Subgroups — C₂×#6104 #88185

Order 416.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#6104	C₂	1	4	yes	maximal, direct product factor
4	C₂×#1055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₁₃	—	2	1	no	—
6	C₂²×D₁₃	—	2	1	no	—
7	D₄×C₁₃	—	2	1	no	—
8	D₄×C₁₃	C₂²	1	2	yes	complemented
9	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	D₅₂	—	2	1	no	—
11	D₅₂	C₂²	1	2	yes	complemented
12	#1055	C₂²	1	2	yes	complemented
13	C₂²×C₁₃	—	2	2	no	—
14	C₂²×C₁₃	—	4	2	no	—
15	C₂²×C₁₃	D₄	1	1	yes	characteristic
16	C₂×D₁₃	—	2	2	no	—
17	C₂×D₁₃	—	4	2	no	—
18	C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₄×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×D₈	—	13	1	no	maximal, Sylow
21	C₂×C₁₃	—	4	2	no	—
22	C₂×C₁₃	D₈	1	2	yes	complemented
23	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
24	D₁₃	—	4	2	no	—
25	C₂×D₄	—	13	1	no	—
26	C₂×D₄	D₁₃	1	1	yes	characteristic, complemented
27	D₈	—	13	4	no	—
28	C₂×C₈	—	13	1	no	—
29	C₁₃	C₂×D₈	1	1	yes	characteristic, complemented, Sylow
30	C₂³	—	2	1	no	—
31	C₂³	—	26	1	no	—
32	D₄	—	2	1	no	—
33	D₄	—	13	2	no	—
34	D₄	—	26	1	no	—
35	D₄	C₂×D₁₃	1	2	yes	complemented
36	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
37	C₈	—	13	2	no	—
38	C₂²	—	2	2	no	—
39	C₂²	—	4	2	no	—
40	C₂²	—	26	2	no	—
41	C₂²	—	52	2	no	—
42	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
43	C₄	C₂²⋊D₁₃	1	1	yes	characteristic
44	C₄	C₂²×D₁₃	1	1	yes	characteristic
45	C₂	—	4	2	no	—
46	C₂	—	52	2	no	—
47	C₂	#6104	1	2	yes	direct product factor
48	C₂	C₂×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₁₃
commutator, cosocle	C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₁₃
Fitting	C₂×D₄×C₁₃	C₂
socle	C₂²×C₁₃	D₄
hypercenter	C₂×D₄	D₁₃
hypocenter	C₁₃	C₂×D₈
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
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×D₄×C₁₃	C₂	semidirect
2. C₂×D₅₂	C₂	semidirect
3. #6104	C₂	direct (N × H)
4. C₂×#1055	C₂	semidirect
8. D₄×C₁₃	C₂²	semidirect
11. D₅₂	C₂²	semidirect
12. #1055	C₂²	semidirect
22. C₂×C₁₃	D₈	semidirect
26. C₂×D₄	D₁₃	semidirect
29. C₁₃	C₂×D₈	semidirect
35. D₄	C₂×D₁₃	semidirect
47. C₂	#6104	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×D₄×C₁₃	2
C₂×D₅₂	2
#6104	2
C₂×#1055	2
C₂×D₈	13

Subgroups — C2×#6104 #88185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#6104 #88185