Subgroups — #46777710

Order 33632.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681233	C₂	1	1	yes	maximal, characteristic
2	#30681223	C₂	1	2	yes	maximal, complemented
3	#30681220	C₂	1	2	yes	maximal, complemented
4	#30681217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₁₀₅₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₂₁₀₂	C₂²	1	1	yes	characteristic
7	D₄₂₀₄	C₂²	1	1	yes	characteristic
8	C₂²⋊D₁₀₅₁	—	2	1	no	—
9	C₄×D₁₀₅₁	—	2	1	no	—
10	C₁₀₅₁⋊C₈	C₂²	1	2	yes	—
11	Q₈×C₁₀₅₁	—	2	1	no	—
12	Q₈×C₁₀₅₁	C₂²	1	2	yes	—
13	C₂×C₄×C₁₀₅₁	—	2	1	no	—
14	C₂×C₄×C₁₀₅₁	C₂²	1	1	yes	characteristic
15	C₂²×C₁₀₅₁	D₄	1	1	yes	characteristic
16	C₂×D₁₀₅₁	—	2	1	no	—
17	C₄×C₁₀₅₁	—	2	2	no	—
18	C₄×C₁₀₅₁	D₄	1	1	yes	characteristic
19	C₄×C₁₀₅₁	C₂³	1	1	yes	characteristic
20	Dic₁₀₅₁	—	2	1	no	—
21	C₂×C₁₀₅₁	—	2	1	no	—
22	C₂×C₁₀₅₁	C₂×D₄	1	1	yes	characteristic
23	D₁₀₅₁	—	4	1	no	—
24	C₁₀₅₁	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	1051	1	no	maximal, Sylow
26	#41	—	1051	1	no	—
27	C₂×Q₈	D₁₀₅₁	1	1	yes	characteristic, complemented
28	Q₁₆	—	1051	2	no	—
29	SD₁₆	—	1051	2	no	—
30	M₁₆	—	1051	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	1051	1	no	—
33	Q₈	C₂×D₁₀₅₁	1	2	yes	—
34	D₄	—	1051	1	no	—
35	D₄	—	2102	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2102	1	no	—
38	C₂×C₄	C₂×D₁₀₅₁	1	1	yes	characteristic
39	C₈	—	1051	2	no	—
40	C₂²	—	2102	1	no	—
41	C₂²	C₂²⋊D₁₀₅₁	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	2102	1	no	—
44	C₄	C₂²⋊D₁₀₅₁	1	1	yes	characteristic
45	C₄	C₂²×D₁₀₅₁	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4204	1	no	—
48	C₂	C₂×C₂²⋊D₁₀₅₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₁₀₅₁
commutator, cosocle	C₄×C₁₀₅₁	C₂³
Frattini	C₄	C₂²×D₁₀₅₁
Fitting	C₂×Q₈×C₁₀₅₁	C₂
socle	C₂×C₁₀₅₁	C₂×D₄
prime radical	#30681233	C₂
hypercenter	C₂×Q₈	D₁₀₅₁
hypocenter	C₁₀₅₁	#137
LCS	G ▷ C₄×C₁₀₅₁ ▷ C₂×C₁₀₅₁ ▷ C₁₀₅₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #30681223	C₂	semidirect
3. #30681220	C₂	semidirect
4. #30681217	C₂	semidirect
5. C₂×Q₈×C₁₀₅₁	C₂	semidirect
24. C₁₀₅₁	#137	semidirect
27. C₂×Q₈	D₁₀₅₁	semidirect

Maximal subgroups

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

subgroup	index
#30681233	2
#30681223	2
#30681220	2
#30681217	2
C₂×Q₈×C₁₀₅₁	2
#137	1051