Finite Group Databasebeta

← C31×#18445 #21475204

Subgroups — C31×#18445 #21475204

Order 7936.

848 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3564C211yesmaximal, characteristic
2C31×#3236C211yesmaximal, characteristic, complemented
3C31×#3232C211yesmaximal, characteristic, complemented
4C31×#2664C211yesmaximal, characteristic, complemented
5C31×#1618C211yesmaximal, characteristic
6C31×#1617C211yesmaximal, characteristic, complemented
7C31×#1615C211yesmaximal, characteristic, complemented
8C31×#1614C211yesmaximal, characteristic, complemented
9C31×#1612C211yesmaximal, characteristic
10C31×#1611C211yesmaximal, characteristic, complemented
11C31×#1609C211yesmaximal, characteristic, complemented
12C31×#1608C211yesmaximal, characteristic, complemented
13C31×#1509C211yesmaximal, characteristic, complemented
14C31×#1503C211yesmaximal, characteristic, complemented
15C31×#1473C211yesmaximal, characteristic, complemented
16C31×#563—21no—
17C31×#563—21no—
18C31×#556—21no—
19C31×#554—21no—
20C31×#552—21no—
21C31×#552—21no—
22C31×#551—21no—
23C31×#551—21no—
24C31×#544C2211yescharacteristic
25C31×#543C2211yescharacteristic
26C31×#542—21no—
27C31×#541—21no—
28C31×#541—21no—
29C31×#539—21no—
30C31×#539C2211yescharacteristic
31C31×#538C2211yescharacteristic
32C31×#533C2211yescharacteristic
33C31×#529C2211yescharacteristic
34C2×C31×#126C2211yescharacteristic
35C2×C31×#125C2211yescharacteristic
36C31×#501—21no—
37C31×#499—21no—
38C31×#491—21no—
39C31×#488—21no—
40C31×#484C2211yescharacteristic
41C31×#484C2211yescharacteristic
42C31×#484C2211yescharacteristic
43C31×#483C2211yescharacteristic
44C31×#483C2211yescharacteristic
45C31×#483C2211yescharacteristic
46C31×#481C2211yescharacteristic
47C31×#480C2211yescharacteristic
48C31×#479—21no—
49C31×#479—21no—
50C31×#479—21no—
51C31×#478—21no—
52C31×#432C2211yescharacteristic
53C31×#431C2211yescharacteristic
54C31×#400C2211yescharacteristic
55C31×#399C2211yescharacteristic
56C31×#398—21no—
57C31×#398C2211yescharacteristic
58C31×#397C2211yescharacteristic
59C31×#396—21no—
60C31×#389—21no—
61C31×#388—21no—
62C4×C4⋊C4×C31C2211yescharacteristic
63C31×#328C2211yescharacteristic
64C31×#328C2211yescharacteristic
65C31×#328C2211yescharacteristic
66C31×#328C2211yescharacteristic
67C31×#328C2211yescharacteristic
68C31×#328C2211yescharacteristic
69C31×#327C2211yescharacteristic
70C31×#327C2211yescharacteristic
71C31×#324C2211yescharacteristic
72C31×#324C2211yescharacteristic
73C31×#323C2211yescharacteristic
74C31×#323C2211yescharacteristic
75C31×C4⋊Q8—21no—
76C31×C4⋊Q8—21no—
77C31×C4⋊Q8—21no—
78C31×C4⋊Q8D411yescharacteristic
79C31×C4⋊Q8D411yescharacteristic
80C31×#126—21no—
81C31×#126—21no—
82C31×#126—21no—
83C31×#126—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#126—21no—
90C31×#126—21no—
91C31×#126—21no—
92C31×#126—21no—
93C31×#125—21no—
94C31×#125—21no—
95C31×#125—21no—
96C31×#125—21no—
97C31×#125—21no—
98C31×#125—21no—
99C31×#125—21no—
100C31×#125—21no—
101C31×#125—21no—
102C31×#125—21no—
103C31×#125—21no—
104C31×#125—21no—
105C31×#125—21no—
106C31×#125D411yescharacteristic
107C31×#124—21no—
