Finite Group Databasebeta

← C31×#8489 #21465248

Subgroups — C31×#8489 #21465248

Order 7936.

690 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3560C211yesmaximal, characteristic
2C31×#1553C211yesmaximal, characteristic, complemented
3C31×#1535C211yesmaximal, characteristic, complemented
4C31×#1496C211yesmaximal, characteristic, complemented
5C31×#1482C211yesmaximal, characteristic, complemented
6C31×#1473C211yesmaximal, characteristic, complemented
7C31×#1473C211yesmaximal, characteristic, complemented
8C31×#563—21no—
9C31×#560—21no—
10C31×#553—21no—
11C31×#553—21no—
12C31×#551—21no—
13C31×#547—21no—
14C31×#546—21no—
15C31×#546—21no—
16C31×#542—21no—
17C31×#539—21no—
18C31×#539C411yescharacteristic
19C31×#538—21no—
20C31×#538—21no—
21C31×#538C411yescharacteristic
22C31×#537C411yescharacteristic
23C31×#534C411yescharacteristic
24C31×#532C2211yescharacteristic
25C31×#529C2211yescharacteristic
26C2×C31×#126C2211yescharacteristic
27C31×#432C2211yescharacteristic, complemented
28C31×#432C2211yescharacteristic, complemented
29C31×#431C2211yescharacteristic, complemented
30C31×#431C2211yescharacteristic, complemented
31C31×#332—21no—
32C31×#331—21no—
33C31×#330—21no—
34C31×#329—21no—
35C31×Q8⋊C8—21no—
36C31×D4⋊C8—21no—
37C31×D4⋊C8—21no—
38C31×D4⋊C8—21no—
39C31×#324—21no—
40C31×#324—21no—
41C31×#323—21no—
42C31×#323—21no—
43C2×#41×C31—21no—
44C2×#41×C31—21no—
45C22×D4×C31—21no—
46C31×C4⋊Q8—21no—
47C31×C4⋊Q8D411yescharacteristic
48C31×#127D411yescharacteristic
49C31×#126—21no—
50C31×#126—21no—
51C31×#126—21no—
52C31×#126—21no—
53C31×#126—21no—
54C31×#126—21no—
55C31×#126—21no—
56C31×#126—21no—
57C31×#126—21no—
58C31×#125—21no—
59C31×#125—21no—
60C31×#125D411yescharacteristic
61C31×#124—21no—
62C31×#124—21no—
63C31×#124—21no—
64C31×#124—21no—
65C31×#124D411yescharacteristic
66C31×#123—21no—
67C31×#123—21no—
68C31×#123—21no—
69C31×#123—21no—
70C31×#123—21no—
71C31×#123—21no—
72C31×#123—21no—
73C31×#123—21no—
74C31×#123—21no—
75C31×#123—21no—
76C31×#123—21no—
77C31×#123—21no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8C2×C411yescharacteristic
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121—21no—
92C31×#121—21no—
93C31×#121—21no—
94C31×#121—21no—
95C31×#121—21no—
96C31×#121—21no—
97C31×#121—21no—
98C31×#121C2×C411yescharacteristic
99C31×#121C2×C411yescharacteristic
100C31×#121C2×C411yescharacteristic
101C31×#120—21no—
102C31×#120—21no—
103C31×#120—21no—
104C31×#120—21no—
105C31×#120—21no—
106C4×Q8×C31D411yescharacteristic
107C4×D4×C31—21no—
108C4×D4×C31—21no—
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31—21no—
115C4×D4×C31D411yescharacteristic
116C4×D4×C31D411yescharacteristic
117C4×D4×C31D411yescharacteristic
118C31×#117—21no—
119C31×#117—21no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31C2×C411yescharacteristic
122C2×C4⋊C4×C31D411yescharacteristic
123C2×C4⋊C4×C31D411yescharacteristic
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31C2×C411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C42×C31C2311yescharacteristic
130C31×C4⋊C8—21no—
131C31×C4⋊C8—21no—
132C31×C4⋊C8—21no—
133C31×C4⋊C8—21no—
134C31×C22⋊C8—21no—
135C31×C22⋊C8—21no—
136C31×C22⋊C8—21no—
137C31×C22⋊C8—21no—
