Finite Group Databasebeta

← C31×#19028 #21475787

Subgroups — C31×#19028 #21475787

Order 7936.

888 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3563C211yesmaximal, characteristic, complemented
2C31×#3217C211yesmaximal, characteristic
3C31×#3138C211yesmaximal, characteristic, complemented
4C2×C31×#490C211yesmaximal, characteristic, complemented
5C31×#1658C214yesmaximal, complemented
6C31×#1657C214yesmaximal, complemented
7C31×#1531C211yesmaximal, characteristic, complemented
8C31×#1528C211yesmaximal, characteristic, complemented
9C31×#1524C211yesmaximal, characteristic, complemented
10C31×#564C2212yescomplemented
11C31×#563C2212yescomplemented
12C31×#557—21no—
13C31×#554—21no—
14C31×#552—21no—
15C31×#552—22no—
16C31×#552—21no—
17C31×#544—21no—
18C31×#544—21no—
19C31×#541—21no—
20C31×#541—22no—
21C31×#539—21no—
22C31×#533C2211yescharacteristic
23C2×C31×#127C2211yescharacteristic
24C31×#529C2211yescharacteristic
25C2×C31×#125C2211yescharacteristic
26C31×#496C2212yes—
27C31×#490—22no—
28C31×#490C2214yes—
29C31×#490C2214yes—
30C31×#490C2212yes—
31C31×#486—21no—
32C31×#486—21no—
33C31×#460—21no—
34C31×#459—21no—
35C31×#450—21no—
36C31×#447—21no—
37C31×#432C2211yescharacteristic
38C31×#418—22no—
39C2×C31×#102—21no—
40C2×C31×#102—21no—
41C4×M16×C31C2211yescharacteristic
42C2×C31×#97C2211yescharacteristic
43C31×#330C2214yescomplemented
44C31×#330C2214yescomplemented
45C31×#330C2212yescomplemented
46C31×#329C2212yescomplemented
47C22×D4×C31—21no—
48C22×D4×C31—21no—
49C22×D4×C31—21no—
50C2×SD16×C31—22no—
51C2×D8×C31—22no—
52C2×M16×C31—21no—
53C22×C8×C31—21no—
54C31×C4⋊Q8—22no—
55C31×C4⋊Q8—21no—
56C31×C4⋊Q8—22no—
57C31×C4⋊Q8D411yescharacteristic
58C31×C4⋊Q8D411yescharacteristic
59C31×#127—21no—
60C31×#127—21no—
61C31×#127—21no—
62C31×#127C2312yes—
63C31×#126—22no—
64C31×#126—22no—
65C31×#126—22no—
66C31×#126—22no—
67C31×#126—21no—
68C31×#125—22no—
69C31×#125—22no—
70C31×#125—21no—
71C31×#125—22no—
72C31×#125—22no—
73C31×#125—22no—
74C31×#125—22no—
75C31×#125—22no—
76C31×#125—22no—
77C31×#125—21no—
78C31×#125—21no—
79C31×#125D412yes—
80C31×#125C2312yes—
81C31×#125C2311yescharacteristic
82C31×#125C2312yes—
83C31×#124C2311yescharacteristic
84C31×#123—22no—
85C31×#123—22no—
86C31×#123—21no—
87C31×C22⋊Q8—22no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—22no—
94C31×C22⋊Q8—22no—
95C31×C22⋊Q8D411yescharacteristic
96C31×#121D411yescharacteristic
97C4×Q8×C31—21no—
98C4×Q8×C31—22no—
99C4×Q8×C31—21no—
100C4×Q8×C31—21no—
101C4×Q8×C31—21no—
102C4×Q8×C31D411yescharacteristic
103C4×D4×C31—22no—
104C4×D4×C31—21no—
105C4×D4×C31D411yescharacteristic
106C31×#117—22no—
107C31×#117—21no—
108C31×#117—22no—
109C31×#117—21no—
110C31×#117D412yes—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—21no—
114C2×C4⋊C4×C31D411yescharacteristic
115C2×C4⋊C4×C31D411yescharacteristic
116C2×C42×C31C2311yescharacteristic
117C31×C4⋊C8—21no—
118C31×#102—24no—
119C31×#102—24no—
120C31×#102—24no—
121C31×#102—24no—
122C31×#102—22no—
123C31×#102—22no—
124C31×C22⋊C8—21no—
