Finite Group Databasebeta

← C31×#61933 #21518692

Subgroups — C31×#61933 #21518692

Order 7936.

1754 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3556C211yesmaximal, characteristic, complemented
2C31×#3508C211yesmaximal, characteristic
3C31×#3400C214yesmaximal, complemented
4C31×#3392C214yesmaximal, complemented
5C31×#3368C214yesmaximal, complemented
6C31×#3365C214yesmaximal, complemented
7C31×#3222C214yesmaximal, complemented
8C31×#3208C212yesmaximal, complemented
9C31×#3123C214yesmaximal, complemented
10C31×#3107C212yesmaximal, complemented
11C31×#2986C211yesmaximal, characteristic, complemented
12C31×#564—22no—
13C31×#559C2214yes—
14C31×#557—22no—
15C31×#557C2214yescomplemented
16C31×#557C2214yescomplemented
17C31×#550C2214yes—
18C31×#546—24no—
19C31×#541—24no—
20C31×#541C2214yes—
21C31×#540—22no—
22C31×#535C2212yes—
23C31×#533C2212yes—
24C31×#533C2211yescharacteristic
25C31×#532—22no—
26C2×C31×#127C2211yescharacteristic
27C31×#518C2212yes—
28C4×#41×C31C2211yescharacteristic
29C31×#497C2214yescomplemented
30C31×#492C2214yes—
31C31×#492C2214yescomplemented
32C31×#490C2214yescomplemented
33C31×#488C2214yescomplemented
34C31×#486C2214yes—
35C31×#485C2214yes—
36C31×#478C2218yescomplemented
37C31×#475C2212yescomplemented
38C31×#474C2212yescomplemented
39C31×#464C2218yescomplemented
40C31×#462C2212yescomplemented
41C31×#461C2212yescomplemented
42C31×#461C2218yescomplemented
43C31×#460C2214yes—
44C31×#460C2214yes—
45C31×#460C2218yescomplemented
46C31×#452C2214yes—
47C31×#450C2218yes—
48C31×#446C2214yescomplemented
49C8×Q8×C31C2214yescomplemented
50C31×#440C2218yescomplemented
51C4×Q16×C31C2214yescomplemented
52C4×SD16×C31C2214yescomplemented
53C4×SD16×C31C2218yescomplemented
54C31×#433C2214yes—
55C31×#431C2212yes—
56C2×#41×C31—24no—
57C2×#41×C31C2311yescharacteristic
58C22×D4×C31—22no—
59C22×D4×C31C2312yes—
60C2×Q16×C31C2314yes—
61C2×SD16×C31C2318yes—
62C2×SD16×C31C2314yes—
63C2×SD16×C31C2318yes—
64C31×C4⋊Q8—24no—
65C31×C4⋊Q8D412yes—
66C31×C4⋊Q8C2314yes—
67C31×C4⋊Q8C2312yes—
68C31×C4⋊Q8C2312yes—
69C31×#127—21no—
70C31×#127—21no—
71C31×#127C2314yes—
72C31×#127C2314yes—
73C31×#126—28no—
74C31×#125—24no—
75C31×#125—28no—
76C31×#125—28no—
77C31×#125—28no—
78C31×#125—22no—
79C31×#125D412yes—
80C31×#125C2314yes—
81C31×#124—24no—
82C31×#124C2314yes—
83C31×#123—28no—
84C31×C22⋊Q8—22no—
85C31×C22⋊Q8D414yes—
86C31×C22⋊Q8C2314yes—
87C31×#121—24no—
88C31×#121—24no—
89C31×#121—28no—
90C31×#120—24no—
91C4×Q8×C31—24no—
92C4×Q8×C31—24no—
93C4×Q8×C31—22no—
94C4×Q8×C31C2314yes—
95C4×Q8×C31C2318yes—
96C4×Q8×C31C2312yes—
97C4×Q8×C31C2314yes—
98C4×D4×C31—22no—
99C4×D4×C31—24no—
100C4×D4×C31—24no—
101C4×D4×C31C2312yes—
102C4×D4×C31C2318yes—
103C31×#117—22no—
104C31×#117—21no—
105C31×#117C2311yescharacteristic
106C31×#117C2312yes—
107C2×C22⋊C4×C31—24no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C31×#107C2314yes—
111C31×#106C2314yes—
112C31×C4⋊C8C2312yes—
113C31×C4⋊C8C2312yes—
114C31×C4⋊C8C2318yes—
115C31×#103C2314yes—
116C31×#103C2314yes—
117C31×#103C2314yes—
118C31×#102C2318yes—
119C31×#102C2314yes—
120C31×#102C2318yes—
121C31×C22⋊C8C2314yes—
