Subgroups — C₄×D₂₆₁₂ #35229691

Order 20896.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₆₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₆₅₃	C₂	1	2	yes	maximal, complemented
3	C₄⋊Dic₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#23782582	C₂	1	2	yes	maximal, complemented
5	C₄²×C₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₆₅₃	C₂²	1	2	yes	—
7	D₂₆₁₂	C₄	1	4	yes	direct product factor
8	C₂×Dic₆₅₃	C₂²	1	2	yes	—
9	C₄×D₆₅₃	—	2	4	no	—
10	C₂×C₄×C₆₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₆₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₆₅₃	C₂²	1	1	yes	characteristic
13	C₂²×C₆₅₃	C₂³	1	1	yes	characteristic
14	C₂×D₆₅₃	—	2	2	no	—
15	C₂×D₆₅₃	—	2	2	no	—
16	C₂×D₆₅₃	C₂×C₄	1	4	yes	complemented
17	C₄×C₆₅₃	—	2	1	no	—
18	C₄×C₆₅₃	C₂×C₄	1	2	yes	complemented
19	C₄×C₆₅₃	D₄	1	2	yes	complemented
20	Dic₆₅₃	—	2	2	no	—
21	C₂×C₆₅₃	C₂²×C₄	1	1	yes	characteristic
22	C₂×C₆₅₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₆₅₃	#41	1	1	yes	characteristic
24	D₆₅₃	—	2	4	no	—
25	C₆₅₃	C₄×D₄	1	1	yes	characteristic, complemented, Sylow
26	C₄×D₄	—	653	1	no	maximal, Sylow
27	C₂×D₄	—	653	1	no	—
28	C₂²×C₄	—	653	2	no	—
29	C₄⋊C₄	—	653	1	no	—
30	C₂²⋊C₄	—	653	2	no	—
31	C₄²	D₆₅₃	1	1	yes	characteristic, complemented
32	C₂³	—	653	2	no	—
33	D₄	—	653	4	no	—
34	C₂×C₄	—	1306	4	no	—
35	C₂×C₄	—	653	2	no	—
36	C₂×C₄	C₂×D₆₅₃	1	1	yes	characteristic
37	C₂×C₄	C₂×D₆₅₃	1	1	yes	characteristic
38	C₂×C₄	C₂×D₆₅₃	1	1	yes	characteristic
39	C₂²	—	1306	2	no	—
40	C₂²	—	1306	2	no	—
41	C₂²	—	653	4	no	—
42	C₂²	C₂²×D₆₅₃	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	1306	2	no	—
45	C₄	C₄×D₆₅₃	1	2	yes	complemented
46	C₄	D₂₆₁₂	1	2	yes	direct product factor
47	C₂	—	1306	4	no	—
48	C₂	C₂×C₄×D₆₅₃	1	1	yes	characteristic
49	C₂	C₂×D₂₆₁₂	1	1	yes	characteristic
50	C₂	#23782605	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₅₃
commutator	C₂×C₆₅₃	C₂²×C₄
Frattini	C₂²	C₂²×D₆₅₃
Fitting	C₄²×C₆₅₃	C₂
socle, cosocle	C₂²×C₆₅₃	C₂³
prime radical	C₂×D₂₆₁₂	C₂
hypercenter	C₄²	D₆₅₃
hypocenter	C₆₅₃	C₄×D₄
LCS	G ▷ C₂×C₆₅₃ ▷ C₆₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₆₅₃	C₂	semidirect
3. C₄⋊Dic₆₅₃	C₂	semidirect
4. #23782582	C₂	semidirect
5. C₄²×C₆₅₃	C₂	semidirect
7. D₂₆₁₂	C₄	direct (N × H)
16. C₂×D₆₅₃	C₂×C₄	semidirect
18. C₄×C₆₅₃	C₂×C₄	semidirect
19. C₄×C₆₅₃	D₄	semidirect
25. C₆₅₃	C₄×D₄	semidirect
31. C₄²	D₆₅₃	semidirect
45. C₄	C₄×D₆₅₃	semidirect
46. C₄	D₂₆₁₂	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×D₂₆₁₂	2
C₂×C₄×D₆₅₃	2
C₄⋊Dic₆₅₃	2
#23782582	2
C₄²×C₆₅₃	2
C₄×D₄	653

Subgroups — C4×D2612 #35229691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₂₆₁₂ #35229691