Finite Group Databasebeta

← C31×#18231 #21474990

Subgroups — C31×#18231 #21474990

Order 7936.

1200 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×#3536C211yesmaximal, characteristic, complemented
2C31×#3006C211yesmaximal, characteristic, complemented
3C31×#3002C211yesmaximal, characteristic, complemented
4C31×#2616C211yesmaximal, characteristic, complemented
5C31×#1604C212yesmaximal, complemented
6C31×#1603C212yesmaximal, complemented
7C31×#1598C212yesmaximal, complemented
8C31×#1597C212yesmaximal, complemented
9C31×#1519C211yesmaximal, characteristic, complemented
10C31×#1513C211yesmaximal, characteristic, complemented
11C31×#1472C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C2×C31×AGL(1,ℤ/8)—21no—
14C2×C31×#135—21no—
15C31×#562—22no—
16C31×#554—21no—
17C31×#548—21no—
18C31×#547—21no—
19C31×#546—21no—
20C31×#546—22no—
21C31×#543—21no—
22C31×#542—21no—
23C31×#539C2212yes—
24C31×#538—21no—
25C31×#537—21no—
26C31×#537C2212yes—
27C31×#525C2211yescharacteristic
28C2×C31×C22⋊Q8—21no—
29C2×C31×C22⋊Q8C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C31×#452—21no—
32C31×#451C2211yescharacteristic, complemented
33C31×#450C2211yescharacteristic, complemented
34C31×#449—21no—
35C31×#449—22no—
36C31×#448C2212yes—
37C31×#448C2211yescharacteristic, complemented
38C31×#447C2212yes—
39C31×#447C2211yescharacteristic, complemented
40C31×#417—21no—
41C31×#416—21no—
42C31×#407C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C31×#395C2212yescomplemented
45C31×#394—22no—
46C31×#394C2212yescomplemented
47C31×#380—21no—
48C31×#380C2211yescharacteristic
49C31×#328C2212yescomplemented
50C31×#327C2212yes—
51C31×#327C2212yes—
52C31×#327C2212yescomplemented
53C31×#324C2212yescomplemented
54C31×#324C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31—22no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—21no—
60C2×#41×C31—21no—
61C2×#41×C31—44no—
62C2×#41×C31D411yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31—21no—
67C22×D4×C31D411yescharacteristic
68C22×D4×C31C2311yescharacteristic
69C23×C4×C31—21no—
70C23×C4×C31C2311yescharacteristic
71C31×AGL(1,ℤ/8)—44no—
72C31×#135—44no—
73C2×Q16×C31—21no—
74C2×SD16×C31—21no—
75C2×SD16×C31—22no—
76C2×SD16×C31—21no—
77C2×D8×C31—22no—
78C2×D8×C31—21no—
79C2×M16×C31—21no—
80C22×C8×C31—21no—
81C31×C4⋊Q8—21no—
82C31×#126—22no—
83C31×#125—22no—
84C31×#124—22no—
85C31×#124—21no—
86C31×#124—22no—
87C31×#123—22no—
88C31×#123—22no—
89C31×#123—22no—
90C31×#123—21no—
91C31×#123—22no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8—44no—
104C31×C22⋊Q8D411yescharacteristic
105C31×C22⋊Q8C2311yescharacteristic
106C31×#121—21no—
107C31×#121—22no—
108C31×#121—22no—
109C31×#121—22no—
110C31×#121—22no—
111C31×#121—21no—
112C31×#121—21no—
113C31×#121—22no—
114C31×#121D412yes—
115C31×#121D411yescharacteristic
116C31×#121C2312yes—
117C31×#121C2311yescharacteristic
118C31×#120—22no—
119C31×#120—21no—
120C4×Q8×C31—21no—
121C4×D4×C31—22no—
122C4×D4×C31—21no—
123C4×D4×C31—21no—
124C4×D4×C31—21no—
125C4×D4×C31—22no—
126C31×#117D411yescharacteristic
127C2×C4⋊C4×C31—21no—
128C2×C4⋊C4×C31—22no—
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31D411yescharacteristic
131C2×C4⋊C4×C31D411yescharacteristic
132C2×C4⋊C4×C31C2312yes—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31D412yes—
139C31×#103—21no—
140C31×#103—21no—
141C31×#103—22no—
142C31×#102—21no—
143C31×#102—21no—
144C31×#102—22no—
145C31×C22⋊C8—21no—
146C31×C22⋊C8—21no—
147C31×C22⋊C8C2311yescharacteristic
148C31×C22⋊C8C2311yescharacteristic
149C31×C22⋊C8C2312yes—
150C31×#95—22no—
151C31×#95C2312yes—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31C2×D411yescharacteristic
155#41×C31—24no—
156#41×C31—24no—
157#41×C31—42no—
158#41×C31—42no—
159#41×C31—42no—
160#41×C31—42no—
161#41×C31—42no—
162#41×C31—42no—
163#41×C31—42no—
164#41×C31—82no—
