Finite Group Databasebeta

← C31×#24140 #21480899

Subgroups — C31×#24140 #21480899

Order 7936.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3505C211yesmaximal, characteristic, complemented
2C31×#2848C211yesmaximal, characteristic, complemented
3C31×#2847C211yesmaximal, characteristic, complemented
4C4×C31×#120C211yesmaximal, characteristic, complemented
5C31×#2044C212yesmaximal, complemented
6C31×#2021C212yesmaximal, complemented
7C31×#1996C211yesmaximal, characteristic, complemented
8C31×#1964C211yesmaximal, characteristic, complemented
9C31×#1889C212yesmaximal, complemented
10C31×#1867C212yesmaximal, complemented
11C31×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C31C2211yescharacteristic
13C31×#553—21no—
14C31×#553—22no—
15C31×#552—21no—
16C31×#551—22no—
17C31×#548—21no—
18C31×#546—21no—
19C31×#539—21no—
20C31×#538—21no—
21C31×#534C2212yes—
22C31×#529—21no—
23C31×#525—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121C2211yescharacteristic
28C2×C31×#120C2211yescharacteristic
29C2×C31×#120C2212yes—
30C31×#518C2212yes—
31C2×C4×D4×C31—21no—
32C2×C4×D4×C31C2211yescharacteristic
33C2×C31×#99C2212yes—
34C2×C31×#99C2212yes—
35C2×C31×#99C2212yes—
36C31×#386—22no—
37C31×#386—21no—
38C31×#386C2212yes—
39C31×#386C2211yescharacteristic
40C31×#385—22no—
41C31×#385—21no—
42C31×#385C2212yes—
43C31×#385C2211yescharacteristic
44C31×#380—21no—
45C31×#380—21no—
46C31×#380C2211yescharacteristic
47C31×#380C2211yescharacteristic
48C31×#379C2212yes—
49C31×#379C2211yescharacteristic
50C4×C22⋊C4×C31—21no—
51C4×C22⋊C4×C31C2211yescharacteristic
52C31×#342C2212yes—
53C31×#342C2212yes—
54C31×#342C2212yes—
55C25×C31C2311yescharacteristic
56C2×#41×C31—21no—
57C22×Q8×C31D411yescharacteristic, complemented
58C22×D4×C31—21no—
59C22×D4×C31—22no—
60C22×D4×C31D411yescharacteristic, complemented
61C22×D4×C31C2311yescharacteristic
62C22×D4×C31C2312yes—
63C23×C4×C31—21no—
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—44no—
70C23×C4×C31D411yescharacteristic, complemented
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C31×#126—22no—
74C31×#126—22no—
75C31×#126—22no—
76C31×#125—21no—
77C31×#125—22no—
78C31×#124—21no—
79C31×#124—22no—
80C31×#123—22no—
81C31×#123—22no—
82C31×#123—22no—
83C31×#123—22no—
84C31×#123—22no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—22no—
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—21no—
91C31×C22⋊Q8—44no—
92C31×#121—21no—
93C31×#121—22no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121—22no—
99C31×#121—22no—
100C31×#121—44no—
101C31×#120—22no—
102C31×#120—22no—
103C31×#120—22no—
104C31×#120—22no—
105C31×#120—24no—
106C31×#120—42no—
107C4×Q8×C31—21no—
108C4×D4×C31—22no—
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—22no—
115C4×D4×C31—22no—
116C4×D4×C31—22no—
117C4×D4×C31—22no—
118C4×D4×C31—44no—
119C31×#117—21no—
120C31×#117—22no—
121C31×#117—22no—
122C2×C4⋊C4×C31—21no—
123C2×C4⋊C4×C31—21no—
124C2×C4⋊C4×C31—21no—
125C2×C4⋊C4×C31—22no—
126C2×C4⋊C4×C31D411yescharacteristic, complemented
127C2×C4⋊C4×C31D411yescharacteristic, complemented
128C2×C4⋊C4×C31D411yescharacteristic, complemented
129C2×C4⋊C4×C31D412yescomplemented
