Subgroups — C₂×#24902357 #35232543

Order 21152.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₆₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#24902357	C₂	1	4	yes	maximal, direct product factor
3	C₂×#19126971	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄×C₆₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₆₁	—	2	1	no	—
6	D₂₆₄₄	—	2	1	no	—
7	D₂₆₄₄	C₂²	1	2	yes	complemented
8	#19126971	C₂²	1	2	yes	complemented
9	C₂³×C₆₆₁	—	2	1	no	—
10	D₄×C₆₆₁	—	2	1	no	—
11	D₄×C₆₆₁	C₂²	1	2	yes	complemented
12	C₂×C₄×C₆₆₁	C₂²	1	1	yes	characteristic
13	C₂²×C₆₆₁	—	2	2	no	—
14	C₂²×C₆₆₁	—	4	2	no	—
15	C₂²×C₆₆₁	D₄	1	1	yes	characteristic
16	C₂×D₆₆₁	—	2	2	no	—
17	C₂×D₆₆₁	—	4	2	no	—
18	C₄×C₆₆₁	D₄	1	1	yes	characteristic
19	C₄×C₆₆₁	C₂³	1	1	yes	characteristic
20	C₂×C₆₆₁	—	4	2	no	—
21	C₂×C₆₆₁	D₈	1	2	yes	complemented
22	C₂×C₆₆₁	C₂×D₄	1	1	yes	characteristic
23	D₆₆₁	—	4	2	no	—
24	C₆₆₁	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
25	C₂×D₈	—	661	1	no	maximal, Sylow
26	C₂×D₄	—	661	1	no	—
27	C₂×D₄	D₆₆₁	1	1	yes	characteristic, complemented
28	D₈	—	661	4	no	—
29	C₂×C₈	—	661	1	no	—
30	C₂³	—	2	1	no	—
31	C₂³	—	1322	1	no	—
32	D₄	—	2	1	no	—
33	D₄	—	1322	1	no	—
34	D₄	—	661	2	no	—
35	D₄	C₂×D₆₆₁	1	2	yes	complemented
36	C₂×C₄	C₂×D₆₆₁	1	1	yes	characteristic
37	C₈	—	661	2	no	—
38	C₂²	—	2	2	no	—
39	C₂²	—	4	2	no	—
40	C₂²	—	1322	2	no	—
41	C₂²	—	2644	2	no	—
42	C₂²	C₂²⋊D₆₆₁	1	1	yes	characteristic
43	C₄	C₂²⋊D₆₆₁	1	1	yes	characteristic
44	C₄	C₂²×D₆₆₁	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	—	2644	2	no	—
47	C₂	#24902357	1	2	yes	direct product factor
48	C₂	C₂×C₂²⋊D₆₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₆₆₁
commutator, cosocle	C₄×C₆₆₁	C₂³
Frattini	C₄	C₂²×D₆₆₁
Fitting	C₂×D₄×C₆₆₁	C₂
socle	C₂²×C₆₆₁	D₄
hypercenter	C₂×D₄	D₆₆₁
hypocenter	C₆₆₁	C₂×D₈
LCS	G ▷ C₄×C₆₆₁ ▷ C₂×C₆₆₁ ▷ C₆₆₁
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×D₂₆₄₄	C₂	semidirect
2. #24902357	C₂	direct (N × H)
3. C₂×#19126971	C₂	semidirect
4. C₂×D₄×C₆₆₁	C₂	semidirect
7. D₂₆₄₄	C₂²	semidirect
8. #19126971	C₂²	semidirect
11. D₄×C₆₆₁	C₂²	semidirect
21. C₂×C₆₆₁	D₈	semidirect
24. C₆₆₁	C₂×D₈	semidirect
27. C₂×D₄	D₆₆₁	semidirect
35. D₄	C₂×D₆₆₁	semidirect
47. C₂	#24902357	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×D₂₆₄₄	2
#24902357	2
C₂×#19126971	2
C₂×D₄×C₆₆₁	2
C₂×D₈	661

Subgroups — C2×#24902357 #35232543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#24902357 #35232543