108C31×#124—21no—
109C31×#124—21no—
110C31×#124D411yescharacteristic
111C31×#123—21no—
112C31×#123—21no—
113C31×#123—21no—
114C31×#123—21no—
115C31×#123—21no—
116C31×#123—21no—
117C31×#123—21no—
118C31×#123—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×C22⋊Q8—21no—
130C31×C22⋊Q8—21no—
131C31×C22⋊Q8—21no—
132C31×C22⋊Q8—21no—
133C31×C22⋊Q8C2311yescharacteristic
134C31×C22⋊Q8C2311yescharacteristic
135C31×C22⋊Q8C2311yescharacteristic
136C31×#121—21no—
137C31×#121C2311yescharacteristic
138C31×#120—21no—
139C4×Q8×C31—21no—
140C4×Q8×C31—21no—
141C4×Q8×C31—21no—
142C4×Q8×C31D411yescharacteristic
143C4×Q8×C31D411yescharacteristic
144C4×Q8×C31D411yescharacteristic
145C4×D4×C31—21no—
146C4×D4×C31—21no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C4×D4×C31D411yescharacteristic
151C31×#117—21no—
152C31×#117—21no—
153C31×#117—21no—
154C31×#117—21no—
155C31×#117—21no—
156C31×#117—21no—
157C2×C4⋊C4×C31—21no—
158C2×C4⋊C4×C31—21no—
159C2×C4⋊C4×C31—21no—
160C2×C4⋊C4×C31—21no—
161C2×C4⋊C4×C31—21no—
162C2×C4⋊C4×C31—21no—
163C2×C4⋊C4×C31D411yescharacteristic
164C2×C4⋊C4×C31D411yescharacteristic
165C2×C4⋊C4×C31C2311yescharacteristic
166C2×C4⋊C4×C31C2311yescharacteristic
167C2×C4⋊C4×C31C2311yescharacteristic
168C2×C22⋊C4×C31—21no—
169C2×C22⋊C4×C31—21no—
170C2×C22⋊C4×C31—21no—
171C2×C22⋊C4×C31D411yescharacteristic
172C2×C22⋊C4×C31D411yescharacteristic
173C2×C22⋊C4×C31C2311yescharacteristic
174C2×C42×C31—21no—
175C2×C42×C31C2311yescharacteristic
176C31×#107—21no—
177C31×#107—21no—
178C31×#107—21no—
179C31×#107—21no—
180C31×#106—21no—
181C31×#106—21no—
182C31×#106—21no—
183C31×#106—21no—
184C31×C4⋊C8—21no—
185C31×C4⋊C8—21no—
186C31×#103—21no—
187C31×#103—21no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#103—21no—
191C31×#103—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×C22⋊C8C2311yescharacteristic
195C31×C22⋊C8C2311yescharacteristic
196C31×C22⋊C8C2311yescharacteristic
197C31×C22⋊C8C2311yescharacteristic
198C31×#97—21no—
199C4×C8×C31—21no—
200C31×#95—21no—
201C31×#95—21no—
202C31×#95—21no—
203C31×#95—21no—
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31C2×D411yescharacteristic
207C2×Q8×C31—21no—
208C2×Q8×C31—21no—
209C2×Q8×C31—21no—
210C2×Q8×C31C2×D411yescharacteristic
211C2×Q8×C31C2×D411yescharacteristic
212C2×Q8×C31C2×D411yescharacteristic
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31C2×D411yescharacteristic
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2411yescharacteristic
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—42no—
270C4⋊C4×C31—42no—
271C4⋊C4×C31—41no—
272C4⋊C4×C31—41no—
273C4⋊C4×C31—41no—
274C4⋊C4×C31—41no—
275C4⋊C4×C31—81no—
276C4⋊C4×C31C2×D411yescharacteristic
277C4⋊C4×C31C2×D411yescharacteristic
278C4⋊C4×C31C2×D411yescharacteristic
279C4⋊C4×C31C2×D411yescharacteristic
280C22⋊C4×C31—21no—
281C22⋊C4×C31—21no—
282C22⋊C4×C31—21no—
283C22⋊C4×C31—21no—
284C22⋊C4×C31—21no—
285C22⋊C4×C31—21no—
286C22⋊C4×C31—21no—
287C22⋊C4×C31—21no—
288C22⋊C4×C31—21no—
289C22⋊C4×C31—21no—
290C22⋊C4×C31—21no—
291C22⋊C4×C31—21no—
292C22⋊C4×C31—21no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C22⋊C4×C31—21no—
