Finite Group Databasebeta

← C31×#24029 #21480788

Subgroups — C31×#24029 #21480788

Order 7936.

1264 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3489C211yesmaximal, characteristic
2C31×#3092C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C31×#2503C211yesmaximal, characteristic, complemented
5C31×#2040C212yesmaximal, complemented
6C31×#2038C212yesmaximal, complemented
7C31×#1901C211yesmaximal, characteristic, complemented
8C31×#1871C211yesmaximal, characteristic, complemented
9C31×#1860C212yesmaximal, complemented
10C31×#1793C212yesmaximal, complemented
11C31×#1789C211yesmaximal, characteristic, complemented
12C2×C31×2−1+4C2211yescharacteristic
13C22×#41×C31C2211yescharacteristic
14C22×M16×C31C2211yescharacteristic
15D4×Q8×C31—21no—
16C31×#548—21no—
17C31×#547—21no—
18C31×#547—22no—
19C31×#546—21no—
20C31×#546—22no—
21C31×#537—21no—
22C31×#537C2211yescharacteristic
23C31×#536—21no—
24C31×#536C2211yescharacteristic
25C31×#525—21no—
26C31×#525C2211yescharacteristic
27C2×C31×C22⋊Q8—21no—
28C2×C31×C22⋊Q8C2211yescharacteristic
29C31×#520C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#484—21no—
32C31×#483—21no—
33C31×#481—21no—
34C31×#480—21no—
35C31×#428C2212yescomplemented
36C2×C31×#104C2212yes—
37C2×C31×#104C2212yes—
38C2×C31×#104C2212yescomplemented
39C31×#417—21no—
40C31×#417—21no—
41C31×#417C2212yes—
42C31×#417C2212yes—
43C31×#417C2212yescomplemented
44C2×C31×#103—21no—
45C2×C31×#102—21no—
46C2×C31×#101C2212yescomplemented
47C31×#407C2211yescharacteristic
48C31×#400—22no—
49C31×#391C2212yescomplemented
50C31×#382C2212yescomplemented
51C31×#381—22no—
52C4×C22⋊C4×C31C2211yescharacteristic
53C31×#343C2212yescomplemented
54C31×#339C2212yescomplemented
55C31×2−1+4—24no—
56C31×2−1+4—42no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—21no—
60C2×#41×C31—22no—
61C2×#41×C31—21no—
62C2×#41×C31—24no—
63C2×#41×C31—42no—
64C2×#41×C31D411yescharacteristic
65C2×#41×C31D411yescharacteristic
66C2×#41×C31C2311yescharacteristic
67C2×#41×C31C2311yescharacteristic
68C2×#41×C31C2311yescharacteristic
69C22×Q8×C31—21no—
70C22×Q8×C31—21no—
71C22×Q8×C31D411yescharacteristic
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31D411yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×M16×C31—21no—
79C2×M16×C31—42no—
80C2×M16×C31C2312yes—
81C2×M16×C31C2312yes—
82C22×C8×C31—21no—
83C31×C4⋊Q8—22no—
84C31×C4⋊Q8—21no—
85C31×#124—22no—
86C31×#124—21no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—21no—
91C31×#123—22no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—21no—
102C31×C22⋊Q8—21no—
103C31×C22⋊Q8D411yescharacteristic
104C31×C22⋊Q8D411yescharacteristic
105C31×#121—22no—
106C31×#121—22no—
107C31×#121—22no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#121—22no—
111C31×#121D411yescharacteristic
112C31×#121D411yescharacteristic
113C31×#120—22no—
114C31×#120—21no—
115C4×Q8×C31—21no—
116C4×D4×C31—22no—
117C4×D4×C31—22no—
118C4×D4×C31—21no—
119C4×D4×C31—22no—
120C4×D4×C31—21no—
121C4×D4×C31—21no—
122C31×#117—21no—
123C31×#117C2311yescharacteristic
124C2×C4⋊C4×C31—22no—
125C2×C4⋊C4×C31—21no—
126C2×C4⋊C4×C31—21no—
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31D412yes—
