Finite Group Databasebeta

← C31×#18465 #21475224

Subgroups — C31×#18465 #21475224

Order 7936.

870 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3564C211yesmaximal, characteristic
2C31×#3218C211yesmaximal, characteristic, complemented
3C31×#3209C211yesmaximal, characteristic, complemented
4C31×#2821C211yesmaximal, characteristic, complemented
5C31×#1606C212yesmaximal
6C31×#1605C212yesmaximal, complemented
7C31×#1603C212yesmaximal, complemented
8C31×#1602C212yesmaximal, complemented
9C31×#1521C211yesmaximal, characteristic, complemented
10C31×#1515C211yesmaximal, characteristic, complemented
11C31×#1473C211yesmaximal, characteristic, complemented
12C31×#563—21no—
13C31×#563—21no—
14C31×#556—21no—
15C31×#554—21no—
16C31×#552—21no—
17C31×#552—21no—
18C31×#551—21no—
19C31×#551—21no—
20C31×#544C2211yescharacteristic
21C31×#543C2211yescharacteristic
22C31×#542—21no—
23C31×#541—21no—
24C31×#541—21no—
25C31×#539—21no—
26C31×#539C2211yescharacteristic
27C31×#538C2211yescharacteristic
28C31×#533C2211yescharacteristic
29C2×C31×C4⋊Q8C2211yescharacteristic
30C31×#529C2211yescharacteristic
31C2×C31×#126C2211yescharacteristic
32C31×#497—21no—
33C31×#494—21no—
34C31×#491—21no—
35C31×#487—21no—
36C31×#462—21no—
37C31×#462—21no—
38C31×#462—21no—
39C31×#461—21no—
40C31×#451C2212yes—
41C31×#451C2212yes—
42C31×#451C2212yes—
43C31×#448C2212yes—
44C31×#432C2211yescharacteristic
45C31×#431C2211yescharacteristic
46C31×#400—21no—
47C31×#399—21no—
48C31×#398—21no—
49C31×#397—21no—
50C31×#395C2212yes—
51C31×#393C2212yes—
52C31×#383C2211yescharacteristic
53C31×#328C2212yes—
54C31×#328C2212yes—
55C31×#328C2212yes—
56C31×#327C2212yes—
57C31×#324C2212yes—
58C31×#323C2212yes—
59C22×Q8×C31C2312yes—
60C2×Q16×C31—22no—
61C2×Q16×C31—22no—
62C2×Q16×C31—22no—
63C2×SD16×C31—22no—
64C31×C4⋊Q8—21no—
65C31×C4⋊Q8—21no—
66C31×C4⋊Q8—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—21no—
70C31×C4⋊Q8—21no—
71C31×C4⋊Q8D411yescharacteristic
72C31×C4⋊Q8D411yescharacteristic
73C31×#126—21no—
74C31×#126—21no—
75C31×#126—21no—
76C31×#126—21no—
77C31×#126—21no—
78C31×#126—21no—
79C31×#126—21no—
80C31×#126—21no—
81C31×#126—21no—
82C31×#126—21no—
83C31×#126—21no—
84C31×#126—21no—
85C31×#126—21no—
86C31×#125—21no—
87C31×#125—21no—
88C31×#125—21no—
89C31×#125—21no—
90C31×#125—21no—
91C31×#125—21no—
92C31×#125—21no—
93C31×#125—21no—
94C31×#125—21no—
95C31×#125D411yescharacteristic
96C31×#124—21no—
97C31×#124—21no—
98C31×#124—21no—
99C31×#124D411yescharacteristic
100C31×#123—21no—
101C31×#123—21no—
102C31×#123—21no—
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8—21no—
114C31×C22⋊Q8—21no—
115C31×C22⋊Q8—21no—
116C31×C22⋊Q8—21no—
117C31×C22⋊Q8—21no—
118C31×C22⋊Q8—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8C2311yescharacteristic
123C31×C22⋊Q8C2311yescharacteristic
124C31×C22⋊Q8C2311yescharacteristic
125C31×#121—21no—
126C31×#121C2311yescharacteristic
127C31×#120—21no—
128C4×Q8×C31—21no—
129C4×Q8×C31—21no—
130C4×Q8×C31—21no—
131C4×Q8×C31D411yescharacteristic
132C4×Q8×C31D411yescharacteristic
133C4×Q8×C31D411yescharacteristic
134C4×D4×C31—21no—
135C4×D4×C31—21no—
136C4×D4×C31—21no—
137C4×D4×C31—21no—
138C4×D4×C31—21no—
139C4×D4×C31D411yescharacteristic
140C31×#117—21no—
141C31×#117—21no—
142C31×#117—21no—
143C31×#117—21no—
144C31×#117—21no—
145C31×#117—21no—
146C2×C4⋊C4×C31—21no—
147C2×C4⋊C4×C31—21no—
148C2×C4⋊C4×C31—21no—
149C2×C4⋊C4×C31—22no—
150C2×C4⋊C4×C31D411yescharacteristic
151C2×C4⋊C4×C31D411yescharacteristic
152C2×C4⋊C4×C31C2311yescharacteristic
