Finite Group Databasebeta

← C31×#19092 #21475851

Subgroups — C31×#19092 #21475851

Order 7936.

816 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3563C211yesmaximal, characteristic, complemented
2C31×#3235C211yesmaximal, characteristic, complemented
3C31×#3234C211yesmaximal, characteristic, complemented
4C31×#3219C211yesmaximal, characteristic
5C31×#1663C212yesmaximal, complemented
6C31×#1660C212yesmaximal, complemented
7C31×#1658C212yesmaximal, complemented
8C31×#1657C212yesmaximal, complemented
9C31×#1537C211yesmaximal, characteristic, complemented
10C31×#1535C211yesmaximal, characteristic, complemented
11C31×#1534C211yesmaximal, characteristic, complemented
12C31×#564C2212yes—
13C31×#563C2212yes—
14C31×#557—21no—
15C31×#554—21no—
16C31×#552—21no—
17C31×#552—22no—
18C31×#552—21no—
19C31×#544—21no—
20C31×#544—21no—
21C31×#541—21no—
22C31×#541—22no—
23C31×#539—21no—
24C31×#533C2211yescharacteristic
25C31×#532C2211yescharacteristic
26C31×#529C2211yescharacteristic
27C2×C31×#125C2211yescharacteristic
28C31×#501C2212yes—
29C31×#501C2212yes—
30C31×#497C2211yescharacteristic
31C31×#496C2211yescharacteristic
32C31×#491C2211yescharacteristic
33C31×#490C2212yes—
34C31×#490C2212yes—
35C31×#490C2211yescharacteristic
36C31×#482—22no—
37C31×#481—21no—
38C31×#480—21no—
39C31×#478—22no—
40C31×#476—21no—
41C31×#474—21no—
42C31×#464—21no—
43C31×#463—21no—
44C31×#452—21no—
45C31×#449—21no—
46C31×#432C2211yescharacteristic
47C31×#432C2211yescharacteristic
48C31×#432C2211yescharacteristic
49C31×#330C2212yes—
50C31×#330C2212yes—
51C31×#330C2212yes—
52C31×#330C2212yes—
53C31×#330C2212yes—
54C31×#329C2212yes—
55C2×#41×C31—21no—
56C2×Q16×C31—21no—
57C2×SD16×C31—21no—
58C2×SD16×C31—21no—
59C2×D8×C31—21no—
60C31×C4⋊Q8—22no—
61C31×C4⋊Q8—21no—
62C31×C4⋊Q8—22no—
63C31×C4⋊Q8D411yescharacteristic
64C31×C4⋊Q8D411yescharacteristic
65C31×C4⋊Q8C2311yescharacteristic
66C31×#127C2311yescharacteristic
67C31×#126—22no—
68C31×#126—22no—
69C31×#126—22no—
70C31×#126—22no—
71C31×#126—21no—
72C31×#125—22no—
73C31×#125—22no—
74C31×#125—21no—
75C31×#125—22no—
76C31×#125—22no—
77C31×#125—22no—
78C31×#125—22no—
79C31×#125—22no—
80C31×#125—22no—
81C31×#125—21no—
82C31×#125—21no—
83C31×#125D412yes—
84C31×#125C2311yescharacteristic
85C31×#125C2312yes—
86C31×#125C2312yes—
87C31×#124—21no—
88C31×#124C2311yescharacteristic
89C31×#123—22no—
90C31×#123—22no—
91C31×#123—21no—
92C31×C22⋊Q8—22no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—22no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8—21no—
98C31×C22⋊Q8—22no—
99C31×C22⋊Q8—22no—
100C31×C22⋊Q8D411yescharacteristic
101C31×#121—21no—
102C31×#121—21no—
103C31×#121D411yescharacteristic
104C4×Q8×C31—21no—
105C4×Q8×C31—22no—
106C4×Q8×C31—21no—
107C4×Q8×C31—21no—
108C4×Q8×C31—21no—
109C4×Q8×C31D411yescharacteristic
110C4×D4×C31—22no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31D411yescharacteristic
115C31×#117—22no—
116C31×#117—21no—
117C31×#117—22no—
118C31×#117—21no—
119C31×#117D412yes—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31—21no—
123C2×C4⋊C4×C31D411yescharacteristic