300C22⋊C4×C31—21no—
301C22⋊C4×C31—42no—
302C22⋊C4×C31—81no—
303C42×C31—21no—
304C42×C31—21no—
305C42×C31—21no—
306C42×C31—21no—
307C42×C31—21no—
308C42×C31—21no—
309C42×C31—21no—
310C42×C31—81no—
311C42×C31C2×D411yescharacteristic
312C42×C31C2×D411yescharacteristic
313C42×C31C2×D411yescharacteristic
314C42×C31C2×D411yescharacteristic
315#18445C3111yesmaximal, characteristic, direct product factor, Sylow
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31C22×D411yescharacteristic
323Q8×C31—41no—
324Q8×C31—41no—
325Q8×C31—41no—
326Q8×C31—81no—
327Q8×C31—81no—
328Q8×C31—81no—
329D4×C31—41no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—81no—
333D4×C31—81no—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—22no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—81no—
365C2×C4×C31—81no—
366C2×C4×C31—81no—
367C2×C4×C31—81no—
368C2×C4×C31—81no—
369C2×C4×C31#12011yescharacteristic
370C2×C4×C31#12011yescharacteristic
371C2×C4×C31#12011yescharacteristic
372C2×C4×C31#12011yescharacteristic
373C2×C4×C31C22×D411yescharacteristic
374C2×C4×C31C22×D411yescharacteristic
375C8×C31—41no—
376C8×C31—41no—
377C8×C31—41no—
378C8×C31—41no—
379#3564C2×C3111yescharacteristic
380#3236C2×C3111yescharacteristic, complemented
381#3232C2×C3111yescharacteristic, complemented
382#2664C2×C3111yescharacteristic, complemented
383#1618C2×C3111yescharacteristic
384#1617C2×C3111yescharacteristic, complemented
385#1615C2×C3111yescharacteristic, complemented
386#1614C2×C3111yescharacteristic, complemented
387#1612C2×C3111yescharacteristic
388#1611C2×C3111yescharacteristic, complemented
389#1609C2×C3111yescharacteristic, complemented
390#1608C2×C3111yescharacteristic, complemented
391#1509C2×C3111yescharacteristic, complemented
392#1503C2×C3111yescharacteristic, complemented
393#1473C2×C3111yescharacteristic, complemented
394C22×C31—21no—
395C22×C31—21no—
396C22×C31—41no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31C2×#12011yescharacteristic
405C22×C31#57711yescharacteristic
406C22×C31#57811yescharacteristic
407C4×C31—21no—
408C4×C31—21no—
409C4×C31—21no—
410C4×C31—21no—
411C4×C31—21no—
412C4×C31—21no—
413C4×C31—42no—
414C4×C31—41no—
415C4×C31—41no—
416C4×C31—41no—
417C4×C31—41no—
418C4×C31—41no—
419C4×C31—41no—
420C4×C31—41no—
421C4×C31—41no—
422C4×C31—41no—
423C4×C31—41no—
424C4×C31—81no—
425C4×C31—81no—
426C4×C31—81no—
427#563—21no—
428#563—21no—
429#556—21no—
430#554—21no—
431#552—21no—
432#552—21no—
433#551—21no—
434#551—21no—
435#544C22×C3111yescharacteristic
436#543C22×C3111yescharacteristic
437#542—21no—
438#541—21no—
439#541—21no—
440#539—21no—
441#539C22×C3111yescharacteristic
442#538C22×C3111yescharacteristic
443#533C22×C3111yescharacteristic
444#529C22×C3111yescharacteristic
445C2×#126C22×C3111yescharacteristic
446C2×#125C22×C3111yescharacteristic
447#501—21no—
448#499—21no—
449#491—21no—
450#488—21no—
451#484C22×C3111yescharacteristic
452#484C22×C3111yescharacteristic
453#484C22×C3111yescharacteristic
454#483C22×C3111yescharacteristic
455#483C22×C3111yescharacteristic
456#483C22×C3111yescharacteristic
457#481C22×C3111yescharacteristic
