Subgroups — #14521173

Order 1984.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₆₂	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₃₁⋊C₈	C₂	1	2	yes	maximal
4	C₈×Dic₃₁	C₂	1	2	yes	maximal
5	C₄×C₃₁⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₆₂	C₄	1	1	yes	characteristic
7	C₂×C₈×C₃₁	C₂²	1	2	yes	—
8	C₄²×C₃₁	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₃₁	C₄	1	1	yes	characteristic
10	Dic₃₁⋊C₄	C₄	1	2	yes	—
11	C₄×Dic₃₁	C₂²	1	2	yes	—
12	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃₁⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
17	C₂×Dic₃₁	C₂×C₄	1	2	yes	—
18	C₂×Dic₃₁	C₂×C₄	1	2	yes	—
19	Dic₆₂	C₈	1	4	yes	complemented
20	C₈×C₃₁	—	2	2	no	—
21	C₃₁⋊C₈	—	2	1	no	—
22	C₃₁⋊C₈	Q₈	1	2	yes	complemented
23	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₃₁	—	2	1	no	—
25	C₄×C₃₁	C₂×C₈	1	2	yes	—
26	C₄×C₃₁	C₂×Q₈	1	1	yes	characteristic
27	C₄×C₃₁	#41	1	1	yes	characteristic
28	Dic₃₁	—	2	2	no	—
29	Dic₃₁	C₂×C₈	1	4	yes	—
30	C₈×Q₈	—	31	1	no	maximal, Sylow
31	C₂×C₃₁	C₄×Q₈	1	1	yes	characteristic
32	C₂×C₃₁	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₃₁	#131	1	1	yes	characteristic
34	C₄×Q₈	—	31	1	no	—
35	C₄⋊C₈	—	31	2	no	—
36	C₄⋊C₈	D₃₁	1	1	yes	characteristic
37	C₄×C₈	—	31	2	no	—
38	C₄×C₈	—	31	1	no	—
39	C₃₁	C₈×Q₈	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	—	31	1	no	—
41	C₂×C₈	—	31	1	no	—
42	C₂×C₈	—	31	1	no	—
43	C₂×C₈	C₂×D₃₁	1	2	yes	—
44	C₄⋊C₄	—	31	2	no	—
45	C₄⋊C₄	—	31	1	no	—
46	C₄²	—	31	2	no	—
47	C₄²	C₂×D₃₁	1	1	yes	characteristic
48	Q₈	—	31	4	no	—
49	C₂×C₄	—	31	2	no	—
50	C₂×C₄	—	31	2	no	—
51	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
52	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
53	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	31	2	no	—
56	C₈	—	62	1	no	—
57	C₂²	C₂×C₄×D₃₁	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	31	4	no	—
60	C₄	—	62	2	no	—
61	C₄	C₈×D₃₁	1	2	yes	—
62	C₄	#92497	1	1	yes	characteristic
63	C₄	Q₈×D₃₁	1	1	yes	characteristic
64	C₂	#11758464	1	1	yes	characteristic
65	C₂	C₂×C₈×D₃₁	1	1	yes	characteristic
66	C₂	#11758484	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃₁
commutator	C₂×C₃₁	C₂²×C₈
Fitting	C₃₁×C₄⋊C₈	C₂
socle, prime radical	C₂²×C₃₁	C₂²×C₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₄⋊C₈	D₃₁
hypocenter	C₃₁	C₈×Q₈
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
19. Dic₆₂	C₈	semidirect
22. C₃₁⋊C₈	Q₈	semidirect
39. C₃₁	C₈×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₆₂	2
C₃₁×C₄⋊C₈	2
Dic₃₁⋊C₈	2
C₈×Dic₃₁	2
C₄×C₃₁⋊C₈	2
C₈×Q₈	31