Finite Group Databasebeta

← C31×#18228 #21474987

Subgroups — C31×#18228 #21474987

Order 7936.

1300 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3537C211yesmaximal, characteristic, complemented
2C31×#3006C211yesmaximal, characteristic, complemented
3C31×#3002C211yesmaximal, characteristic, complemented
4C31×#2615C211yesmaximal, characteristic, complemented
5C31×#1606C212yesmaximal, complemented
6C31×#1601C212yesmaximal, complemented
7C31×#1600C212yesmaximal, complemented
8C31×#1595C212yesmaximal, complemented
9C31×#1519C211yesmaximal, characteristic, complemented
10C31×#1513C211yesmaximal, characteristic, complemented
11C31×#1471C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic, complemented
13C2×C31×AGL(1,ℤ/8)—21no—
14C2×C31×#135—21no—
15C31×#560—22no—
16C31×#553—21no—
17C31×#553—21no—
18D42×C31—22no—
19D42×C31—21no—
20D42×C31—21no—
21C31×#540—21no—
22C31×#538—21no—
23C31×#538C2212yes—
24C31×#535—21no—
25C31×#534—21no—
26C31×#534C2212yes—
27C31×#525C2211yescharacteristic
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C31×#452—21no—
32C31×#451C2211yescharacteristic, complemented
33C31×#450C2211yescharacteristic, complemented
34C31×#449—21no—
35C31×#449—22no—
36C31×#448C2211yescharacteristic, complemented
37C31×#448C2212yescomplemented
38C31×#447C2211yescharacteristic, complemented
39C31×#447C2212yescomplemented
40C31×#417—21no—
41C31×#416—21no—
42C31×#407C2211yescharacteristic, complemented
43C2×C31×C22⋊C8C2211yescharacteristic, complemented
44C31×#393C2212yescomplemented
45C31×#392—22no—
46C31×#392C2212yescomplemented
47C31×#380—21no—
48C31×#380C2211yescharacteristic, complemented
49C31×#328C2212yescomplemented
50C31×#327C2212yescomplemented
51C31×#327C2212yescomplemented
52C31×#327C2212yescomplemented
53C31×#323C2212yescomplemented
54C31×#323C2212yescomplemented
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—44no—
60C2×#41×C31D411yescharacteristic, complemented
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—22no—
63C22×D4×C31—21no—
64C22×D4×C31—21no—
65C22×D4×C31—22no—
66C22×D4×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31D411yescharacteristic
69C22×D4×C31D412yes—
70C22×D4×C31D411yescharacteristic, complemented
71C22×D4×C31C2311yescharacteristic
72C23×C4×C31—21no—
73C23×C4×C31C2311yescharacteristic
74C31×AGL(1,ℤ/8)—44no—
75C31×#135—44no—
76C2×Q16×C31—21no—
77C2×SD16×C31—21no—
78C2×SD16×C31—21no—
79C2×SD16×C31—22no—
80C2×D8×C31—21no—
81C2×D8×C31—22no—
82C2×M16×C31—21no—
83C22×C8×C31—21no—
84C31×#127—22no—
85C31×#127—21no—
86C31×#126—22no—
87C31×#126—22no—
88C31×#125—21no—
89C31×#124—22no—
90C31×#123—22no—
91C31×#123—21no—
92C31×#123—22no—
93C31×#123—22no—
94C31×#123—22no—
95C31×C22⋊Q8D411yescharacteristic, complemented
96C31×C22⋊Q8C2311yescharacteristic
97C31×#121—22no—
98C31×#121—21no—
99C31×#121—21no—
100C31×#121—22no—
101C31×#121—22no—
102C31×#121—22no—
103C31×#121—22no—
104C31×#121—21no—
105C31×#121—21no—
106C31×#121—21no—
107C31×#121—21no—
108C31×#121—21no—
109C31×#121—21no—
110C31×#121—22no—
111C31×#121—44no—
112C31×#121D412yescomplemented
113C31×#121D411yescharacteristic, complemented
114C31×#121C2312yes—
115C31×#121C2311yescharacteristic
116C31×#120—22no—
117C31×#120—22no—
118C31×#120—22no—
119C31×#120—21no—
120C31×#120—22no—
121C31×#120—22no—
122C31×#120—22no—
123C4×D4×C31—22no—
124C4×D4×C31—21no—
125C4×D4×C31—21no—
126C4×D4×C31—21no—
127C4×D4×C31—21no—
128C4×D4×C31—22no—
129C31×#117—21no—
130C31×#117D411yescharacteristic, complemented
