Subgroups — #14520809

Order 1984.

110 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	#11758503	C₂	1	1	yes	maximal, characteristic
3	C₂×#92474	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₃₁	—	2	1	no	—
5	C₂²×C₄×C₃₁	C₂²	1	1	yes	characteristic
6	C₄²×C₃₁	—	2	1	no	—
7	C₄²×C₃₁	C₄	1	2	yes	complemented
8	C₂²⋊Dic₃₁	—	2	1	no	—
9	C₄⋊Dic₃₁	C₄	1	2	yes	complemented
10	C₄×Dic₃₁	—	2	1	no	—
11	#92474	—	2	1	no	—
12	#92474	C₄	1	2	yes	complemented
13	C₂×C₃₁⋊C₈	—	2	1	no	—
14	C₂³×C₃₁	D₄	1	1	yes	characteristic
15	C₂×C₄×C₃₁	—	2	4	no	—
16	C₂×C₄×C₃₁	—	2	2	no	—
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	D₄	1	1	yes	characteristic
21	C₂×C₄×C₃₁	D₄	1	1	yes	characteristic
22	C₂×C₄×C₃₁	Q₈	1	1	yes	characteristic
23	C₂×Dic₃₁	—	2	2	no	—
24	C₃₁⋊C₈	—	2	2	no	—
25	C₂²×C₃₁	—	2	2	no	—
26	C₂²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₃₁	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₃₁	—	2	4	no	—
30	C₄×C₃₁	C₄²	1	1	yes	characteristic
31	C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₃₁	C₄⋊C₄	1	1	yes	characteristic
34	Dic₃₁	—	4	2	no	—
35	#339	—	31	1	no	maximal, Sylow
36	C₂×C₃₁	—	2	1	no	—
37	C₂×C₃₁	—	2	1	no	—
38	C₂×C₃₁	#95	1	1	yes	characteristic
39	C₂×C₃₁	#104	1	2	yes	—
40	C₂×M₁₆	—	31	1	no	—
41	#117	—	31	1	no	—
42	C₂×C₄²	D₃₁	1	1	yes	characteristic
43	C₃₁	#339	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	2	1	no	—
45	C₂²×C₄	C₂×D₃₁	1	1	yes	characteristic
46	M₁₆	—	31	2	no	—
47	M₁₆	—	62	1	no	—
48	C₂×C₈	—	62	1	no	—
49	C₄⋊C₄	—	31	2	no	—
50	C₂²⋊C₄	—	62	1	no	—
51	C₄²	—	2	1	no	—
52	C₄²	—	62	1	no	—
53	C₄²	Dic₃₁	1	2	yes	complemented
54	C₂³	C₂²⋊D₃₁	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	62	2	no	—
58	C₂×C₄	Dic₆₂	1	1	yes	characteristic
59	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
60	C₂×C₄	C₄×D₃₁	1	1	yes	characteristic
61	C₂×C₄	D₁₂₄	1	1	yes	characteristic
62	C₂×C₄	C₂×Dic₃₁	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₃₁	1	1	yes	characteristic
64	C₈	—	62	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	Dic₃₁⋊C₄	1	1	yes	characteristic
67	C₂²	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
68	C₂²	C₂²⋊Dic₃₁	1	1	yes	characteristic
69	C₄	—	2	4	no	—
70	C₄	—	124	2	no	—
71	C₄	C₄×Dic₃₁	1	1	yes	characteristic
72	C₄	Dic₃₁⋊C₄	1	1	yes	characteristic
73	C₄	C₄⋊Dic₃₁	1	1	yes	characteristic
74	C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	2	1	no	—
77	C₂	#11758393	1	2	yes	—
78	C₂	C₃₁⋊#95	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₂₄
commutator	C₄×C₃₁	C₄²
Frattini	C₂²×C₄	C₂×D₃₁
Fitting	C₂×C₄²×C₃₁	C₂
socle	C₂²×C₃₁	C₂²⋊C₄
prime radical	C₂³×C₃₁	D₄
cosocle	C₂²×C₄×C₃₁	C₂²
hypercenter	C₂×C₄²	D₃₁
hypocenter	C₃₁	#339
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
7. C₄²×C₃₁	C₄	semidirect
9. C₄⋊Dic₃₁	C₄	semidirect
12. #92474	C₄	semidirect
43. C₃₁	#339	semidirect
53. C₄²	Dic₃₁	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
#11758503	2
C₂×#92474	2
#339	31