132C2×C4⋊C4×C31C2312yes—
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31D412yes—
137C2×C42×C31C2312yes—
138C31×#107—22no—
139C31×#106—22no—
140C31×#104—24no—
141C31×#104—42no—
142C31×#104—42no—
143C31×#103—22no—
144C31×#103—22no—
145C31×#103—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—22no—
149C31×#101—42no—
150C31×C22⋊C8—21no—
151C31×C22⋊C8—21no—
152C31×#95—21no—
153C31×#95—24no—
154C31×#95—24no—
155C24×C31—21no—
156C24×C31C2×D411yescharacteristic
157#41×C31—22no—
158#41×C31—22no—
159#41×C31—22no—
160#41×C31—22no—
161#41×C31—22no—
162#41×C31—22no—
163#41×C31—22no—
164#41×C31—44no—
165#41×C31—41no—
166#41×C31—41no—
167#41×C31—44no—
168#41×C31—44no—
169#41×C31—48no—
170#41×C31—42no—
171#41×C31—42no—
172#41×C31#4114yes—
173C2×Q8×C31—22no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—22no—
178C2×Q8×C31—22no—
179C2×Q8×C31—22no—
180C2×Q8×C31—41no—
181C2×Q8×C31—44no—
182C2×Q8×C31—42no—
183C2×Q8×C31—42no—
184C2×Q8×C31C2×D411yescharacteristic
185C2×Q8×C31C2×D411yescharacteristic
186C2×Q8×C31C2×D411yescharacteristic
187C2×D4×C31—21no—
188C2×D4×C31—22no—
189C2×D4×C31—22no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—22no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—41no—
199C2×D4×C31—44no—
200C2×D4×C31C2×D411yescharacteristic
201C2×D4×C31C2×D411yescharacteristic
202C2×D4×C31C2×D411yescharacteristic
203C22×C4×C31—21no—
204C22×C4×C31—22no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—22no—
208C22×C4×C31—21no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—22no—
215C22×C4×C31—22no—
216C22×C4×C31—44no—
217C22×C4×C31—44no—
218C22×C4×C31—41no—
219C22×C4×C31—41no—
220C22×C4×C31C2×D412yes—
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2×D411yescharacteristic
224C22×C4×C31C2×D411yescharacteristic
225C22×C4×C31C2×D411yescharacteristic
226C22×C4×C31C2×D412yes—
227C22×C4×C31C2411yescharacteristic
228M16×C31—22no—
229M16×C31—22no—
230M16×C31—22no—
231M16×C31—22no—
232M16×C31—42no—
233C2×C8×C31—22no—
234C2×C8×C31—22no—
235C2×C8×C31—42no—
236C4⋊C4×C31—22no—
237C4⋊C4×C31—22no—
238C4⋊C4×C31—22no—
239C4⋊C4×C31—22no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—22no—
242C4⋊C4×C31—22no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—22no—
247C4⋊C4×C31—22no—
248C4⋊C4×C31—41no—
249C4⋊C4×C31—41no—
250C4⋊C4×C31C2×D411yescharacteristic
251C4⋊C4×C31C2×D411yescharacteristic
252C22⋊C4×C31—22no—
253C22⋊C4×C31—22no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—22no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—21no—
261C22⋊C4×C31—21no—
262C22⋊C4×C31—21no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—42no—
265C42×C31—22no—
266C42×C31—21no—
267C42×C31—22no—
268C42×C31—22no—
269#24029C3111yesmaximal, characteristic, direct product factor, Sylow
270C23×C31—21no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—41no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—81no—
279C23×C31#12011yescharacteristic
280C23×C31#12011yescharacteristic
281C23×C31C22×D411yescharacteristic
282Q8×C31—21no—
283Q8×C31—21no—
284Q8×C31—21no—
285Q8×C31—22no—
286Q8×C31—42no—
287Q8×C31—44no—
288Q8×C31—41no—