165#41×C31—82no—
166#41×C31—82no—
167C2×Q8×C31—22no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31—42no—
173C2×Q8×C31—42no—
174C2×Q8×C31C2×D411yescharacteristic
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—22no—
180C2×D4×C31—21no—
181C2×D4×C31—22no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—41no—
190C2×D4×C31—41no—
191C2×D4×C31—81no—
192C2×D4×C31—81no—
193C2×D4×C31C2×D411yescharacteristic
194C2×D4×C31C2×D412yes—
195C22×C4×C31—24no—
196C22×C4×C31—21no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—22no—
203C22×C4×C31—42no—
204C22×C4×C31—42no—
205C22×C4×C31—41no—
206C22×C4×C31—41no—
207C22×C4×C31C2×D412yes—
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D412yes—
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2411yescharacteristic
215Q16×C31—42no—
216SD16×C31—42no—
217SD16×C31—42no—
218SD16×C31—44no—
219D8×C31—42no—
220D8×C31—44no—
221M16×C31—42no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—22no—
225C2×C8×C31—42no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—22no—
228C4⋊C4×C31—22no—
229C4⋊C4×C31—22no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—22no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—42no—
238C4⋊C4×C31—44no—
239C4⋊C4×C31C2×D412yes—
240C4⋊C4×C31C2×D411yescharacteristic
241C4⋊C4×C31C2×D411yescharacteristic
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—22no—
245C22⋊C4×C31—22no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—21no—
256C22⋊C4×C31—44no—
257C22⋊C4×C31—82no—
258C22⋊C4×C31—81no—
259C42×C31—22no—
260C42×C31—21no—
261#18231C3111yesmaximal, characteristic, direct product factor, Sylow
262C23×C31—21no—
263C23×C31—21no—
264C23×C31—22no—
265C23×C31—22no—
266C23×C31—21no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—42no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—81no—
277C23×C31—81no—
278C23×C31#12011yescharacteristic
279C23×C31#12011yescharacteristic
280C23×C31C22×D411yescharacteristic
281Q8×C31—22no—
282Q8×C31—22no—
283Q8×C31—41no—
284Q8×C31—41no—
285Q8×C31—41no—
286Q8×C31—42no—
287Q8×C31—81no—
288Q8×C31—82no—
289D4×C31—22no—
290D4×C31—22no—
291D4×C31—42no—
292D4×C31—41no—
293D4×C31—41no—
294D4×C31—41no—
295D4×C31—42no—
296D4×C31—44no—
297D4×C31—44no—
298D4×C31—42no—
299D4×C31—41no—
300D4×C31—42no—
301D4×C31—41no—
302D4×C31—42no—
303D4×C31—82no—
304D4×C31—81no—
305D4×C31—82no—
306D4×C31—82no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—21no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—44no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—44no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—81no—
332C2×C4×C31—82no—
333C2×C4×C31—82no—
334C2×C4×C31—82no—
335C2×C4×C31#12011yescharacteristic
336C2×C4×C31#12011yescharacteristic
337C2×C4×C31C22×D411yescharacteristic
338C2×C4×C31C22×D411yescharacteristic
339C8×C31—41no—
340C8×C31—41no—
341C8×C31—42no—
342#3536C2×C3111yescharacteristic, complemented
343#3006C2×C3111yescharacteristic, complemented
344#3002C2×C3111yescharacteristic, complemented
345#2616C2×C3111yescharacteristic, complemented
346#1604C2×C3112yescomplemented
347#1603C2×C3112yescomplemented
348#1598C2×C3112yescomplemented
349#1597C2×C3112yescomplemented
350#1519C2×C3111yescharacteristic, complemented
351#1513C2×C3111yescharacteristic, complemented
352#1472C2×C3111yescharacteristic, complemented
353C22×C31—21no—
354C22×C31—21no—
355C22×C31—21no—
356C22×C31—21no—
357C22×C31—21no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—41no—
364C22×C31—42no—
365C22×C31—41no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—41no—
369C22×C31—42no—
370C22×C31—81no—
371C22×C31—81no—
372C22×C31—81no—
373C22×C31—81no—
374C22×C31—81no—
375C22×C31—81no—
376C22×C31—162no—
377C22×C31C2×#12011yescharacteristic
378C22×C31#57611yescharacteristic
379C22×C31#57711yescharacteristic
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—21no—
