Subgroups — C₂×C₄⋊Dic₁₀₁ #15692210

Order 3232.

92 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀₁	C₂	1	2	yes	maximal
2	C₄⋊Dic₁₀₁	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₁₀₁	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₁₀₁	C₄	1	4	yes	complemented
6	C₂×C₄×C₁₀₁	C₂²	1	2	yes	—
7	C₂×Dic₁₀₁	—	2	4	no	—
8	C₂×Dic₁₀₁	C₂²	1	4	yes	—
9	C₂²×C₁₀₁	C₂×C₄	1	2	yes	—
10	C₂²×C₁₀₁	D₄	1	2	yes	—
11	C₂²×C₁₀₁	Q₈	1	2	yes	—
12	C₂²×C₁₀₁	C₂³	1	1	yes	characteristic
13	C₄×C₁₀₁	C₂×C₄	1	4	yes	complemented
14	Dic₁₀₁	—	2	4	no	—
15	C₂×C₁₀₁	C₄⋊C₄	1	4	yes	complemented
16	C₂×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
18	C₂×C₁₀₁	C₂×Q₈	1	1	yes	characteristic
19	C₁₀₁	C₂×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₄⋊C₄	—	101	1	no	maximal, Sylow
21	C₂²×C₄	—	101	2	no	—
22	C₂²×C₄	D₁₀₁	1	1	yes	characteristic
23	C₄⋊C₄	—	101	4	no	—
24	C₂³	C₂×D₁₀₁	1	1	yes	characteristic
25	C₂×C₄	—	101	4	no	—
26	C₂×C₄	—	202	4	no	—
27	C₂×C₄	Dic₁₀₁	1	4	yes	complemented
28	C₂×C₄	C₂×D₁₀₁	1	2	yes	—
29	C₂²	Dic₂₀₂	1	2	yes	—
30	C₂²	D₄₀₄	1	2	yes	—
31	C₂²	C₂×Dic₁₀₁	1	2	yes	—
32	C₂²	C₂²×D₁₀₁	1	1	yes	characteristic
33	C₄	—	202	4	no	—
34	C₄	C₂×Dic₁₀₁	1	4	yes	complemented
35	C₂	C₄⋊Dic₁₀₁	1	4	yes	direct product factor
36	C₂	C₂²×Dic₁₀₁	1	1	yes	characteristic
37	C₂	C₂×D₄₀₄	1	1	yes	characteristic
38	C₂	C₂×Dic₂₀₂	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄⋊Dic₁₀₁	C₂	direct (N × H)
5. C₂×C₄×C₁₀₁	C₄	semidirect
13. C₄×C₁₀₁	C₂×C₄	semidirect
15. C₂×C₁₀₁	C₄⋊C₄	semidirect
19. C₁₀₁	C₂×C₄⋊C₄	semidirect
27. C₂×C₄	Dic₁₀₁	semidirect
34. C₄	C₂×Dic₁₀₁	semidirect
35. C₂	C₄⋊Dic₁₀₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₀₁	2
C₄⋊Dic₁₀₁	2
C₂²×C₄×C₁₀₁	2
C₂×C₄⋊C₄	101

Subgroups — C2×C4⋊Dic101 #15692210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊Dic₁₀₁ #15692210