Subgroups — #46777698

Order 33632.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681232	C₂	1	2	yes	maximal, complemented
2	Dic₄₂₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#30681221	C₂	1	2	yes	maximal, complemented
4	C₈×D₁₀₅₁	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×C₁₀₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₂₁₀₂	C₂²	1	2	yes	—
7	C₂²⋊D₁₀₅₁	—	2	2	no	—
8	C₂×Dic₁₀₅₁	—	2	2	no	—
9	C₄×D₁₀₅₁	C₂²	1	1	yes	characteristic
10	C₁₀₅₁⋊C₈	C₂²	1	1	yes	characteristic
11	D₄×C₁₀₅₁	C₂²	1	2	yes	—
12	C₈×C₁₀₅₁	C₂²	1	1	yes	characteristic
13	C₂²×C₁₀₅₁	—	2	2	no	—
14	C₂×D₁₀₅₁	D₄	1	1	yes	characteristic
15	C₄×C₁₀₅₁	C₂³	1	1	yes	characteristic
16	Dic₁₀₅₁	—	2	2	no	—
17	Dic₁₀₅₁	D₄	1	1	yes	characteristic
18	C₂×C₁₀₅₁	—	4	2	no	—
19	C₂×C₁₀₅₁	C₂×D₄	1	1	yes	characteristic
20	D₁₀₅₁	—	2	1	no	—
21	C₁₀₅₁	#135	1	1	yes	characteristic, complemented, Sylow
22	#135	—	1051	1	no	maximal, Sylow
23	#41	—	1051	2	no	—
24	Q₁₆	—	1051	1	no	—
25	SD₁₆	—	1051	2	no	—
26	D₈	D₁₀₅₁	1	1	yes	characteristic, complemented
27	C₂×C₈	—	1051	1	no	—
28	Q₈	—	1051	2	no	—
29	D₄	—	2102	2	no	—
30	D₄	C₂×D₁₀₅₁	1	2	yes	—
31	C₂×C₄	—	1051	1	no	—
32	C₂×C₄	—	2102	2	no	—
33	C₈	—	1051	1	no	—
34	C₈	C₂×D₁₀₅₁	1	1	yes	characteristic
35	C₂²	—	2	2	no	—
36	C₂²	—	1051	1	no	—
37	C₄	—	1051	1	no	—
38	C₄	—	2102	2	no	—
39	C₄	C₂²×D₁₀₅₁	1	1	yes	characteristic
40	C₂	—	4	2	no	—
41	C₂	—	2102	1	no	—
42	C₂	D₄×D₁₀₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₀₅₁
commutator, cosocle	C₄×C₁₀₅₁	C₂³
Frattini	C₄	C₂²×D₁₀₅₁
Fitting	D₈×C₁₀₅₁	C₂
socle	C₂×C₁₀₅₁	C₂×D₄
hypercenter	D₈	D₁₀₅₁
hypocenter	C₁₀₅₁	#135
LCS	G ▷ C₄×C₁₀₅₁ ▷ C₂×C₁₀₅₁ ▷ C₁₀₅₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #30681232	C₂	semidirect
2. Dic₄₂₀₄	C₂	semidirect
3. #30681221	C₂	semidirect
4. C₈×D₁₀₅₁	C₂	semidirect
5. D₈×C₁₀₅₁	C₂	semidirect
21. C₁₀₅₁	#135	semidirect
26. D₈	D₁₀₅₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#30681232	2
Dic₄₂₀₄	2
#30681221	2
C₈×D₁₀₅₁	2
D₈×C₁₀₅₁	2
#135	1051