Subgroups — #15692275

Order 3232.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108074	C₂	1	1	yes	maximal, characteristic, complemented
2	#13108064	C₂	1	1	yes	maximal, characteristic, complemented
3	#13108062	C₂	1	1	yes	maximal, characteristic, complemented
4	#13108061	C₂	1	1	yes	maximal, characteristic, complemented
5	#13108059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
7	#41×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
9	D₄×C₁₀₁	—	2	1	no	—
10	D₄×C₁₀₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₁₀₁	—	2	1	no	—
12	C₂×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
13	C₂²⋊D₁₀₁	—	2	1	no	—
14	D₄₀₄	C₂²	1	1	yes	characteristic
15	C₄×D₁₀₁	—	2	1	no	—
16	Dic₂₀₂	C₂²	1	1	yes	characteristic
17	#11717579	C₂²	1	1	yes	characteristic
18	#11717579	C₂²	1	1	yes	characteristic
19	C₂²×C₁₀₁	—	2	1	no	—
20	C₂²×C₁₀₁	D₄	1	1	yes	characteristic
21	C₂×D₁₀₁	—	2	1	no	—
22	C₄×C₁₀₁	—	2	1	no	—
23	C₄×C₁₀₁	D₄	1	1	yes	characteristic
24	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
25	Dic₁₀₁	—	2	1	no	—
26	C₂×C₁₀₁	—	2	1	no	—
27	C₂×C₁₀₁	—	4	1	no	—
28	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
29	D₁₀₁	—	4	1	no	—
30	C₁₀₁	#135	1	1	yes	characteristic, complemented, Sylow
31	#135	—	101	1	no	maximal, Sylow
32	#41	—	101	1	no	—
33	#41	D₁₀₁	1	1	yes	characteristic, complemented
34	Q₁₆	—	101	1	no	—
35	SD₁₆	—	101	1	no	—
36	SD₁₆	—	101	1	no	—
37	D₈	—	101	1	no	—
38	C₂×C₈	—	101	1	no	—
39	Q₈	—	101	1	no	—
40	Q₈	C₂×D₁₀₁	1	1	yes	characteristic
41	D₄	—	2	1	no	—
42	D₄	—	101	1	no	—
43	D₄	—	202	1	no	—
44	D₄	C₂×D₁₀₁	1	1	yes	characteristic
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	202	1	no	—
47	C₂×C₄	C₂×D₁₀₁	1	1	yes	characteristic
48	C₈	—	101	1	no	—
49	C₈	—	101	1	no	—
50	C₂²	—	2	1	no	—
51	C₂²	—	202	1	no	—
52	C₂²	C₂²⋊D₁₀₁	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	202	1	no	—
55	C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
56	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	—	4	1	no	—
59	C₂	—	404	1	no	—
60	C₂	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²⋊D₁₀₁
commutator, cosocle	C₄×C₁₀₁	C₂³
Frattini	C₄	C₂²×D₁₀₁
Fitting	#41×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂×D₄
hypercenter	#41	D₁₀₁
hypocenter	C₁₀₁	#135
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
1. #13108074	C₂	semidirect
2. #13108064	C₂	semidirect
3. #13108062	C₂	semidirect
4. #13108061	C₂	semidirect
5. #13108059	C₂	semidirect
6. C₂×#11717579	C₂	semidirect
7. #41×C₁₀₁	C₂	semidirect
30. C₁₀₁	#135	semidirect
33. #41	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
#13108062	2
#13108061	2
#13108059	2
C₂×#11717579	2
#41×C₁₀₁	2
#135	101