Subgroups — #44536936

Order 31424.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₉₆₄	C₂	1	2	yes	maximal
2	#30628337	C₂	1	1	yes	maximal, characteristic
3	C₄×Dic₉₈₂	C₂	1	1	yes	maximal, characteristic
4	#30628262	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₉₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₉₈₂	C₂²	1	2	yes	—
7	C₂×Dic₉₈₂	C₂²	1	1	yes	characteristic
8	Dic₁₉₆₄	—	2	4	no	—
9	C₄⋊Dic₄₉₁	—	2	1	no	—
10	C₄⋊Dic₄₉₁	—	2	1	no	—
11	C₄⋊Dic₄₉₁	C₂²	1	1	yes	characteristic
12	Dic₄₉₁⋊C₄	—	2	1	no	—
13	C₄×Dic₄₉₁	—	2	1	no	—
14	C₂×C₈×C₄₉₁	C₂²	1	2	yes	—
15	C₄²×C₄₉₁	C₂²	1	1	yes	characteristic
16	Dic₉₈₂	—	2	1	no	—
17	Dic₉₈₂	—	2	2	no	—
18	Dic₉₈₂	—	2	2	no	—
19	Dic₉₈₂	D₄	1	2	yes	—
20	C₂×Dic₄₉₁	—	2	1	no	—
21	C₂×Dic₄₉₁	—	2	1	no	—
22	C₂×Dic₄₉₁	—	2	2	no	—
23	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₉₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₄₉₁	C₂³	1	1	yes	characteristic
26	C₈×C₄₉₁	—	2	2	no	—
27	C₂²×C₄₉₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₉₁	—	2	1	no	—
29	C₄×C₄₉₁	Q₁₆	1	2	yes	complemented
30	C₄×C₄₉₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₄₉₁	#41	1	1	yes	characteristic
32	Dic₄₉₁	—	2	2	no	—
33	Dic₄₉₁	—	4	2	no	—
34	Dic₄₉₁	—	4	1	no	—
35	C₂×C₄₉₁	#121	1	1	yes	characteristic
36	C₂×C₄₉₁	C₂×Q₁₆	1	1	yes	characteristic
37	C₂×C₄₉₁	#137	1	1	yes	characteristic
38	C₄₉₁	#462	1	1	yes	characteristic, complemented, Sylow
39	#462	—	491	1	no	maximal, Sylow
40	C₂×Q₁₆	—	491	2	no	—
41	C₄⋊Q₈	—	491	1	no	—
42	C₄×Q₈	—	491	1	no	—
43	C₄⋊C₈	D₄₉₁	1	1	yes	characteristic
44	#103	—	491	2	no	—
45	C₂×Q₈	—	491	2	no	—
46	C₂×Q₈	—	491	1	no	—
47	Q₁₆	—	982	4	no	—
48	C₂×C₈	C₂×D₄₉₁	1	2	yes	—
49	C₄⋊C₄	—	982	1	no	—
50	C₄⋊C₄	—	982	1	no	—
51	C₄⋊C₄	—	982	1	no	—
52	C₄⋊C₄	—	491	1	no	—
53	C₄²	—	982	1	no	—
54	C₄²	C₂×D₄₉₁	1	1	yes	characteristic
55	Q₈	—	982	2	no	—
56	Q₈	—	982	2	no	—
57	Q₈	—	982	1	no	—
58	Q₈	—	491	2	no	—
59	C₂×C₄	—	982	1	no	—
60	C₂×C₄	—	982	2	no	—
61	C₂×C₄	—	982	1	no	—
62	C₂×C₄	D₁₉₆₄	1	1	yes	characteristic
63	C₂×C₄	D₁₉₆₄	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₄₉₁	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₂²	C₂×D₁₉₆₄	1	1	yes	characteristic
67	C₄	—	2	1	no	—
68	C₄	—	1964	1	no	—
69	C₄	—	1964	2	no	—
70	C₄	—	982	2	no	—
71	C₄	Dic₁₉₆₄	1	2	yes	complemented
72	C₄	D₄×D₄₉₁	1	1	yes	characteristic
73	C₄	#21463329	1	1	yes	characteristic
74	C₂	#30628312	1	1	yes	characteristic
75	C₂	C₂×Dic₁₉₆₄	1	1	yes	characteristic
76	C₂	#30628370	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₉₆₄
commutator, cosocle	C₂×C₄×C₄₉₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₉₁
Fitting	C₄⋊C₈×C₄₉₁	C₂
socle, prime radical	C₂²×C₄₉₁	C₂×D₄
hypercenter	C₄⋊C₈	D₄₉₁
hypocenter	C₄₉₁	#462
LCS	G ▷ C₂×C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
29. C₄×C₄₉₁	Q₁₆	semidirect
38. C₄₉₁	#462	semidirect
71. C₄	Dic₁₉₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₁₉₆₄	2
#30628337	2
C₄×Dic₉₈₂	2
#30628262	2
C₄⋊C₈×C₄₉₁	2
#462	491