Subgroups — C₃₁×#392 #14520573

Order 1984.

322 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×C₃₁	C₂	1	3	yes	maximal, complemented
2	C₂×C₂²⋊C₄×C₃₁	C₂	1	3	yes	maximal, complemented
3	C₃₁×#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×C₃₁	C₂²	1	3	yes	—
5	C₂×D₄×C₃₁	—	2	12	no	—
6	C₂×D₄×C₃₁	—	2	6	no	—
7	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄×C₃₁	C₂²	1	3	yes	—
9	C₂²⋊C₄×C₃₁	—	2	6	no	—
10	C₂³×C₃₁	—	2	3	no	—
11	C₂³×C₃₁	—	2	6	no	—
12	C₂³×C₃₁	—	2	6	no	—
13	C₂³×C₃₁	—	2	3	no	—
14	C₂³×C₃₁	D₄	1	6	yes	complemented
15	C₂³×C₃₁	C₂³	1	1	yes	characteristic
16	D₄×C₃₁	—	2	24	no	—
17	C₂×C₄×C₃₁	—	2	6	no	—
18	C₂×C₄×C₃₁	—	2	3	no	—
19	C₂×C₄×C₃₁	D₄	1	6	yes	complemented
20	C₂²×C₃₁	—	2	12	no	—
21	C₂²×C₃₁	—	2	6	no	—
22	C₂²×C₃₁	—	4	3	no	—
23	C₂²×C₃₁	—	4	6	no	—
24	C₂²×C₃₁	—	4	3	no	—
25	C₂²×C₃₁	C₂×D₄	1	3	yes	—
26	C₂²×C₃₁	C₂×D₄	1	3	yes	—
27	C₂²×C₃₁	#41	1	1	yes	characteristic
28	C₄×C₃₁	—	2	6	no	—
29	C₄×C₃₁	—	4	1	no	—
30	#392	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₃₁	—	4	6	no	—
32	C₂×C₃₁	#120	1	3	yes	—
33	C₂×C₃₁	#121	1	3	yes	—
34	C₂×C₃₁	#127	1	1	yes	characteristic
35	C₂²×D₄	C₂×C₃₁	1	3	yes	complemented
36	C₂×C₂²⋊C₄	C₂×C₃₁	1	3	yes	complemented
37	#95	C₂×C₃₁	1	1	yes	characteristic, complemented
38	C₃₁	#392	1	1	yes	characteristic, direct product factor, Sylow
39	C₂⁴	C₂²×C₃₁	1	3	yes	—
40	C₂×D₄	—	2	12	no	—
41	C₂×D₄	—	2	6	no	—
42	C₂²×C₄	C₂²×C₃₁	1	1	yes	characteristic
43	C₂²×C₄	C₂²×C₃₁	1	3	yes	—
44	C₂²⋊C₄	—	2	6	no	—
45	C₂³	—	2	3	no	—
46	C₂³	—	2	6	no	—
47	C₂³	—	2	6	no	—
48	C₂³	—	2	3	no	—
49	C₂³	D₄×C₃₁	1	6	yes	complemented
50	C₂³	C₂³×C₃₁	1	1	yes	characteristic
51	D₄	—	2	24	no	—
52	C₂×C₄	—	2	6	no	—
53	C₂×C₄	—	2	3	no	—
54	C₂×C₄	D₄×C₃₁	1	6	yes	complemented
55	C₂²	—	2	12	no	—
56	C₂²	—	2	6	no	—
57	C₂²	—	4	3	no	—
58	C₂²	—	4	6	no	—
59	C₂²	—	4	3	no	—
60	C₂²	C₂×D₄×C₃₁	1	3	yes	—
61	C₂²	C₂×D₄×C₃₁	1	3	yes	—
62	C₂²	#41×C₃₁	1	1	yes	characteristic
63	C₄	—	2	6	no	—
64	C₄	—	4	1	no	—
65	C₂	—	4	6	no	—
66	C₂	C₃₁×#120	1	3	yes	—
67	C₂	C₃₁×#121	1	3	yes	—
68	C₂	C₃₁×#127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂³
commutator, Frattini, cosocle	C₂³	C₂³×C₃₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×C₃₁	C₂	semidirect
2. C₂×C₂²⋊C₄×C₃₁	C₂	semidirect
3. C₃₁×#95	C₂	semidirect
14. C₂³×C₃₁	D₄	semidirect
19. C₂×C₄×C₃₁	D₄	semidirect
30. #392	C₃₁	direct (N × H)
35. C₂²×D₄	C₂×C₃₁	semidirect
36. C₂×C₂²⋊C₄	C₂×C₃₁	semidirect
37. #95	C₂×C₃₁	semidirect
38. C₃₁	#392	direct (N × H)
49. C₂³	D₄×C₃₁	semidirect
54. C₂×C₄	D₄×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×C₃₁	2
C₂×C₂²⋊C₄×C₃₁	2
C₃₁×#95	2
#392	31

Subgroups — C31×#392 #14520573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#392 #14520573