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—21no—
138C2×C22⋊C4×C31—22no—
139C2×C22⋊C4×C31D411yescharacteristic, complemented
140C2×C22⋊C4×C31D412yescomplemented
141C2×C22⋊C4×C31C2312yes—
142C2×C22⋊C4×C31C2311yescharacteristic
143C2×C22⋊C4×C31C2312yes—
144C2×C22⋊C4×C31C2311yescharacteristic
145C2×C22⋊C4×C31C2312yes—
146C2×C22⋊C4×C31C2311yescharacteristic
147C2×C42×C31—21no—
148C2×C42×C31D411yescharacteristic, complemented
149C31×#99—24no—
150C31×#99—42no—
151C31×#99—42no—
152C31×#95—21no—
153C31×#95—21no—
154C31×#95—21no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—21no—
158C31×#95—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—21no—
165C24×C31—42no—
166C24×C31—42no—
167C24×C31C2×D412yes—
168C24×C31C2×D411yescharacteristic
169C24×C31#4112yescomplemented
170C24×C31C2411yescharacteristic
171#41×C31—82no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31—42no—
175C2×D4×C31—24no—
176C2×D4×C31—21no—
177C2×D4×C31—22no—
178C2×D4×C31—21no—
179C2×D4×C31—22no—
180C2×D4×C31—22no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—22no—
184C2×D4×C31—21no—
185C2×D4×C31—22no—
186C2×D4×C31—21no—
187C2×D4×C31—22no—
188C2×D4×C31—22no—
189C2×D4×C31—22no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—42no—
193C2×D4×C31—42no—
194C2×D4×C31—42no—
195C2×D4×C31—44no—
196C2×D4×C31—44no—
197C2×D4×C31—44no—
198C22×C4×C31—24no—
199C22×C4×C31—24no—
200C22×C4×C31—24no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—22no—
206C22×C4×C31—22no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—22no—
211C22×C4×C31—22no—
212C22×C4×C31—42no—
213C22×C4×C31—42no—
214C22×C4×C31—42no—
215C22×C4×C31—42no—
216C22×C4×C31—42no—
217C22×C4×C31—42no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—42no—
224C22×C4×C31—41no—
225C22×C4×C31—41no—
226C22×C4×C31—41no—
227C22×C4×C31—41no—
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D412yes—
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D412yes—
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D411yescharacteristic
240C4⋊C4×C31—22no—
241C4⋊C4×C31—22no—
242C4⋊C4×C31—22no—
243C4⋊C4×C31—22no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—22no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—22no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—42no—
253C4⋊C4×C31—42no—
254C4⋊C4×C31—42no—
255C4⋊C4×C31—44no—
256C22⋊C4×C31—22no—
257C22⋊C4×C31—22no—
258C22⋊C4×C31—24no—
259C22⋊C4×C31—22no—
260C22⋊C4×C31—22no—
261C22⋊C4×C31—22no—
262C22⋊C4×C31—22no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—22no—
265C22⋊C4×C31—21no—
266C22⋊C4×C31—22no—
267C22⋊C4×C31—21no—
268C22⋊C4×C31—22no—
269C22⋊C4×C31—21no—
270C22⋊C4×C31—21no—
271C22⋊C4×C31—22no—
272C22⋊C4×C31—22no—
273C22⋊C4×C31—22no—
274C22⋊C4×C31—21no—
275C22⋊C4×C31—22no—
276C22⋊C4×C31—22no—
277C22⋊C4×C31—21no—
278C22⋊C4×C31—44no—
279C22⋊C4×C31—42no—
280C22⋊C4×C31—44no—
281C22⋊C4×C31—44no—
282C22⋊C4×C31—42no—
283C22⋊C4×C31—42no—
284C22⋊C4×C31—44no—
285C22⋊C4×C31#4112yescomplemented
286C42×C31—22no—
287C42×C31—22no—
288C42×C31—21no—
289C42×C31—21no—
290C42×C31—42no—
291#24140C3111yesmaximal, characteristic, direct product factor, Sylow