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31D411yescharacteristic
156C2×C22⋊C4×C31D411yescharacteristic
157C2×C22⋊C4×C31C2311yescharacteristic
158C2×C42×C31C2311yescharacteristic
159C31×C4⋊C8—21no—
160C31×C4⋊C8—21no—
161C31×#103—22no—
162C31×#103—22no—
163C31×#103—22no—
164C31×#103—22no—
165C31×C22⋊C8C2312yes—
166C31×C22⋊C8C2312yes—
167C31×#97—21no—
168C4×C8×C31—21no—
169C31×#95—22no—
170C31×#95—21no—
171C31×#95—22no—
172C31×#95—21no—
173C31×#95C2312yes—
174C24×C31C2×D411yescharacteristic
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—22no—
179C2×Q8×C31—22no—
180C2×Q8×C31—82no—
181C2×Q8×C31C2×D411yescharacteristic
182C2×Q8×C31C2×D411yescharacteristic
183C2×Q8×C31C2×D411yescharacteristic
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31C2×D411yescharacteristic
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31C2×D411yescharacteristic
196C22×C4×C31C2×D411yescharacteristic
197C22×C4×C31C2×D411yescharacteristic
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2411yescharacteristic
201Q16×C31—82no—
202Q16×C31—82no—
203Q16×C31—82no—
204SD16×C31—82no—
205C2×C8×C31—22no—
206C2×C8×C31—22no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—21no—
213C4⋊C4×C31—21no—
214C4⋊C4×C31—21no—
215C4⋊C4×C31—21no—
216C4⋊C4×C31—21no—
217C4⋊C4×C31—21no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—21no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—21no—
230C4⋊C4×C31—21no—
231C4⋊C4×C31—21no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—41no—
237C4⋊C4×C31—41no—
238C4⋊C4×C31—41no—
239C4⋊C4×C31—41no—
240C4⋊C4×C31—82no—
241C4⋊C4×C31C2×D411yescharacteristic
242C4⋊C4×C31C2×D411yescharacteristic
243C4⋊C4×C31C2×D411yescharacteristic
244C4⋊C4×C31C2×D411yescharacteristic
245C22⋊C4×C31—21no—
246C22⋊C4×C31—21no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—21no—
251C22⋊C4×C31—21no—
252C22⋊C4×C31—21no—
253C22⋊C4×C31—21no—
254C22⋊C4×C31—21no—
255C22⋊C4×C31—21no—
256C22⋊C4×C31—21no—
257C22⋊C4×C31—21no—
258C22⋊C4×C31—21no—
259C22⋊C4×C31—21no—
260C22⋊C4×C31—21no—
261C22⋊C4×C31—21no—
262C22⋊C4×C31—21no—
263C22⋊C4×C31—21no—
264C22⋊C4×C31—21no—
265C22⋊C4×C31—21no—
266C22⋊C4×C31—82no—
267C42×C31—21no—
268C42×C31—21no—
269C42×C31—21no—
270C42×C31—21no—
271C42×C31—21no—
272C42×C31—21no—
273C42×C31—21no—
274C42×C31C2×D411yescharacteristic
275C42×C31C2×D411yescharacteristic
276C42×C31C2×D411yescharacteristic
277C42×C31C2×D411yescharacteristic
278#18465C3111yesmaximal, characteristic, direct product factor, Sylow
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—22no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31C22×D411yescharacteristic
285Q8×C31—41no—
286Q8×C31—41no—
287Q8×C31—41no—
288Q8×C31—42no—
289Q8×C31—42no—
290Q8×C31—42no—
291Q8×C31—42no—
292Q8×C31—81no—
293Q8×C31—81no—
294Q8×C31—81no—
295D4×C31—41no—
296D4×C31—42no—
297D4×C31—81no—
298D4×C31—81no—
299C2×C4×C31—22no—
300C2×C4×C31—21no—
301C2×C4×C31—21no—
302C2×C4×C31—21no—
303C2×C4×C31—21no—
304C2×C4×C31—21no—
305C2×C4×C31—21no—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—22no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—42no—
321C2×C4×C31—81no—
322C2×C4×C31—81no—
323C2×C4×C31—81no—
324C2×C4×C31—81no—
325C2×C4×C31—81no—
326C2×C4×C31#12011yescharacteristic
327C2×C4×C31#12011yescharacteristic
328C2×C4×C31#12011yescharacteristic
329C2×C4×C31#12011yescharacteristic
330C2×C4×C31C22×D411yescharacteristic
331C2×C4×C31C22×D411yescharacteristic
332C8×C31—42no—
333C8×C31—42no—
334#3564C2×C3111yescharacteristic
335#3218C2×C3111yescharacteristic, complemented
336#3209C2×C3111yescharacteristic, complemented