124C2×C4⋊C4×C31D411yescharacteristic
125C2×C42×C31C2311yescharacteristic
126C31×#107—22no—
127C31×#107—22no—
128C31×#106—22no—
129C31×#106—22no—
130C31×C4⋊C8—21no—
131C31×C4⋊C8—21no—
132C31×C4⋊C8—21no—
133C31×#103—21no—
134C31×#103—21no—
135C31×#102—21no—
136C31×#102—21no—
137C31×#102—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×C22⋊C8—21no—
142C31×C22⋊C8—21no—
143C31×C22⋊C8—21no—
144C31×#97C2311yescharacteristic
145C31×#97C2312yes—
146C31×#97C2312yes—
147C31×#97C2311yescharacteristic
148#41×C31—81no—
149#41×C31—81no—
150C2×Q8×C31—22no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31C2×D411yescharacteristic
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31—21no—
159C2×D4×C31—41no—
160C2×D4×C31C2×D411yescharacteristic
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—41no—
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169Q16×C31—81no—
170SD16×C31—81no—
171SD16×C31—81no—
172D8×C31—81no—
173C2×C8×C31—22no—
174C2×C8×C31—22no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31—22no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—22no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—22no—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—22no—
194C4⋊C4×C31—22no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31C2×D411yescharacteristic
202C4⋊C4×C31C2×D411yescharacteristic
203C4⋊C4×C31C2×D412yes—
204C4⋊C4×C31C2×D412yes—
205C4⋊C4×C31C2×D412yes—
206C4⋊C4×C31C2×D412yes—
207C22⋊C4×C31—22no—
208C22⋊C4×C31—22no—
209C22⋊C4×C31—22no—
210C22⋊C4×C31—21no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—21no—
213C22⋊C4×C31—21no—
214C22⋊C4×C31—21no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—41no—
217C22⋊C4×C31—41no—
218C42×C31—22no—
219C42×C31—22no—
220C42×C31—22no—
221C42×C31—22no—
222C42×C31—21no—
223C42×C31C2×D411yescharacteristic
224C42×C31C2×D411yescharacteristic
225C42×C31C2×D411yescharacteristic
226C42×C31C2411yescharacteristic
227#19092C3111yesmaximal, characteristic, direct product factor, Sylow
228C23×C31—21no—
229C23×C31—41no—
230C23×C31#12011yescharacteristic
231Q8×C31—41no—
232Q8×C31—42no—
233Q8×C31—41no—
234Q8×C31—41no—
235Q8×C31—81no—
236Q8×C31—82no—
237D4×C31—41no—
238D4×C31—41no—
239D4×C31—41no—
240D4×C31—42no—
241D4×C31—42no—
242D4×C31—42no—
243D4×C31—82no—
244C2×C4×C31—22no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—42no—
255C2×C4×C31—42no—
256C2×C4×C31—41no—
257C2×C4×C31—82no—
258C2×C4×C31—81no—
259C2×C4×C31—82no—
260C2×C4×C31#12011yescharacteristic
261C2×C4×C31#12011yescharacteristic
262C2×C4×C31#12011yescharacteristic
263C2×C4×C31C22×D411yescharacteristic
264C2×C4×C31C22×D411yescharacteristic
265C2×C4×C31C22×D411yescharacteristic
266C8×C31—42no—
267C8×C31—42no—
268C8×C31—41no—
269C8×C31—41no—
270#3563C2×C3111yescharacteristic, complemented
271#3235C2×C3111yescharacteristic, complemented
272#3234C2×C3111yescharacteristic, complemented
273#3219C2×C3111yescharacteristic
274#1663C2×C3112yescomplemented
275#1660C2×C3112yescomplemented
276#1658C2×C3112yescomplemented
277#1657C2×C3112yescomplemented
278#1537C2×C3111yescharacteristic, complemented
279#1535C2×C3111yescharacteristic, complemented
