Finite Group Databasebeta

← C31×#18230 #21474989

Subgroups — C31×#18230 #21474989

Order 7936.

1140 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3538C211yesmaximal, characteristic, complemented
2C31×#3007C211yesmaximal, characteristic, complemented
3C31×#3002C211yesmaximal, characteristic
4C31×#2616C211yesmaximal, characteristic, complemented
5C31×#1605C212yesmaximal, complemented
6C31×#1603C212yesmaximal, complemented
7C31×#1599C212yesmaximal, complemented
8C31×#1597C212yesmaximal, complemented
9C31×#1520C211yesmaximal, characteristic, complemented
10C31×#1513C211yesmaximal, characteristic, complemented
11C31×#1472C211yesmaximal, characteristic, complemented
12C22×#41×C31C2211yescharacteristic
13C2×C31×#137—21no—
14C2×C31×#135—21no—
15C31×#563—22no—
16C31×#552—21no—
17C31×#552—21no—
18C31×#551—22no—
19D4×Q8×C31—21no—
20D4×Q8×C31—21no—
21C31×#544—21no—
22C31×#544C2212yes—
23C31×#541—21no—
24C31×#539—21no—
25C31×#539C2212yes—
26C31×#536—21no—
27C31×#525C2211yescharacteristic
28C2×C31×C22⋊Q8—21no—
29C2×C31×C22⋊Q8C2211yescharacteristic
30C2×C31×C22⋊Q8C2211yescharacteristic
31C31×#452—21no—
32C31×#452—22no—
33C31×#451C2212yes—
34C31×#451C2211yescharacteristic
35C31×#450C2212yes—
36C31×#450C2211yescharacteristic
37C31×#449—21no—
38C31×#448C2211yescharacteristic
39C31×#447C2211yescharacteristic
40C31×#417—21no—
41C31×#416—21no—
42C31×#407C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C31×#395C2212yes—
45C31×#394—22no—
46C31×#394C2212yes—
47C31×#380—21no—
48C31×#380C2211yescharacteristic
49C31×#328C2212yes—
50C31×#328C2212yes—
51C31×#328C2212yes—
52C31×#327C2212yes—
53C31×#324C2212yes—
54C31×#324C2212yes—
55C2×#41×C31—21no—
56C2×#41×C31—21no—
57C2×#41×C31—21no—
58C2×#41×C31—21no—
59C2×#41×C31—44no—
60C2×#41×C31D411yescharacteristic
61C22×Q8×C31—21no—
62C22×Q8×C31D411yescharacteristic
63C22×Q8×C31D411yescharacteristic
64C22×Q8×C31C2311yescharacteristic
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31C2311yescharacteristic
69C31×#137—44no—
70C31×#135—44no—
71C2×Q16×C31—21no—
72C2×Q16×C31—22no—
73C2×SD16×C31—21no—
74C2×SD16×C31—22no—
75C2×SD16×C31—21no—
76C2×D8×C31—21no—
77C2×M16×C31—21no—
78C22×C8×C31—21no—
79C31×C4⋊Q8—21no—
80C31×C4⋊Q8—22no—
81C31×C4⋊Q8—22no—
82C31×C4⋊Q8—22no—
83C31×#126—22no—
84C31×#126—22no—
85C31×#126—22no—
86C31×#126—22no—
87C31×#125—21no—
88C31×#125—22no—
89C31×#125—22no—
90C31×#125—22no—
91C31×#125—22no—
92C31×#124—22no—
93C31×#123—22no—
94C31×#123—22no—
95C31×#123—22no—
96C31×#123—21no—
97C31×#123—22no—
98C31×C22⋊Q8—21no—
99C31×C22⋊Q8—21no—
100C31×C22⋊Q8—22no—
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8—22no—
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—22no—
110C31×C22⋊Q8—44no—
111C31×C22⋊Q8D412yes—
112C31×C22⋊Q8D411yescharacteristic
113C31×C22⋊Q8C2312yes—
114C31×C22⋊Q8C2311yescharacteristic
115C31×#121D411yescharacteristic
116C31×#121C2311yescharacteristic
117C31×#120—21no—
118C4×Q8×C31—21no—
119C4×Q8×C31—21no—
120C4×D4×C31—22no—
121C4×D4×C31—21no—
122C4×D4×C31—21no—
123C4×D4×C31—22no—
124C31×#117—21no—
125C31×#117—22no—
126C31×#117—22no—
127C31×#117D411yescharacteristic
128C2×C4⋊C4×C31—21no—
129C2×C4⋊C4×C31—22no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31D411yescharacteristic
132C2×C4⋊C4×C31D411yescharacteristic
133C2×C4⋊C4×C31C2312yes—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31D412yes—
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—21no—
153C24×C31C2×D411yescharacteristic
154#41×C31—24no—
155#41×C31—24no—
156#41×C31—42no—
157#41×C31—42no—
158#41×C31—42no—
159#41×C31—42no—
160#41×C31—42no—