337#2821C2×C3111yescharacteristic, complemented
338#1606C2×C3112yes—
339#1605C2×C3112yescomplemented
340#1603C2×C3112yescomplemented
341#1602C2×C3112yescomplemented
342#1521C2×C3111yescharacteristic, complemented
343#1515C2×C3111yescharacteristic, complemented
344#1473C2×C3111yescharacteristic, complemented
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—41no—
348C22×C31—41no—
349C22×C31—41no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—41no—
353C22×C31—82no—
354C22×C31C2×#12011yescharacteristic
355C22×C31#57812yes—
356C4×C31—21no—
357C4×C31—21no—
358C4×C31—21no—
359C4×C31—21no—
360C4×C31—21no—
361C4×C31—21no—
362C4×C31—41no—
363C4×C31—41no—
364C4×C31—41no—
365C4×C31—41no—
366C4×C31—41no—
367C4×C31—41no—
368C4×C31—41no—
369C4×C31—41no—
370C4×C31—41no—
371C4×C31—41no—
372C4×C31—82no—
373C4×C31—82no—
374#563—21no—
375#563—21no—
376#556—21no—
377#554—21no—
378#552—21no—
379#552—21no—
380#551—21no—
381#551—21no—
382#544C22×C3111yescharacteristic
383#543C22×C3111yescharacteristic
384#542—21no—
385#541—21no—
386#541—21no—
387#539—21no—
388#539C22×C3111yescharacteristic
389#538C22×C3111yescharacteristic
390#533C22×C3111yescharacteristic
391C2×C4⋊Q8C22×C3111yescharacteristic
392#529C22×C3111yescharacteristic
393C2×#126C22×C3111yescharacteristic
394#497—21no—
395#494—21no—
396#491—21no—
397#487—21no—
398#462—21no—
399#462—21no—
400#462—21no—
401#461—21no—
402#451C22×C3112yes—
403#451C22×C3112yes—
404#451C22×C3112yes—
405#448C22×C3112yes—
406#432C22×C3111yescharacteristic
407#431C22×C3111yescharacteristic
408#400—21no—
409#399—21no—
410#398—21no—
411#397—21no—
412#395C22×C3112yes—
413#393C22×C3112yes—
414#383C22×C3111yescharacteristic
415#328C22×C3112yes—
416#328C22×C3112yes—
417#328C22×C3112yes—
418#327C22×C3112yes—
419#324C22×C3112yes—
420#323C22×C3112yes—
421C2×C31—22no—
422C2×C31—81no—
423C2×C31—81no—
424C2×C31#301111yescharacteristic
425C2×C31#302211yescharacteristic
426C2×C31#302711yescharacteristic
427C22×Q8C23×C3112yes—
428C2×Q16—22no—
429C2×Q16—22no—
430C2×Q16—22no—
431C2×SD16—22no—
432C4⋊Q8—21no—
433C4⋊Q8—21no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8—21no—
437C4⋊Q8—21no—
438C4⋊Q8—21no—
439C4⋊Q8D4×C3111yescharacteristic
440C4⋊Q8D4×C3111yescharacteristic
441#126—21no—
442#126—21no—
443#126—21no—
444#126—21no—
445#126—21no—
446#126—21no—
447#126—21no—
448#126—21no—
449#126—21no—
450#126—21no—
451#126—21no—
452#126—21no—
453#126—21no—
454#125—21no—
455#125—21no—
456#125—21no—
457#125—21no—
458#125—21no—
459#125—21no—
460#125—21no—
461#125—21no—
462#125—21no—
463#125D4×C3111yescharacteristic
464#124—21no—
465#124—21no—
466#124—21no—
467#124D4×C3111yescharacteristic
468#123—21no—
469#123—21no—
470#123—21no—
471#123—21no—
472#123—21no—
473#123—21no—
474#123—21no—
475#123—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8—21no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8C23×C3111yescharacteristic
491C22⋊Q8C23×C3111yescharacteristic
492C22⋊Q8C23×C3111yescharacteristic
493#121—21no—
494#121C23×C3111yescharacteristic
495#120—21no—
496C4×Q8—21no—
497C4×Q8—21no—
498C4×Q8—21no—
499C4×Q8D4×C3111yescharacteristic
500C4×Q8D4×C3111yescharacteristic
501C4×Q8D4×C3111yescharacteristic
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4D4×C3111yescharacteristic
508#117—21no—
509#117—21no—
510#117—21no—
511#117—21no—
512#117—21no—
513#117—21no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—21no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4D4×C3111yescharacteristic
519C2×C4⋊C4D4×C3111yescharacteristic
