Finite Group Databasebeta

← C31×#24115 #21480874

Subgroups — C31×#24115 #21480874

Order 7936.

1078 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3491C211yesmaximal, characteristic
2C31×#2623C212yesmaximal, complemented
3C31×#2317C211yesmaximal, characteristic, complemented
4C31×#2062C212yesmaximal, complemented
5C31×#2044C212yesmaximal
6C31×#1899C212yesmaximal, complemented
7C31×#1867C214yesmaximal, complemented
8C31×#1820C211yesmaximal, characteristic, complemented
9C31×#552—22no—
10C31×#552—22no—
11C31×#551—22no—
12C31×#551—22no—
13C31×#543C2211yescharacteristic
14C31×#539—21no—
15C31×#539—21no—
16C31×#534C2211yescharacteristic
17C31×#529—21no—
18C31×#529—21no—
19C2×C31×#123C2212yes—
20C31×#518C2212yes—
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C2×C31×#99C2214yes—
25C31×#400—22no—
26C31×#399—22no—
27C31×#398—22no—
28C31×#397—22no—
29C31×#389—21no—
30C31×#389—21no—
31C31×#386C2214yes—
32C31×#385C2212yes—
33C31×#385C2212yes—
34C31×#385C2214yes—
35C31×#384—21no—
36C31×#382—21no—
37C31×#381C2212yes—
38C31×#342C2212yes—
39C31×#342C2214yes—
40C31×#342C2212yes—
41C22×D4×C31C2312yes—
42C23×C4×C31C2312yes—
43C23×C4×C31C2311yescharacteristic
44C31×#126—22no—
45C31×#126—22no—
46C31×#126—22no—
47C31×#126—22no—
48C31×#125—21no—
49C31×#125—21no—
50C31×#125—22no—
51C31×#125—22no—
52C31×#124—21no—
53C31×#124—21no—
54C31×#123—22no—
55C31×#123—22no—
56C31×#123—22no—
57C31×#123—22no—
58C31×#123—22no—
59C31×#123—22no—
60C31×#123—22no—
61C31×C22⋊Q8—22no—
62C31×C22⋊Q8—22no—
63C31×C22⋊Q8—21no—
64C31×C22⋊Q8—21no—
65C31×C22⋊Q8—22no—
66C31×C22⋊Q8—22no—
67C31×#121—21no—
68C31×#121—21no—
69C31×#120—22no—
70C4×Q8×C31—21no—
71C4×Q8×C31—21no—
72C4×D4×C31—21no—
73C4×D4×C31—21no—
74C4×D4×C31—22no—
75C4×D4×C31—22no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C31×#117—22no—
79C31×#117—22no—
80C31×#117—22no—
81C31×#117—22no—
82C31×#117—22no—
83C31×#117—24no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—24no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31D412yes—
93C2×C4⋊C4×C31D412yes—
94C2×C4⋊C4×C31D411yescharacteristic
95C2×C4⋊C4×C31D411yescharacteristic
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31D412yes—
99C2×C22⋊C4×C31D412yes—
100C2×C22⋊C4×C31C2314yes—
101C2×C22⋊C4×C31C2311yescharacteristic
102C2×C22⋊C4×C31C2311yescharacteristic
103C2×C22⋊C4×C31C2312yes—
104C2×C22⋊C4×C31C2312yes—
105C2×C42×C31—21no—
106C2×C42×C31D411yescharacteristic
107C2×C42×C31D411yescharacteristic
108C31×#99—28no—
109C31×#95—22no—
110C31×#95—24no—
111C31×#95—24no—
112C31×#95—22no—
113C31×#95—22no—
114C31×#95—22no—
115C24×C31C2×D412yes—
116C24×C31C2411yescharacteristic
117C2×Q8×C31—21no—
118C2×Q8×C31—21no—
119C2×D4×C31—22no—
120C2×D4×C31—22no—
121C2×D4×C31—24no—
122C2×D4×C31—24no—
123C2×D4×C31—21no—
124C2×D4×C31—21no—
125C22×C4×C31—22no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—22no—
130C22×C4×C31—24no—
131C22×C4×C31—24no—
132C22×C4×C31—22no—
133C22×C4×C31—82no—
134C22×C4×C31C2×D412yes—
135C22×C4×C31C2×D412yes—
136C22×C4×C31C2×D412yes—
137C22×C4×C31C2×D411yescharacteristic
138C22×C4×C31C2×D411yescharacteristic
139C22×C4×C31C2×D411yescharacteristic
140C22×C4×C31C2×D411yescharacteristic
141C22×C4×C31C2×D412yes—
142C22×C4×C31C2×D411yescharacteristic
143C22×C4×C31C2×D411yescharacteristic
144C22×C4×C31C2×D412yes—
145C4⋊C4×C31—24no—
146C4⋊C4×C31—22no—
147C4⋊C4×C31—22no—
148C4⋊C4×C31—22no—
149C4⋊C4×C31—22no—
150C4⋊C4×C31—21no—
151C4⋊C4×C31—21no—
152C4⋊C4×C31—21no—
153C4⋊C4×C31—21no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—22no—
157C4⋊C4×C31—22no—
158C4⋊C4×C31—22no—
159C4⋊C4×C31—22no—