138C31×#97—21no—
139C31×#97—21no—
140C4×C8×C31—21no—
141C4×C8×C31—21no—
142C24×C31—21no—
143C24×C31C22⋊C411yescharacteristic
144#41×C31—82no—
145#41×C31—82no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31C22⋊C411yescharacteristic
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—21no—
160C2×D4×C31—21no—
161C2×D4×C31—82no—
162C2×D4×C31C22⋊C411yescharacteristic
163C2×D4×C31C22⋊C411yescharacteristic
164C2×D4×C31C22⋊C411yescharacteristic
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31C22⋊C411yescharacteristic
174C22×C4×C31C22⋊C411yescharacteristic
175C22×C4×C31C22⋊C411yescharacteristic
176C22×C4×C31C22×C411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C2×C8×C31—41no—
180C2×C8×C31—41no—
181C2×C8×C31—41no—
182C2×C8×C31—41no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31C22⋊C411yescharacteristic
201C4⋊C4×C31C22⋊C411yescharacteristic
202C4⋊C4×C31C22⋊C411yescharacteristic
203C4⋊C4×C31C22⋊C411yescharacteristic
204C22⋊C4×C31—21no—
205C22⋊C4×C31—21no—
206C22⋊C4×C31—21no—
207C22⋊C4×C31—21no—
208C22⋊C4×C31—21no—
209C22⋊C4×C31—21no—
210C22⋊C4×C31—21no—
211C22⋊C4×C31—21no—
212C22⋊C4×C31—21no—
213C22⋊C4×C31—21no—
214C22⋊C4×C31—21no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—21no—
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×C31—21no—
227C22⋊C4×C31—21no—
228C22⋊C4×C31—21no—
229C42×C31—21no—
230C42×C31—21no—
231C42×C31—21no—
232C42×C31C2×D411yescharacteristic
233C42×C31C2×D411yescharacteristic
234C42×C31C2×D411yescharacteristic
235C42×C31C2×D411yescharacteristic
236#8489C3111yesmaximal, characteristic, direct product factor, Sylow
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—21no—
240C23×C31—21no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—81no—
245C23×C31—81no—
246C23×C31—81no—
247C23×C31C2×C22⋊C411yescharacteristic
248Q8×C31—41no—
249Q8×C31—81no—
250Q8×C31—81no—
251D4×C31—41no—
252D4×C31—41no—
253D4×C31—41no—
254D4×C31—42no—
255D4×C31—42no—
256D4×C31—42no—
257D4×C31—81no—
258D4×C31—81no—
259D4×C31—81no—
260D4×C31—81no—
261D4×C31—81no—
262D4×C31—81no—
263D4×C31—81no—
264D4×C31—81no—
265D4×C31—81no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—81no—
281C2×C4×C31—81no—
282C2×C4×C31—81no—
283C2×C4×C31—81no—
284C2×C4×C31—81no—
285C2×C4×C31—81no—
286C2×C4×C31—81no—
287C2×C4×C31—81no—
288C2×C4×C31C2×C22⋊C411yescharacteristic
289C2×C4×C31C2×C22⋊C411yescharacteristic
290C2×C4×C31#12011yescharacteristic
291C2×C4×C31#12011yescharacteristic
292C2×C4×C31#12011yescharacteristic
293C2×C4×C31#12011yescharacteristic
294C8×C31—81no—
295C8×C31—81no—
296C8×C31—81no—
297C8×C31—81no—
298#3560C2×C3111yescharacteristic
299#1553C2×C3111yescharacteristic, complemented
300#1535C2×C3111yescharacteristic, complemented
301#1496C2×C3111yescharacteristic, complemented
302#1482C2×C3111yescharacteristic, complemented
303#1473C2×C3111yescharacteristic, complemented
304#1473C2×C3111yescharacteristic, complemented
305C22×C31—21no—
306C22×C31—21no—
307C22×C31—21no—
308C22×C31—41no—
309C22×C31—41no—
310C22×C31—41no—
311C22×C31—41no—
312C22×C31—41no—
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31—161no—
321C22×C31—162no—
322C22×C31#37911yescharacteristic
323C4×C31—21no—