125C31×#97—21no—
126C31×#97C2312yes—
127C31×#97C2312yes—
128C31×#97C2312yes—
129C4×C8×C31—21no—
130C24×C31—41no—
131C2×Q8×C31—22no—
132C2×Q8×C31—21no—
133C2×Q8×C31—21no—
134C2×Q8×C31C2×D411yescharacteristic
135C2×D4×C31—21no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—44no—
140C2×D4×C31—44no—
141C2×D4×C31—41no—
142C2×D4×C31—41no—
143C2×D4×C31—41no—
144C2×D4×C31—82no—
145C2×D4×C31C2×D411yescharacteristic
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31C2×D411yescharacteristic
151C22×C4×C31C2×D411yescharacteristic
152C22×C4×C31C2×D411yescharacteristic
153SD16×C31—82no—
154D8×C31—82no—
155M16×C31—42no—
156C2×C8×C31—22no—
157C2×C8×C31—22no—
158C2×C8×C31—22no—
159C2×C8×C31—42no—
160C4⋊C4×C31—22no—
161C4⋊C4×C31—22no—
162C4⋊C4×C31—22no—
163C4⋊C4×C31—22no—
164C4⋊C4×C31—22no—
165C4⋊C4×C31—22no—
166C4⋊C4×C31—22no—
167C4⋊C4×C31—22no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—22no—
171C4⋊C4×C31—22no—
172C4⋊C4×C31—21no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—22no—
177C4⋊C4×C31—22no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—22no—
181C4⋊C4×C31—22no—
182C4⋊C4×C31C2×D412yes—
183C4⋊C4×C31C2×D412yes—
184C4⋊C4×C31C2×D412yes—
185C4⋊C4×C31C2×D412yes—
186C4⋊C4×C31C2×D411yescharacteristic
187C4⋊C4×C31C2×D411yescharacteristic
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—21no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—21no—
194C22⋊C4×C31—21no—
195C22⋊C4×C31—21no—
196C22⋊C4×C31—21no—
197C42×C31—22no—
198C42×C31—22no—
199C42×C31—22no—
200C42×C31—22no—
201C42×C31—21no—
202C42×C31C2×D411yescharacteristic
203C42×C31C2×D411yescharacteristic
204C42×C31C2×D411yescharacteristic
205C42×C31C2411yescharacteristic
206#19028C3111yesmaximal, characteristic, direct product factor, Sylow
207C23×C31—21no—
208C23×C31—42no—
209C23×C31—82no—
210C23×C31—82no—
211C23×C31—82no—
212C23×C31#12011yescharacteristic
213Q8×C31—41no—
214Q8×C31—42no—
215Q8×C31—81no—
216Q8×C31—82no—
217D4×C31—41no—
218D4×C31—42no—
219D4×C31—42no—
220D4×C31—44no—
221D4×C31—44no—
222D4×C31—42no—
223D4×C31—82no—
224D4×C31—82no—
225D4×C31—82no—
226C2×C4×C31—22no—
227C2×C4×C31—22no—
228C2×C4×C31—22no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—41no—
236C2×C4×C31—42no—
237C2×C4×C31—42no—
238C2×C4×C31—81no—
239C2×C4×C31—82no—
240C2×C4×C31#12011yescharacteristic
241C2×C4×C31#12011yescharacteristic
242C2×C4×C31#12011yescharacteristic
243C2×C4×C31C22×D411yescharacteristic
244C2×C4×C31C22×D411yescharacteristic
245C2×C4×C31C22×D411yescharacteristic
246C8×C31—42no—
247C8×C31—42no—
248C8×C31—42no—
249#3563C2×C3111yescharacteristic, complemented
250#3217C2×C3111yescharacteristic
251#3138C2×C3111yescharacteristic, complemented
252C2×#490C2×C3111yescharacteristic, complemented
253#1658C2×C3114yescomplemented
254#1657C2×C3114yescomplemented
255#1531C2×C3111yescharacteristic, complemented
256#1528C2×C3111yescharacteristic, complemented
257#1524C2×C3111yescharacteristic, complemented
258C22×C31—21no—
259C22×C31—21no—
260C22×C31—41no—
