Finite Group Databasebeta

← C31×#18234 #21474993

Subgroups — C31×#18234 #21474993

Order 7936.

938 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3535C211yesmaximal, characteristic
2C31×#3092C211yesmaximal, characteristic, complemented
3C2×C31×#483C211yesmaximal, characteristic, complemented
4C31×#2623C211yesmaximal, characteristic, complemented
5C31×#1612C212yesmaximal, complemented
6C31×#1611C212yesmaximal, complemented
7C31×#1609C212yesmaximal, complemented
8C31×#1608C212yesmaximal, complemented
9C31×#1516C211yesmaximal, characteristic, complemented
10C31×#1511C211yesmaximal, characteristic, complemented
11C31×#1468C211yesmaximal, characteristic, complemented
12C31×#563—21no—
13C31×#562—21no—
14C31×#554—21no—
15C31×#552—21no—
16C31×#551—21no—
17C31×#551—21no—
18C31×#547—21no—
19C31×#546—21no—
20C31×#544C2211yescharacteristic
21C31×#543C2211yescharacteristic
22C31×#542—21no—
23C31×#539—21no—
24C31×#539—21no—
25C31×#539C2211yescharacteristic
26C31×#538C2211yescharacteristic
27C31×#536—21no—
28C31×#525C2211yescharacteristic
29C2×C31×#123C2211yescharacteristic
30C2×C31×C22⋊Q8C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C31×#484—21no—
33C31×#483—21no—
34C31×#483—21no—
35C31×#483C2212yes—
36C31×#483C2212yes—
37C31×#483C2212yes—
38C31×#481—21no—
39C31×#480C2212yes—
40C31×#428—21no—
41C2×C31×#106—21no—
42C31×#417—21no—
43C2×C31×#103—21no—
44C31×#407C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C31×#400—21no—
47C31×#399—21no—
48C31×#398C2212yes—
49C31×#397C2212yes—
50C31×#386—21no—
51C31×#385—21no—
52C31×#381C2211yescharacteristic
53C31×#328C2212yes—
54C31×#328C2212yes—
55C31×#328C2212yes—
56C31×#327C2212yes—
57C31×#324C2212yes—
58C31×#323C2212yes—
59C2×#41×C31—21no—
60C2×#41×C31D411yescharacteristic
61C22×Q8×C31D411yescharacteristic
62C22×D4×C31D411yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31C2311yescharacteristic
65C2×M16×C31—21no—
66C22×C8×C31—21no—
67C31×C4⋊Q8—21no—
68C31×C4⋊Q8—21no—
69C31×C4⋊Q8—21no—
70C31×#126—21no—
71C31×#126—21no—
72C31×#126—21no—
73C31×#126—21no—
74C31×#126—21no—
75C31×#126—21no—
76C31×#125—21no—
77C31×#125—21no—
78C31×#125—21no—
79C31×#125—21no—
80C31×#125—21no—
81C31×#124—21no—
82C31×#124—21no—
83C31×#124—21no—
84C31×#124—21no—
85C31×#123—21no—
86C31×#123—21no—
87C31×#123—21no—
88C31×#123—21no—
89C31×#123—21no—
90C31×#123—21no—
91C31×#123—21no—
92C31×#123—21no—
93C31×#123—21no—
94C31×#123—21no—
95C31×#123—21no—
96C31×#123—21no—
97C31×#123—21no—
98C31×#123—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—21no—
101C31×C22⋊Q8—21no—
102C31×C22⋊Q8—21no—
103C31×C22⋊Q8—21no—
104C31×C22⋊Q8—21no—
105C31×C22⋊Q8—21no—
106C31×C22⋊Q8—21no—
107C31×C22⋊Q8—21no—
108C31×C22⋊Q8—21no—
109C31×C22⋊Q8—21no—
110C31×C22⋊Q8—21no—
111C31×C22⋊Q8—21no—
112C31×C22⋊Q8—21no—
113C31×C22⋊Q8D411yescharacteristic
114C31×C22⋊Q8D411yescharacteristic
115C31×C22⋊Q8D411yescharacteristic
116C31×C22⋊Q8C2311yescharacteristic
117C31×C22⋊Q8C2311yescharacteristic
118C31×C22⋊Q8C2311yescharacteristic
119C31×#121—21no—
120C31×#121—21no—
121C31×#121—21no—
122C31×#121—21no—
123C31×#121D411yescharacteristic
124C31×#121C2311yescharacteristic
125C31×#120—21no—
126C31×#120—21no—
127C4×Q8×C31—21no—
128C4×D4×C31—21no—
129C4×D4×C31—21no—
130C4×D4×C31—21no—
131C4×D4×C31—21no—
132C4×D4×C31—21no—
133C4×D4×C31—21no—
134C4×D4×C31—21no—
135C31×#117—21no—
136C31×#117—21no—
137C31×#117—21no—
138C31×#117D411yescharacteristic
139C2×C4⋊C4×C31—21no—
140C2×C4⋊C4×C31—21no—
141C2×C4⋊C4×C31—21no—
142C2×C4⋊C4×C31—21no—
