Subgroups — #20266034

Order 6464.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692310	C₂	1	1	yes	maximal, characteristic
2	#15692310	C₂	1	1	yes	maximal, characteristic
3	#15692246	C₂	1	1	yes	maximal, characteristic
4	C₂×#11717581	—	2	1	no	—
5	C₂×#11717581	—	2	1	no	—
6	C₄⋊Dic₁₀₁	—	2	1	no	—
7	C₄⋊Dic₁₀₁	C₄	1	1	yes	characteristic
8	#13108053	—	2	1	no	—
9	C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₁₀₁	C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₀₁	—	2	1	no	—
12	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₁₀₁	—	2	1	no	—
14	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
15	C₂×Dic₁₀₁	D₄	1	1	yes	characteristic
16	#11717581	—	2	2	no	—
17	#11717581	—	2	2	no	—
18	C₂²×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₁₀₁	—	2	1	no	—
20	C₄×C₁₀₁	—	4	1	no	—
21	Dic₁₀₁	—	2	1	no	—
22	Dic₁₀₁	—	2	1	no	—
23	Dic₁₀₁	—	4	1	no	—
24	C₂×C₁₀₁	#101	1	1	yes	characteristic
25	C₂×C₁₀₁	#104	1	1	yes	characteristic
26	C₂×C₁₀₁	#104	1	1	yes	characteristic
27	C₁₀₁	#330	1	1	yes	characteristic, complemented, Sylow
28	#330	—	101	1	no	maximal, Sylow
29	#125	—	101	1	no	—
30	#97	—	101	1	no	—
31	#97	—	101	1	no	—
32	C₂×C₈	—	202	1	no	—
33	C₂×C₈	—	202	1	no	—
34	C₄⋊C₄	—	101	1	no	—
35	C₄⋊C₄	—	202	1	no	—
36	C₄⋊C₄	—	202	1	no	—
37	C₄⋊C₄	#87938	1	1	yes	characteristic
38	C₄²	—	101	1	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	101	1	no	—
41	C₂×C₄	—	101	1	no	—
42	C₂×C₄	—	202	1	no	—
43	C₂×C₄	C₂×#87938	1	1	yes	characteristic
44	C₈	—	202	2	no	—
45	C₈	—	202	2	no	—
46	C₂²	C₂²⋊#87938	1	1	yes	characteristic
47	C₄	—	2	1	no	—
48	C₄	—	4	1	no	—
49	C₄	—	404	1	no	—
50	C₄	—	202	1	no	—
51	C₄	—	202	1	no	—
52	C₂	#15692316	1	1	yes	characteristic
53	C₂	#15692319	1	1	yes	characteristic
54	C₂	#15692320	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#87938
commutator	C₂×C₄×C₁₀₁	C₂×C₄
Frattini	C₂×C₄	C₂×#87938
Fitting	C₄⋊C₄×C₁₀₁	C₄
socle	C₂²×C₁₀₁	C₂²⋊C₄
hypercenter	C₄⋊C₄	#87938
hypocenter	C₁₀₁	#330
LCS	G ▷ C₂×C₄×C₁₀₁ ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
27. C₁₀₁	#330	semidirect