161#41×C31—42no—
162#41×C31—42no—
163C2×Q8×C31—22no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—42no—
170C2×Q8×C31—42no—
171C2×Q8×C31—42no—
172C2×Q8×C31—82no—
173C2×Q8×C31C2×D412yes—
174C2×Q8×C31C2×D411yescharacteristic
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—42no—
181C2×D4×C31—42no—
182C2×D4×C31—42no—
183C2×D4×C31—41no—
184C2×D4×C31—41no—
185C2×D4×C31C2×D411yescharacteristic
186C22×C4×C31—24no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—22no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—22no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—41no—
196C22×C4×C31—41no—
197C22×C4×C31C2×D412yes—
198C22×C4×C31C2×D411yescharacteristic
199C22×C4×C31C2×D411yescharacteristic
200C22×C4×C31C2×D411yescharacteristic
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2411yescharacteristic
205Q16×C31—42no—
206Q16×C31—44no—
207SD16×C31—42no—
208SD16×C31—44no—
209SD16×C31—42no—
210D8×C31—42no—
211M16×C31—42no—
212C2×C8×C31—21no—
213C2×C8×C31—21no—
214C2×C8×C31—22no—
215C2×C8×C31—42no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—22no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—22no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—21no—
226C4⋊C4×C31—21no—
227C4⋊C4×C31—21no—
228C4⋊C4×C31—21no—
229C4⋊C4×C31—22no—
230C4⋊C4×C31—22no—
231C4⋊C4×C31—22no—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—42no—
234C4⋊C4×C31—44no—
235C4⋊C4×C31C2×D412yes—
236C4⋊C4×C31C2×D411yescharacteristic
237C4⋊C4×C31C2×D411yescharacteristic
238C22⋊C4×C31—22no—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—22no—
241C22⋊C4×C31—22no—
242C22⋊C4×C31—22no—
243C22⋊C4×C31—22no—
244C22⋊C4×C31—21no—
245C22⋊C4×C31—21no—
246C22⋊C4×C31—22no—
247C22⋊C4×C31—21no—
248C22⋊C4×C31—21no—
249C22⋊C4×C31—21no—
250C22⋊C4×C31—44no—
251C22⋊C4×C31—82no—
252C22⋊C4×C31—81no—
253C42×C31—22no—
254C42×C31—22no—
255C42×C31—22no—
256C42×C31—21no—
257#18230C3111yesmaximal, characteristic, direct product factor, Sylow
258C23×C31—21no—
259C23×C31—21no—
260C23×C31—22no—
261C23×C31—21no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31#12011yescharacteristic
271C23×C31#12011yescharacteristic
272C23×C31C22×D411yescharacteristic
273Q8×C31—22no—
274Q8×C31—22no—
275Q8×C31—42no—
276Q8×C31—41no—
277Q8×C31—41no—
278Q8×C31—41no—
279Q8×C31—42no—
280Q8×C31—42no—
281Q8×C31—81no—
282Q8×C31—82no—
283D4×C31—22no—
284D4×C31—22no—
285D4×C31—41no—
286D4×C31—41no—
287D4×C31—41no—
288D4×C31—42no—
289D4×C31—44no—
290D4×C31—44no—
291D4×C31—41no—
292D4×C31—41no—
293D4×C31—81no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—21no—
299C2×C4×C31—21no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—21no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—44no—
311C2×C4×C31—42no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—44no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—42no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—81no—
321C2×C4×C31—82no—
322C2×C4×C31#12011yescharacteristic
323C2×C4×C31#12011yescharacteristic
324C2×C4×C31C22×D411yescharacteristic
325C2×C4×C31C22×D411yescharacteristic
326C8×C31—41no—
327C8×C31—41no—
328C8×C31—42no—
329#3538C2×C3111yescharacteristic, complemented
330#3007C2×C3111yescharacteristic, complemented
331#3002C2×C3111yescharacteristic
332#2616C2×C3111yescharacteristic, complemented
333#1605C2×C3112yescomplemented
334#1603C2×C3112yescomplemented
335#1599C2×C3112yescomplemented
336#1597C2×C3112yescomplemented
337#1520C2×C3111yescharacteristic, complemented
338#1513C2×C3111yescharacteristic, complemented
339#1472C2×C3111yescharacteristic, complemented