143C2×C4⋊C4×C31—21no—
144C2×C4⋊C4×C31—21no—
145C2×C4⋊C4×C31—21no—
146C2×C4⋊C4×C31—22no—
147C2×C4⋊C4×C31D411yescharacteristic
148C2×C4⋊C4×C31D411yescharacteristic
149C2×C4⋊C4×C31C2312yes—
150C2×C4⋊C4×C31C2311yescharacteristic
151C2×C22⋊C4×C31—21no—
152C2×C22⋊C4×C31—21no—
153C2×C22⋊C4×C31—21no—
154C2×C22⋊C4×C31—22no—
155C2×C22⋊C4×C31D411yescharacteristic
156C2×C22⋊C4×C31D411yescharacteristic
157C2×C22⋊C4×C31C2311yescharacteristic
158C31×#107—22no—
159C31×#106—22no—
160C31×#106—22no—
161C31×#106—22no—
162C31×#103—22no—
163C31×#103—22no—
164C31×#103—22no—
165C31×#102—22no—
166C31×C22⋊C8—21no—
167C31×C22⋊C8—21no—
168C31×C22⋊C8C2312yes—
169C31×C22⋊C8C2312yes—
170C31×#95—22no—
171C31×#95—22no—
172C31×#95—21no—
173C31×#95C2312yes—
174C24×C31C2×D411yescharacteristic
175C24×C31C2×D411yescharacteristic
176#41×C31—42no—
177#41×C31—82no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31—21no—
181C2×Q8×C31—42no—
182C2×Q8×C31C2×D411yescharacteristic
183C2×Q8×C31C2×D411yescharacteristic
184C2×Q8×C31C2×D411yescharacteristic
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—42no—
193C2×D4×C31C2×D411yescharacteristic
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—42no—
204C22×C4×C31—41no—
205C22×C4×C31—41no—
206C22×C4×C31—82no—
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2411yescharacteristic
216M16×C31—42no—
217C2×C8×C31—22no—
218C2×C8×C31—22no—
219C2×C8×C31—42no—
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—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—22no—
244C4⋊C4×C31—22no—
245C4⋊C4×C31—41no—
246C4⋊C4×C31—41no—
247C4⋊C4×C31—82no—
248C4⋊C4×C31C2×D411yescharacteristic
249C4⋊C4×C31C2×D411yescharacteristic
250C4⋊C4×C31C2×D411yescharacteristic
251C4⋊C4×C31C2×D411yescharacteristic
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—21no—
267C22⋊C4×C31—21no—
268C22⋊C4×C31—21no—
269C22⋊C4×C31—21no—
270C22⋊C4×C31—21no—
271C22⋊C4×C31—21no—
272C22⋊C4×C31—21no—
273C22⋊C4×C31—21no—
274C22⋊C4×C31—21no—
275C22⋊C4×C31—42no—
276C22⋊C4×C31—82no—
277C42×C31—21no—
278C42×C31—21no—
279C42×C31—21no—
280C42×C31—21no—
281C42×C31—21no—
282#18234C3111yesmaximal, characteristic, direct product factor, Sylow
283C23×C31—22no—
284C23×C31—22no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—22no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31#12011yescharacteristic
292C23×C31#12011yescharacteristic
293C23×C31C22×D411yescharacteristic
294Q8×C31—41no—
295Q8×C31—41no—
296Q8×C31—41no—
297Q8×C31—81no—
298Q8×C31—81no—
299Q8×C31—81no—
300D4×C31—41no—
301D4×C31—42no—
302D4×C31—42no—
303D4×C31—42no—
304D4×C31—81no—
305D4×C31—81no—
306D4×C31—81no—
307D4×C31—81no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—42no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—81no—
335C2×C4×C31—81no—
336C2×C4×C31—81no—
337C2×C4×C31—81no—
338C2×C4×C31—81no—
339C2×C4×C31—81no—
340C2×C4×C31—82no—
341C2×C4×C31—82no—
342C2×C4×C31#12011yescharacteristic
343C2×C4×C31#12011yescharacteristic
344C2×C4×C31C22×D411yescharacteristic
345C2×C4×C31C22×D411yescharacteristic
346C8×C31—42no—
347C8×C31—42no—
348#3535C2×C3111yescharacteristic
349#3092C2×C3111yescharacteristic, complemented
350C2×#483C2×C3111yescharacteristic, complemented
351#2623C2×C3111yescharacteristic, complemented
352#1612C2×C3112yescomplemented
353#1611C2×C3112yescomplemented
354#1609C2×C3112yescomplemented
355#1608C2×C3112yescomplemented
356#1516C2×C3111yescharacteristic, complemented
357#1511C2×C3111yescharacteristic, complemented
358#1468C2×C3111yescharacteristic, complemented