122C31×#97C2314yes—
123C4×C8×C31C2314yes—
124C4×C8×C31C2314yes—
125C24×C31—22no—
126#41×C31—42no—
127#41×C31—88no—
128C2×Q8×C31—22no—
129C2×Q8×C31C2×D414yes—
130C2×Q8×C31C2411yescharacteristic
131C2×Q8×C31C2414yes—
132C2×D4×C31—21no—
133C2×D4×C31—22no—
134C2×D4×C31—24no—
135C2×D4×C31—28no—
136C2×D4×C31—24no—
137C2×D4×C31—44no—
138C2×D4×C31—84no—
139C2×D4×C31C2414yes—
140C2×D4×C31C2411yescharacteristic
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—28no—
144C22×C4×C31C2×D412yes—
145C22×C4×C31C2411yescharacteristic
146Q16×C31—44no—
147SD16×C31—48no—
148SD16×C31—44no—
149SD16×C31—48no—
150C2×C8×C31C2414yes—
151C2×C8×C31C2414yes—
152C4⋊C4×C31—22no—
153C4⋊C4×C31—22no—
154C4⋊C4×C31—22no—
155C4⋊C4×C31—22no—
156C4⋊C4×C31—24no—
157C4⋊C4×C31—28no—
158C4⋊C4×C31—28no—
159C4⋊C4×C31—24no—
160C4⋊C4×C31—28no—
161C4⋊C4×C31C2×D414yes—
162C4⋊C4×C31C2×D414yes—
163C4⋊C4×C31C2×D418yes—
164C4⋊C4×C31C2414yes—
165C4⋊C4×C31C2412yes—
166C22⋊C4×C31—21no—
167C22⋊C4×C31—24no—
168C22⋊C4×C31—28no—
169C22⋊C4×C31—22no—
170C22⋊C4×C31—28no—
171C22⋊C4×C31C2×D414yes—
172C42×C31—21no—
173C42×C31—22no—
174C42×C31—24no—
175C42×C31—28no—
176C42×C31C2×D411yescharacteristic
177C42×C31C2×D411yescharacteristic
178C42×C31C2412yes—
179C42×C31C2414yes—
180#61933C3111yesmaximal, characteristic, direct product factor, Sylow
181C23×C31—24no—
182C23×C31—21no—
183C23×C31—44no—
184C23×C31—84no—
185C23×C31C22×D411yescharacteristic
186Q8×C31—28no—
187Q8×C31—24no—
188Q8×C31—24no—
189Q8×C31—22no—
190Q8×C31—44no—
191D4×C31—28no—
192D4×C31—22no—
193D4×C31—44no—
194D4×C31—42no—
195D4×C31—48no—
196D4×C31—84no—
197D4×C31—88no—
198C2×C4×C31—24no—
199C2×C4×C31—22no—
200C2×C4×C31—24no—
201C2×C4×C31—24no—
202C2×C4×C31—21no—
203C2×C4×C31—22no—
204C2×C4×C31—42no—
205C2×C4×C31—44no—
206C2×C4×C31—88no—
207C2×C4×C31C22×D411yescharacteristic
208C2×C4×C31C22×D418yes—
209C2×C4×C31C22×D412yes—
210C2×C4×C31C22×D412yes—
211C2×C4×C31C2511yescharacteristic
212C8×C31—24no—
213C8×C31—24no—
214#3556C2×C3111yescharacteristic, complemented
215#3508C2×C3111yescharacteristic
216#3400C2×C3114yescomplemented
217#3392C2×C3114yescomplemented
218#3368C2×C3114yescomplemented
219#3365C2×C3114yescomplemented
220#3222C2×C3114yescomplemented
221#3208C2×C3112yescomplemented
222#3123C2×C3114yescomplemented
223#3107C2×C3112yescomplemented
224#2986C2×C3111yescharacteristic, complemented
225C22×C31—21no—
226C22×C31—22no—
227C22×C31—41no—
228C22×C31—44no—
229C22×C31—42no—
230C22×C31—48no—
231C22×C31—164no—
232C22×C31C23×D411yescharacteristic
233C4×C31—21no—
234C4×C31—22no—
235C4×C31—28no—
236C4×C31—41no—
237C4×C31—44no—
238C4×C31—42no—
239C4×C31—44no—
240C4×C31#57714yes—
241C4×C31#58512yes—
242#564—22no—
243#559C22×C3114yes—
244#557—22no—
245#557C22×C3114yescomplemented
246#557C22×C3114yescomplemented
247#550C22×C3114yes—
248#546—24no—
249#541—24no—
250#541C22×C3114yes—
251#540—22no—
252#535C22×C3112yes—
253#533C22×C3112yes—
254#533C22×C3111yescharacteristic
255#532—22no—
256C2×#127C22×C3111yescharacteristic
257#518C22×C3112yes—
258C4×#41C22×C3111yescharacteristic
259#497C22×C3114yescomplemented
260#492C22×C3114yes—