289Q8×C31—41no—
290Q8×C31—42no—
291Q8×C31#12312yes—
292D4×C31—24no—
293D4×C31—21no—
294D4×C31—21no—
295D4×C31—21no—
296D4×C31—22no—
297D4×C31—42no—
298D4×C31—42no—
299D4×C31—42no—
300D4×C31—44no—
301D4×C31—42no—
302D4×C31—42no—
303D4×C31—42no—
304D4×C31—81no—
305D4×C31—82no—
306D4×C31#12312yes—
307C2×C4×C31—21no—
308C2×C4×C31—22no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—24no—
316C2×C4×C31—21no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—21no—
322C2×C4×C31—24no—
323C2×C4×C31—42no—
324C2×C4×C31—42no—
325C2×C4×C31—42no—
326C2×C4×C31—44no—
327C2×C4×C31—44no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—44no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—82no—
338C2×C4×C31—82no—
339C2×C4×C31—82no—
340C2×C4×C31#12011yescharacteristic
341C2×C4×C31#12011yescharacteristic
342C2×C4×C31C22×D411yescharacteristic
343C2×C4×C31C22×D411yescharacteristic
344C2×C4×C31C2×#4112yes—
345C2×C4×C31H(5,𝔽2)12yes—
346C8×C31—42no—
347C8×C31—42no—
348#3489C2×C3111yescharacteristic
349#3092C2×C3111yescharacteristic, complemented
350C2×#417C2×C3111yescharacteristic, complemented
351#2503C2×C3111yescharacteristic, complemented
352#2040C2×C3112yescomplemented
353#2038C2×C3112yescomplemented
354#1901C2×C3111yescharacteristic, complemented
355#1871C2×C3111yescharacteristic, complemented
356#1860C2×C3112yescomplemented
357#1793C2×C3112yescomplemented
358#1789C2×C3111yescharacteristic, complemented
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—22no—
365C22×C31—21no—
366C22×C31—21no—
367C22×C31—44no—
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—84no—
377C22×C31#45412yes—
378C22×C31C2×#12011yescharacteristic
379C22×C31#54612yes—
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—22no—
383C4×C31—42no—
384C4×C31—41no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—42no—
388C4×C31—41no—
389C4×C31—82no—
390C4×C31—82no—
391C4×C31C2×#12311yescharacteristic
392C4×C31#53411yescharacteristic
393C4×C31#54612yes—
394C2×2−1+4C22×C3111yescharacteristic
395C22×#41C22×C3111yescharacteristic
396C22×M16C22×C3111yescharacteristic
397D4×Q8—21no—
398#548—21no—
399#547—21no—
400#547—22no—
401#546—21no—
402#546—22no—
403#537—21no—
404#537C22×C3111yescharacteristic
405#536—21no—
406#536C22×C3111yescharacteristic
407#525—21no—
408#525C22×C3111yescharacteristic
409C2×C22⋊Q8—21no—
410C2×C22⋊Q8C22×C3111yescharacteristic
411#520C22×C3111yescharacteristic
412C22×C4⋊C4C22×C3111yescharacteristic
413#484—21no—
414#483—21no—
415#481—21no—
416#480—21no—
417#428C22×C3112yescomplemented
418C2×#104C22×C3112yes—
419C2×#104C22×C3112yes—
420C2×#104C22×C3112yescomplemented
421#417—21no—
422#417—21no—
423#417C22×C3112yes—
424#417C22×C3112yes—
425#417C22×C3112yescomplemented
426C2×#103—21no—
427C2×#102—21no—
428C2×#101C22×C3112yescomplemented
429#407C22×C3111yescharacteristic
430#400—22no—
431#391C22×C3112yescomplemented
432#382C22×C3112yescomplemented
433#381—22no—
434C4×C22⋊C4C22×C3111yescharacteristic
435#343C22×C3112yescomplemented
436#339C22×C3112yescomplemented
437C2×C31—22no—
438C2×C31—22no—
439C2×C31—41no—
440C2×C31—42no—
441C2×C31—81no—
442C2×C31—81no—
443C2×C31#240511yescharacteristic