280#1534C2×C3111yescharacteristic, complemented
281C22×C31—21no—
282C22×C31—21no—
283C22×C31—21no—
284C22×C31—41no—
285C22×C31—41no—
286C22×C31—41no—
287C22×C31—81no—
288C22×C31—81no—
289C22×C31—81no—
290C22×C31C2×#12011yescharacteristic
291C4×C31—21no—
292C4×C31—21no—
293C4×C31—21no—
294C4×C31—21no—
295C4×C31—21no—
296C4×C31—21no—
297C4×C31—41no—
298C4×C31—42no—
299C4×C31—41no—
300C4×C31—42no—
301C4×C31—42no—
302C4×C31—42no—
303C4×C31—41no—
304C4×C31—81no—
305#564C22×C3112yes—
306#563C22×C3112yes—
307#557—21no—
308#554—21no—
309#552—21no—
310#552—22no—
311#552—21no—
312#544—21no—
313#544—21no—
314#541—21no—
315#541—22no—
316#539—21no—
317#533C22×C3111yescharacteristic
318#532C22×C3111yescharacteristic
319#529C22×C3111yescharacteristic
320C2×#125C22×C3111yescharacteristic
321#501C22×C3112yes—
322#501C22×C3112yes—
323#497C22×C3111yescharacteristic
324#496C22×C3111yescharacteristic
325#491C22×C3111yescharacteristic
326#490C22×C3112yes—
327#490C22×C3112yes—
328#490C22×C3111yescharacteristic
329#482—22no—
330#481—21no—
331#480—21no—
332#478—22no—
333#476—21no—
334#474—21no—
335#464—21no—
336#463—21no—
337#452—21no—
338#449—21no—
339#432C22×C3111yescharacteristic
340#432C22×C3111yescharacteristic
341#432C22×C3111yescharacteristic
342#330C22×C3112yes—
343#330C22×C3112yes—
344#330C22×C3112yes—
345#330C22×C3112yes—
346#330C22×C3112yes—
347#329C22×C3112yes—
348C2×C31—41no—
349C2×C31—81no—
350C2×C31—161no—
351C2×C31#302011yescharacteristic
352C2×C31#302011yescharacteristic
353C2×C31#302111yescharacteristic
354C2×#41—21no—
355C2×Q16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×D8—21no—
359C4⋊Q8—22no—
360C4⋊Q8—21no—
361C4⋊Q8—22no—
362C4⋊Q8D4×C3111yescharacteristic
363C4⋊Q8D4×C3111yescharacteristic
364C4⋊Q8C23×C3111yescharacteristic
365#127C23×C3111yescharacteristic
366#126—22no—
367#126—22no—
368#126—22no—
369#126—22no—
370#126—21no—
371#125—22no—
372#125—22no—
373#125—21no—
374#125—22no—
375#125—22no—
376#125—22no—
377#125—22no—
378#125—22no—
379#125—22no—
380#125—21no—
381#125—21no—
382#125D4×C3112yes—
383#125C23×C3112yes—
384#125C23×C3111yescharacteristic
385#125C23×C3112yes—
386#124—21no—
387#124C23×C3111yescharacteristic
388#123—22no—
389#123—22no—
390#123—21no—
391C22⋊Q8—22no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—22no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8D4×C3111yescharacteristic
400#121—21no—
401#121—21no—
402#121D4×C3111yescharacteristic
403C4×Q8—21no—
404C4×Q8—22no—
405C4×Q8—21no—
406C4×Q8—21no—
407C4×Q8—21no—
408C4×Q8D4×C3111yescharacteristic
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4D4×C3111yescharacteristic
414#117—22no—
415#117—21no—
416#117—22no—
417#117—21no—
418#117D4×C3112yes—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4D4×C3111yescharacteristic
423C2×C4⋊C4D4×C3111yescharacteristic
424C2×C42C23×C3111yescharacteristic
425#107—22no—
426#107—22no—
427#106—22no—
428#106—22no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8—21no—
432#103—21no—
433#103—21no—
434#102—21no—
435#102—21no—
436#102—22no—
437#102—22no—
438#102—22no—
439#102—22no—