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—21no—
365C22×C31—21no—
366C22×C31—44no—
367C22×C31—41no—
368C22×C31—41no—
369C22×C31—41no—
370C22×C31—41no—
371C22×C31—41no—
372C22×C31—41no—
373C22×C31—82no—
374C22×C31#45812yes—
375C22×C31C2×#12011yescharacteristic
376C22×C31#57712yes—
377C4×C31—21no—
378C4×C31—21no—
379C4×C31—21no—
380C4×C31—21no—
381C4×C31—41no—
382C4×C31—41no—
383C4×C31—41no—
384C4×C31—41no—
385C4×C31—41no—
386C4×C31—41no—
387C4×C31—41no—
388C4×C31—41no—
389C4×C31—41no—
390C4×C31—41no—
391C4×C31—82no—
392C4×C31—82no—
393#563—21no—
394#562—21no—
395#554—21no—
396#552—21no—
397#551—21no—
398#551—21no—
399#547—21no—
400#546—21no—
401#544C22×C3111yescharacteristic
402#543C22×C3111yescharacteristic
403#542—21no—
404#539—21no—
405#539—21no—
406#539C22×C3111yescharacteristic
407#538C22×C3111yescharacteristic
408#536—21no—
409#525C22×C3111yescharacteristic
410C2×#123C22×C3111yescharacteristic
411C2×C22⋊Q8C22×C3111yescharacteristic
412C22×C4⋊C4C22×C3111yescharacteristic
413#484—21no—
414#483—21no—
415#483—21no—
416#483C22×C3112yes—
417#483C22×C3112yes—
418#483C22×C3112yes—
419#481—21no—
420#480C22×C3112yes—
421#428—21no—
422C2×#106—21no—
423#417—21no—
424C2×#103—21no—
425#407C22×C3111yescharacteristic
426C2×C22⋊C8C22×C3111yescharacteristic
427#400—21no—
428#399—21no—
429#398C22×C3112yes—
430#397C22×C3112yes—
431#386—21no—
432#385—21no—
433#381C22×C3111yescharacteristic
434#328C22×C3112yes—
435#328C22×C3112yes—
436#328C22×C3112yes—
437#327C22×C3112yes—
438#324C22×C3112yes—
439#323C22×C3112yes—
440C2×C31—22no—
441C2×C31—22no—
442C2×C31—41no—
443C2×C31—81no—
444C2×C31—81no—
445C2×C31#301011yescharacteristic
446C2×C31#302211yescharacteristic
447C2×C31C2×#45811yescharacteristic
448C2×#41—21no—
449C2×#41D4×C3111yescharacteristic
450C22×Q8D4×C3111yescharacteristic
451C22×D4D4×C3111yescharacteristic
452C23×C4—21no—
453C23×C4C23×C3111yescharacteristic
454C2×M16—21no—
455C22×C8—21no—
456C4⋊Q8—21no—
457C4⋊Q8—21no—
458C4⋊Q8—21no—
459#126—21no—
460#126—21no—
461#126—21no—
462#126—21no—
463#126—21no—
464#126—21no—
465#125—21no—
466#125—21no—
467#125—21no—
468#125—21no—
469#125—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124—21no—
474#123—21no—
475#123—21no—
476#123—21no—
477#123—21no—
478#123—21no—
479#123—21no—
480#123—21no—
481#123—21no—
482#123—21no—
483#123—21no—
484#123—21no—
485#123—21no—
486#123—21no—
487#123—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493C22⋊Q8—21no—
494C22⋊Q8—21no—
495C22⋊Q8—21no—
496C22⋊Q8—21no—
497C22⋊Q8—21no—
498C22⋊Q8—21no—
499C22⋊Q8—21no—
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8D4×C3111yescharacteristic
503C22⋊Q8D4×C3111yescharacteristic
504C22⋊Q8D4×C3111yescharacteristic
505C22⋊Q8C23×C3111yescharacteristic
506C22⋊Q8C23×C3111yescharacteristic
507C22⋊Q8C23×C3111yescharacteristic
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121D4×C3111yescharacteristic
513#121C23×C3111yescharacteristic
514#120—21no—
515#120—21no—
516C4×Q8—21no—
517C4×D4—21no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524#117—21no—
525#117—21no—
526#117—21no—
527#117D4×C3111yescharacteristic
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4D4×C3111yescharacteristic
537C2×C4⋊C4D4×C3111yescharacteristic
538C2×C4⋊C4C23×C3112yes—
539C2×C4⋊C4C23×C3111yescharacteristic
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—22no—
544C2×C22⋊C4D4×C3111yescharacteristic
545C2×C22⋊C4D4×C3111yescharacteristic
546C2×C22⋊C4C23×C3111yescharacteristic
547#107—22no—
