Subgroups — #20265507

Order 6464.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692234	C₂	1	1	yes	maximal, characteristic
2	#15692186	C₂	1	2	yes	maximal, complemented
3	#15692178	C₂	1	2	yes	maximal, complemented
4	C₂²⋊#11717579	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₀₂	C₂²	1	1	yes	characteristic
7	C₂×#11717579	C₂²	1	2	yes	—
8	C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
9	#13108053	—	2	1	no	—
10	C₂²⋊Dic₁₀₁	—	2	1	no	—
11	C₂²×C₄×C₁₀₁	—	2	1	no	—
12	C₂²×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₀₁	—	2	1	no	—
14	C₄⋊C₄×C₁₀₁	C₂²	1	2	yes	—
15	C₂³×C₁₀₁	D₄	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	—	2	2	no	—
17	C₂×C₄×C₁₀₁	—	2	2	no	—
18	C₂×C₄×C₁₀₁	—	4	2	no	—
19	C₂×C₄×C₁₀₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
21	C₂×Dic₁₀₁	—	2	1	no	—
22	C₂×Dic₁₀₁	—	2	1	no	—
23	Dic₂₀₂	—	2	2	no	—
24	#11717579	—	2	2	no	—
25	C₂²×C₁₀₁	—	2	1	no	—
26	C₂²×C₁₀₁	—	2	1	no	—
27	C₂²×C₁₀₁	SD₁₆	1	2	yes	—
28	C₂²×C₁₀₁	C₂×D₄	1	1	yes	characteristic
29	C₄×C₁₀₁	—	2	1	no	—
30	C₄×C₁₀₁	—	4	2	no	—
31	C₄×C₁₀₁	#41	1	2	yes	—
32	Dic₁₀₁	—	4	1	no	—
33	Dic₁₀₁	—	4	1	no	—
34	C₂×C₁₀₁	—	2	2	no	—
35	C₂×C₁₀₁	#123	1	1	yes	characteristic
36	C₂×C₁₀₁	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×C₁₀₁	#137	1	1	yes	characteristic
38	C₁₀₁	#483	1	1	yes	characteristic, complemented, Sylow
39	#483	—	101	1	no	maximal, Sylow
40	C₂²⋊Q₈	—	101	1	no	—
41	C₂×C₄⋊C₄	D₁₀₁	1	1	yes	characteristic
42	#106	—	101	2	no	—
43	#103	—	101	2	no	—
44	C₂²⋊C₈	—	101	1	no	—
45	C₂×Q₈	—	101	1	no	—
46	C₂²×C₄	—	2	1	no	—
47	C₂²×C₄	C₂×D₁₀₁	1	1	yes	characteristic
48	C₂×C₈	—	101	2	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	—	101	1	no	—
51	C₄⋊C₄	—	202	1	no	—
52	C₄⋊C₄	C₂×D₁₀₁	1	2	yes	—
53	C₂²⋊C₄	—	202	1	no	—
54	C₂³	C₂²⋊D₁₀₁	1	1	yes	characteristic
55	Q₈	—	202	2	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	4	2	no	—
59	C₂×C₄	—	202	1	no	—
60	C₂×C₄	—	202	1	no	—
61	C₂×C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
63	C₈	—	202	2	no	—
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	#13108062	1	2	yes	—
67	C₂²	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	4	2	no	—
70	C₄	—	404	1	no	—
71	C₄	—	404	1	no	—
72	C₄	#13108074	1	2	yes	—
73	C₂	—	2	2	no	—
74	C₂	#15692238	1	1	yes	characteristic
75	C₂	C₂×#13108062	1	1	yes	characteristic
76	C₂	#15692286	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₁₀₁
commutator	C₂×C₄×C₁₀₁	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₁
Fitting	C₂×C₄⋊C₄×C₁₀₁	C₂
socle	C₂²×C₁₀₁	C₂×D₄
hypercenter	C₂×C₄⋊C₄	D₁₀₁
hypocenter	C₁₀₁	#483
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #15692186	C₂	semidirect
3. #15692178	C₂	semidirect
38. C₁₀₁	#483	semidirect