Subgroups — #14521099

Order 1984.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊(C₃₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
4	Dic₃₁⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₃₁	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₁	C₄	1	1	yes	characteristic
8	C₂²×Dic₃₁	C₄	1	1	yes	characteristic
9	C₂×C₈×C₃₁	C₂²	1	2	yes	—
10	C₄×Dic₃₁	C₄	1	1	yes	characteristic
11	C₄×Dic₃₁	C₄	1	1	yes	characteristic
12	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
13	C₄×Dic₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₃₁⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₃₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₁	—	2	2	no	—
17	C₂×C₄×C₃₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₃₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₃₁	—	2	2	no	—
20	C₂×Dic₃₁	C₈	1	4	yes	complemented
21	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₃₁	C₂×C₄	1	1	yes	characteristic
25	C₈×C₃₁	—	2	2	no	—
26	C₃₁⋊C₈	—	2	2	no	—
27	C₂²×C₃₁	—	2	1	no	—
28	C₂²×C₃₁	—	2	1	no	—
29	C₂²×C₃₁	C₂×C₈	1	2	yes	—
30	C₂²×C₃₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₃₁	—	2	1	no	—
32	C₄×C₃₁	#41	1	2	yes	—
33	Dic₃₁	—	2	1	no	—
34	Dic₃₁	C₂×C₈	1	2	yes	—
35	Dic₃₁	C₂×C₈	1	2	yes	—
36	Dic₃₁	M₁₆	1	2	yes	—
37	#431	—	31	1	no	maximal, Sylow
38	C₂×C₃₁	—	2	2	no	—
39	C₂×C₃₁	#117	1	1	yes	characteristic
40	C₂×C₃₁	C₂²×C₈	1	1	yes	characteristic
41	C₂×C₃₁	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₄²	—	31	1	no	—
43	C₄⋊C₈	—	31	2	no	—
44	C₂²⋊C₈	—	31	1	no	—
45	C₂²⋊C₈	D₃₁	1	1	yes	characteristic
46	C₄×C₈	—	31	2	no	—
47	C₃₁	#431	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	31	1	no	—
49	C₂²×C₄	—	31	1	no	—
50	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
51	C₂×C₈	—	31	2	no	—
52	C₂×C₈	C₂×D₃₁	1	2	yes	—
53	C₄²	—	31	1	no	—
54	C₄²	—	31	1	no	—
55	C₄²	—	31	1	no	—
56	C₄²	—	31	1	no	—
57	C₂³	C₄×D₃₁	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	31	4	no	—
60	C₂×C₄	—	31	1	no	—
61	C₂×C₄	—	31	1	no	—
62	C₂×C₄	—	31	1	no	—
63	C₂×C₄	—	31	1	no	—
64	C₂×C₄	—	62	2	no	—
65	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₃₁	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	62	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	C₈×D₃₁	1	2	yes	—
72	C₂²	C₂×C₄×D₃₁	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	31	2	no	—
75	C₄	—	31	2	no	—
76	C₄	—	31	2	no	—
77	C₄	—	62	1	no	—
78	C₄	#92497	1	2	yes	—
79	C₂	—	2	2	no	—
80	C₂	#11758454	1	1	yes	characteristic
81	C₂	C₂×C₈×D₃₁	1	1	yes	characteristic
82	C₂	M₁₆×D₃₁	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. Dic₃₁⋊C₈	C₂	semidirect
5. C₈×Dic₃₁	C₂	semidirect
20. C₂×Dic₃₁	C₈	semidirect
47. C₃₁	#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₃₁	2
C₃₁×C₂²⋊C₈	2
C₂²⋊(C₃₁⋊C₈)	2
Dic₃₁⋊C₈	2
C₈×Dic₃₁	2
#431	31