Subgroups — #16843691

Order 3968.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Dic₆₂	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₆×C₃₁	C₂	1	1	yes	maximal, characteristic
4	C₄×Dic₆₂	C₄	1	1	yes	characteristic
5	C₂×C₁₆×C₃₁	—	2	1	no	—
6	C₄×C₈×C₃₁	C₂²	1	1	yes	characteristic
7	Dic₃₁⋊C₈	—	2	1	no	—
8	C₈×Dic₃₁	—	2	1	no	—
9	C₂×C₃₁⋊C₁₆	—	2	1	no	—
10	C₄⋊(C₃₁⋊C₈)	C₄	1	1	yes	characteristic
11	C₂×Dic₆₂	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₃₁	D₄	1	1	yes	characteristic
14	C₄²×C₃₁	C₂×C₄	1	1	yes	characteristic
15	C₄⋊Dic₃₁	C₈	1	1	yes	characteristic
16	Dic₃₁⋊C₄	—	2	1	no	—
17	C₄×Dic₃₁	—	2	1	no	—
18	C₂×C₃₁⋊C₈	—	2	1	no	—
19	C₁₆×C₃₁	—	2	2	no	—
20	C₃₁⋊C₁₆	—	4	1	no	—
21	C₂×C₄×C₃₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₁	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₃₁	M₁₆	1	1	yes	characteristic
24	C₂×Dic₃₁	—	2	1	no	—
25	C₂×Dic₃₁	—	2	1	no	—
26	Dic₆₂	—	2	1	no	—
27	Dic₆₂	C₁₆	1	2	yes	complemented
28	C₈×C₃₁	—	2	1	no	—
29	C₈×C₃₁	SD₁₆	1	1	yes	characteristic
30	C₈×C₃₁	Q₁₆	1	1	yes	characteristic
31	C₃₁⋊C₈	—	4	1	no	—
32	Q₈⋊C₁₆	—	31	1	no	maximal, Sylow
33	C₂²×C₃₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₄×C₃₁	—	2	1	no	—
35	C₄×C₃₁	#103	1	1	yes	characteristic
36	C₄×C₃₁	#104	1	1	yes	characteristic
37	C₄×C₃₁	C₂×C₁₆	1	1	yes	characteristic
38	C₄×C₃₁	M₃₂	1	1	yes	characteristic
39	Dic₃₁	—	2	2	no	—
40	Dic₃₁	—	4	1	no	—
41	C₈×Q₈	—	31	1	no	—
42	C₄⋊C₁₆	—	31	1	no	—
43	C₄×C₁₆	D₃₁	1	1	yes	characteristic
44	C₂×C₃₁	Q₈⋊C₈	1	1	yes	characteristic
45	C₂×C₃₁	C₂²⋊C₁₆	1	1	yes	characteristic
46	C₂×C₃₁	#350	1	1	yes	characteristic
47	C₄×Q₈	—	31	1	no	—
48	C₂×C₁₆	—	2	1	no	—
49	C₂×C₁₆	—	62	1	no	—
50	C₄⋊C₈	—	31	1	no	—
51	C₄⋊C₈	—	62	1	no	—
52	C₄×C₈	—	62	1	no	—
53	C₄×C₈	C₂×D₃₁	1	1	yes	characteristic
54	C₃₁	Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	31	1	no	—
56	C₂×C₈	—	62	1	no	—
57	C₂×C₈	D₁₂₄	1	1	yes	characteristic
58	C₂×C₈	C₂²⋊D₃₁	1	1	yes	characteristic
59	C₄⋊C₄	—	31	1	no	—
60	C₄⋊C₄	—	62	1	no	—
61	C₄²	—	62	1	no	—
62	C₄²	C₄×D₃₁	1	1	yes	characteristic
63	C₁₆	—	2	2	no	—
64	C₁₆	—	124	1	no	—
65	Q₈	—	31	2	no	—
66	Q₈	—	62	1	no	—
67	C₂×C₄	—	62	1	no	—
68	C₂×C₄	—	62	1	no	—
69	C₂×C₄	C₈×D₃₁	1	1	yes	characteristic
70	C₂×C₄	#92469	1	1	yes	characteristic
71	C₂×C₄	(C₂×D₃₁)⋊C₄	1	1	yes	characteristic
72	C₈	—	2	1	no	—
73	C₈	—	124	1	no	—
74	C₈	#92470	1	1	yes	characteristic
75	C₈	Dic₁₂₄	1	1	yes	characteristic
76	C₂²	(C₂×D₃₁)⋊C₈	1	1	yes	characteristic
77	C₄	—	2	1	no	—
78	C₄	—	62	2	no	—
79	C₄	—	124	1	no	—
80	C₄	C₁₆×D₃₁	1	1	yes	characteristic
81	C₄	#11758386	1	1	yes	characteristic
82	C₄	#11758393	1	1	yes	characteristic
83	C₄	#11758404	1	1	yes	characteristic
84	C₂	#14520781	1	1	yes	characteristic
85	C₂	(C₂×D₃₁)⋊C₁₆	1	1	yes	characteristic
86	C₂	#14520832	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₁₂₄
commutator	C₄×C₃₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₃₁
Fitting	C₄×C₁₆×C₃₁	C₂
socle, prime radical	C₂²×C₃₁	C₂²⋊C₈
cosocle	C₄×C₈×C₃₁	C₂²
hypercenter	C₄×C₁₆	D₃₁
hypocenter	C₃₁	Q₈⋊C₁₆
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
27. Dic₆₂	C₁₆	semidirect
54. C₃₁	Q₈⋊C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₈×Dic₆₂	2
C₄⋊(C₃₁⋊C₁₆)	2
C₄×C₁₆×C₃₁	2
Q₈⋊C₁₆	31