Subgroups — D₁₀₁⋊M₃₂ #20266233

Order 6464.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15692330	C₂	1	2	yes	maximal, complemented
2	#15692329	C₂	1	2	yes	maximal, complemented
3	D₁₀₁⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×D₁₀₁	C₂	1	1	yes	maximal, characteristic
5	#13108077	C₂²	1	4	yes	complemented
6	C₂×C₄×D₁₀₁	C₄	1	1	yes	characteristic
7	C₂×#11717579	C₂²	1	1	yes	characteristic
8	C₈×D₁₀₁	C₄	1	1	yes	characteristic
9	C₈×D₁₀₁	C₄	1	1	yes	characteristic
10	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
11	C₈×D₁₀₁	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₀₁	C₄	1	1	yes	characteristic
13	C₂²×D₁₀₁	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₁₀₁	C₈	1	1	yes	characteristic
16	C₄×D₁₀₁	C₈	1	1	yes	characteristic
17	C₄×D₁₀₁	C₈	1	1	yes	characteristic
18	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
19	C₄×D₁₀₁	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
22	#11717579	C₂×C₄	1	1	yes	characteristic
23	#11717579	C₂³	1	1	yes	characteristic
24	C₂²×C₁₀₁	C₂×C₈	1	1	yes	characteristic
25	C₂×D₁₀₁	—	2	2	no	—
26	C₂×D₁₀₁	C₂×C₈	1	1	yes	characteristic
27	C₂×D₁₀₁	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₀₁	C₂×C₈	1	1	yes	characteristic
31	Dic₁₀₁	C₂×C₈	1	1	yes	characteristic
32	C₂×C₁₀₁	—	2	1	no	—
33	C₂×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
34	D₁₀₁	—	2	1	no	—
35	D₁₀₁	M₃₂	1	2	yes	complemented
36	C₁₀₁	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
37	C₂×M₃₂	—	101	1	no	maximal, Sylow
38	C₂²×C₈	—	101	1	no	—
39	M₃₂	—	101	2	no	—
40	M₃₂	—	101	2	no	—
41	C₂×C₁₆	—	101	2	no	—
42	C₂²×C₄	—	101	1	no	—
43	C₂×C₈	—	101	1	no	—
44	C₂×C₈	—	101	1	no	—
45	C₂×C₈	—	101	1	no	—
46	C₂×C₈	—	101	1	no	—
47	C₂×C₈	—	101	1	no	—
48	C₂×C₈	#87938	1	1	yes	characteristic
49	C₁₆	—	101	4	no	—
50	C₂³	—	101	1	no	—
51	C₂×C₄	—	101	1	no	—
52	C₂×C₄	—	101	1	no	—
53	C₂×C₄	—	101	1	no	—
54	C₂×C₄	—	101	1	no	—
55	C₂×C₄	—	101	1	no	—
56	C₂×C₄	C₂×#87938	1	1	yes	characteristic
57	C₈	—	101	1	no	—
58	C₈	—	101	1	no	—
59	C₈	C₂×#87938	1	1	yes	characteristic
60	C₈	C₂×#87938	1	1	yes	characteristic
61	C₂²	—	101	1	no	—
62	C₂²	—	101	1	no	—
63	C₂²	—	202	2	no	—
64	C₂²	D₁₀₁⋊C₈	1	1	yes	characteristic
65	C₄	—	101	1	no	—
66	C₄	—	101	1	no	—
67	C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
68	C₄	C₂²×#87938	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	101	2	no	—
71	C₂	—	202	1	no	—
72	C₂	C₂×D₁₀₁⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#87938
commutator, socle	C₂×C₁₀₁	C₂²×C₈
Frattini	C₄	C₂²×#87938
Fitting	C₂×C₈×C₁₀₁	C₄
hypercenter	C₂×C₈	#87938
hypocenter	C₁₀₁	C₂×M₃₂
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #15692330	C₂	semidirect
2. #15692329	C₂	semidirect
3. D₁₀₁⋊C₁₆	C₂	semidirect
5. #13108077	C₂²	semidirect
35. D₁₀₁	M₃₂	semidirect
36. C₁₀₁	C₂×M₃₂	semidirect

Subgroups — D101⋊M32 #20266233

Conjugacy classes of subgroups

Complements

Subgroups — D₁₀₁⋊M₃₂ #20266233