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—21no—
302C23×C31—22no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—41no—
308C23×C31—44no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—44no—
317C23×C31—44no—
318C23×C31—44no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—42no—
322C23×C31—42no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31C22×D411yescharacteristic
328C23×C31C22×D411yescharacteristic
329C23×C31C22×D411yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31C2×#4111yescharacteristic
332C23×C31H(5,𝔽2)11yescharacteristic
333C23×C312−1+411yescharacteristic
334Q8×C31—42no—
335Q8×C31—81no—
336D4×C31—48no—
337D4×C31—42no—
338D4×C31—42no—
339D4×C31—41no—
340D4×C31—41no—
341D4×C31—41no—
342D4×C31—42no—
343D4×C31—42no—
344D4×C31—41no—
345D4×C31—42no—
346D4×C31—81no—
347D4×C31—82no—
348D4×C31—82no—
349D4×C31—88no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—21no—
357C2×C4×C31—22no—
358C2×C4×C31—21no—
359C2×C4×C31—21no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—21no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—44no—
371C2×C4×C31—44no—
372C2×C4×C31—44no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—44no—
380C2×C4×C31—42no—
381C2×C4×C31—41no—
382C2×C4×C31—42no—
383C2×C4×C31—41no—
384C2×C4×C31—42no—
385C2×C4×C31—41no—
386C2×C4×C31—42no—
387C2×C4×C31—42no—
388C2×C4×C31—42no—
389C2×C4×C31—41no—
390C2×C4×C31—42no—
391C2×C4×C31—41no—
392C2×C4×C31—42no—
393C2×C4×C31—42no—
394C2×C4×C31—81no—
395C2×C4×C31—82no—
396C2×C4×C31—82no—
397C2×C4×C31#12011yescharacteristic
398C2×C4×C31#12011yescharacteristic
399C2×C4×C31#12011yescharacteristic
400C2×C4×C31#12011yescharacteristic
401#3505C2×C3111yescharacteristic, complemented
402#2848C2×C3111yescharacteristic, complemented
403#2847C2×C3111yescharacteristic, complemented
404C4×#120C2×C3111yescharacteristic, complemented
405#2044C2×C3112yescomplemented
406#2021C2×C3112yescomplemented
407#1996C2×C3111yescharacteristic, complemented
408#1964C2×C3111yescharacteristic, complemented
409#1889C2×C3112yescomplemented
410#1867C2×C3112yescomplemented
411#1799C2×C3111yescharacteristic, complemented
412C22×C31—21no—
413C22×C31—21no—
414C22×C31—21no—
415C22×C31—21no—
416C22×C31—21no—
417C22×C31—21no—
418C22×C31—24no—
419C22×C31—24no—
420C22×C31—24no—
421C22×C31—41no—
422C22×C31—41no—
423C22×C31—41no—
424C22×C31—41no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—42no—
430C22×C31—42no—
431C22×C31—42no—
432C22×C31—42no—
433C22×C31—42no—
434C22×C31—42no—
435C22×C31—42no—
436C22×C31—42no—
437C22×C31—42no—
438C22×C31—41no—
439C22×C31—42no—
440C22×C31—41no—
441C22×C31—42no—
442C22×C31—42no—
443C22×C31—41no—
444C22×C31—82no—
445C22×C31—81no—
446C22×C31—82no—
447C22×C31C2×#12011yescharacteristic
448C22×C31#52511yescharacteristic
449C22×C31#53711yescharacteristic
450C22×C31#54611yescharacteristic
451C22×C31#54711yescharacteristic
452C22×C31#54811yescharacteristic
453C22×C31#55011yescharacteristic
454C4×C31—21no—
455C4×C31—21no—
456C4×C31—21no—
457C4×C31—42no—
458C4×C31—41no—
459C4×C31—42no—
460C4×C31—42no—
461C4×C31—41no—
462C4×C31—42no—
463C4×C31—41no—
464C4×C31—42no—
465C4×C31—82no—
466C4×C31—81no—
