋊Q8—21no—
456C4⋊Q8C23×C3112yes—
457#126—21no—
458#126—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#125C23×C3111yescharacteristic
464#125C23×C3111yescharacteristic
465#124—21no—
466#124—21no—
467#124—21no—
468#124—21no—
469#124—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124D4×C3111yescharacteristic
474#124D4×C3111yescharacteristic
475#124C23×C3111yescharacteristic
476#124C23×C3111yescharacteristic
477#124C23×C3111yescharacteristic
478#124C23×C3111yescharacteristic
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488#123—21no—
489#123—21no—
490#123—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8D4×C3111yescharacteristic
500C22⋊Q8D4×C3111yescharacteristic
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121D4×C3111yescharacteristic
510#121D4×C3111yescharacteristic
511#120—21no—
512#120—21no—
513#120—21no—
514#120—21no—
515#120—21no—
516#120—21no—
517C4×Q8D4×C3111yescharacteristic
518C4×Q8D4×C3111yescharacteristic
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4D4×C3111yescharacteristic
526C4×D4D4×C3111yescharacteristic
527#117—21no—
528#117—21no—
529#117—21no—
530#117—21no—
531#117—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C42C23×C3111yescharacteristic
540#107—22no—
541#106—22no—
542C4⋊C8—21no—
543C4⋊C8—21no—
544#103—22no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552C22⋊C8—21no—
553C22⋊C8—21no—
554#97—21no—
555#97C23×C3112yes—
556#97C23×C3112yes—
557#97C23×C3112yes—
558C31#1905511yescharacteristic, direct product factor, Sylow
559C24—21no—
560C24—21no—
561#41—82no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—42no—
566C2×Q8—41no—
567C2×Q8—82no—
568C2×Q8C2×D4×C3111yescharacteristic
569C2×Q8C2×D4×C3111yescharacteristic
570C2×Q8C2×D4×C3111yescharacteristic
571C2×Q8C2×D4×C3111yescharacteristic
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—42no—
583C2×D4—82no—
584C2×D4C2×D4×C3111yescharacteristic
585C2×D4C2×D4×C3111yescharacteristic
586C2×D4C2×D4×C3111yescharacteristic
587C2×D4C2×D4×C3111yescharacteristic
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—41no—
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600Q16—82no—
601SD16—82no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—42no—
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—22no—
621C4⋊C4—22no—
622C4⋊C4—41no—
623C4⋊C4—41no—
624C4⋊C4C2×D4×C3111yescharacteristic
625C4⋊C4C2×D4×C3111yescharacteristic
626C4⋊C4C2×D4×C3111yescharacteristic
627C4⋊C4C2×D4×C3111yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
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—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42C2×D4×C3111yescharacteristic
661C42C2×D4×C3111yescharacteristic
662C42C2×D4×C3111yescharacteristic
663C42C24×C3111yescharacteristic
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—42no—
669C23—81no—
670C23—81no—
671C23—81no—
672C23—81no—
673C23—81no—
674C23C31×#12011yescharacteristic
675Q8—41no—
676Q8—41no—
677Q8—41no—
678Q8—41no—
679Q8—42no—
680Q8—42no—
681Q8—81no—
682Q8—82no—
683Q8—81no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—42no—
689D4—42no—
690D4—81no—
691D4—81no—
692D4—81no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697D4—81no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—81no—
712C2×C4—81no—
713C2×C4—81no—
714C2×C4—81no—
715C2×C4—81no—
716C2×C4—81no—
717C2×C4—81no—
718C2×C4—82no—
719C2×C4C31×#12011yescharacteristic
720C2×C4C31×#12011yescharacteristic
721C2×C4C31×#12011yescharacteristic
722C2×C4C22×D4×C3111yescharacteristic
723C2×C4C22×D4×C3111yescharacteristic
724C2×C4C22×D4×C3111yescharacteristic
725C8—42no—
726C8—42no—
727C8—42no—
728C22—21no—
729C22—21no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—162no—
743C22—162no—
744C22C31×#45512yes—
745C22C2×C31×#12011yescharacteristic
746C4—21no—
747C4—21no—
748C4—21no—
749C4—21no—
750C4—21no—
751C4—21no—
752C4—41no—
753C4—41no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—41no—
760C4—82no—
761C2—22no—
762C2—81no—
763C2—81no—
764C2—81no—
765C2—81no—
766C2C2×C31×#45511yescharacteristic
767C2C31×#302111yescharacteristic
768C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3545C2
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×#3239C2semidirect
3. C31×#3218C2semidirect
4. C2×C31×#489C2semidirect
5. C31×#1664C2semidirect
6. C31×#1662C2semidirect
7. C31×#1661C2semidirect
8. C31×#1659C2semidirect
9. C31×#1533C2semidirect
10. C31×#1532C2semidirect
11. C31×#1532C2semidirect
28. C2×C31×C4⋊Q8C22semidirect
32. C31×#501C22semidirect
33. C31×#497C22semidirect
34. C31×#491C22semidirect
38. C31×#489C22semidirect
39. C31×#489C22semidirect
48. C31×#432C22semidirect
49. C31×#432C22semidirect
52. C2×C31×#97C22semidirect
53. C31×#330C22semidirect
54. C31×#330C22semidirect
56. C31×#329C22semidirect
57. C31×#329C22semidirect
58. C31×#329C22semidirect
279. #19055C31direct (N × H)
345. #3239C2×C31semidirect
346. #3218C2×C31semidirect
347. C2×#489C2×C31semidirect
348. #1664C2×C31semidirect
349. #1662C2×C31semidirect
350. #1661C2×C31semidirect
351. #1659C2×C31semidirect
352. #1533C2×C31semidirect
353. #1532C2×C31semidirect
354. #1532C2×C31semidirect
404. C2×C4⋊Q8C22×C31semidirect
408. #501C22×C31semidirect
409. #497C22×C31semidirect
410. #491C22×C31semidirect
414. #489C22×C31semidirect
415. #489C22×C31semidirect
424. #432C22×C31semidirect
425. #432C22×C31semidirect
428. C2×#97C22×C31semidirect
429. #330C22×C31semidirect
430. #330C22×C31semidirect
432. #329C22×C31semidirect
433. #329C22×C31semidirect
434. #329C22×C31semidirect
558. C31#19055direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35452
C31×#32392
C31×#32182
C2×C31×#4892
C31×#16642
C31×#16622
C31×#16612
C31×#16592
C31×#15332
C31×#15322
#1905531