261C22×C31—41no—
262C22×C31—41no—
263C22×C31—82no—
264C22×C31—82no—
265C22×C31—82no—
266C22×C31—164no—
267C22×C31#45412yes—
268C22×C31C2×#12011yescharacteristic
269C4×C31—21no—
270C4×C31—21no—
271C4×C31—21no—
272C4×C31—21no—
273C4×C31—21no—
274C4×C31—42no—
275C4×C31—41no—
276C4×C31—41no—
277C4×C31—42no—
278C4×C31—42no—
279C4×C31—42no—
280C4×C31—41no—
281C4×C31#45412yes—
282#564C22×C3112yescomplemented
283#563C22×C3112yescomplemented
284#557—21no—
285#554—21no—
286#552—21no—
287#552—22no—
288#552—21no—
289#544—21no—
290#544—21no—
291#541—21no—
292#541—22no—
293#539—21no—
294#533C22×C3111yescharacteristic
295C2×#127C22×C3111yescharacteristic
296#529C22×C3111yescharacteristic
297C2×#125C22×C3111yescharacteristic
298#496C22×C3112yes—
299#490—22no—
300#490C22×C3114yes—
301#490C22×C3114yes—
302#490C22×C3112yes—
303#486—21no—
304#486—21no—
305#460—21no—
306#459—21no—
307#450—21no—
308#447—21no—
309#432C22×C3111yescharacteristic
310#418—22no—
311C2×#102—21no—
312C2×#102—21no—
313C4×M16C22×C3111yescharacteristic
314C2×#97C22×C3111yescharacteristic
315#330C22×C3114yescomplemented
316#330C22×C3114yescomplemented
317#330C22×C3112yescomplemented
318#329C22×C3112yescomplemented
319C2×C31—22no—
320C2×C31—81no—
321C2×C31—162no—
322C2×C31C2×#45411yescharacteristic
323C2×C31C2×#45411yescharacteristic
324C2×C31#302111yescharacteristic
325C22×D4—21no—
326C22×D4—21no—
327C22×D4—21no—
328C2×SD16—22no—
329C2×D8—22no—
330C2×M16—21no—
331C22×C8—21no—
332C4⋊Q8—22no—
333C4⋊Q8—21no—
334C4⋊Q8—22no—
335C4⋊Q8D4×C3111yescharacteristic
336C4⋊Q8D4×C3111yescharacteristic
337#127—21no—
338#127—21no—
339#127—21no—
340#127C23×C3112yes—
341#126—22no—
342#126—22no—
343#126—22no—
344#126—22no—
345#126—21no—
346#125—22no—
347#125—22no—
348#125—21no—
349#125—22no—
350#125—22no—
351#125—22no—
352#125—22no—
353#125—22no—
354#125—22no—
355#125—21no—
356#125—21no—
357#125D4×C3112yes—
358#125C23×C3112yes—
359#125C23×C3111yescharacteristic
360#125C23×C3112yes—
361#124C23×C3111yescharacteristic
362#123—22no—
363#123—22no—
364#123—21no—
365C22⋊Q8—22no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—21no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8D4×C3111yescharacteristic
374#121D4×C3111yescharacteristic
375C4×Q8—21no—
376C4×Q8—22no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8D4×C3111yescharacteristic
381C4×D4—22no—
382C4×D4—21no—
383C4×D4D4×C3111yescharacteristic
384#117—22no—
385#117—21no—
386#117—22no—
387#117—21no—
388#117D4×C3112yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4D4×C3111yescharacteristic
393C2×C4⋊C4D4×C3111yescharacteristic
394C2×C42C23×C3111yescharacteristic
395C4⋊C8—21no—
396#102—24no—
397#102—24no—
398#102—24no—
399#102—24no—
400#102—22no—
401#102—22no—
402C22⋊C8—21no—
403#97—21no—
404#97C23×C3112yes—
405#97C23×C3112yes—
406#97C23×C3112yes—
407C4×C8—21no—
408C31#1902811yescharacteristic, direct product factor, Sylow
409C24—41no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8C2×D4×C3111yescharacteristic
