Subgroups — #20266158

Order 6464.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692334	C₂	1	2	yes	maximal, complemented
2	#15692314	C₂	1	4	yes	maximal, complemented
3	C₂×#13108075	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#87938	—	2	2	no	—
5	C₂²⋊#87938	C₂²	1	4	yes	—
6	C₄×#87938	—	2	2	no	—
7	#13108075	—	2	2	no	—
8	#13108075	—	2	2	no	—
9	C₂×D₄₀₄	C₄	1	1	yes	characteristic, complemented
10	C₂×D₄₀₄	C₂²	1	2	yes	—
11	C₂×C₄×D₁₀₁	C₄	1	2	yes	complemented
12	C₂×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
14	C₂²×D₁₀₁	C₂×C₄	1	2	yes	—
15	C₂²×D₁₀₁	C₂³	1	1	yes	characteristic
16	C₂×#87938	—	2	4	no	—
17	Q₈×C₁₀₁	—	2	2	no	—
18	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₀₁	C₂×C₄	1	1	yes	characteristic
21	D₄₀₄	—	2	4	no	—
22	D₄₀₄	—	2	2	no	—
23	C₄×D₁₀₁	—	2	2	no	—
24	C₄×D₁₀₁	—	2	2	no	—
25	C₄×D₁₀₁	D₄	1	2	yes	—
26	C₄×D₁₀₁	D₄	1	2	yes	—
27	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×D₁₀₁	—	2	2	no	—
29	C₂×D₁₀₁	—	4	1	no	—
30	C₂×D₁₀₁	—	4	2	no	—
31	C₂×D₁₀₁	C₂×D₄	1	2	yes	—
32	#87938	—	4	4	no	—
33	C₄×C₁₀₁	—	2	2	no	—
34	C₄×C₁₀₁	C₂²⋊C₄	1	2	yes	—
35	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
36	Dic₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₁₀₁	—	2	1	no	—
38	C₂×C₁₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	D₁₀₁	—	2	2	no	—
40	D₁₀₁	—	4	2	no	—
41	C₁₀₁	#410	1	1	yes	characteristic, complemented, Sylow
42	#410	—	101	1	no	maximal, Sylow
43	C₂×#41	—	101	1	no	—
44	#117	—	101	2	no	—
45	#99	—	101	4	no	—
46	#41	—	202	2	no	—
47	#41	—	202	2	no	—
48	C₂×Q₈	#87938	1	1	yes	characteristic, complemented
49	C₂×D₄	—	101	2	no	—
50	C₂×D₄	—	101	1	no	—
51	C₂²×C₄	—	101	1	no	—
52	C₂²×C₄	—	101	2	no	—
53	C₄⋊C₄	—	202	2	no	—
54	C₂²⋊C₄	—	101	4	no	—
55	C₄²	—	202	2	no	—
56	C₂³	—	101	1	no	—
57	C₂³	—	101	2	no	—
58	Q₈	—	2	2	no	—
59	D₄	—	202	4	no	—
60	D₄	—	202	2	no	—
61	C₂×C₄	—	101	1	no	—
62	C₂×C₄	—	101	2	no	—
63	C₂×C₄	—	101	2	no	—
64	C₂×C₄	—	202	2	no	—
65	C₂×C₄	—	202	2	no	—
66	C₂×C₄	—	202	4	no	—
67	C₂×C₄	C₂×#87938	1	2	yes	—
68	C₂×C₄	C₂×#87938	1	1	yes	characteristic
69	C₂²	—	101	2	no	—
70	C₂²	—	404	2	no	—
71	C₂²	—	404	1	no	—
72	C₂²	—	202	2	no	—
73	C₂²	C₂²×#87938	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	101	1	no	—
76	C₄	—	101	1	no	—
77	C₄	—	404	4	no	—
78	C₄	C₂²⋊#87938	1	2	yes	—
79	C₂	—	2	1	no	—
80	C₂	—	404	2	no	—
81	C₂	—	202	2	no	—
82	C₂	C₂×C₂²⋊#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊#87938
commutator	C₂²×C₁₀₁	C₂²×C₄
Frattini	C₂²	C₂²×#87938
Fitting	C₂×Q₈×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₂×C₂²⋊C₄
hypercenter	C₂×Q₈	#87938
hypocenter	C₁₀₁	#410
LCS	G ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #15692334	C₂	semidirect
2. #15692314	C₂	semidirect
9. C₂×D₄₀₄	C₄	semidirect
11. C₂×C₄×D₁₀₁	C₄	semidirect
13. C₂×Q₈×C₁₀₁	C₄	semidirect
41. C₁₀₁	#410	semidirect
48. C₂×Q₈	#87938	semidirect