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—42no—
349C22×C31—42no—
350C22×C31—41no—
351C22×C31—41no—
352C22×C31—42no—
353C22×C31—41no—
354C22×C31—81no—
355C22×C31—81no—
356C22×C31—81no—
357C22×C31—81no—
358C22×C31—81no—
359C22×C31—81no—
360C22×C31C2×#12011yescharacteristic
361C22×C31#57711yescharacteristic
362C22×C31#57811yescharacteristic
363C4×C31—21no—
364C4×C31—21no—
365C4×C31—21no—
366C4×C31—42no—
367C4×C31—41no—
368C4×C31—42no—
369C4×C31—41no—
370C4×C31—42no—
371C4×C31—41no—
372C4×C31—42no—
373C4×C31—42no—
374C4×C31—82no—
375C4×C31B(4,𝔽2)12yes—
376C22×#41C22×C3111yescharacteristic
377C2×#137—21no—
378C2×#135—21no—
379#563—22no—
380#552—21no—
381#552—21no—
382#551—22no—
383D4×Q8—21no—
384D4×Q8—21no—
385#544—21no—
386#544C22×C3112yes—
387#541—21no—
388#539—21no—
389#539C22×C3112yes—
390#536—21no—
391#525C22×C3111yescharacteristic
392C2×C22⋊Q8—21no—
393C2×C22⋊Q8C22×C3111yescharacteristic
394C2×C22⋊Q8C22×C3111yescharacteristic
395#452—21no—
396#452—22no—
397#451C22×C3112yes—
398#451C22×C3111yescharacteristic
399#450C22×C3112yes—
400#450C22×C3111yescharacteristic
401#449—21no—
402#448C22×C3111yescharacteristic
403#447C22×C3111yescharacteristic
404#417—21no—
405#416—21no—
406#407C22×C3111yescharacteristic
407C2×C22⋊C8C22×C3111yescharacteristic
408#395C22×C3112yes—
409#394—22no—
410#394C22×C3112yes—
411#380—21no—
412#380C22×C3111yescharacteristic
413#328C22×C3112yes—
414#328C22×C3112yes—
415#328C22×C3112yes—
416#327C22×C3112yes—
417#324C22×C3112yes—
418#324C22×C3112yes—
419C2×C31—21no—
420C2×C31—21no—
421C2×C31—41no—
422C2×C31—41no—
423C2×C31—81no—
424C2×C31—82no—
425C2×C31#301311yescharacteristic
426C2×C31#302011yescharacteristic
427C2×C31C2×B(4,𝔽2)11yescharacteristic
428C2×#41—21no—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—44no—
433C2×#41D4×C3111yescharacteristic
434C22×Q8—21no—
435C22×Q8D4×C3111yescharacteristic
436C22×Q8D4×C3111yescharacteristic
437C22×Q8C23×C3111yescharacteristic
438C22×D4—21no—
439C22×D4C23×C3111yescharacteristic
440C23×C4—21no—
441C23×C4C23×C3111yescharacteristic
442#137—44no—
443#135—44no—
444C2×Q16—21no—
445C2×Q16—22no—
446C2×SD16—21no—
447C2×SD16—22no—
448C2×SD16—21no—
449C2×D8—21no—
450C2×M16—21no—
451C22×C8—21no—
452C4⋊Q8—21no—
453C4⋊Q8—22no—
454C4⋊Q8—22no—
455C4⋊Q8—22no—
456#126—22no—
457#126—22no—
458#126—22no—
459#126—22no—
460#125—21no—
461#125—22no—
462#125—22no—
463#125—22no—
464#125—22no—
465#124—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—21no—
470#123—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482C22⋊Q8—22no—
483C22⋊Q8—44no—
484C22⋊Q8D4×C3112yes—
485C22⋊Q8D4×C3111yescharacteristic
486C22⋊Q8C23×C3112yes—
487C22⋊Q8C23×C3111yescharacteristic
488#121D4×C3111yescharacteristic
489#121C23×C3111yescharacteristic
490#120—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4—22no—
497#117—21no—
498#117—22no—
499#117—22no—
500#117D4×C3111yescharacteristic
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—22no—
504C2×C4⋊C4D4×C3111yescharacteristic
505C2×C4⋊C4D4×C3111yescharacteristic
506C2×C4⋊C4C23×C3112yes—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4D4×C3112yes—
512#103—21no—
513#103—21no—
514#103—22no—
515#102—21no—
516#102—21no—
517#102—22no—
518C22⋊C8—21no—
519C22⋊C8—21no—
520C22⋊C8C23×C3112yes—
521C22⋊C8C23×C3111yescharacteristic
522C22⋊C8C23×C3111yescharacteristic
523#95—22no—
524#95C23×C3112yes—
525C31#1823011yescharacteristic, direct product factor, Sylow
526C24—21no—
527C24C2×D4×C3111yescharacteristic
528#41—24no—
529#41—24no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—42no—