414C2×D4—21no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—44no—
419C2×D4—44no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—82no—
424C2×D4C2×D4×C3111yescharacteristic
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4C2×D4×C3111yescharacteristic
430C22×C4C2×D4×C3111yescharacteristic
431C22×C4C2×D4×C3111yescharacteristic
432SD16—82no—
433D8—82no—
434M16—42no—
435C2×C8—22no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—42no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4C2×D4×C3112yes—
462C4⋊C4C2×D4×C3112yes—
463C4⋊C4C2×D4×C3112yes—
464C4⋊C4C2×D4×C3112yes—
465C4⋊C4C2×D4×C3111yescharacteristic
466C4⋊C4C2×D4×C3111yescharacteristic
467C22⋊C4—22no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—22no—
472C22⋊C4—21no—
473C22⋊C4—21no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42C2×D4×C3111yescharacteristic
482C42C2×D4×C3111yescharacteristic
483C42C2×D4×C3111yescharacteristic
484C42C24×C3111yescharacteristic
485C23—21no—
486C23—42no—
487C23—82no—
488C23—82no—
489C23—82no—
490C23C31×#12011yescharacteristic
491Q8—41no—
492Q8—42no—
493Q8—81no—
494Q8—82no—
495D4—41no—
496D4—42no—
497D4—42no—
498D4—44no—
499D4—44no—
500D4—42no—
501D4—82no—
502D4—82no—
503D4—82no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—81no—
517C2×C4—82no—
518C2×C4C31×#12011yescharacteristic
519C2×C4C31×#12011yescharacteristic
520C2×C4C31×#12011yescharacteristic
521C2×C4C22×D4×C3111yescharacteristic
522C2×C4C22×D4×C3111yescharacteristic
523C2×C4C22×D4×C3111yescharacteristic
524C8—42no—
525C8—42no—
526C8—42no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—82no—
533C22—82no—
534C22—82no—
535C22—164no—
536C22C31×#45412yes—
537C22C2×C31×#12011yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—42no—
544C4—41no—
545C4—41no—
546C4—42no—
547C4—42no—
548C4—42no—
549C4—41no—
550C4C31×#45412yes—
551C2—22no—
552C2—81no—
553C2—162no—
554C2C2×C31×#45411yescharacteristic
555C2C2×C31×#45411yescharacteristic
556C2C31×#302111yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC42C24×C31
prime radicalC31×#3217C2
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
3. C31×#3138C2semidirect
4. C2×C31×#490C2semidirect
5. C31×#1658C2semidirect
6. C31×#1657C2semidirect
7. C31×#1531C2semidirect
8. C31×#1528C2semidirect
9. C31×#1524C2semidirect
10. C31×#564C22semidirect
11. C31×#563C22semidirect
43. C31×#330C22semidirect
44. C31×#330C22semidirect
45. C31×#330C22semidirect
46. C31×#329C22semidirect
206. #19028C31direct (N × H)
249. #3563C2×C31semidirect
251. #3138C2×C31semidirect
252. C2×#490C2×C31semidirect
253. #1658C2×C31semidirect
254. #1657C2×C31semidirect
255. #1531C2×C31semidirect
256. #1528C2×C31semidirect
257. #1524C2×C31semidirect
282. #564C22×C31semidirect
283. #563C22×C31semidirect
315. #330C22×C31semidirect
316. #330C22×C31semidirect
317. #330C22×C31semidirect
318. #329C22×C31semidirect
408. C31#19028direct (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×#32172
C31×#31382
C2×C31×#4902
C31×#16582
C31×#16572
C31×#15312
C31×#15282
C31×#15242
#1902831