458#480C22×C3111yescharacteristic
459#479—21no—
460#479—21no—
461#479—21no—
462#478—21no—
463#432C22×C3111yescharacteristic
464#431C22×C3111yescharacteristic
465#400C22×C3111yescharacteristic
466#399C22×C3111yescharacteristic
467#398—21no—
468#398C22×C3111yescharacteristic
469#397C22×C3111yescharacteristic
470#396—21no—
471#389—21no—
472#388—21no—
473C4×C4⋊C4C22×C3111yescharacteristic
474#328C22×C3111yescharacteristic
475#328C22×C3111yescharacteristic
476#328C22×C3111yescharacteristic
477#328C22×C3111yescharacteristic
478#328C22×C3111yescharacteristic
479#328C22×C3111yescharacteristic
480#327C22×C3111yescharacteristic
481#327C22×C3111yescharacteristic
482#324C22×C3111yescharacteristic
483#324C22×C3111yescharacteristic
484#323C22×C3111yescharacteristic
485#323C22×C3111yescharacteristic
486C2×C31—21no—
487C2×C31—21no—
488C2×C31—81no—
489C2×C31—81no—
490C2×C31#301311yescharacteristic
491C2×C31#301811yescharacteristic
492C2×C31#302811yescharacteristic
493C4⋊Q8—21no—
494C4⋊Q8—21no—
495C4⋊Q8—21no—
496C4⋊Q8D4×C3111yescharacteristic
497C4⋊Q8D4×C3111yescharacteristic
498#126—21no—
499#126—21no—
500#126—21no—
501#126—21no—
502#126—21no—
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#126—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125—21no—
520#125—21no—
521#125—21no—
522#125—21no—
523#125—21no—
524#125D4×C3111yescharacteristic
525#124—21no—
526#124—21no—
527#124—21no—
528#124D4×C3111yescharacteristic
529#123—21no—
530#123—21no—
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537C22⋊Q8—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8C23×C3111yescharacteristic
552C22⋊Q8C23×C3111yescharacteristic
553C22⋊Q8C23×C3111yescharacteristic
554#121—21no—
555#121C23×C3111yescharacteristic
556#120—21no—
557C4×Q8—21no—
558C4×Q8—21no—
559C4×Q8—21no—
560C4×Q8D4×C3111yescharacteristic
561C4×Q8D4×C3111yescharacteristic
562C4×Q8D4×C3111yescharacteristic
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—21no—
567C4×D4—21no—
568C4×D4D4×C3111yescharacteristic
569#117—21no—
570#117—21no—
571#117—21no—
572#117—21no—
573#117—21no—
574#117—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4D4×C3111yescharacteristic
582C2×C4⋊C4D4×C3111yescharacteristic
583C2×C4⋊C4C23×C3111yescharacteristic
584C2×C4⋊C4C23×C3111yescharacteristic
585C2×C4⋊C4C23×C3111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4D4×C3111yescharacteristic
590C2×C22⋊C4D4×C3111yescharacteristic
591C2×C22⋊C4C23×C3111yescharacteristic
592C2×C42—21no—
593C2×C42C23×C3111yescharacteristic
594#107—21no—
595#107—21no—
596#107—21no—
597#107—21no—
598#106—21no—
599#106—21no—
600#106—21no—
601#106—21no—
602C4⋊C8—21no—
603C4⋊C8—21no—
604#103—21no—
605#103—21no—
606#103—21no—
607#103—21no—
608#103—21no—
609#103—21no—
610#102—21no—
611#102—21no—
612C22⋊C8C23×C3111yescharacteristic
613C22⋊C8C23×C3111yescharacteristic
614C22⋊C8C23×C3111yescharacteristic
615C22⋊C8C23×C3111yescharacteristic
616#97—21no—
617C4×C8—21no—
618#95—21no—
619#95—21no—
620#95—21no—
621#95—21no—
622#95C23×C3111yescharacteristic
623#95C23×C3111yescharacteristic
624C31#1844511yescharacteristic, direct product factor, Sylow
