Subgroups — #27187556

Order 12928.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266110	C₂	1	2	yes	maximal, complemented
2	#20266109	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₀₁⋊C₃₂	C₂	1	2	yes	maximal, complemented
4	C₂×#15692305	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265595	C₂	1	1	yes	maximal, characteristic
6	#15692305	C₂²	1	1	yes	characteristic
7	#15692305	C₂²	1	1	yes	characteristic
8	#15692305	C₂²	1	2	yes	—
9	#15692261	C₄	1	1	yes	characteristic
10	#15692194	C₄	1	2	yes	—
11	C₂×#13108049	C₂²	1	1	yes	characteristic
12	C₁₆×D₁₀₁	C₂²	1	2	yes	—
13	M₃₂×C₁₀₁	C₄	1	1	yes	characteristic
14	#13108074	C₈	1	1	yes	characteristic
15	#13108058	C₈	1	1	yes	characteristic
16	#13108057	C₈	1	2	yes	—
17	C₈×D₁₀₁	C₂×C₄	1	2	yes	—
18	#13108049	C₂×C₄	1	1	yes	characteristic
19	#13108049	C₂³	1	1	yes	characteristic
20	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
21	C₁₆×C₁₀₁	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
23	C₂²⋊D₁₀₁	C₁₆	1	2	yes	—
24	D₄₀₄	C₁₆	1	1	yes	characteristic
25	C₄×D₁₀₁	C₂×C₈	1	2	yes	—
26	Dic₂₀₂	C₁₆	1	1	yes	characteristic
27	C₈×C₁₀₁	C₂×C₈	1	1	yes	characteristic
28	C₈×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
29	#11717579	C₂×C₈	1	2	yes	—
30	C₂²×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
31	C₂×D₁₀₁	C₂×C₁₆	1	2	yes	—
32	C₄×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
33	C₄×C₁₀₁	C₂²×C₈	1	1	yes	characteristic
34	Dic₁₀₁	C₂×C₁₆	1	2	yes	—
35	C₂×C₁₀₁	—	2	1	no	—
36	C₂×C₁₀₁	C₂²×C₁₆	1	1	yes	characteristic
37	D₁₀₁	—	2	2	no	—
38	#2258	—	101	1	no	maximal, Sylow
39	C₁₀₁	#2258	1	1	yes	characteristic, complemented, Sylow
40	#504	—	101	1	no	—
41	M₆₄	—	101	1	no	—
42	M₆₄	—	101	2	no	—
43	C₂×C₃₂	—	101	1	no	—
44	C₂×C₃₂	—	101	2	no	—
45	#131	—	101	1	no	—
46	M₃₂	—	101	2	no	—
47	M₃₂	#87938	1	1	yes	characteristic
48	C₂×C₁₆	—	101	1	no	—
49	C₂×C₁₆	—	101	2	no	—
50	C₃₂	—	101	1	no	—
51	C₃₂	—	101	1	no	—
52	C₃₂	—	101	2	no	—
53	#41	—	101	1	no	—
54	M₁₆	—	101	1	no	—
55	M₁₆	—	101	2	no	—
56	C₂×C₈	—	101	2	no	—
57	C₂×C₈	C₂×#87938	1	1	yes	characteristic
58	C₁₆	—	101	1	no	—
59	C₁₆	—	101	1	no	—
60	C₁₆	C₂×#87938	1	2	yes	—
61	Q₈	—	101	1	no	—
62	D₄	—	101	2	no	—
63	D₄	—	101	1	no	—
64	C₂×C₄	—	101	2	no	—
65	C₂×C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
66	C₈	—	101	2	no	—
67	C₈	D₁₀₁⋊C₈	1	1	yes	characteristic
68	C₈	C₂²×#87938	1	1	yes	characteristic
69	C₂²	—	101	2	no	—
70	C₂²	D₁₀₁⋊C₁₆	1	1	yes	characteristic
71	C₄	—	101	2	no	—
72	C₄	D₁₀₁⋊C₁₆	1	1	yes	characteristic
73	C₄	C₂×D₁₀₁⋊C₈	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	202	2	no	—
76	C₂	C₂×D₁₀₁⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#87938
commutator, socle	C₂×C₁₀₁	C₂²×C₁₆
Fitting	M₃₂×C₁₀₁	C₄
prime radical	#13108074	C₈
cosocle	#13108049	C₂³
hypercenter	M₃₂	#87938
hypocenter	C₁₀₁	#2258
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #20266110	C₂	semidirect
2. #20266109	C₂	semidirect
3. D₁₀₁⋊C₃₂	C₂	semidirect
4. C₂×#15692305	C₂	semidirect
39. C₁₀₁	#2258	semidirect

Maximal subgroups

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

subgroup	index
#20266110	2
#20266109	2
D₁₀₁⋊C₃₂	2
C₂×#15692305	2
#20265595	2
#2258	101