160C4⋊C4×C31—41no—
161C4⋊C4×C31—41no—
162C4⋊C4×C31—42no—
163C4⋊C4×C31—82no—
164C4⋊C4×C31—82no—
165C4⋊C4×C31—84no—
166C22⋊C4×C31—22no—
167C22⋊C4×C31—22no—
168C22⋊C4×C31—22no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—22no—
171C22⋊C4×C31—22no—
172C22⋊C4×C31—22no—
173C22⋊C4×C31—22no—
174C22⋊C4×C31—22no—
175C22⋊C4×C31—22no—
176C22⋊C4×C31—22no—
177C22⋊C4×C31—22no—
178C22⋊C4×C31—22no—
179C22⋊C4×C31—24no—
180C22⋊C4×C31—24no—
181C22⋊C4×C31—84no—
182C22⋊C4×C31#4114yes—
183C42×C31—24no—
184C42×C31—22no—
185C42×C31—22no—
186C42×C31—21no—
187C42×C31—21no—
188C42×C31—21no—
189C42×C31—21no—
190#24115C3111yesmaximal, characteristic, direct product factor, Sylow
191C23×C31—22no—
192C23×C31—24no—
193C23×C31—41no—
194C23×C31—41no—
195C23×C31—42no—
196C23×C31—42no—
197C23×C31C22×D411yescharacteristic
198C23×C31C22×D412yes—
199C23×C31C2×#4112yes—
200C23×C312−1+412yes—
201Q8×C31—81no—
202Q8×C31—81no—
203D4×C31—42no—
204D4×C31—42no—
205D4×C31—44no—
206D4×C31—81no—
207D4×C31—81no—
208C2×C4×C31—21no—
209C2×C4×C31—21no—
210C2×C4×C31—21no—
211C2×C4×C31—21no—
212C2×C4×C31—24no—
213C2×C4×C31—24no—
214C2×C4×C31—21no—
215C2×C4×C31—21no—
216C2×C4×C31—21no—
217C2×C4×C31—21no—
218C2×C4×C31—22no—
219C2×C4×C31—22no—
220C2×C4×C31—22no—
221C2×C4×C31—24no—
222C2×C4×C31—24no—
223C2×C4×C31—42no—
224C2×C4×C31—42no—
225C2×C4×C31—41no—
226C2×C4×C31—42no—
227C2×C4×C31—41no—
228C2×C4×C31—41no—
229C2×C4×C31—42no—
230C2×C4×C31—41no—
231C2×C4×C31—44no—
232C2×C4×C31—44no—
233C2×C4×C31—42no—
234C2×C4×C31—42no—
235C2×C4×C31—44no—
236C2×C4×C31—44no—
237C2×C4×C31—42no—
238C2×C4×C31—44no—
239C2×C4×C31—82no—
240C2×C4×C31—82no—
241C2×C4×C31#12011yescharacteristic
242C2×C4×C31#12011yescharacteristic
243C2×C4×C31#12012yes—
244#3491C2×C3111yescharacteristic
245#2623C2×C3112yescomplemented
246#2317C2×C3111yescharacteristic, complemented
247#2062C2×C3112yescomplemented
248#2044C2×C3112yes—
249#1899C2×C3112yescomplemented
250#1867C2×C3114yescomplemented
251#1820C2×C3111yescharacteristic, complemented
252C22×C31—21no—
253C22×C31—22no—
254C22×C31—21no—
255C22×C31—22no—
256C22×C31—42no—
257C22×C31—42no—
258C22×C31—42no—
259C22×C31—42no—
260C22×C31—42no—
261C22×C31—84no—
262C22×C31C2×#12011yescharacteristic
263C22×C31#52511yescharacteristic
264C22×C31#53611yescharacteristic
265C22×C31#54714yes—
266C4×C31—22no—
267C4×C31—21no—
268C4×C31—21no—
269C4×C31—44no—
270C4×C31—42no—
271C4×C31—41no—
272C4×C31—42no—
273C4×C31—41no—
274C4×C31—41no—
275C4×C31—42no—
276C4×C31—41no—
277C4×C31—84no—
278C4×C31—82no—
279#552—22no—
280#552—22no—
281#551—22no—
282#551—22no—
283#543C22×C3111yescharacteristic
284#539—21no—
285#539—21no—
286#534C22×C3111yescharacteristic
287#529—21no—
288#529—21no—
289C2×#123C22×C3112yes—
290#518C22×C3112yes—
291C2×#117C22×C3111yescharacteristic
292C2×#117C22×C3111yescharacteristic
293C22×C4⋊C4C22×C3111yescharacteristic
294C2×#99C22×C3114yes—
295#400—22no—
296#399—22no—
297#398—22no—
298#397—22no—
299#389—21no—
300#389—21no—
301#386C22×C3114yes—
302#385C22×C3112yes—
303#385C22×C3112yes—
304#385C22×C3114yes—
305#384—21no—
306#382—21no—
307#381C22×C3112yes—
308#342C22×C3112yes—
309#342C22×C3114yes—
310#342C22×C3112yes—
311C2×C31—21no—
312C2×C31—24no—
313C2×C31—21no—
314C2×C31—82no—
315C2×C31#240611yescharacteristic
316C2×C31#302711yescharacteristic
317C2×C31#302811yescharacteristic
318C22×D4C23×C3112yes—
319C23×C4C23×C3111yescharacteristic
320C23×C4C23×C3112yes—
321#126—22no—
322#126—22no—
323#126—22no—
324#126—22no—
325#125—21no—
326#125—21no—
327#125—22no—
328#125—22no—
329#124—21no—
330#124—21no—
331#123—22no—
332#123—22no—