535#41—42no—
536#41—42no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—42no—
544C2×Q8—42no—
545C2×Q8—42no—
546C2×Q8—82no—
547C2×Q8C2×D4×C3112yes—
548C2×Q8C2×D4×C3111yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—42no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4C2×D4×C3111yescharacteristic
560C22×C4—24no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4C2×D4×C3112yes—
572C22×C4C2×D4×C3111yescharacteristic
573C22×C4C2×D4×C3111yescharacteristic
574C22×C4C2×D4×C3111yescharacteristic
575C22×C4C2×D4×C3112yes—
576C22×C4C2×D4×C3111yescharacteristic
577C22×C4C2×D4×C3111yescharacteristic
578C22×C4C24×C3111yescharacteristic
579Q16—42no—
580Q16—44no—
581SD16—42no—
582SD16—44no—
583SD16—42no—
584D8—42no—
585M16—42no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—22no—
589C2×C8—42no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—22no—
596C4⋊C4—22no—
597C4⋊C4—22no—
598C4⋊C4—22no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—42no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C3112yes—
610C4⋊C4C2×D4×C3111yescharacteristic
611C4⋊C4C2×D4×C3111yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—21no—
623C22⋊C4—21no—
624C22⋊C4—44no—
625C22⋊C4—82no—
626C22⋊C4—81no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—21no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23C31×#12011yescharacteristic
644C23C31×#12011yescharacteristic
645C23C22×D4×C3111yescharacteristic
646Q8—22no—
647Q8—22no—
648Q8—42no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—42no—
653Q8—42no—
654Q8—81no—
655Q8—82no—
656D4—22no—
657D4—22no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—42no—
662D4—44no—
663D4—44no—
664D4—41no—
665D4—41no—
666D4—81no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—44no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—44no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—81no—
694C2×C4—82no—
695C2×C4C31×#12011yescharacteristic
696C2×C4C31×#12011yescharacteristic
697C2×C4C22×D4×C3111yescharacteristic
698C2×C4C22×D4×C3111yescharacteristic
699C8—41no—
700C8—41no—
701C8—42no—
702C22—21no—
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—42no—
711C22—42no—
712C22—41no—
713C22—41no—
714C22—42no—
715C22—41no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22C2×C31×#12011yescharacteristic
723C22C31×#57711yescharacteristic
724C22C31×#57811yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—42no—
729C4—41no—
730C4—42no—
731C4—41no—
732C4—42no—
733C4—41no—
734C4—42no—
735C4—42no—
736C4—82no—
737C4C31×B(4,𝔽2)12yes—
738C2—21no—
739C2—21no—
740C2—41no—
741C2—41no—
742C2—82no—
743C2—81no—
744C2C31×#301311yescharacteristic
745C2C31×#302011yescharacteristic
746C2C2×C31×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3002C2
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×#3538C2semidirect
2. C31×#3007C2semidirect
4. C31×#2616C2semidirect
5. C31×#1605C2semidirect
6. C31×#1603C2semidirect
7. C31×#1599C2semidirect
8. C31×#1597C2semidirect
9. C31×#1520C2semidirect
10. C31×#1513C2semidirect
11. C31×#1472C2semidirect
257. #18230C31direct (N × H)
329. #3538C2×C31semidirect
330. #3007C2×C31semidirect
332. #2616C2×C31semidirect
333. #1605C2×C31semidirect
334. #1603C2×C31semidirect
335. #1599C2×C31semidirect
336. #1597C2×C31semidirect
337. #1520C2×C31semidirect
338. #1513C2×C31semidirect
339. #1472C2×C31semidirect
525. C31#18230direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35382
C31×#30072
C31×#30022
C31×#26162
C31×#16052
C31×#16032
C31×#15992
C31×#15972
C31×#15202
C31×#15132
C31×#14722
#1823031