Subgroups — #14521102

Order 1984.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal
3	C₄⋊(C₃₁⋊C₈)	C₂	1	2	yes	maximal, complemented
4	C₄×C₃₁⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₃₁	C₄	1	1	yes	characteristic
6	C₂²×C₄×C₃₁	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
8	C₄²×C₃₁	C₄	1	1	yes	characteristic
9	C₄²×C₃₁	C₄	1	1	yes	characteristic
10	C₄²×C₃₁	C₂²	1	1	yes	characteristic
11	C₄²×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁⋊C₈	C₂²	1	4	yes	—
13	C₂³×C₃₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₁	—	2	2	no	—
15	C₂×C₄×C₃₁	—	2	2	no	—
16	C₂×C₄×C₃₁	C₈	1	4	yes	complemented
17	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
23	C₃₁⋊C₈	—	2	4	no	—
24	C₂²×C₃₁	—	2	1	no	—
25	C₂²×C₃₁	—	2	1	no	—
26	C₂²×C₃₁	C₂×C₈	1	2	yes	—
27	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₃₁	—	2	1	no	—
29	C₄×C₃₁	—	2	1	no	—
30	C₄×C₃₁	C₂×C₈	1	2	yes	—
31	C₄×C₃₁	C₂×C₈	1	2	yes	—
32	C₄×C₃₁	M₁₆	1	2	yes	—
33	C₄×C₃₁	#41	1	2	yes	—
34	#431	—	31	1	no	maximal, Sylow
35	C₂×C₃₁	—	2	2	no	—
36	C₂×C₃₁	#117	1	1	yes	characteristic
37	C₂×C₃₁	C₂²×C₈	1	1	yes	characteristic
38	C₂×C₃₁	C₂×M₁₆	1	1	yes	characteristic
39	C₂×C₄²	D₃₁	1	1	yes	characteristic
40	C₄⋊C₈	—	31	2	no	—
41	C₂²⋊C₈	—	31	2	no	—
42	C₄×C₈	—	31	2	no	—
43	C₃₁	#431	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	Dic₃₁	1	1	yes	characteristic
45	C₂²×C₄	Dic₃₁	1	1	yes	characteristic
46	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
47	C₂×C₈	—	31	4	no	—
48	C₄²	Dic₃₁	1	1	yes	characteristic
49	C₄²	Dic₃₁	1	1	yes	characteristic
50	C₄²	C₂×D₃₁	1	1	yes	characteristic
51	C₄²	C₂×D₃₁	1	1	yes	characteristic
52	C₂³	C₂×Dic₃₁	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	C₃₁⋊C₈	1	4	yes	complemented
56	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
57	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
58	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
59	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
61	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
62	C₈	—	62	4	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	2	1	no	—
65	C₂²	C₂×C₃₁⋊C₈	1	2	yes	—
66	C₂²	C₂²×Dic₃₁	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	2	1	no	—
69	C₄	C₂×C₃₁⋊C₈	1	2	yes	—
70	C₄	C₂×C₃₁⋊C₈	1	2	yes	—
71	C₄	#92474	1	2	yes	—
72	C₄	#92495	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	C₂²×C₃₁⋊C₈	1	1	yes	characteristic
75	C₂	C₂×#92474	1	1	yes	characteristic
76	C₂	#11758503	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×D₃₁
commutator	C₂×C₃₁	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₃₁
Fitting	C₂×C₄²×C₃₁	C₂
socle	C₂²×C₃₁	C₂²×C₄
prime radical	C₂³×C₃₁	C₂×C₄
cosocle	C₂×C₄×C₃₁	C₂³
hypercenter	C₂×C₄²	D₃₁
hypocenter	C₃₁	#431
LCS	G ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
3. C₄⋊(C₃₁⋊C₈)	C₂	semidirect
4. C₄×C₃₁⋊C₈	C₂	semidirect
16. C₂×C₄×C₃₁	C₈	semidirect
43. C₃₁	#431	semidirect
55. C₂×C₄	C₃₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×C₃₁	2
C₂²⋊(C₃₁⋊C₈)	2
C₄⋊(C₃₁⋊C₈)	2
C₄×C₃₁⋊C₈	2
#431	31