Subgroups — C₃₁×#492 #14520673

Order 1984.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×C₃₁	C₂	1	4	yes	maximal, complemented
2	C₃₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₁×#127	C₂	1	1	yes	maximal, characteristic
4	C₄×C₈×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₃₁	C₂²	1	2	yes	—
6	C₂×D₄×C₃₁	—	2	2	no	—
7	C₂×D₄×C₃₁	C₂²	1	2	yes	—
8	SD₁₆×C₃₁	—	2	8	no	—
9	C₂×C₈×C₃₁	C₂²	1	2	yes	—
10	C₄⋊C₄×C₃₁	—	2	2	no	—
11	C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂³×C₃₁	—	2	2	no	—
13	Q₈×C₃₁	—	2	4	no	—
14	D₄×C₃₁	—	2	4	no	—
15	D₄×C₃₁	—	4	4	no	—
16	C₂×C₄×C₃₁	—	2	2	no	—
17	C₂×C₄×C₃₁	D₄	1	2	yes	—
18	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₈×C₃₁	D₄	1	4	yes	complemented
20	C₂²×C₃₁	—	4	2	no	—
21	C₂²×C₃₁	—	4	4	no	—
22	C₂²×C₃₁	C₂×D₄	1	1	yes	characteristic
23	C₄×C₃₁	—	4	2	no	—
24	C₄×C₃₁	SD₁₆	1	4	yes	complemented
25	C₄×C₃₁	C₂×D₄	1	2	yes	—
26	#492	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
27	C₂×C₃₁	—	8	2	no	—
28	C₂×C₃₁	#127	1	1	yes	characteristic
29	C₂×C₃₁	C₂×SD₁₆	1	2	yes	—
30	C₂×SD₁₆	C₂×C₃₁	1	4	yes	complemented
31	C₄⋊Q₈	C₂×C₃₁	1	1	yes	characteristic, complemented
32	#127	C₂×C₃₁	1	1	yes	characteristic
33	C₄×C₈	C₂×C₃₁	1	1	yes	characteristic, complemented
34	C₃₁	#492	1	1	yes	characteristic, direct product factor, Sylow
35	C₂×Q₈	C₂²×C₃₁	1	2	yes	—
36	C₂×D₄	—	2	2	no	—
37	C₂×D₄	C₂²×C₃₁	1	2	yes	—
38	SD₁₆	—	2	8	no	—
39	C₂×C₈	C₂²×C₃₁	1	2	yes	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄²	C₂²×C₃₁	1	1	yes	characteristic
42	C₂³	—	2	2	no	—
43	Q₈	—	2	4	no	—
44	D₄	—	2	4	no	—
45	D₄	—	4	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	D₄×C₃₁	1	2	yes	—
48	C₂×C₄	C₂³×C₃₁	1	1	yes	characteristic
49	C₈	D₄×C₃₁	1	4	yes	complemented
50	C₂²	—	4	2	no	—
51	C₂²	—	4	4	no	—
52	C₂²	C₂×D₄×C₃₁	1	1	yes	characteristic
53	C₄	—	4	2	no	—
54	C₄	SD₁₆×C₃₁	1	4	yes	complemented
55	C₄	C₂×D₄×C₃₁	1	2	yes	—
56	C₂	—	8	2	no	—
57	C₂	C₃₁×#127	1	1	yes	characteristic
58	C₂	C₂×SD₁₆×C₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃₁
prime radical	C₃₁×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃₁ ◁ C₄²×C₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×C₃₁	C₂	semidirect
2. C₃₁×C₄⋊Q₈	C₂	semidirect
4. C₄×C₈×C₃₁	C₂	semidirect
19. C₈×C₃₁	D₄	semidirect
24. C₄×C₃₁	SD₁₆	semidirect
26. #492	C₃₁	direct (N × H)
30. C₂×SD₁₆	C₂×C₃₁	semidirect
31. C₄⋊Q₈	C₂×C₃₁	semidirect
33. C₄×C₈	C₂×C₃₁	semidirect
34. C₃₁	#492	direct (N × H)
49. C₈	D₄×C₃₁	semidirect
54. C₄	SD₁₆×C₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×C₃₁	2
C₃₁×C₄⋊Q₈	2
C₃₁×#127	2
C₄×C₈×C₃₁	2
#492	31

Subgroups — C31×#492 #14520673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#492 #14520673