625C24C2×D4×C3111yescharacteristic
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8C2×D4×C3111yescharacteristic
630C2×Q8C2×D4×C3111yescharacteristic
631C2×Q8C2×D4×C3111yescharacteristic
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4C2×D4×C3111yescharacteristic
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×C4C2×D4×C3111yescharacteristic
646C22×C4C2×D4×C3111yescharacteristic
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C24×C3111yescharacteristic
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—41no—
693C4⋊C4—41no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C3111yescharacteristic
696C4⋊C4C2×D4×C3111yescharacteristic
697C4⋊C4C2×D4×C3111yescharacteristic
698C4⋊C4C2×D4×C3111yescharacteristic
699C22⋊C4—21no—
700C22⋊C4—21no—
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—42no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42—21no—
728C42—21no—
729C42—81no—
730C42C2×D4×C3111yescharacteristic
731C42C2×D4×C3111yescharacteristic
732C42C2×D4×C3111yescharacteristic
733C42C2×D4×C3111yescharacteristic
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—41no—
740C23C22×D4×C3111yescharacteristic
741Q8—41no—
742Q8—41no—
743Q8—41no—
744Q8—81no—
745Q8—81no—
746Q8—81no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—81no—
783C2×C4—81no—
784C2×C4—81no—
785C2×C4—81no—
786C2×C4—81no—
787C2×C4C31×#12011yescharacteristic
788C2×C4C31×#12011yescharacteristic
789C2×C4C31×#12011yescharacteristic
790C2×C4C31×#12011yescharacteristic
791C2×C4C22×D4×C3111yescharacteristic
792C2×C4C22×D4×C3111yescharacteristic
793C8—41no—
794C8—41no—
795C8—41no—
796C8—41no—
797C22—21no—
798C22—21no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22C2×C31×#12011yescharacteristic
808C22C31×#57711yescharacteristic
809C22C31×#57811yescharacteristic
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—21no—
816C4—42no—
817C4—41no—
818C4—41no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C2—21no—
831C2—21no—
832C2—81no—
833C2—81no—
834C2C31×#301311yescharacteristic
835C2C31×#301811yescharacteristic
836C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#538C22
LCSG ▷ C22×C4 ▷ 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×#3236C2semidirect
3. C31×#3232C2semidirect
4. C31×#2664C2semidirect
6. C31×#1617C2semidirect
7. C31×#1615C2semidirect
8. C31×#1614C2semidirect
10. C31×#1611C2semidirect
11. C31×#1609C2semidirect
12. C31×#1608C2semidirect
13. C31×#1509C2semidirect
14. C31×#1503C2semidirect
15. C31×#1473C2semidirect
315. #18445C31direct (N × H)
380. #3236C2×C31semidirect
381. #3232C2×C31semidirect
382. #2664C2×C31semidirect
384. #1617C2×C31semidirect
385. #1615C2×C31semidirect
386. #1614C2×C31semidirect
388. #1611C2×C31semidirect
389. #1609C2×C31semidirect
390. #1608C2×C31semidirect
391. #1509C2×C31semidirect
392. #1503C2×C31semidirect
393. #1473C2×C31semidirect
624. C31#18445direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35642
C31×#32362
C31×#32322
C31×#26642
C31×#16182
C31×#16172
C31×#16152
C31×#16142
C31×#16122
C31×#16112
C31×#16092
C31×#16082
C31×#15092
C31×#15032
C31×#14732
#1844531