Subgroups — #44536979

Order 31424.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₉₂₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#21463311	C₂	1	1	yes	maximal, characteristic, complemented
3	#30628312	C₂	1	2	yes	maximal, complemented
4	#30628257	C₂	1	2	yes	maximal, complemented
5	#106×C₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₉₆₄	—	2	2	no	—
7	C₂×D₁₉₆₄	C₂²	1	2	yes	—
8	C₂×C₄×D₄₉₁	C₂²	1	1	yes	characteristic
9	D₃₉₂₈	—	2	2	no	—
10	#21463311	—	2	2	no	—
11	C₂×C₄₉₁⋊C₈	C₂²	1	1	yes	characteristic
12	(C₂×D₄₉₁)⋊C₄	—	2	2	no	—
13	C₂×C₈×C₄₉₁	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₄₉₁	C₂²	1	2	yes	—
15	C₂²×D₄₉₁	—	2	2	no	—
16	C₂²×D₄₉₁	D₄	1	1	yes	characteristic
17	D₁₉₆₄	—	2	2	no	—
18	D₁₉₆₄	—	2	2	no	—
19	D₁₉₆₄	—	4	4	no	—
20	C₂×Dic₄₉₁	D₄	1	1	yes	characteristic
21	C₄×D₄₉₁	—	2	1	no	—
22	C₄×D₄₉₁	—	2	1	no	—
23	C₄₉₁⋊C₈	—	2	1	no	—
24	C₂×C₄×C₄₉₁	—	2	2	no	—
25	C₂×C₄×C₄₉₁	C₂³	1	1	yes	characteristic
26	C₈×C₄₉₁	D₄	1	2	yes	complemented
27	C₂²×C₄₉₁	C₂×D₄	1	1	yes	characteristic
28	C₂×D₄₉₁	—	2	1	no	—
29	C₂×D₄₉₁	—	2	2	no	—
30	C₂×D₄₉₁	—	4	2	no	—
31	C₂×D₄₉₁	—	4	2	no	—
32	C₂×D₄₉₁	—	4	2	no	—
33	C₄×C₄₉₁	—	4	2	no	—
34	C₄×C₄₉₁	C₂×D₄	1	1	yes	characteristic
35	C₄×C₄₉₁	#41	1	1	yes	characteristic
36	Dic₄₉₁	—	2	1	no	—
37	C₂×C₄₉₁	#121	1	1	yes	characteristic
38	C₂×C₄₉₁	AGL(1,ℤ/8)	1	2	yes	—
39	D₄₉₁	—	4	1	no	—
40	D₄₉₁	—	8	2	no	—
41	C₄₉₁	#469	1	1	yes	characteristic, complemented, Sylow
42	#469	—	491	1	no	maximal, Sylow
43	C₂×D₈	—	491	1	no	—
44	C₂×M₁₆	—	491	1	no	—
45	#121	—	491	2	no	—
46	#106	D₄₉₁	1	1	yes	characteristic, complemented
47	#102	—	491	2	no	—
48	C₂×D₄	—	982	2	no	—
49	C₂×D₄	—	491	2	no	—
50	C₂²×C₄	—	491	1	no	—
51	D₈	—	982	2	no	—
52	M₁₆	—	982	2	no	—
53	C₂×C₈	—	491	1	no	—
54	C₂×C₈	C₂×D₄₉₁	1	1	yes	characteristic
55	C₄⋊C₄	C₂×D₄₉₁	1	2	yes	—
56	C₂²⋊C₄	—	982	2	no	—
57	C₂³	—	982	2	no	—
58	C₂³	—	491	1	no	—
59	D₄	—	1964	4	no	—
60	D₄	—	982	2	no	—
61	D₄	—	982	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	982	1	no	—
64	C₂×C₄	—	982	1	no	—
65	C₂×C₄	—	491	1	no	—
66	C₂×C₄	C₂²×D₄₉₁	1	1	yes	characteristic
67	C₈	—	982	1	no	—
68	C₈	D₁₉₆₄	1	2	yes	complemented
69	C₂²	—	1964	2	no	—
70	C₂²	—	1964	2	no	—
71	C₂²	—	1964	2	no	—
72	C₂²	—	982	2	no	—
73	C₂²	—	982	1	no	—
74	C₂²	D₄×D₄₉₁	1	1	yes	characteristic
75	C₄	—	4	2	no	—
76	C₄	—	982	1	no	—
77	C₄	C₂×D₁₉₆₄	1	1	yes	characteristic
78	C₄	#21463329	1	1	yes	characteristic
79	C₂	—	3928	2	no	—
80	C₂	—	1964	1	no	—
81	C₂	#30628312	1	1	yes	characteristic
82	C₂	#30628364	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₄₉₁
commutator, cosocle	C₂×C₄×C₄₉₁	C₂³
Frattini	C₂×C₄	C₂²×D₄₉₁
Fitting	#106×C₄₉₁	C₂
socle	C₂²×C₄₉₁	C₂×D₄
hypercenter	#106	D₄₉₁
hypocenter	C₄₉₁	#469
LCS	G ▷ C₂×C₄×C₄₉₁ ▷ C₂×C₄₉₁ ▷ C₄₉₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
1. C₂×D₃₉₂₈	C₂	semidirect
2. C₂×#21463311	C₂	semidirect
3. #30628312	C₂	semidirect
4. #30628257	C₂	semidirect
5. #106×C₄₉₁	C₂	semidirect
26. C₈×C₄₉₁	D₄	semidirect
41. C₄₉₁	#469	semidirect
46. #106	D₄₉₁	semidirect
68. C₈	D₁₉₆₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₉₂₈	2
C₂×#21463311	2
#30628312	2
#30628257	2
#106×C₄₉₁	2
#469	491