467C4×C31—82no—
468C4×C31B(4,𝔽2)12yes—
469C24×C4C22×C3111yescharacteristic
470#553—21no—
471#553—22no—
472#552—21no—
473#551—22no—
474#548—21no—
475#546—21no—
476#539—21no—
477#538—21no—
478#534C22×C3112yes—
479#529—21no—
480#525—21no—
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C3111yescharacteristic
483C2×#121—21no—
484C2×#121C22×C3111yescharacteristic
485C2×#120C22×C3111yescharacteristic
486C2×#120C22×C3112yes—
487#518C22×C3112yes—
488C2×C4×D4—21no—
489C2×C4×D4C22×C3111yescharacteristic
490C2×#99C22×C3112yes—
491C2×#99C22×C3112yes—
492C2×#99C22×C3112yes—
493#386—22no—
494#386—21no—
495#386C22×C3112yes—
496#386C22×C3111yescharacteristic
497#385—22no—
498#385—21no—
499#385C22×C3112yes—
500#385C22×C3111yescharacteristic
501#380—21no—
502#380—21no—
503#380C22×C3111yescharacteristic
504#380C22×C3111yescharacteristic
505#379C22×C3112yes—
506#379C22×C3111yescharacteristic
507C4×C22⋊C4—21no—
508C4×C22⋊C4C22×C3111yescharacteristic
509#342C22×C3112yes—
510#342C22×C3112yes—
511#342C22×C3112yes—
512C2×C31—21no—
513C2×C31—21no—
514C2×C31—21no—
515C2×C31—21no—
516C2×C31—21no—
517C2×C31—21no—
518C2×C31—44no—
519C2×C31—81no—
520C2×C31—82no—
521C2×C31#240711yescharacteristic
522C2×C31C2×B(4,𝔽2)11yescharacteristic
523C2×C31#302511yescharacteristic
524C25C23×C3111yescharacteristic
525C2×#41—21no—
526C22×Q8D4×C3111yescharacteristic, complemented
527C22×D4—21no—
528C22×D4—22no—
529C22×D4D4×C3111yescharacteristic, complemented
530C22×D4C23×C3111yescharacteristic
531C22×D4C23×C3112yes—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—44no—
539C23×C4D4×C3111yescharacteristic, complemented
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542#126—22no—
543#126—22no—
544#126—22no—
545#125—21no—
546#125—22no—
547#124—21no—
548#124—22no—
549#123—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554C22⋊Q8—21no—
555C22⋊Q8—22no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—44no—
561#121—21no—
562#121—22no—
563#121—21no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—22no—
568#121—22no—
569#121—44no—
570#120—22no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—24no—
575#120—42no—
576C4×Q8—21no—
577C4×D4—22no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—44no—
588#117—21no—
589#117—22no—
590#117—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4D4×C3111yescharacteristic, complemented
596C2×C4⋊C4D4×C3111yescharacteristic, complemented
597C2×C4⋊C4D4×C3111yescharacteristic, complemented
598C2×C4⋊C4D4×C3112yescomplemented
599C2×C22⋊C4—22no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4D4×C3111yescharacteristic, complemented
609C2×C22⋊C4D4×C3112yescomplemented
610C2×C22⋊C4C23×C3112yes—
611C2×C22⋊C4C23×C3111yescharacteristic
612C2×C22⋊C4C23×C3112yes—
613C2×C22⋊C4C23×C3111yescharacteristic
614C2×C22⋊C4C23×C3112yes—
615C2×C22⋊C4C23×C3111yescharacteristic
616C2×C42—21no—
617C2×C42D4×C3111yescharacteristic, complemented
618#99—24no—
619#99—42no—
620#99—42no—
621#95—21no—
622#95—21no—
623#95—21no—
624#95—22no—
625#95—22no—
626#95—21no—
627#95—21no—
628C31#2414011yescharacteristic, direct product factor, Sylow
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C3112yes—