383C4×C31—42no—
384C4×C31—42no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—42no—
388C4×C31—41no—
389C4×C31—42no—
390C4×C31—82no—
391C4×C31B(4,𝔽2)12yes—
392C22×#41C22×C3111yescharacteristic
393C2×AGL(1,ℤ/8)—21no—
394C2×#135—21no—
395#562—22no—
396#554—21no—
397#548—21no—
398#547—21no—
399#546—21no—
400#546—22no—
401#543—21no—
402#542—21no—
403#539C22×C3112yes—
404#538—21no—
405#537—21no—
406#537C22×C3112yes—
407#525C22×C3111yescharacteristic
408C2×C22⋊Q8—21no—
409C2×C22⋊Q8C22×C3111yescharacteristic
410C2×#121C22×C3111yescharacteristic
411#452—21no—
412#451C22×C3111yescharacteristic, complemented
413#450C22×C3111yescharacteristic, complemented
414#449—21no—
415#449—22no—
416#448C22×C3112yes—
417#448C22×C3111yescharacteristic, complemented
418#447C22×C3112yes—
419#447C22×C3111yescharacteristic, complemented
420#417—21no—
421#416—21no—
422#407C22×C3111yescharacteristic
423C2×C22⋊C8C22×C3111yescharacteristic
424#395C22×C3112yescomplemented
425#394—22no—
426#394C22×C3112yescomplemented
427#380—21no—
428#380C22×C3111yescharacteristic
429#328C22×C3112yescomplemented
430#327C22×C3112yes—
431#327C22×C3112yes—
432#327C22×C3112yescomplemented
433#324C22×C3112yescomplemented
434#324C22×C3112yescomplemented
435C2×C31—21no—
436C2×C31—21no—
437C2×C31—41no—
438C2×C31—41no—
439C2×C31—81no—
440C2×C31—82no—
441C2×C31—82no—
442C2×C31#301211yescharacteristic
443C2×C31#302011yescharacteristic
444C2×C31C2×B(4,𝔽2)11yescharacteristic
445C2×#41—21no—
446C2×#41—22no—
447C2×#41—21no—
448C2×#41—21no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41—44no—
452C2×#41D4×C3111yescharacteristic
453C22×Q8D4×C3111yescharacteristic
454C22×Q8C23×C3111yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4D4×C3111yescharacteristic
458C22×D4C23×C3111yescharacteristic
459C23×C4—21no—
460C23×C4C23×C3111yescharacteristic
461AGL(1,ℤ/8)—44no—
462#135—44no—
463C2×Q16—21no—
464C2×SD16—21no—
465C2×SD16—21no—
466C2×SD16—22no—
467C2×D8—21no—
468C2×D8—22no—
469C2×M16—21no—
470C22×C8—21no—
471C4⋊Q8—21no—
472#126—22no—
473#125—22no—
474#124—22no—
475#124—21no—
476#124—22no—
477#123—22no—
478#123—22no—
479#123—22no—
480#123—21no—
481#123—22no—
482C22⋊Q8—21no—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—22no—
492C22⋊Q8—22no—
493C22⋊Q8—44no—
494C22⋊Q8D4×C3111yescharacteristic
495C22⋊Q8C23×C3111yescharacteristic
496#121—21no—
497#121—22no—
498#121—22no—
499#121—22no—
500#121—22no—
501#121—21no—
502#121—21no—
503#121—22no—
504#121D4×C3112yes—
505#121D4×C3111yescharacteristic
506#121C23×C3112yes—
507#121C23×C3111yescharacteristic
508#120—22no—
509#120—21no—
510C4×Q8—21no—
511C4×D4—22no—
512C4×D4—21no—
513C4×D4—21no—
514C4×D4—21no—
515C4×D4—22no—
516#117D4×C3111yescharacteristic
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4D4×C3111yescharacteristic
521C2×C4⋊C4D4×C3111yescharacteristic
522C2×C4⋊C4C23×C3112yes—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4D4×C3112yes—
529#103—21no—
530#103—21no—
531#103—22no—
532#102—21no—
533#102—21no—
534#102—22no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8C23×C3111yescharacteristic
538C22⋊C8C23×C3111yescharacteristic
539C22⋊C8C23×C3112yes—
540#95—22no—
541#95C23×C3112yes—
542C31#1823111yescharacteristic, direct product factor, Sylow
543C24—21no—
544C24—21no—
545C24C2×D4×C3111yescharacteristic
546#41—24no—
547#41—24no—
548#41—42no—
549#41—42no—
550#41—42no—
551#41—42no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—82no—
556#41—82no—
557#41—82no—
558C2×Q8—22no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8C2×D4×C3111yescharacteristic
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—22no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—42no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4C2×D4×C3111yescharacteristic
585C2×D4C2×D4×C3112yes—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—41no—
