Subgroups — #20266025

Order 6464.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11717581	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11717581	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692217	C₂	1	1	yes	maximal, characteristic
4	C₂×#11717581	—	2	1	no	—
5	C₂×#11717581	—	2	1	no	—
6	C₂×D₄₀₄	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₀₁	—	2	1	no	—
8	#13108051	—	2	1	no	—
9	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
11	C₂²×D₁₀₁	—	2	1	no	—
12	C₂×C₄×C₁₀₁	—	2	1	no	—
13	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
16	D₄₀₄	—	2	1	no	—
17	D₄₀₄	C₈	1	2	yes	complemented
18	C₄×D₁₀₁	—	4	1	no	—
19	C₄×D₁₀₁	—	4	1	no	—
20	#11717581	—	2	2	no	—
21	#11717581	—	4	1	no	—
22	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₀₁	—	2	2	no	—
24	C₂×D₁₀₁	—	4	1	no	—
25	C₂×D₁₀₁	—	4	1	no	—
26	C₄×C₁₀₁	—	4	1	no	—
27	C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₀₁	M₁₆	1	1	yes	characteristic
29	Dic₁₀₁	—	2	1	no	—
30	Dic₁₀₁	D₈	1	1	yes	characteristic
31	Dic₁₀₁	SD₁₆	1	1	yes	characteristic
32	C₂×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₂×C₁₀₁	#102	1	1	yes	characteristic
34	C₂×C₁₀₁	#104	1	1	yes	characteristic
35	D₁₀₁	—	4	2	no	—
36	C₁₀₁	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	101	1	no	maximal, Sylow
38	C₄×D₄	—	101	1	no	—
39	C₄⋊C₈	—	101	1	no	—
40	C₄×C₈	—	101	1	no	—
41	C₂×D₄	—	101	1	no	—
42	C₂²×C₄	—	202	1	no	—
43	C₂×C₈	—	202	1	no	—
44	C₂×C₈	—	202	1	no	—
45	C₄⋊C₄	#87938	1	1	yes	characteristic
46	C₂²⋊C₄	—	202	1	no	—
47	C₄²	—	101	1	no	—
48	C₂³	—	202	1	no	—
49	D₄	—	101	2	no	—
50	D₄	—	202	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	101	1	no	—
53	C₂×C₄	—	101	1	no	—
54	C₂×C₄	—	404	1	no	—
55	C₂×C₄	—	404	1	no	—
56	C₂×C₄	C₂×#87938	1	1	yes	characteristic
57	C₈	—	404	1	no	—
58	C₈	—	202	2	no	—
59	C₂²	—	404	1	no	—
60	C₂²	—	404	1	no	—
61	C₂²	—	202	2	no	—
62	C₂²	C₂²⋊#87938	1	1	yes	characteristic
63	C₄	—	4	1	no	—
64	C₄	—	101	1	no	—
65	C₄	—	101	1	no	—
66	C₄	—	202	1	no	—
67	C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
68	C₄	#13108084	1	1	yes	characteristic
69	C₂	—	404	2	no	—
70	C₂	#15692312	1	1	yes	characteristic
71	C₂	#15692317	1	1	yes	characteristic
72	C₂	#15692320	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87938
commutator	C₄×C₁₀₁	C₂×C₈
Frattini	C₂×C₄	C₂×#87938
Fitting	C₄⋊C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	D₄⋊C₈
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11717581	C₂	semidirect
2. C₄×#11717581	C₂	semidirect
17. D₄₀₄	C₈	semidirect
36. C₁₀₁	D₄⋊C₈	semidirect