261#492C22×C3114yescomplemented
262#490C22×C3114yescomplemented
263#488C22×C3114yescomplemented
264#486C22×C3114yes—
265#485C22×C3114yes—
266#478C22×C3118yescomplemented
267#475C22×C3112yescomplemented
268#474C22×C3112yescomplemented
269#464C22×C3118yescomplemented
270#462C22×C3112yescomplemented
271#461C22×C3112yescomplemented
272#461C22×C3118yescomplemented
273#460C22×C3114yes—
274#460C22×C3114yes—
275#460C22×C3118yescomplemented
276#452C22×C3114yes—
277#450C22×C3118yes—
278#446C22×C3114yescomplemented
279C8×Q8C22×C3114yescomplemented
280#440C22×C3118yescomplemented
281C4×Q16C22×C3114yescomplemented
282C4×SD16C22×C3114yescomplemented
283C4×SD16C22×C3118yescomplemented
284#433C22×C3114yes—
285#431C22×C3112yes—
286C2×C31—41no—
287C2×C31—81no—
288C2×C31—84no—
289C2×C31#348711yescharacteristic
290C2×C31C2×#57712yes—
291C2×#41—24no—
292C2×#41C23×C3111yescharacteristic
293C22×D4—22no—
294C22×D4C23×C3112yes—
295C2×Q16C23×C3114yes—
296C2×SD16C23×C3118yes—
297C2×SD16C23×C3114yes—
298C2×SD16C23×C3118yes—
299C4⋊Q8—24no—
300C4⋊Q8D4×C3112yes—
301C4⋊Q8C23×C3112yes—
302C4⋊Q8C23×C3114yes—
303C4⋊Q8C23×C3112yes—
304#127—21no—
305#127—21no—
306#127C23×C3114yes—
307#127C23×C3114yes—
308#126—28no—
309#125—24no—
310#125—28no—
311#125—28no—
312#125—28no—
313#125—22no—
314#125D4×C3112yes—
315#125C23×C3114yes—
316#124—24no—
317#124C23×C3114yes—
318#123—28no—
319C22⋊Q8—22no—
320C22⋊Q8D4×C3114yes—
321C22⋊Q8C23×C3114yes—
322#121—24no—
323#121—24no—
324#121—28no—
325#120—24no—
326C4×Q8—24no—
327C4×Q8—24no—
328C4×Q8—22no—
329C4×Q8C23×C3112yes—
330C4×Q8C23×C3114yes—
331C4×Q8C23×C3118yes—
332C4×Q8C23×C3114yes—
333C4×D4—22no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4C23×C3112yes—
337C4×D4C23×C3118yes—
338#117—22no—
339#117—21no—
340#117C23×C3111yescharacteristic
341#117C23×C3112yes—
342C2×C22⋊C4—24no—
343C2×C42—21no—
344C2×C42C23×C3111yescharacteristic
345#107C23×C3114yes—
346#106C23×C3114yes—
347C4⋊C8C23×C3112yes—
348C4⋊C8C23×C3112yes—
349C4⋊C8C23×C3118yes—
350#103C23×C3114yes—
351#103C23×C3114yes—
352#103C23×C3114yes—
353#102C23×C3118yes—
354#102C23×C3114yes—
355#102C23×C3118yes—
356C22⋊C8C23×C3114yes—
357#97C23×C3114yes—
358C4×C8C23×C3114yes—
359C4×C8C23×C3114yes—
360C31#6193311yescharacteristic, direct product factor, Sylow
361C24—22no—
362#41—42no—
363#41—88no—
364C2×Q8—22no—
365C2×Q8C2×D4×C3114yes—
366C2×Q8C24×C3111yescharacteristic
367C2×Q8C24×C3114yes—
368C2×D4—21no—
369C2×D4—22no—
370C2×D4—24no—
371C2×D4—28no—
372C2×D4—24no—
373C2×D4—44no—
374C2×D4—84no—
375C2×D4C24×C3114yes—
376C2×D4C24×C3111yescharacteristic
377C22×C4—21no—
378C22×C4—22no—
379C22×C4—28no—
380C22×C4C2×D4×C3112yes—
381C22×C4C24×C3111yescharacteristic
382Q16—44no—
383SD16—48no—
384SD16—44no—
385SD16—48no—
386C2×C8C24×C3114yes—
387C2×C8C24×C3114yes—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—24no—
393C4⋊C4—28no—
394C4⋊C4—28no—
395C4⋊C4—24no—
396C4⋊C4—28no—
397C4⋊C4C2×D4×C3114yes—
398C4⋊C4C2×D4×C3114yes—
399C4⋊C4C2×D4×C3118yes—
400C4⋊C4C24×C3114yes—
401C4⋊C4C24×C3112yes—
402C22⋊C4—21no—
403C22⋊C4—24no—
404C22⋊C4—28no—
405C22⋊C4—22no—
406C22⋊C4—28no—
407C22⋊C4C2×D4×C3114yes—
