Subgroups — #20264949

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13108058	C₂	1	1	yes	maximal, characteristic
2	#15692214	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	#13108058	—	2	1	no	—
5	#13108058	—	2	1	no	—
6	C₂×#11717579	C₄	1	2	yes	complemented
7	C₄⋊Dic₁₀₁	—	2	1	no	—
8	C₂²⋊Dic₁₀₁	C₄	1	2	yes	—
9	C₄×Dic₁₀₁	—	2	1	no	—
10	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	M₁₆×C₁₀₁	—	2	1	no	—
12	M₁₆×C₁₀₁	C₄	1	2	yes	complemented
13	C₂×C₈×C₁₀₁	—	2	1	no	—
14	C₂³×C₁₀₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
18	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	Q₈	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	2	no	—
22	C₈×C₁₀₁	—	2	2	no	—
23	#11717579	—	2	2	no	—
24	C₂²×C₁₀₁	—	4	1	no	—
25	C₂²×C₁₀₁	C₄²	1	1	yes	characteristic
26	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
29	C₄×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₄⋊C₄	1	1	yes	characteristic
32	Dic₁₀₁	—	4	2	no	—
33	C₂×C₁₀₁	—	2	1	no	—
34	C₂×C₁₀₁	—	2	1	no	—
35	C₂×C₁₀₁	—	2	1	no	—
36	C₂×C₁₀₁	#95	1	1	yes	characteristic
37	C₁₀₁	#344	1	1	yes	characteristic, complemented, Sylow
38	#344	—	101	1	no	maximal, Sylow
39	C₂×M₁₆	—	101	1	no	—
40	C₂×M₁₆	D₁₀₁	1	1	yes	characteristic
41	#117	—	101	1	no	—
42	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
43	M₁₆	—	2	1	no	—
44	M₁₆	—	202	1	no	—
45	M₁₆	—	202	1	no	—
46	M₁₆	Dic₁₀₁	1	2	yes	complemented
47	C₂×C₈	—	2	1	no	—
48	C₂×C₈	—	101	2	no	—
49	C₄⋊C₄	—	202	1	no	—
50	C₂²⋊C₄	—	101	2	no	—
51	C₄²	—	202	1	no	—
52	C₂³	C₄×D₁₀₁	1	1	yes	characteristic
53	C₂×C₄	—	202	2	no	—
54	C₂×C₄	Dic₂₀₂	1	1	yes	characteristic
55	C₂×C₄	C₄×D₁₀₁	1	1	yes	characteristic
56	C₂×C₄	D₄₀₄	1	1	yes	characteristic
57	C₂×C₄	C₂×Dic₁₀₁	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
59	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	202	2	no	—
62	C₂²	—	4	1	no	—
63	C₂²	C₄×Dic₁₀₁	1	1	yes	characteristic
64	C₂²	#13108051	1	1	yes	characteristic
65	C₂²	#13108053	1	1	yes	characteristic
66	C₄	—	404	2	no	—
67	C₄	#13108051	1	1	yes	characteristic
68	C₄	C₂²⋊Dic₁₀₁	1	1	yes	characteristic
69	C₄	#13108053	1	1	yes	characteristic
70	C₄	C₄⋊Dic₁₀₁	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	—	2	1	no	—
74	C₂	#15692162	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13108051
commutator	C₂²×C₁₀₁	C₄²
Frattini	C₂²×C₄	C₂×D₁₀₁
Fitting	C₂×M₁₆×C₁₀₁	C₂
socle	C₂×C₁₀₁	#95
hypercenter	C₂×M₁₆	D₁₀₁
hypocenter	C₁₀₁	#344
LCS	G ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
6. C₂×#11717579	C₄	semidirect
12. M₁₆×C₁₀₁	C₄	semidirect
37. C₁₀₁	#344	semidirect
46. M₁₆	Dic₁₀₁	semidirect