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31D411yescharacteristic
133C2×C4⋊C4×C31D411yescharacteristic, complemented
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31C2312yes—
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—22no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31C2×D412yes—
156C24×C31C2×D411yescharacteristic
157#41×C31—24no—
158#41×C31—24no—
159#41×C31—42no—
160#41×C31—42no—
161#41×C31—42no—
162#41×C31—42no—
163#41×C31—42no—
164#41×C31—42no—
165#41×C31—42no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—42no—
169C2×Q8×C31C2×D411yescharacteristic
170C2×D4×C31—22no—
171C2×D4×C31—21no—
172C2×D4×C31—21no—
173C2×D4×C31—22no—
174C2×D4×C31—22no—
175C2×D4×C31—22no—
176C2×D4×C31—22no—
177C2×D4×C31—22no—
178C2×D4×C31—22no—
179C2×D4×C31—21no—
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31—42no—
190C2×D4×C31—42no—
191C2×D4×C31—42no—
192C2×D4×C31—41no—
193C2×D4×C31—41no—
194C2×D4×C31—44no—
195C2×D4×C31—82no—
196C2×D4×C31—82no—
197C2×D4×C31—82no—
198C2×D4×C31—82no—
199C2×D4×C31—81no—
200C2×D4×C31—81no—
201C2×D4×C31—82no—
202C2×D4×C31—82no—
203C2×D4×C31—84no—
204C2×D4×C31C2×D411yescharacteristic
205C2×D4×C31C2×D412yes—
206C22×C4×C31—24no—
207C22×C4×C31—21no—
208C22×C4×C31—22no—
209C22×C4×C31—22no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—22no—
213C22×C4×C31—42no—
214C22×C4×C31—42no—
215C22×C4×C31—41no—
216C22×C4×C31—41no—
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2×D412yes—
221C22×C4×C31C2×D411yescharacteristic
222C22×C4×C31C2×D411yescharacteristic
223C22×C4×C31C2411yescharacteristic
224Q16×C31—42no—
225SD16×C31—42no—
226SD16×C31—42no—
227SD16×C31—44no—
228D8×C31—42no—
229D8×C31—44no—
230M16×C31—42no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—22no—
234C2×C8×C31—42no—
235C4⋊C4×C31—22no—
236C4⋊C4×C31—22no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—42no—
243C4⋊C4×C31C2×D412yes—
244C4⋊C4×C31C2×D411yescharacteristic
245C4⋊C4×C31C2×D411yescharacteristic
246C22⋊C4×C31—22no—
247C22⋊C4×C31—22no—
248C22⋊C4×C31—22no—
249C22⋊C4×C31—22no—
250C22⋊C4×C31—22no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—21no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—22no—
255C22⋊C4×C31—21no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—22no—
259C22⋊C4×C31—21no—
260C22⋊C4×C31—44no—
261C22⋊C4×C31—81no—
262C22⋊C4×C31—82no—
263C42×C31—22no—
264C42×C31—21no—
265#18228C3111yesmaximal, characteristic, direct product factor, Sylow
266C23×C31—21no—
267C23×C31—21no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—22no—
271C23×C31—21no—
272C23×C31—22no—
273C23×C31—22no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—42no—
280C23×C31—42no—
281C23×C31—42no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—81no—
286C23×C31—81no—
287C23×C31—82no—
288C23×C31—82no—
289C23×C31—82no—
290C23×C31#12011yescharacteristic
291C23×C31#12011yescharacteristic
292C23×C31C22×D411yescharacteristic
293Q8×C31—22no—
294Q8×C31—22no—
295Q8×C31—41no—
296Q8×C31—41no—
297Q8×C31—41no—
298D4×C31—22no—
299D4×C31—22no—
300D4×C31—42no—
301D4×C31—41no—
302D4×C31—41no—
303D4×C31—41no—
304D4×C31—44no—
305D4×C31—42no—
306D4×C31—44no—
307D4×C31—44no—
308D4×C31—42no—
309D4×C31—41no—
310D4×C31—42no—
311D4×C31—41no—
312D4×C31—42no—
313D4×C31—42no—
314D4×C31—81no—
315D4×C31—82no—
316D4×C31—82no—
317D4×C31—81no—
318D4×C31—82no—
319D4×C31—82no—
320D4×C31—82no—
321D4×C31—82no—
322D4×C31—82no—
