Subgroups — #20265213

Order 6464.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11717579	C₂	1	1	yes	maximal, characteristic
2	#15692214	C₂	1	1	yes	maximal, characteristic
3	#15692188	C₂	1	2	yes	maximal, complemented
4	#15692186	C₂	1	2	yes	maximal, complemented
5	#117×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11717579	C₄	1	4	yes	complemented
7	C₂×#11717579	C₂²	1	1	yes	characteristic
8	C₂×#11717579	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₀₁	C₂²	1	2	yes	—
10	C₂²⋊Dic₁₀₁	—	2	1	no	—
11	C₄×Dic₁₀₁	—	2	1	no	—
12	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
14	C₂²⋊C₄×C₁₀₁	—	2	1	no	—
15	C₄²×C₁₀₁	—	2	1	no	—
16	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₁₀₁	—	2	2	no	—
18	C₂×C₄×C₁₀₁	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	Q₈	1	2	yes	—
21	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₀₁	—	2	2	no	—
23	#11717579	C₂×C₄	1	2	yes	—
24	#11717579	C₂×C₄	1	2	yes	—
25	C₂²×C₁₀₁	—	2	2	no	—
26	C₂²×C₁₀₁	C₄⋊C₄	1	2	yes	—
27	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
28	C₄×C₁₀₁	—	4	2	no	—
29	C₄×C₁₀₁	C₄⋊C₄	1	2	yes	—
30	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
32	Dic₁₀₁	—	4	2	no	—
33	C₂×C₁₀₁	—	2	2	no	—
34	C₂×C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₁₀₁	#135	1	2	yes	—
36	C₁₀₁	#427	1	1	yes	characteristic, complemented, Sylow
37	#427	—	101	1	no	maximal, Sylow
38	C₂²×C₈	—	101	1	no	—
39	#117	—	101	1	no	—
40	#117	D₁₀₁	1	1	yes	characteristic
41	#107	—	101	2	no	—
42	#106	—	101	2	no	—
43	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
44	C₂×C₈	—	101	4	no	—
45	C₂×C₈	—	101	1	no	—
46	C₂×C₈	—	101	1	no	—
47	C₄⋊C₄	—	101	2	no	—
48	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
49	C₂²⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	—	202	1	no	—
51	C₄²	—	2	1	no	—
52	C₄²	—	202	1	no	—
53	C₂³	C₂²⋊D₁₀₁	1	1	yes	characteristic
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	202	2	no	—
56	C₂×C₄	Dic₂₀₂	1	2	yes	—
57	C₂×C₄	C₄×D₁₀₁	1	2	yes	—
58	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
60	C₈	—	101	2	no	—
61	C₈	—	101	2	no	—
62	C₂²	—	2	2	no	—
63	C₂²	#13108053	1	2	yes	—
64	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
65	C₄	—	4	2	no	—
66	C₄	—	404	2	no	—
67	C₄	#13108053	1	2	yes	—
68	C₄	C₂×C₄×D₁₀₁	1	1	yes	characteristic
69	C₄	C₂×Dic₂₀₂	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	C₂×#13108053	1	1	yes	characteristic
72	C₂	#15692275	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₀₁
commutator	C₄×C₁₀₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	#117×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	#117	D₁₀₁
hypocenter	C₁₀₁	#427
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. #15692188	C₂	semidirect
4. #15692186	C₂	semidirect
6. C₂×#11717579	C₄	semidirect
36. C₁₀₁	#427	semidirect