324C4×C31—21no—
325C4×C31—21no—
326C4×C31—21no—
327C4×C31—21no—
328C4×C31—21no—
329C4×C31—41no—
330C4×C31—41no—
331C4×C31—41no—
332C4×C31—41no—
333C4×C31—41no—
334C4×C31—41no—
335C4×C31—41no—
336C4×C31—41no—
337#563—21no—
338#560—21no—
339#553—21no—
340#553—21no—
341#551—21no—
342#547—21no—
343#546—21no—
344#546—21no—
345#542—21no—
346#539—21no—
347#539C4×C3111yescharacteristic
348#538—21no—
349#538—21no—
350#538C4×C3111yescharacteristic
351#537C4×C3111yescharacteristic
352#534C4×C3111yescharacteristic
353#532C22×C3111yescharacteristic
354#529C22×C3111yescharacteristic
355C2×#126C22×C3111yescharacteristic
356#432C22×C3111yescharacteristic, complemented
357#432C22×C3111yescharacteristic, complemented
358#431C22×C3111yescharacteristic, complemented
359#431C22×C3111yescharacteristic, complemented
360#332—21no—
361#331—21no—
362#330—21no—
363#329—21no—
364Q8⋊C8—21no—
365D4⋊C8—21no—
366D4⋊C8—21no—
367D4⋊C8—21no—
368#324—21no—
369#324—21no—
370#323—21no—
371#323—21no—
372C2×C31—41no—
373C2×C31—81no—
374C2×C31—81no—
375C2×C31—81no—
376C2×C31—81no—
377C2×C31#179111yescharacteristic
378C2×C31#179411yescharacteristic
379C2×C31#179511yescharacteristic
380C2×#41—21no—
381C2×#41—21no—
382C22×D4—21no—
383C4⋊Q8—21no—
384C4⋊Q8D4×C3111yescharacteristic
385#127D4×C3111yescharacteristic
386#126—21no—
387#126—21no—
388#126—21no—
389#126—21no—
390#126—21no—
391#126—21no—
392#126—21no—
393#126—21no—
394#126—21no—
395#125—21no—
396#125—21no—
397#125D4×C3111yescharacteristic
398#124—21no—
399#124—21no—
400#124—21no—
401#124—21no—
402#124D4×C3111yescharacteristic
403#123—21no—
404#123—21no—
405#123—21no—
406#123—21no—
407#123—21no—
408#123—21no—
409#123—21no—
410#123—21no—
411#123—21no—
412#123—21no—
413#123—21no—
414#123—21no—
415C22⋊Q8—21no—
416C22⋊Q8—21no—
417C22⋊Q8—21no—
418C22⋊Q8—21no—
419C22⋊Q8—21no—
420C22⋊Q8—21no—
421C22⋊Q8—21no—
422C22⋊Q8C2×C4×C3111yescharacteristic
423#121—21no—
424#121—21no—
425#121—21no—
426#121—21no—
427#121—21no—
428#121—21no—
429#121—21no—
430#121—21no—
431#121—21no—
432#121—21no—
433#121—21no—
434#121—21no—
435#121C2×C4×C3111yescharacteristic
436#121C2×C4×C3111yescharacteristic
437#121C2×C4×C3111yescharacteristic
438#120—21no—
439#120—21no—
440#120—21no—
441#120—21no—
442#120—21no—
443C4×Q8D4×C3111yescharacteristic
444C4×D4—21no—
445C4×D4—21no—
446C4×D4—21no—
447C4×D4—21no—
448C4×D4—21no—
449C4×D4—21no—
450C4×D4—21no—
451C4×D4—21no—
452C4×D4D4×C3111yescharacteristic
453C4×D4D4×C3111yescharacteristic
454C4×D4D4×C3111yescharacteristic
455#117—21no—
456#117—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4C2×C4×C3111yescharacteristic
459C2×C4⋊C4D4×C3111yescharacteristic
460C2×C4⋊C4D4×C3111yescharacteristic
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4C2×C4×C3111yescharacteristic
464C2×C22⋊C4D4×C3111yescharacteristic
465C2×C22⋊C4D4×C3111yescharacteristic
466C2×C42C23×C3111yescharacteristic
467C4⋊C8—21no—
468C4⋊C8—21no—
469C4⋊C8—21no—
470C4⋊C8—21no—
471C22⋊C8—21no—
472C22⋊C8—21no—
473C22⋊C8—21no—
474C22⋊C8—21no—
475#97—21no—
476#97—21no—
477C4×C8—21no—
478C4×C8—21no—
479C31#848911yescharacteristic, direct product factor, Sylow
480C24—21no—
481C24C22⋊C4×C3111yescharacteristic
482#41—82no—
