Subgroups — #20265254

Order 6464.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108057	C₂	1	2	yes	maximal, complemented
2	C₄×D₄₀₄	C₂	1	1	yes	maximal, characteristic
3	#15692167	C₂	1	2	yes	maximal, complemented
4	C₄×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄₀₄	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₀₁	C₂²	1	2	yes	—
8	#13108057	—	2	4	no	—
9	C₂×#11717579	C₂²	1	1	yes	characteristic
10	C₂×#11717579	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₁	C₄	1	1	yes	characteristic
12	#13108051	C₄	1	2	yes	—
13	C₂×C₈×C₁₀₁	C₂²	1	2	yes	—
14	C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
15	C₂²×D₁₀₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₁₀₁	C₂×C₄	1	2	yes	—
20	D₄₀₄	—	2	2	no	—
21	C₄×D₁₀₁	—	2	2	no	—
22	C₄×D₁₀₁	—	2	2	no	—
23	C₈×C₁₀₁	—	2	2	no	—
24	#11717579	—	2	1	no	—
25	#11717579	D₄	1	2	yes	complemented
26	C₂²×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₁₀₁	—	2	2	no	—
28	C₂×D₁₀₁	—	2	2	no	—
29	C₂×D₁₀₁	—	2	2	no	—
30	C₄×C₁₀₁	—	2	1	no	—
31	C₄×C₁₀₁	M₁₆	1	2	yes	complemented
32	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₀₁	#41	1	1	yes	characteristic
34	Dic₁₀₁	—	2	2	no	—
35	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
36	C₂×C₁₀₁	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₁₀₁	#131	1	1	yes	characteristic
38	D₁₀₁	—	4	2	no	—
39	C₁₀₁	#436	1	1	yes	characteristic, complemented, Sylow
40	#436	—	101	1	no	maximal, Sylow
41	C₂×M₁₆	—	101	2	no	—
42	C₄×D₄	—	101	1	no	—
43	C₄⋊C₈	D₁₀₁	1	1	yes	characteristic, complemented
44	C₂²⋊C₈	—	101	2	no	—
45	C₄×C₈	—	101	1	no	—
46	C₂×D₄	—	101	1	no	—
47	C₂²×C₄	—	101	2	no	—
48	M₁₆	—	202	4	no	—
49	C₂×C₈	—	101	1	no	—
50	C₂×C₈	—	101	1	no	—
51	C₂×C₈	C₂×D₁₀₁	1	2	yes	—
52	C₄⋊C₄	—	101	1	no	—
53	C₂²⋊C₄	—	101	2	no	—
54	C₄²	C₂×D₁₀₁	1	1	yes	characteristic
55	C₂³	—	101	2	no	—
56	D₄	—	202	2	no	—
57	C₂×C₄	—	101	2	no	—
58	C₂×C₄	—	202	2	no	—
59	C₂×C₄	—	202	2	no	—
60	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
61	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
63	C₈	—	2	2	no	—
64	C₈	—	101	2	no	—
65	C₈	—	202	1	no	—
66	C₂²	—	202	2	no	—
67	C₂²	—	202	2	no	—
68	C₂²	—	202	2	no	—
69	C₂²	C₂×C₄×D₁₀₁	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	202	2	no	—
72	C₄	#13108057	1	2	yes	complemented
73	C₄	D₄×D₁₀₁	1	1	yes	characteristic
74	C₄	#13108075	1	1	yes	characteristic
75	C₂	—	404	2	no	—
76	C₂	#15692217	1	1	yes	characteristic
77	C₂	C₂×#13108057	1	1	yes	characteristic
78	C₂	#15692263	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₀₁
commutator, socle	C₂²×C₁₀₁	C₂²×C₄
Fitting	C₄⋊C₈×C₁₀₁	C₂
hypercenter	C₄⋊C₈	D₁₀₁
hypocenter	C₁₀₁	#436
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#13108057	C₂	semidirect
3. #15692167	C₂	semidirect
4. C₄×#11717579	C₂	semidirect
5. C₄⋊C₈×C₁₀₁	C₂	semidirect
25. #11717579	D₄	semidirect
31. C₄×C₁₀₁	M₁₆	semidirect
39. C₁₀₁	#436	semidirect
43. C₄⋊C₈	D₁₀₁	semidirect
72. C₄	#13108057	semidirect