323D4×C31—88no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—21no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—21no—
332C2×C4×C31—21no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—44no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—44no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—81no—
346C2×C4×C31—82no—
347C2×C4×C31—82no—
348C2×C4×C31#12011yescharacteristic
349C2×C4×C31#12011yescharacteristic
350C2×C4×C31C22×D411yescharacteristic
351C2×C4×C31C22×D411yescharacteristic
352C8×C31—41no—
353C8×C31—41no—
354C8×C31—42no—
355#3537C2×C3111yescharacteristic, complemented
356#3006C2×C3111yescharacteristic, complemented
357#3002C2×C3111yescharacteristic, complemented
358#2615C2×C3111yescharacteristic, complemented
359#1606C2×C3112yescomplemented
360#1601C2×C3112yescomplemented
361#1600C2×C3112yescomplemented
362#1595C2×C3112yescomplemented
363#1519C2×C3111yescharacteristic, complemented
364#1513C2×C3111yescharacteristic, complemented
365#1471C2×C3111yescharacteristic, complemented
366C22×C31—21no—
367C22×C31—21no—
368C22×C31—21no—
369C22×C31—21no—
370C22×C31—21no—
371C22×C31—21no—
372C22×C31—21no—
373C22×C31—21no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31—41no—
382C22×C31—42no—
383C22×C31—41no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—81no—
387C22×C31—81no—
388C22×C31—82no—
389C22×C31—82no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—162no—
395C22×C31—164no—
396C22×C31C2×#12011yescharacteristic
397C22×C31#57611yescharacteristic
398C22×C31#57711yescharacteristic
399C4×C31—21no—
400C4×C31—21no—
401C4×C31—21no—
402C4×C31—42no—
403C4×C31—41no—
404C4×C31—42no—
405C4×C31—41no—
406C4×C31—42no—
407C4×C31—41no—
408C4×C31—82no—
409C4×C31B(4,𝔽2)12yes—
410C22×#41C22×C3111yescharacteristic, complemented
411C2×AGL(1,ℤ/8)—21no—
412C2×#135—21no—
413#560—22no—
414#553—21no—
415#553—21no—
416D42—22no—
417D42—21no—
418D42—21no—
419#540—21no—
420#538—21no—
421#538C22×C3112yes—
422#535—21no—
423#534—21no—
424#534C22×C3112yes—
425#525C22×C3111yescharacteristic
426C2×#121—21no—
427C2×#121C22×C3111yescharacteristic
428C2×#121C22×C3111yescharacteristic
429#452—21no—
430#451C22×C3111yescharacteristic, complemented
431#450C22×C3111yescharacteristic, complemented
432#449—21no—
433#449—22no—
434#448C22×C3111yescharacteristic, complemented
435#448C22×C3112yescomplemented
436#447C22×C3111yescharacteristic, complemented
437#447C22×C3112yescomplemented
438#417—21no—
439#416—21no—
440#407C22×C3111yescharacteristic, complemented
441C2×C22⋊C8C22×C3111yescharacteristic, complemented
442#393C22×C3112yescomplemented
443#392—22no—
444#392C22×C3112yescomplemented
445#380—21no—
446#380C22×C3111yescharacteristic, complemented
447#328C22×C3112yescomplemented
448#327C22×C3112yescomplemented
449#327C22×C3112yescomplemented
450#327C22×C3112yescomplemented
451#323C22×C3112yescomplemented
452#323C22×C3112yescomplemented
453C2×C31—21no—
454C2×C31—21no—
455C2×C31—41no—
456C2×C31—41no—
457C2×C31—82no—
458C2×C31—82no—
459C2×C31—82no—
460C2×C31—81no—
461C2×C31#301211yescharacteristic
462C2×C31#301911yescharacteristic
463C2×C31C2×B(4,𝔽2)11yescharacteristic
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—44no—
469C2×#41D4×C3111yescharacteristic, complemented
470C22×Q8C23×C3111yescharacteristic
471C22×D4—22no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—22no—
477C22×D4D4×C3111yescharacteristic
478C22×D4D4×C3112yes—
479C22×D4D4×C3111yescharacteristic, complemented
