Subgroups — #20265294

Order 6464.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692262	C₂	1	2	yes	maximal, complemented
2	#15692191	C₂	1	1	yes	maximal, characteristic, complemented
3	#15692182	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#135×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	#13108058	—	2	2	no	—
7	#13108058	C₂²	1	2	yes	—
8	C₂×#11717579	—	2	2	no	—
9	C₂×#11717579	C₂²	1	1	yes	characteristic
10	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
11	#41×C₁₀₁	C₂²	1	2	yes	—
12	Q₁₆×C₁₀₁	C₄	1	1	yes	characteristic, complemented
13	SD₁₆×C₁₀₁	C₄	1	2	yes	complemented
14	D₈×C₁₀₁	C₄	1	1	yes	characteristic, complemented
15	C₂×C₈×C₁₀₁	C₂²	1	1	yes	characteristic
16	Q₈×C₁₀₁	C₂×C₄	1	2	yes	—
17	D₄×C₁₀₁	—	2	2	no	—
18	D₄×C₁₀₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₀₁	—	2	2	no	—
20	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	1	no	—
22	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
23	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
24	#11717579	—	2	2	no	—
25	#11717579	D₄	1	1	yes	characteristic
26	#11717579	D₄	1	1	yes	characteristic
27	C₂²×C₁₀₁	—	2	2	no	—
28	C₂²×C₁₀₁	#41	1	1	yes	characteristic
29	C₄×C₁₀₁	—	2	2	no	—
30	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂×D₄	1	1	yes	characteristic
32	Dic₁₀₁	—	2	2	no	—
33	C₂×C₁₀₁	—	2	1	no	—
34	C₂×C₁₀₁	—	4	2	no	—
35	C₂×C₁₀₁	C₄×D₄	1	1	yes	characteristic
36	C₁₀₁	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	101	1	no	maximal, Sylow
38	#135	D₁₀₁	1	1	yes	characteristic
39	#131	—	101	2	no	—
40	#108	—	101	1	no	—
41	#104	—	101	2	no	—
42	C₄×C₈	—	101	1	no	—
43	#41	C₂×D₁₀₁	1	2	yes	—
44	Q₁₆	Dic₁₀₁	1	1	yes	characteristic, complemented
45	SD₁₆	Dic₁₀₁	1	2	yes	complemented
46	D₈	Dic₁₀₁	1	1	yes	characteristic, complemented
47	M₁₆	—	101	2	no	—
48	M₁₆	—	202	2	no	—
49	C₂×C₈	—	101	1	no	—
50	C₂×C₈	—	202	2	no	—
51	C₂×C₈	C₂×D₁₀₁	1	1	yes	characteristic
52	C₄²	—	101	1	no	—
53	Q₈	C₂×Dic₁₀₁	1	2	yes	—
54	D₄	—	2	2	no	—
55	D₄	C₂×Dic₁₀₁	1	2	yes	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	202	1	no	—
58	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
59	C₈	—	101	1	no	—
60	C₈	—	101	1	no	—
61	C₈	—	202	2	no	—
62	C₈	C₂×Dic₁₀₁	1	1	yes	characteristic
63	C₈	C₂×Dic₁₀₁	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#13108073	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	202	2	no	—
68	C₄	C₂²×Dic₁₀₁	1	1	yes	characteristic
69	C₄	D₄×D₁₀₁	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	4	2	no	—
72	C₂	D₄×Dic₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#135×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₄×D₄
hypercenter	#135	D₁₀₁
hypocenter	C₁₀₁	#443
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #15692262	C₂	semidirect
2. #15692191	C₂	semidirect
3. #15692182	C₂	semidirect
4. C₈×Dic₁₀₁	C₂	semidirect
12. Q₁₆×C₁₀₁	C₄	semidirect
13. SD₁₆×C₁₀₁	C₄	semidirect
14. D₈×C₁₀₁	C₄	semidirect
36. C₁₀₁	#443	semidirect
44. Q₁₆	Dic₁₀₁	semidirect
45. SD₁₆	Dic₁₀₁	semidirect
46. D₈	Dic₁₀₁	semidirect