Subgroups — C₂×#13108059 #15692265

Order 3232.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#13108059	C₂	1	4	yes	maximal, direct product factor
3	C₂×#11717579	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₀₁	—	2	1	no	—
6	C₂²×D₁₀₁	—	2	1	no	—
7	D₄×C₁₀₁	—	2	1	no	—
8	D₄×C₁₀₁	C₂²	1	2	yes	complemented
9	C₂×C₄×C₁₀₁	C₂²	1	1	yes	characteristic
10	D₄₀₄	—	2	1	no	—
11	D₄₀₄	C₂²	1	2	yes	complemented
12	#11717579	C₂²	1	2	yes	complemented
13	C₂²×C₁₀₁	—	2	2	no	—
14	C₂²×C₁₀₁	—	4	2	no	—
15	C₂²×C₁₀₁	D₄	1	1	yes	characteristic
16	C₂×D₁₀₁	—	2	2	no	—
17	C₂×D₁₀₁	—	4	2	no	—
18	C₄×C₁₀₁	D₄	1	1	yes	characteristic
19	C₄×C₁₀₁	C₂³	1	1	yes	characteristic
20	C₂×C₁₀₁	—	4	2	no	—
21	C₂×C₁₀₁	D₈	1	2	yes	complemented
22	C₂×C₁₀₁	C₂×D₄	1	1	yes	characteristic
23	D₁₀₁	—	4	2	no	—
24	C₁₀₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₈	—	101	1	no	maximal, Sylow
26	C₂×D₄	—	101	1	no	—
27	C₂×D₄	D₁₀₁	1	1	yes	characteristic, complemented
28	D₈	—	101	4	no	—
29	C₂×C₈	—	101	1	no	—
30	C₂³	—	2	1	no	—
31	C₂³	—	202	1	no	—
32	D₄	—	2	1	no	—
33	D₄	—	101	2	no	—
34	D₄	—	202	1	no	—
35	D₄	C₂×D₁₀₁	1	2	yes	complemented
36	C₂×C₄	C₂×D₁₀₁	1	1	yes	characteristic
37	C₈	—	101	2	no	—
38	C₂²	—	2	2	no	—
39	C₂²	—	4	2	no	—
40	C₂²	—	404	2	no	—
41	C₂²	—	202	2	no	—
42	C₂²	C₂²⋊D₁₀₁	1	1	yes	characteristic
43	C₄	C₂²⋊D₁₀₁	1	1	yes	characteristic
44	C₄	C₂²×D₁₀₁	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	—	404	2	no	—
47	C₂	#13108059	1	2	yes	direct product factor
48	C₂	C₂×C₂²⋊D₁₀₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₁₀₁
commutator, cosocle	C₄×C₁₀₁	C₂³
Frattini	C₄	C₂²×D₁₀₁
Fitting	C₂×D₄×C₁₀₁	C₂
socle	C₂²×C₁₀₁	D₄
hypercenter	C₂×D₄	D₁₀₁
hypocenter	C₁₀₁	C₂×D₈
LCS	G ▷ C₄×C₁₀₁ ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₄₀₄	C₂	semidirect
2. #13108059	C₂	direct (N × H)
3. C₂×#11717579	C₂	semidirect
4. C₂×D₄×C₁₀₁	C₂	semidirect
8. D₄×C₁₀₁	C₂²	semidirect
11. D₄₀₄	C₂²	semidirect
12. #11717579	C₂²	semidirect
21. C₂×C₁₀₁	D₈	semidirect
24. C₁₀₁	C₂×D₈	semidirect
27. C₂×D₄	D₁₀₁	semidirect
35. D₄	C₂×D₁₀₁	semidirect
47. C₂	#13108059	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₄₀₄	2
#13108059	2
C₂×#11717579	2
C₂×D₄×C₁₀₁	2
C₂×D₈	101

Subgroups — C2×#13108059 #15692265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13108059 #15692265