480C22×D4C23×C3111yescharacteristic
481C23×C4—21no—
482C23×C4C23×C3111yescharacteristic
483AGL(1,ℤ/8)—44no—
484#135—44no—
485C2×Q16—21no—
486C2×SD16—21no—
487C2×SD16—21no—
488C2×SD16—22no—
489C2×D8—21no—
490C2×D8—22no—
491C2×M16—21no—
492C22×C8—21no—
493#127—22no—
494#127—21no—
495#126—22no—
496#126—22no—
497#125—21no—
498#124—22no—
499#123—22no—
500#123—21no—
501#123—22no—
502#123—22no—
503#123—22no—
504C22⋊Q8D4×C3111yescharacteristic, complemented
505C22⋊Q8C23×C3111yescharacteristic
506#121—22no—
507#121—21no—
508#121—21no—
509#121—22no—
510#121—22no—
511#121—22no—
512#121—22no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#121—22no—
520#121—44no—
521#121D4×C3112yescomplemented
522#121D4×C3111yescharacteristic, complemented
523#121C23×C3112yes—
524#121C23×C3111yescharacteristic
525#120—22no—
526#120—22no—
527#120—22no—
528#120—21no—
529#120—22no—
530#120—22no—
531#120—22no—
532C4×D4—22no—
533C4×D4—21no—
534C4×D4—21no—
535C4×D4—21no—
536C4×D4—21no—
537C4×D4—22no—
538#117—21no—
539#117D4×C3111yescharacteristic, complemented
540C2×C4⋊C4—21no—
541C2×C4⋊C4D4×C3111yescharacteristic
542C2×C4⋊C4D4×C3111yescharacteristic, complemented
543C2×C22⋊C4—21no—
544C2×C22⋊C4—22no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—22no—
547C2×C22⋊C4C23×C3112yes—
548#103—21no—
549#103—21no—
550#103—22no—
551#102—21no—
552#102—21no—
553#102—22no—
554C22⋊C8—21no—
555C22⋊C8—21no—
556C22⋊C8C23×C3111yescharacteristic
557C22⋊C8C23×C3111yescharacteristic
558C22⋊C8C23×C3112yes—
559#95—22no—
560#95C23×C3112yes—
561C31#1822811yescharacteristic, direct product factor, Sylow
562C24—22no—
563C24—21no—
564C24—21no—
565C24C2×D4×C3112yes—
566C24C2×D4×C3111yescharacteristic
567#41—24no—
568#41—24no—
569#41—42no—
570#41—42no—
571#41—42no—
572#41—42no—
573#41—42no—
574#41—42no—
575#41—42no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—42no—
579C2×Q8C2×D4×C3111yescharacteristic
580C2×D4—22no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4—42no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—44no—
605C2×D4—82no—
606C2×D4—82no—
607C2×D4—82no—
608C2×D4—82no—
609C2×D4—81no—
610C2×D4—81no—
611C2×D4—82no—
612C2×D4—82no—
613C2×D4—84no—
614C2×D4C2×D4×C3111yescharacteristic
615C2×D4C2×D4×C3112yes—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4C2×D4×C3111yescharacteristic
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3111yescharacteristic
632C22×C4C2×D4×C3111yescharacteristic
633C22×C4C24×C3111yescharacteristic
634Q16—42no—
635SD16—42no—
636SD16—42no—
637SD16—44no—
638D8—42no—
639D8—44no—
640M16—42no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—42no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—42no—
653C4⋊C4C2×D4×C3112yes—
654C4⋊C4C2×D4×C3111yescharacteristic
655C4⋊C4C2×D4×C3111yescharacteristic
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—21no—
670C22⋊C4—44no—
671C22⋊C4—81no—
672C22⋊C4—82no—
673C42—22no—
674C42—21no—
675C23—21no—
676C23—21no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—42no—
689C23—42no—
690C23—42no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—81no—
695C23—81no—
696C23—82no—
697C23—82no—
698C23—82no—
699C23C31×#12011yescharacteristic
700C23C31×#12011yescharacteristic
701C23C22×D4×C3111yescharacteristic
702Q8—22no—
703Q8—22no—
704Q8—41no—
705Q8—41no—
706Q8—41no—
707D4—22no—
708D4—22no—
709D4—42no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—44no—
714D4—42no—
715D4—44no—
716D4—44no—
717D4—42no—
718D4—41no—
719D4—42no—
720D4—41no—