444C2×C31C2×#45411yescharacteristic
445C2×C31#302211yescharacteristic
4462−1+4—24no—
4472−1+4—42no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—22no—
452C2×#41—21no—
453C2×#41—24no—
454C2×#41—42no—
455C2×#41D4×C3111yescharacteristic
456C2×#41D4×C3111yescharacteristic
457C2×#41C23×C3111yescharacteristic
458C2×#41C23×C3111yescharacteristic
459C2×#41C23×C3111yescharacteristic
460C22×Q8—21no—
461C22×Q8—21no—
462C22×Q8D4×C3111yescharacteristic
463C22×Q8C23×C3111yescharacteristic
464C22×D4—21no—
465C22×D4D4×C3111yescharacteristic
466C23×C4—21no—
467C23×C4—21no—
468C23×C4C23×C3111yescharacteristic
469C2×M16—21no—
470C2×M16—42no—
471C2×M16C23×C3112yes—
472C2×M16C23×C3112yes—
473C22×C8—21no—
474C4⋊Q8—22no—
475C4⋊Q8—21no—
476#124—22no—
477#124—21no—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—21no—
482#123—22no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8D4×C3111yescharacteristic
495C22⋊Q8D4×C3111yescharacteristic
496#121—22no—
497#121—22no—
498#121—22no—
499#121—21no—
500#121—21no—
501#121—22no—
502#121D4×C3111yescharacteristic
503#121D4×C3111yescharacteristic
504#120—22no—
505#120—21no—
506C4×Q8—21no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—21no—
510C4×D4—22no—
511C4×D4—21no—
512C4×D4—21no—
513#117—21no—
514#117C23×C3111yescharacteristic
515C2×C4⋊C4—22no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4D4×C3112yes—
523C2×C4⋊C4C23×C3112yes—
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C22⋊C4—22no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4D4×C3112yes—
528C2×C42C23×C3112yes—
529#107—22no—
530#106—22no—
531#104—24no—
532#104—42no—
533#104—42no—
534#103—22no—
535#103—22no—
536#103—22no—
537#102—22no—
538#102—22no—
539#102—22no—
540#101—42no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543#95—21no—
544#95—24no—
545#95—24no—
546C31#2402911yescharacteristic, direct product factor, Sylow
547C24—21no—
548C24C2×D4×C3111yescharacteristic
549#41—22no—
550#41—22no—
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—44no—
557#41—41no—
558#41—41no—
559#41—44no—
560#41—44no—
561#41—48no—
562#41—42no—
563#41—42no—
564#41#41×C3114yes—
565C2×Q8—22no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—22no—
572C2×Q8—41no—
573C2×Q8—44no—
574C2×Q8—42no—
575C2×Q8—42no—
576C2×Q8C2×D4×C3111yescharacteristic
577C2×Q8C2×D4×C3111yescharacteristic
578C2×Q8C2×D4×C3111yescharacteristic
579C2×D4—21no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—41no—
591C2×D4—44no—
592C2×D4C2×D4×C3111yescharacteristic
593C2×D4C2×D4×C3111yescharacteristic
594C2×D4C2×D4×C3111yescharacteristic
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—22no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—41no—
611C22×C4—41no—
612C22×C4C2×D4×C3112yes—
613C22×C4C2×D4×C3111yescharacteristic
614C22×C4C2×D4×C3111yescharacteristic
615C22×C4C2×D4×C3111yescharacteristic
616C22×C4C2×D4×C3111yescharacteristic
617C22×C4C2×D4×C3111yescharacteristic
618C22×C4C2×D4×C3112yes—
619C22×C4C24×C3111yescharacteristic
620M16—22no—
621M16—22no—
622M16—22no—
623M16—22no—
624M16—42no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—42no—