333#123—22no—
334#123—22no—
335#123—22no—
336#123—22no—
337#123—22no—
338C22⋊Q8—22no—
339C22⋊Q8—22no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—22no—
343C22⋊Q8—22no—
344#121—21no—
345#121—21no—
346#120—22no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×D4—21no—
350C4×D4—21no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—22no—
355#117—22no—
356#117—22no—
357#117—22no—
358#117—22no—
359#117—22no—
360#117—24no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—24no—
369C2×C4⋊C4D4×C3111yescharacteristic
370C2×C4⋊C4D4×C3111yescharacteristic
371C2×C4⋊C4D4×C3112yes—
372C2×C4⋊C4D4×C3112yes—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4D4×C3112yes—
376C2×C22⋊C4D4×C3112yes—
377C2×C22⋊C4C23×C3114yes—
378C2×C22⋊C4C23×C3111yescharacteristic
379C2×C22⋊C4C23×C3111yescharacteristic
380C2×C22⋊C4C23×C3112yes—
381C2×C22⋊C4C23×C3112yes—
382C2×C42—21no—
383C2×C42D4×C3111yescharacteristic
384C2×C42D4×C3111yescharacteristic
385#99—28no—
386#95—22no—
387#95—22no—
388#95—22no—
389#95—22no—
390#95—24no—
391#95—24no—
392C31#2411511yescharacteristic, direct product factor, Sylow
393C24C2×D4×C3112yes—
394C24C24×C3111yescharacteristic
395C2×Q8—21no—
396C2×Q8—21no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—24no—
400C2×D4—24no—
401C2×D4—21no—
402C2×D4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—22no—
411C22×C4—82no—
412C22×C4C2×D4×C3112yes—
413C22×C4C2×D4×C3112yes—
414C22×C4C2×D4×C3112yes—
415C22×C4C2×D4×C3111yescharacteristic
416C22×C4C2×D4×C3111yescharacteristic
417C22×C4C2×D4×C3111yescharacteristic
418C22×C4C2×D4×C3111yescharacteristic
419C22×C4C2×D4×C3112yes—
420C22×C4C2×D4×C3111yescharacteristic
421C22×C4C2×D4×C3111yescharacteristic
422C22×C4C2×D4×C3112yes—
423C4⋊C4—24no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—42no—
441C4⋊C4—82no—
442C4⋊C4—82no—
443C4⋊C4—84no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—84no—
460C22⋊C4#41×C3114yes—
461C42—24no—
462C42—22no—
463C42—22no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—21no—
468C23—22no—
469C23—24no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23C22×D4×C3111yescharacteristic
475C23C22×D4×C3112yes—
476C23C2×#41×C3112yes—
477C23C31×2−1+412yes—
478Q8—81no—
479Q8—81no—
480D4—42no—
481D4—42no—
482D4—44no—
483D4—81no—
484D4—81no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4C31×#12011yescharacteristic
519C2×C4C31×#12011yescharacteristic
520C2×C4C31×#12012yes—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—22no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22C2×C31×#12011yescharacteristic
532C22C31×#52511yescharacteristic
533C22C31×#53611yescharacteristic
534C22C31×#54714yes—
535C4—22no—
536C4—21no—
537C4—21no—
538C4—44no—
539C4—42no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—42no—
545C4—41no—
546C4—84no—
547C4—82no—
548C2—21no—
549C2—24no—
550C2—21no—
551C2—82no—
552C2C31×#240611yescharacteristic
553C2C31×#302711yescharacteristic
554C2C31×#302811yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC24C24×C31
prime radicalC31×#534C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2623C2semidirect
3. C31×#2317C2semidirect
4. C31×#2062C2semidirect
6. C31×#1899C2semidirect
7. C31×#1867C2semidirect
8. C31×#1820C2semidirect
190. #24115C31direct (N × H)
245. #2623C2×C31semidirect
246. #2317C2×C31semidirect
247. #2062C2×C31semidirect
249. #1899C2×C31semidirect
250. #1867C2×C31semidirect
251. #1820C2×C31semidirect
392. C31#24115direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#34912
C31×#26232
C31×#23172
C31×#20622
C31×#20442
C31×#18992
C31×#18672
C31×#18202
#2411531