Subgroups — #15692288

Order 3232.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13108074	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₀₂	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₄₀₄	C₂	1	2	yes	maximal, complemented
4	#13108063	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
7	C₂²⋊D₁₀₁	—	2	1	no	—
8	C₂×Dic₁₀₁	—	2	1	no	—
9	D₄₀₄	C₂²	1	1	yes	characteristic
10	C₄×D₁₀₁	—	2	1	no	—
11	Dic₂₀₂	—	2	1	no	—
12	Dic₂₀₂	C₂²	1	2	yes	—
13	Dic₂₀₂	C₂²	1	1	yes	characteristic
14	C₈×C₁₀₁	C₂²	1	2	yes	—
15	C₂²×C₁₀₁	D₄	1	1	yes	characteristic
16	C₂×D₁₀₁	—	2	1	no	—
17	C₄×C₁₀₁	D₄	1	1	yes	characteristic
18	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
19	Dic₁₀₁	—	2	2	no	—
20	Dic₁₀₁	—	2	1	no	—
21	C₂×C₁₀₁	—	2	1	no	—
22	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
23	D₁₀₁	—	4	1	no	—
24	C₁₀₁	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	101	1	no	maximal, Sylow
26	#41	—	101	1	no	—
27	C₂×Q₈	—	101	1	no	—
28	Q₁₆	—	101	2	no	—
29	SD₁₆	—	101	2	no	—
30	M₁₆	D₁₀₁	1	1	yes	characteristic, complemented
31	Q₈	—	101	2	no	—
32	Q₈	—	101	1	no	—
33	Q₈	—	202	1	no	—
34	D₄	—	101	1	no	—
35	D₄	—	202	1	no	—
36	C₂×C₄	—	202	1	no	—
37	C₂×C₄	—	202	1	no	—
38	C₂×C₄	C₂×D₁₀₁	1	1	yes	characteristic
39	C₈	C₂×D₁₀₁	1	2	yes	—
40	C₂²	—	202	1	no	—
41	C₂²	D₄₀₄	1	1	yes	characteristic
42	C₄	—	202	1	no	—
43	C₄	—	202	2	no	—
44	C₄	D₄₀₄	1	1	yes	characteristic
45	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	404	1	no	—
48	C₂	C₂×D₄₀₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄₀₄
commutator, cosocle	C₄×C₁₀₁	C₂³
Frattini	C₄	C₂²×D₁₀₁
Fitting	M₁₆×C₁₀₁	C₂
socle	C₂×C₁₀₁	C₂×D₄
prime radical	#13108074	C₂
hypercenter	M₁₆	D₁₀₁
hypocenter	C₁₀₁	#137
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₀₂	C₂	semidirect
3. Dic₄₀₄	C₂	semidirect
4. #13108063	C₂	semidirect
5. M₁₆×C₁₀₁	C₂	semidirect
24. C₁₀₁	#137	semidirect
30. M₁₆	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
C₂×Dic₂₀₂	2
Dic₄₀₄	2
#13108063	2
M₁₆×C₁₀₁	2
#137	101