Subgroups — #27186248

Order 12928.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266109	C₂	1	2	yes	maximal, complemented
2	C₂×#15692194	C₂	1	1	yes	maximal, characteristic
3	#15692305	—	2	2	no	—
4	C₂×C₈×D₁₀₁	C₄	1	1	yes	characteristic
5	#15692194	—	2	2	no	—
6	C₂×#13108049	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₁₀₁	C₄	1	1	yes	characteristic
8	C₂×C₄×D₁₀₁	C₈	1	1	yes	characteristic
9	C₂×#11717579	C₈	1	1	yes	characteristic
10	C₈×D₁₀₁	—	2	1	no	—
11	C₈×D₁₀₁	—	2	1	no	—
12	#13108049	D₄	1	2	yes	—
13	C₂×C₈×C₁₀₁	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₁₀₁	—	2	1	no	—
15	C₂²×D₁₀₁	C₁₆	1	1	yes	characteristic
16	C₂×C₄×C₁₀₁	C₂×C₈	1	1	yes	characteristic
17	C₂×Dic₁₀₁	C₁₆	1	1	yes	characteristic
18	C₄×D₁₀₁	—	2	1	no	—
19	C₄×D₁₀₁	—	2	1	no	—
20	C₈×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₈×C₁₀₁	M₁₆	1	1	yes	characteristic
22	#11717579	—	2	1	no	—
23	C₂²×C₁₀₁	C₂×C₁₆	1	1	yes	characteristic
24	C₂×D₁₀₁	—	2	1	no	—
25	C₂×D₁₀₁	—	4	1	no	—
26	C₄×C₁₀₁	C₂²⋊C₈	1	1	yes	characteristic
27	C₄×C₁₀₁	M₃₂	1	1	yes	characteristic
28	Dic₁₀₁	—	2	1	no	—
29	C₂×C₁₀₁	—	2	1	no	—
30	C₂×C₁₀₁	C₂²⋊C₁₆	1	1	yes	characteristic
31	D₁₀₁	—	4	1	no	—
32	#1400	—	101	1	no	maximal, Sylow
33	C₁₀₁	#1400	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₃₂	—	101	1	no	—
35	M₆₄	—	101	2	no	—
36	C₂²×C₈	—	101	1	no	—
37	M₃₂	—	202	2	no	—
38	C₂×C₁₆	—	101	1	no	—
39	C₂×C₁₆	#87938	1	1	yes	characteristic
40	C₃₂	—	202	2	no	—
41	C₂²×C₄	—	101	1	no	—
42	C₂×C₈	—	101	1	no	—
43	C₂×C₈	—	202	1	no	—
44	C₂×C₈	—	202	1	no	—
45	C₂×C₈	C₂×#87938	1	1	yes	characteristic
46	C₁₆	—	2	1	no	—
47	C₁₆	—	101	2	no	—
48	C₂³	—	101	1	no	—
49	C₂×C₄	—	101	1	no	—
50	C₂×C₄	—	202	1	no	—
51	C₂×C₄	—	202	1	no	—
52	C₂×C₄	D₁₀₁⋊C₈	1	1	yes	characteristic
53	C₈	—	202	1	no	—
54	C₈	C₂²⋊#87938	1	1	yes	characteristic
55	C₈	#13108084	1	1	yes	characteristic
56	C₂²	—	404	1	no	—
57	C₂²	—	202	1	no	—
58	C₂²	D₁₀₁⋊C₁₆	1	1	yes	characteristic
59	C₄	—	202	1	no	—
60	C₄	#15692312	1	1	yes	characteristic
61	C₄	#15692330	1	1	yes	characteristic
62	C₂	—	2	1	no	—
63	C₂	—	404	1	no	—
64	C₂	#20266072	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²⋊#87938
commutator	C₂²×C₁₀₁	C₂×C₁₆
Frattini	C₂×C₈	C₂×#87938
Fitting	C₂×C₁₆×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₂²⋊C₁₆
prime radical	C₂²×D₁₀₁	C₁₆
cosocle	C₂×#13108049	C₂²
hypercenter	C₂×C₁₆	#87938
hypocenter	C₁₀₁	#1400
LCS	G ▷ C₂²×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
1. #20266109	C₂	semidirect
33. C₁₀₁	#1400	semidirect

Maximal subgroups

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

subgroup	index
#20266109	2
C₂×#15692194	2
#1400	101