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—41no—
641C4⋊C4—41no—
642C4⋊C4C2×D4×C3111yescharacteristic
643C4⋊C4C2×D4×C3111yescharacteristic
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—21no—
650C22⋊C4—22no—
651C22⋊C4—22no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—42no—
657C42—22no—
658C42—21no—
659C42—22no—
660C42—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—81no—
670C23C31×#12011yescharacteristic
671C23C31×#12011yescharacteristic
672C23C22×D4×C3111yescharacteristic
673Q8—21no—
674Q8—21no—
675Q8—21no—
676Q8—22no—
677Q8—42no—
678Q8—44no—
679Q8—41no—
680Q8—41no—
681Q8—42no—
682Q8C31×#12312yes—
683D4—24no—
684D4—21no—
685D4—21no—
686D4—21no—
687D4—22no—
688D4—42no—
689D4—42no—
690D4—42no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—42no—
695D4—81no—
696D4—82no—
697D4C31×#12312yes—
698C2×C4—21no—
699C2×C4—22no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—24no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—82no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C31×#12011yescharacteristic
732C2×C4C31×#12011yescharacteristic
733C2×C4C22×D4×C3111yescharacteristic
734C2×C4C22×D4×C3111yescharacteristic
735C2×C4C2×#41×C3112yes—
736C2×C4C31×H(5,𝔽2)12yes—
737C8—42no—
738C8—42no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—22no—
745C22—21no—
746C22—21no—
747C22—44no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—84no—
757C22C31×#45412yes—
758C22C2×C31×#12011yescharacteristic
759C22C31×#54612yes—
760C4—21no—
761C4—21no—
762C4—22no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—42no—
768C4—41no—
769C4—82no—
770C4—82no—
771C4C2×C31×#12311yescharacteristic
772C4C31×#53411yescharacteristic
773C4C31×#54612yes—
774C2—22no—
775C2—22no—
776C2—41no—
777C2—42no—
778C2—81no—
779C2—81no—
780C2C31×#240511yescharacteristic
781C2C2×C31×#45411yescharacteristic
782C2C31×#302211yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3489C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3092C2semidirect
3. C2×C31×#417C2semidirect
4. C31×#2503C2semidirect
5. C31×#2040C2semidirect
6. C31×#2038C2semidirect
7. C31×#1901C2semidirect
8. C31×#1871C2semidirect
9. C31×#1860C2semidirect
10. C31×#1793C2semidirect
11. C31×#1789C2semidirect
35. C31×#428C22semidirect
38. C2×C31×#104C22semidirect
43. C31×#417C22semidirect
46. C2×C31×#101C22semidirect
49. C31×#391C22semidirect
50. C31×#382C22semidirect
53. C31×#343C22semidirect
54. C31×#339C22semidirect
269. #24029C31direct (N × H)
349. #3092C2×C31semidirect
350. C2×#417C2×C31semidirect
351. #2503C2×C31semidirect
352. #2040C2×C31semidirect
353. #2038C2×C31semidirect
354. #1901C2×C31semidirect
355. #1871C2×C31semidirect
356. #1860C2×C31semidirect
357. #1793C2×C31semidirect
358. #1789C2×C31semidirect
417. #428C22×C31semidirect
420. C2×#104C22×C31semidirect
425. #417C22×C31semidirect
428. C2×#101C22×C31semidirect
431. #391C22×C31semidirect
432. #382C22×C31semidirect
435. #343C22×C31semidirect
436. #339C22×C31semidirect
546. C31#24029direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34892
C31×#30922
C2×C31×#4172
C31×#25032
C31×#20402
C31×#20382
C31×#19012
C31×#18712
C31×#18602
C31×#17932
C31×#17892
#2402931