483#41—82no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C22⋊C4×C3111yescharacteristic
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—82no—
500C2×D4C22⋊C4×C3111yescharacteristic
501C2×D4C22⋊C4×C3111yescharacteristic
502C2×D4C22⋊C4×C3111yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4C22⋊C4×C3111yescharacteristic
512C22×C4C22⋊C4×C3111yescharacteristic
513C22×C4C22⋊C4×C3111yescharacteristic
514C22×C4C22×C4×C3111yescharacteristic
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C2×C8—41no—
518C2×C8—41no—
519C2×C8—41no—
520C2×C8—41no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4C22⋊C4×C3111yescharacteristic
539C4⋊C4C22⋊C4×C3111yescharacteristic
540C4⋊C4C22⋊C4×C3111yescharacteristic
541C4⋊C4C22⋊C4×C3111yescharacteristic
542C22⋊C4—21no—
543C22⋊C4—21no—
544C22⋊C4—21no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C22⋊C4—21no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—21no—
564C22⋊C4—21no—
565C22⋊C4—21no—
566C22⋊C4—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42C2×D4×C3111yescharacteristic
571C42C2×D4×C3111yescharacteristic
572C42C2×D4×C3111yescharacteristic
573C42C2×D4×C3111yescharacteristic
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—81no—
582C23—81no—
583C23—81no—
584C23C2×C22⋊C4×C3111yescharacteristic
585Q8—41no—
586Q8—81no—
587Q8—81no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—42no—
592D4—42no—
593D4—42no—
594D4—81no—
595D4—81no—
596D4—81no—
597D4—81no—
598D4—81no—
599D4—81no—
600D4—81no—
601D4—81no—
602D4—81no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—81no—
618C2×C4—81no—
619C2×C4—81no—
620C2×C4—81no—
621C2×C4—81no—
622C2×C4—81no—
623C2×C4—81no—
624C2×C4—81no—
625C2×C4C2×C22⋊C4×C3111yescharacteristic
626C2×C4C2×C22⋊C4×C3111yescharacteristic
627C2×C4C31×#12011yescharacteristic
628C2×C4C31×#12011yescharacteristic
629C2×C4C31×#12011yescharacteristic
630C2×C4C31×#12011yescharacteristic
631C8—81no—
632C8—81no—
633C8—81no—
634C8—81no—
635C22—21no—
636C22—21no—
637C22—21no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—161no—
651C22—162no—
652C22C31×#37911yescharacteristic
653C4—21no—
654C4—21no—
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—41no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C2—41no—
668C2—81no—
669C2—81no—
670C2—81no—
671C2—81no—
672C2C31×#179111yescharacteristic
673C2C31×#179411yescharacteristic
674C2C31×#179511yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#3560C2
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×#1553C2semidirect
3. C31×#1535C2semidirect
4. C31×#1496C2semidirect
5. C31×#1482C2semidirect
6. C31×#1473C2semidirect
7. C31×#1473C2semidirect
27. C31×#432C22semidirect
28. C31×#432C22semidirect
29. C31×#431C22semidirect
30. C31×#431C22semidirect
236. #8489C31direct (N × H)
299. #1553C2×C31semidirect
300. #1535C2×C31semidirect
301. #1496C2×C31semidirect
302. #1482C2×C31semidirect
303. #1473C2×C31semidirect
304. #1473C2×C31semidirect
356. #432C22×C31semidirect
357. #432C22×C31semidirect
358. #431C22×C31semidirect
359. #431C22×C31semidirect
479. C31#8489direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35602
C31×#15532
C31×#15352
C31×#14962
C31×#14822
C31×#14732
#848931