520C2×C4⋊C4C23×C3111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4D4×C3111yescharacteristic
524C2×C22⋊C4D4×C3111yescharacteristic
525C2×C22⋊C4C23×C3111yescharacteristic
526C2×C42C23×C3111yescharacteristic
527C4⋊C8—21no—
528C4⋊C8—21no—
529#103—22no—
530#103—22no—
531#103—22no—
532#103—22no—
533C22⋊C8C23×C3112yes—
534C22⋊C8C23×C3112yes—
535#97—21no—
536C4×C8—21no—
537#95—21no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95C23×C3112yes—
542C31#1846511yescharacteristic, direct product factor, Sylow
543C24C2×D4×C3111yescharacteristic
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—82no—
550C2×Q8C2×D4×C3111yescharacteristic
551C2×Q8C2×D4×C3111yescharacteristic
552C2×Q8C2×D4×C3111yescharacteristic
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4C2×D4×C3111yescharacteristic
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4C2×D4×C3111yescharacteristic
565C22×C4C2×D4×C3111yescharacteristic
566C22×C4C2×D4×C3111yescharacteristic
567C22×C4C2×D4×C3111yescharacteristic
568C22×C4C2×D4×C3111yescharacteristic
569C22×C4C24×C3111yescharacteristic
570Q16—82no—
571Q16—82no—
572Q16—82no—
573SD16—82no—
574C2×C8—22no—
575C2×C8—22no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—41no—
606C4⋊C4—41no—
607C4⋊C4—41no—
608C4⋊C4—41no—
609C4⋊C4—82no—
610C4⋊C4C2×D4×C3111yescharacteristic
611C4⋊C4C2×D4×C3111yescharacteristic
612C4⋊C4C2×D4×C3111yescharacteristic
613C4⋊C4C2×D4×C3111yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—21no—
625C22⋊C4—21no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—82no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42C2×D4×C3111yescharacteristic
644C42C2×D4×C3111yescharacteristic
645C42C2×D4×C3111yescharacteristic
646C42C2×D4×C3111yescharacteristic
647C23—21no—
648C23—21no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23C22×D4×C3111yescharacteristic
653Q8—41no—
654Q8—41no—
655Q8—41no—
656Q8—42no—
657Q8—42no—
658Q8—42no—
659Q8—42no—
660Q8—81no—
661Q8—81no—
662Q8—81no—
663D4—41no—
664D4—42no—
665D4—81no—
666D4—81no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—81no—
690C2×C4—81no—
691C2×C4—81no—
692C2×C4—81no—
693C2×C4—81no—
694C2×C4C31×#12011yescharacteristic
695C2×C4C31×#12011yescharacteristic
696C2×C4C31×#12011yescharacteristic
697C2×C4C31×#12011yescharacteristic
698C2×C4C22×D4×C3111yescharacteristic
699C2×C4C22×D4×C3111yescharacteristic
700C8—42no—
701C8—42no—
702C22—21no—
703C22—21no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—82no—
711C22C2×C31×#12011yescharacteristic
712C22C31×#57812yes—
713C4—21no—
714C4—21no—
715C4—21no—
716C4—21no—
717C4—21no—
718C4—21no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—41no—
728C4—41no—
729C4—82no—
730C4—82no—
731C2—22no—
732C2—81no—
733C2—81no—
734C2C31×#301111yescharacteristic
735C2C31×#302211yescharacteristic
736C2C31×#302711yescharacteristic
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×#3218C2semidirect
3. C31×#3209C2semidirect
4. C31×#2821C2semidirect
6. C31×#1605C2semidirect
7. C31×#1603C2semidirect
8. C31×#1602C2semidirect
9. C31×#1521C2semidirect
10. C31×#1515C2semidirect
11. C31×#1473C2semidirect
278. #18465C31direct (N × H)
335. #3218C2×C31semidirect
336. #3209C2×C31semidirect
337. #2821C2×C31semidirect
339. #1605C2×C31semidirect
340. #1603C2×C31semidirect
341. #1602C2×C31semidirect
342. #1521C2×C31semidirect
343. #1515C2×C31semidirect
344. #1473C2×C31semidirect
542. C31#18465direct (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×#32182
C31×#32092
C31×#28212
C31×#16062
C31×#16052
C31×#16032
C31×#16022
C31×#15212
C31×#15152
C31×#14732
#1846531