721D4—42no—
722D4—42no—
723D4—81no—
724D4—82no—
725D4—82no—
726D4—81no—
727D4—82no—
728D4—82no—
729D4—82no—
730D4—82no—
731D4—82no—
732D4—88no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—21no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—44no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—44no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—81no—
755C2×C4—82no—
756C2×C4—82no—
757C2×C4C31×#12011yescharacteristic
758C2×C4C31×#12011yescharacteristic
759C2×C4C22×D4×C3111yescharacteristic
760C2×C4C22×D4×C3111yescharacteristic
761C8—41no—
762C8—41no—
763C8—42no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—41no—
782C22—42no—
783C22—42no—
784C22—81no—
785C22—81no—
786C22—82no—
787C22—82no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22—81no—
792C22—162no—
793C22—164no—
794C22C2×C31×#12011yescharacteristic
795C22C31×#57611yescharacteristic
796C22C31×#57711yescharacteristic
797C4—21no—
798C4—21no—
799C4—21no—
800C4—42no—
801C4—41no—
802C4—42no—
803C4—41no—
804C4—42no—
805C4—41no—
806C4—82no—
807C4C31×B(4,𝔽2)12yes—
808C2—21no—
809C2—21no—
810C2—41no—
811C2—41no—
812C2—82no—
813C2—82no—
814C2—82no—
815C2—81no—
816C2C31×#301211yescharacteristic
817C2C31×#301911yescharacteristic
818C2C2×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×#3537C2semidirect
2. C31×#3006C2semidirect
3. C31×#3002C2semidirect
4. C31×#2615C2semidirect
5. C31×#1606C2semidirect
6. C31×#1601C2semidirect
7. C31×#1600C2semidirect
8. C31×#1595C2semidirect
9. C31×#1519C2semidirect
10. C31×#1513C2semidirect
11. C31×#1471C2semidirect
12. C22×#41×C31C22semidirect
32. C31×#451C22semidirect
33. C31×#450C22semidirect
36. C31×#448C22semidirect
37. C31×#448C22semidirect
38. C31×#447C22semidirect
39. C31×#447C22semidirect
42. C31×#407C22semidirect
43. C2×C31×C22⋊C8C22semidirect
44. C31×#393C22semidirect
46. C31×#392C22semidirect
48. C31×#380C22semidirect
49. C31×#328C22semidirect
50. C31×#327C22semidirect
51. C31×#327C22semidirect
52. C31×#327C22semidirect
53. C31×#323C22semidirect
54. C31×#323C22semidirect
60. C2×#41×C31D4semidirect
70. C22×D4×C31D4semidirect
95. C31×C22⋊Q8D4semidirect
112. C31×#121D4semidirect
113. C31×#121D4semidirect
130. C31×#117D4semidirect
133. C2×C4⋊C4×C31D4semidirect
265. #18228C31direct (N × H)
355. #3537C2×C31semidirect
356. #3006C2×C31semidirect
357. #3002C2×C31semidirect
358. #2615C2×C31semidirect
359. #1606C2×C31semidirect
360. #1601C2×C31semidirect
361. #1600C2×C31semidirect
362. #1595C2×C31semidirect
363. #1519C2×C31semidirect
364. #1513C2×C31semidirect
365. #1471C2×C31semidirect
410. C22×#41C22×C31semidirect
430. #451C22×C31semidirect
431. #450C22×C31semidirect
434. #448C22×C31semidirect
435. #448C22×C31semidirect
436. #447C22×C31semidirect
437. #447C22×C31semidirect
440. #407C22×C31semidirect
441. C2×C22⋊C8C22×C31semidirect
442. #393C22×C31semidirect
444. #392C22×C31semidirect
446. #380C22×C31semidirect
447. #328C22×C31semidirect
448. #327C22×C31semidirect
449. #327C22×C31semidirect
450. #327C22×C31semidirect
451. #323C22×C31semidirect
452. #323C22×C31semidirect
469. C2×#41D4×C31semidirect
479. C22×D4D4×C31semidirect
504. C22⋊Q8D4×C31semidirect
521. #121D4×C31semidirect
522. #121D4×C31semidirect
539. #117D4×C31semidirect
542. C2×C4⋊C4D4×C31semidirect
561. C31#18228direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35372
C31×#30062
C31×#30022
C31×#26152
C31×#16062
C31×#16012
C31×#16002
C31×#15952
C31×#15192
C31×#15132
C31×#14712
#1822831