Subgroups — #15692286

Order 3232.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108074	C₂	1	1	yes	maximal, characteristic
2	#13108064	C₂	1	2	yes	maximal, complemented
3	#13108061	C₂	1	2	yes	maximal, complemented
4	#13108058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₀₁	—	2	1	no	—
7	Q₈×C₁₀₁	C₂²	1	2	yes	—
8	C₂×C₄×C₁₀₁	—	2	1	no	—
9	C₂×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	C₂²⋊D₁₀₁	—	2	1	no	—
11	D₄₀₄	C₂²	1	1	yes	characteristic
12	C₄×D₁₀₁	—	2	1	no	—
13	Dic₂₀₂	C₂²	1	1	yes	characteristic
14	#11717579	C₂²	1	2	yes	—
15	C₂²×C₁₀₁	D₄	1	1	yes	characteristic
16	C₂×D₁₀₁	—	2	1	no	—
17	C₄×C₁₀₁	—	2	2	no	—
18	C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
20	Dic₁₀₁	—	2	1	no	—
21	C₂×C₁₀₁	—	2	1	no	—
22	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
23	D₁₀₁	—	4	1	no	—
24	C₁₀₁	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	101	1	no	maximal, Sylow
26	#41	—	101	1	no	—
27	C₂×Q₈	D₁₀₁	1	1	yes	characteristic, complemented
28	Q₁₆	—	101	2	no	—
29	SD₁₆	—	101	2	no	—
30	M₁₆	—	101	1	no	—
31	Q₈	—	2	1	no	—
32	Q₈	—	101	1	no	—
33	Q₈	C₂×D₁₀₁	1	2	yes	—
34	D₄	—	101	1	no	—
35	D₄	—	202	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	202	1	no	—
38	C₂×C₄	C₂×D₁₀₁	1	1	yes	characteristic
39	C₈	—	101	2	no	—
40	C₂²	—	202	1	no	—
41	C₂²	C₂²⋊D₁₀₁	1	1	yes	characteristic
42	C₄	—	2	2	no	—
43	C₄	—	202	1	no	—
44	C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
45	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	404	1	no	—
48	C₂	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₁₀₁
commutator, cosocle	C₄×C₁₀₁	C₂³
Frattini	C₄	C₂²×D₁₀₁
Fitting	C₂×Q₈×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂×D₄
prime radical	#13108074	C₂
hypercenter	C₂×Q₈	D₁₀₁
hypocenter	C₁₀₁	#137
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
2. #13108064	C₂	semidirect
3. #13108061	C₂	semidirect
4. #13108058	C₂	semidirect
5. C₂×Q₈×C₁₀₁	C₂	semidirect
24. C₁₀₁	#137	semidirect
27. C₂×Q₈	D₁₀₁	semidirect

Maximal subgroups

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

subgroup	index
#13108074	2
#13108064	2
#13108061	2
#13108058	2
C₂×Q₈×C₁₀₁	2
#137	101