597C22×C4—41no—
598C22×C4C2×D4×C3112yes—
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C2×D4×C3112yes—
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C24×C3111yescharacteristic
606Q16—42no—
607SD16—42no—
608SD16—42no—
609SD16—44no—
610D8—42no—
611D8—44no—
612M16—42no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—22no—
616C2×C8—42no—
617C4⋊C4—22no—
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—22no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—44no—
630C4⋊C4C2×D4×C3112yes—
631C4⋊C4C2×D4×C3111yescharacteristic
632C4⋊C4C2×D4×C3111yescharacteristic
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—22no—
644C22⋊C4—21no—
645C22⋊C4—22no—
646C22⋊C4—21no—
647C22⋊C4—44no—
648C22⋊C4—82no—
649C22⋊C4—81no—
650C42—22no—
651C42—21no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—22no—
656C23—21no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—42no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—81no—
667C23—81no—
668C23C31×#12011yescharacteristic
669C23C31×#12011yescharacteristic
670C23C22×D4×C3111yescharacteristic
671Q8—22no—
672Q8—22no—
673Q8—41no—
674Q8—41no—
675Q8—41no—
676Q8—42no—
677Q8—81no—
678Q8—82no—
679D4—22no—
680D4—22no—
681D4—42no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—42no—
686D4—44no—
687D4—44no—
688D4—42no—
689D4—41no—
690D4—42no—
691D4—41no—
692D4—42no—
693D4—82no—
694D4—81no—
695D4—82no—
696D4—82no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—44no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—81no—
722C2×C4—82no—
723C2×C4—82no—
724C2×C4—82no—
725C2×C4C31×#12011yescharacteristic
726C2×C4C31×#12011yescharacteristic
727C2×C4C22×D4×C3111yescharacteristic
728C2×C4C22×D4×C3111yescharacteristic
729C8—41no—
730C8—41no—
731C8—42no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—42no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—41no—
745C22—42no—
746C22—42no—
747C22—41no—
748C22—42no—
749C22—81no—
750C22—81no—
751C22—81no—
752C22—81no—
753C22—81no—
754C22—81no—
755C22—162no—
756C22C2×C31×#12011yescharacteristic
757C22C31×#57611yescharacteristic
758C22C31×#57711yescharacteristic
759C4—21no—
760C4—21no—
761C4—21no—
762C4—42no—
763C4—42no—
764C4—41no—
765C4—41no—
766C4—42no—
767C4—41no—
768C4—42no—
769C4—82no—
770C4C31×B(4,𝔽2)12yes—
771C2—21no—
772C2—21no—
773C2—41no—
774C2—41no—
775C2—82no—
776C2—82no—
777C2—81no—
778C2C31×#301211yescharacteristic
779C2C31×#302011yescharacteristic
780C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3536C2semidirect
2. C31×#3006C2semidirect
3. C31×#3002C2semidirect
4. C31×#2616C2semidirect
5. C31×#1604C2semidirect
6. C31×#1603C2semidirect
7. C31×#1598C2semidirect
8. C31×#1597C2semidirect
9. C31×#1519C2semidirect
10. C31×#1513C2semidirect
11. C31×#1472C2semidirect
32. C31×#451C22semidirect
33. C31×#450C22semidirect
37. C31×#448C22semidirect
39. C31×#447C22semidirect
44. C31×#395C22semidirect
46. C31×#394C22semidirect
49. C31×#328C22semidirect
52. C31×#327C22semidirect
53. C31×#324C22semidirect
54. C31×#324C22semidirect
261. #18231C31direct (N × H)
342. #3536C2×C31semidirect
343. #3006C2×C31semidirect
344. #3002C2×C31semidirect
345. #2616C2×C31semidirect
346. #1604C2×C31semidirect
347. #1603C2×C31semidirect
348. #1598C2×C31semidirect
349. #1597C2×C31semidirect
350. #1519C2×C31semidirect
351. #1513C2×C31semidirect
352. #1472C2×C31semidirect
412. #451C22×C31semidirect
413. #450C22×C31semidirect
417. #448C22×C31semidirect
419. #447C22×C31semidirect
424. #395C22×C31semidirect
426. #394C22×C31semidirect
429. #328C22×C31semidirect
432. #327C22×C31semidirect
433. #324C22×C31semidirect
434. #324C22×C31semidirect
542. C31#18231direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35362
C31×#30062
C31×#30022
C31×#26162
C31×#16042
C31×#16032
C31×#15982
C31×#15972
C31×#15192
C31×#15132
C31×#14722
#1823131