Subgroups — #15692317

Order 3232.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₀₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#87938	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₁₀₁	—	2	1	no	—
5	C₂×#87938	—	2	1	no	—
6	D₄×C₁₀₁	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊D₁₀₁	—	2	1	no	—
8	D₄₀₄	C₄	1	1	yes	characteristic, complemented
9	C₄×D₁₀₁	C₂²	1	1	yes	characteristic
10	#11717581	—	2	1	no	—
11	C₂²×C₁₀₁	—	2	1	no	—
12	C₂×D₁₀₁	—	2	1	no	—
13	C₂×D₁₀₁	—	4	1	no	—
14	C₂×D₁₀₁	—	4	1	no	—
15	C₂×D₁₀₁	D₄	1	1	yes	characteristic
16	#87938	—	4	1	no	—
17	C₄×C₁₀₁	C₂×C₄	1	1	yes	characteristic
18	Dic₁₀₁	D₄	1	1	yes	characteristic
19	C₂×C₁₀₁	—	4	1	no	—
20	C₂×C₁₀₁	C₂²⋊C₄	1	1	yes	characteristic
21	D₁₀₁	—	4	1	no	—
22	D₁₀₁	D₈	1	1	yes	characteristic
23	D₁₀₁	SD₁₆	1	1	yes	characteristic
24	C₁₀₁	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	101	1	no	maximal, Sylow
26	C₂×D₄	—	101	1	no	—
27	C₂×C₈	—	101	1	no	—
28	C₄⋊C₄	—	101	1	no	—
29	C₂³	—	202	1	no	—
30	D₄	—	101	1	no	—
31	D₄	—	202	1	no	—
32	D₄	#87938	1	1	yes	characteristic, complemented
33	C₂×C₄	—	101	1	no	—
34	C₂×C₄	—	202	1	no	—
35	C₈	—	202	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	101	1	no	—
38	C₂²	—	404	1	no	—
39	C₂²	—	404	1	no	—
40	C₂²	—	202	1	no	—
41	C₄	—	101	1	no	—
42	C₄	—	404	1	no	—
43	C₄	C₂×#87938	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	101	1	no	—
46	C₂	—	101	1	no	—
47	C₂	—	404	1	no	—
48	C₂	C₂²⋊#87938	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#87938
commutator	C₄×C₁₀₁	C₂×C₄
Frattini	C₄	C₂×#87938
Fitting	D₄×C₁₀₁	C₄
socle	C₂×C₁₀₁	C₂²⋊C₄
prime radical	D₄×D₁₀₁	C₂
cosocle	C₄×D₁₀₁	C₂²
hypercenter	D₄	#87938
hypocenter	C₁₀₁	#102
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. D₁₀₁⋊C₈	C₂	semidirect
2. C₄⋊#87938	C₂	semidirect
6. D₄×C₁₀₁	C₄	semidirect
8. D₄₀₄	C₄	semidirect
24. C₁₀₁	#102	semidirect
32. D₄	#87938	semidirect

Maximal subgroups

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

subgroup	index
D₁₀₁⋊C₈	2
C₄⋊#87938	2
D₄×D₁₀₁	2
#102	101