638C24C2×D4×C3111yescharacteristic
639C24#41×C3112yescomplemented
640C24C24×C3111yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C3111yescharacteristic
699C22×C4C2×D4×C3112yes—
700C22×C4C2×D4×C3111yescharacteristic
701C22×C4C2×D4×C3111yescharacteristic
702C22×C4C2×D4×C3111yescharacteristic
703C22×C4C2×D4×C3111yescharacteristic
704C22×C4C2×D4×C3112yes—
705C22×C4C2×D4×C3111yescharacteristic
706C22×C4C2×D4×C3112yes—
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C2×D4×C3111yescharacteristic
709C22×C4C2×D4×C3111yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C3112yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C3111yescharacteristic
797C23C22×D4×C3111yescharacteristic
798C23C22×D4×C3111yescharacteristic
799C23C2×#41×C3111yescharacteristic
800C23C2×#41×C3111yescharacteristic
801C23C31×H(5,𝔽2)11yescharacteristic
802C23C31×2−1+411yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4C31×#12011yescharacteristic
867C2×C4C31×#12011yescharacteristic
868C2×C4C31×#12011yescharacteristic
869C2×C4C31×#12011yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×C31×#12011yescharacteristic
906C22C31×#52511yescharacteristic
907C22C31×#53711yescharacteristic
908C22C31×#54611yescharacteristic
909C22C31×#54711yescharacteristic
910C22C31×#54811yescharacteristic
911C22C31×#55011yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—41no—
917C4—42no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4C31×B(4,𝔽2)12yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C31×#240711yescharacteristic
937C2C2×C31×B(4,𝔽2)11yescharacteristic
938C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3505C2semidirect
2. C31×#2848C2semidirect
3. C31×#2847C2semidirect
4. C4×C31×#120C2semidirect
5. C31×#2044C2semidirect
6. C31×#2021C2semidirect
7. C31×#1996C2semidirect
8. C31×#1964C2semidirect
9. C31×#1889C2semidirect
10. C31×#1867C2semidirect
11. C31×#1799C2semidirect
57. C22×Q8×C31D4semidirect
60. C22×D4×C31D4semidirect
70. C23×C4×C31D4semidirect
126. C2×C4⋊C4×C31D4semidirect
127. C2×C4⋊C4×C31D4semidirect
128. C2×C4⋊C4×C31D4semidirect
129. C2×C4⋊C4×C31D4semidirect
139. C2×C22⋊C4×C31D4semidirect
140. C2×C22⋊C4×C31D4semidirect
148. C2×C42×C31D4semidirect
169. C24×C31#41semidirect
285. C22⋊C4×C31#41semidirect
291. #24140C31direct (N × H)
401. #3505C2×C31semidirect
402. #2848C2×C31semidirect
403. #2847C2×C31semidirect
404. C4×#120C2×C31semidirect
405. #2044C2×C31semidirect
406. #2021C2×C31semidirect
407. #1996C2×C31semidirect
408. #1964C2×C31semidirect
409. #1889C2×C31semidirect
410. #1867C2×C31semidirect
411. #1799C2×C31semidirect
526. C22×Q8D4×C31semidirect
529. C22×D4D4×C31semidirect
539. C23×C4D4×C31semidirect
595. C2×C4⋊C4D4×C31semidirect
596. C2×C4⋊C4D4×C31semidirect
597. C2×C4⋊C4D4×C31semidirect
598. C2×C4⋊C4D4×C31semidirect
608. C2×C22⋊C4D4×C31semidirect
609. C2×C22⋊C4D4×C31semidirect
617. C2×C42D4×C31semidirect
628. C31#24140direct (N × H)
639. C24#41×C31semidirect
755. C22⋊C4#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#35052
C31×#28482
C31×#28472
C4×C31×#1202
C31×#20442
C31×#20212
C31×#19962
C31×#19642
C31×#18892
C31×#18672
C31×#17992
#2414031