Subgroups — #15692254

Order 3232.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₀₂	C₂	1	2	yes	maximal
2	C₄⋊Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	#13108053	C₂	1	2	yes	maximal
4	C₄×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
5	C₄⋊C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₀₁	C₂²	1	2	yes	—
7	C₂×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₀₁	C₂²	1	2	yes	—
9	C₂×Dic₁₀₁	C₂²	1	1	yes	characteristic
10	C₂×Dic₁₀₁	C₂²	1	1	yes	characteristic
11	Dic₂₀₂	—	2	4	no	—
12	C₂²×C₁₀₁	C₂³	1	1	yes	characteristic
13	C₄×C₁₀₁	—	2	2	no	—
14	C₄×C₁₀₁	Q₈	1	2	yes	complemented
15	Dic₁₀₁	—	2	2	no	—
16	Dic₁₀₁	D₄	1	2	yes	—
17	Dic₁₀₁	Q₈	1	2	yes	complemented
18	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
19	C₂×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
21	C₁₀₁	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊Q₈	—	101	1	no	maximal, Sylow
23	C₂×Q₈	—	101	2	no	—
24	C₄⋊C₄	—	101	2	no	—
25	C₄⋊C₄	—	101	1	no	—
26	C₄⋊C₄	D₁₀₁	1	1	yes	characteristic
27	C₄²	—	101	1	no	—
28	Q₈	—	202	4	no	—
29	C₂×C₄	—	101	1	no	—
30	C₂×C₄	—	101	1	no	—
31	C₂×C₄	—	101	2	no	—
32	C₂×C₄	C₂×D₁₀₁	1	2	yes	—
33	C₂×C₄	C₂×D₁₀₁	1	1	yes	characteristic
34	C₂²	C₂²×D₁₀₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	101	2	no	—
37	C₄	—	101	2	no	—
38	C₄	—	202	2	no	—
39	C₄	Dic₂₀₂	1	2	yes	complemented
40	C₂	D₄×D₁₀₁	1	1	yes	characteristic
41	C₂	Q₈×D₁₀₁	1	1	yes	characteristic
42	C₂	C₂×Dic₂₀₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₁₀₁
commutator, socle, prime radical, cosocle	C₂²×C₁₀₁	C₂³
Fitting	C₄⋊C₄×C₁₀₁	C₂
hypercenter	C₄⋊C₄	D₁₀₁
hypocenter	C₁₀₁	C₄⋊Q₈
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
14. C₄×C₁₀₁	Q₈	semidirect
17. Dic₁₀₁	Q₈	semidirect
21. C₁₀₁	C₄⋊Q₈	semidirect
39. C₄	Dic₂₀₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₂₀₂	2
C₄⋊Dic₁₀₁	2
#13108053	2
C₄×Dic₁₀₁	2
C₄⋊C₄×C₁₀₁	2
C₄⋊Q₈	101