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97C23×C3112yes—
444#97C23×C3112yes—
445#97C23×C3111yescharacteristic
446#97C23×C3111yescharacteristic
447C31#1909211yescharacteristic, direct product factor, Sylow
448#41—81no—
449#41—81no—
450C2×Q8—22no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C3111yescharacteristic
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4C2×D4×C3111yescharacteristic
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4C2×D4×C3111yescharacteristic
467C22×C4C2×D4×C3111yescharacteristic
468C22×C4C2×D4×C3111yescharacteristic
469Q16—81no—
470SD16—81no—
471SD16—81no—
472D8—81no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—21no—
476C2×C8—21no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4C2×D4×C3111yescharacteristic
502C4⋊C4C2×D4×C3111yescharacteristic
503C4⋊C4C2×D4×C3112yes—
504C4⋊C4C2×D4×C3112yes—
505C4⋊C4C2×D4×C3112yes—
506C4⋊C4C2×D4×C3112yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—22no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—21no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C42—22no—
519C42—22no—
520C42—22no—
521C42—22no—
522C42—21no—
523C42C2×D4×C3111yescharacteristic
524C42C2×D4×C3111yescharacteristic
525C42C2×D4×C3111yescharacteristic
526C42C24×C3111yescharacteristic
527C23—21no—
528C23—41no—
529C23C31×#12011yescharacteristic
530Q8—41no—
531Q8—42no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535Q8—82no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—42no—
540D4—42no—
541D4—42no—
542D4—82no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—81no—
558C2×C4—82no—
559C2×C4C31×#12011yescharacteristic
560C2×C4C31×#12011yescharacteristic
561C2×C4C31×#12011yescharacteristic
562C2×C4C22×D4×C3111yescharacteristic
563C2×C4C22×D4×C3111yescharacteristic
564C2×C4C22×D4×C3111yescharacteristic
565C8—42no—
566C8—42no—
567C8—41no—
568C8—41no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22C2×C31×#12011yescharacteristic
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—21no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—42no—
589C4—42no—
590C4—42no—
591C4—41no—
592C4—81no—
593C2—41no—
594C2—81no—
595C2—161no—
596C2C31×#302011yescharacteristic
597C2C31×#302011yescharacteristic
598C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3219C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C31×#3563C2semidirect
2. C31×#3235C2semidirect
3. C31×#3234C2semidirect
5. C31×#1663C2semidirect
6. C31×#1660C2semidirect
7. C31×#1658C2semidirect
8. C31×#1657C2semidirect
9. C31×#1537C2semidirect
10. C31×#1535C2semidirect
11. C31×#1534C2semidirect
227. #19092C31direct (N × H)
270. #3563C2×C31semidirect
271. #3235C2×C31semidirect
272. #3234C2×C31semidirect
274. #1663C2×C31semidirect
275. #1660C2×C31semidirect
276. #1658C2×C31semidirect
277. #1657C2×C31semidirect
278. #1537C2×C31semidirect
279. #1535C2×C31semidirect
280. #1534C2×C31semidirect
447. C31#19092direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35632
C31×#32352
C31×#32342
C31×#32192
C31×#16632
C31×#16602
C31×#16582
C31×#16572
C31×#15372
C31×#15352
C31×#15342
#1909231