548#106—22no—
549#106—22no—
550#106—22no—
551#103—22no—
552#103—22no—
553#103—22no—
554#102—22no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8C23×C3112yes—
558C22⋊C8C23×C3112yes—
559#95—21no—
560#95—22no—
561#95—22no—
562#95C23×C3112yes—
563C31#1823411yescharacteristic, direct product factor, Sylow
564C24C2×D4×C3111yescharacteristic
565C24C2×D4×C3111yescharacteristic
566#41—42no—
567#41—82no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8—21no—
571C2×Q8—42no—
572C2×Q8C2×D4×C3111yescharacteristic
573C2×Q8C2×D4×C3111yescharacteristic
574C2×Q8C2×D4×C3111yescharacteristic
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—42no—
583C2×D4C2×D4×C3111yescharacteristic
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—42no—
594C22×C4—41no—
595C22×C4—41no—
596C22×C4—82no—
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C2×D4×C3111yescharacteristic
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C24×C3111yescharacteristic
606M16—42no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—42no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—41no—
636C4⋊C4—41no—
637C4⋊C4—82no—
638C4⋊C4C2×D4×C3111yescharacteristic
639C4⋊C4C2×D4×C3111yescharacteristic
640C4⋊C4C2×D4×C3111yescharacteristic
641C4⋊C4C2×D4×C3111yescharacteristic
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—21no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—42no—
666C22⋊C4—82no—
667C42—21no—
668C42—21no—
669C42—21no—
670C42—21no—
671C42—21no—
672C23—22no—
673C23—22no—
674C23—21no—
675C23—21no—
676C23—22no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C31×#12011yescharacteristic
681C23C31×#12011yescharacteristic
682C23C22×D4×C3111yescharacteristic
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—81no—
687Q8—81no—
688Q8—81no—
689D4—41no—
690D4—42no—
691D4—42no—
692D4—42no—
693D4—81no—
694D4—81no—
695D4—81no—
696D4—81no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—81no—
724C2×C4—81no—
725C2×C4—81no—
726C2×C4—81no—
727C2×C4—81no—
728C2×C4—81no—
729C2×C4—82no—
730C2×C4—82no—
731C2×C4C31×#12011yescharacteristic
732C2×C4C31×#12011yescharacteristic
733C2×C4C22×D4×C3111yescharacteristic
734C2×C4C22×D4×C3111yescharacteristic
735C8—42no—
736C8—42no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—82no—
752C22C31×#45812yes—
753C22C2×C31×#12011yescharacteristic
754C22C31×#57712yes—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—41no—
763C4—41no—
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—82no—
770C4—82no—
771C2—22no—
772C2—22no—
773C2—41no—
774C2—81no—
775C2—81no—
776C2C31×#301011yescharacteristic
777C2C31×#302211yescharacteristic
778C2C2×C31×#45811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3535C2
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
2. C31×#3092C2semidirect
3. C2×C31×#483C2semidirect
4. C31×#2623C2semidirect
5. C31×#1612C2semidirect
6. C31×#1611C2semidirect
7. C31×#1609C2semidirect
8. C31×#1608C2semidirect
9. C31×#1516C2semidirect
10. C31×#1511C2semidirect
11. C31×#1468C2semidirect
282. #18234C31direct (N × H)
349. #3092C2×C31semidirect
350. C2×#483C2×C31semidirect
351. #2623C2×C31semidirect
352. #1612C2×C31semidirect
353. #1611C2×C31semidirect
354. #1609C2×C31semidirect
355. #1608C2×C31semidirect
356. #1516C2×C31semidirect
357. #1511C2×C31semidirect
358. #1468C2×C31semidirect
563. C31#18234direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35352
C31×#30922
C2×C31×#4832
C31×#26232
C31×#16122
C31×#16112
C31×#16092
C31×#16082
C31×#15162
C31×#15112
C31×#14682
#1823431