408C42—21no—
409C42—22no—
410C42—24no—
411C42—28no—
412C42C2×D4×C3111yescharacteristic
413C42C2×D4×C3111yescharacteristic
414C42C24×C3112yes—
415C42C24×C3114yes—
416C23—24no—
417C23—21no—
418C23—44no—
419C23—84no—
420C23C22×D4×C3111yescharacteristic
421Q8—28no—
422Q8—24no—
423Q8—24no—
424Q8—22no—
425Q8—44no—
426D4—28no—
427D4—22no—
428D4—44no—
429D4—42no—
430D4—48no—
431D4—84no—
432D4—88no—
433C2×C4—24no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—24no—
437C2×C4—21no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—88no—
442C2×C4C22×D4×C3111yescharacteristic
443C2×C4C22×D4×C3118yes—
444C2×C4C22×D4×C3112yes—
445C2×C4C22×D4×C3112yes—
446C2×C4C25×C3111yescharacteristic
447C8—24no—
448C8—24no—
449C22—21no—
450C22—22no—
451C22—41no—
452C22—44no—
453C22—42no—
454C22—48no—
455C22—164no—
456C22C23×D4×C3111yescharacteristic
457C4—21no—
458C4—22no—
459C4—28no—
460C4—41no—
461C4—44no—
462C4—42no—
463C4—44no—
464C4C31×#57714yes—
465C4C31×#58512yes—
466C2—41no—
467C2—84no—
468C2—81no—
469C2C31×#348711yescharacteristic
470C2C2×C31×#57712yes—
subgroupG/H
center, socleC22×C31C23×D4
commutator, Frattini, cosocleC2×C4C25×C31
prime radicalC31×#3508C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C31×#533 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3556C2semidirect
3. C31×#3400C2semidirect
4. C31×#3392C2semidirect
5. C31×#3368C2semidirect
6. C31×#3365C2semidirect
7. C31×#3222C2semidirect
8. C31×#3208C2semidirect
9. C31×#3123C2semidirect
10. C31×#3107C2semidirect
11. C31×#2986C2semidirect
15. C31×#557C22semidirect
16. C31×#557C22semidirect
29. C31×#497C22semidirect
31. C31×#492C22semidirect
32. C31×#490C22semidirect
33. C31×#488C22semidirect
36. C31×#478C22semidirect
37. C31×#475C22semidirect
38. C31×#474C22semidirect
39. C31×#464C22semidirect
40. C31×#462C22semidirect
41. C31×#461C22semidirect
42. C31×#461C22semidirect
45. C31×#460C22semidirect
48. C31×#446C22semidirect
49. C8×Q8×C31C22semidirect
50. C31×#440C22semidirect
51. C4×Q16×C31C22semidirect
52. C4×SD16×C31C22semidirect
53. C4×SD16×C31C22semidirect
180. #61933C31direct (N × H)
214. #3556C2×C31semidirect
216. #3400C2×C31semidirect
217. #3392C2×C31semidirect
218. #3368C2×C31semidirect
219. #3365C2×C31semidirect
220. #3222C2×C31semidirect
221. #3208C2×C31semidirect
222. #3123C2×C31semidirect
223. #3107C2×C31semidirect
224. #2986C2×C31semidirect
245. #557C22×C31semidirect
246. #557C22×C31semidirect
259. #497C22×C31semidirect
261. #492C22×C31semidirect
262. #490C22×C31semidirect
263. #488C22×C31semidirect
266. #478C22×C31semidirect
267. #475C22×C31semidirect
268. #474C22×C31semidirect
269. #464C22×C31semidirect
270. #462C22×C31semidirect
271. #461C22×C31semidirect
272. #461C22×C31semidirect
275. #460C22×C31semidirect
278. #446C22×C31semidirect
279. C8×Q8C22×C31semidirect
280. #440C22×C31semidirect
281. C4×Q16C22×C31semidirect
282. C4×SD16C22×C31semidirect
283. C4×SD16C22×C31semidirect
360. C31#61933direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35562
C31×#35082
C31×#34002
C31×#33922
C31×#33682
C31×#33652
C31×#32222
C31×#32082
C31×#31232
C31×#31072
C31×#29862
#6193331