Subgroups — (C₂×#14524194)⋊C₄ #31772679

Order 17312.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14524194	C₂	1	2	yes	maximal
2	C₂×C₄×D₅₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#14524194	—	2	2	no	—
4	C₂×#14524194	—	2	2	no	—
5	C₂×#14524194	C₄	1	4	yes	complemented
6	C₂²×D₅₄₁	C₂²	1	1	yes	characteristic
7	C₂×Dic₅₄₁	C₄	1	1	yes	characteristic, complemented
8	C₄×D₅₄₁	—	2	2	no	—
9	C₂×C₄×C₅₄₁	C₄	1	1	yes	characteristic, complemented
10	C₂²×C₅₄₁	C₂×C₄	1	1	yes	characteristic
11	C₂×D₅₄₁	C₂×C₄	1	2	yes	—
12	C₂×D₅₄₁	D₄	1	1	yes	characteristic
13	C₂×D₅₄₁	D₄	1	2	yes	—
14	C₂×D₅₄₁	Q₈	1	1	yes	characteristic
15	#14524194	—	2	4	no	—
16	C₄×C₅₄₁	—	2	1	no	—
17	Dic₅₄₁	—	2	1	no	—
18	C₂×C₅₄₁	C₄²	1	1	yes	characteristic
19	C₂×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
21	D₅₄₁	C₂²⋊C₄	1	2	yes	—
22	D₅₄₁	C₄⋊C₄	1	2	yes	—
23	C₅₄₁	#95	1	1	yes	characteristic, complemented, Sylow
24	#95	—	541	1	no	maximal, Sylow
25	C₂²×C₄	—	541	2	no	—
26	C₂²×C₄	—	541	1	no	—
27	C₂³	—	541	1	no	—
28	C₂×C₄	—	541	4	no	—
29	C₂×C₄	—	541	1	no	—
30	C₂×C₄	—	1082	2	no	—
31	C₂×C₄	—	1082	2	no	—
32	C₂×C₄	—	1082	2	no	—
33	C₂×C₄	#14524194	1	1	yes	characteristic, complemented
34	C₂²	—	541	2	no	—
35	C₂²	—	541	2	no	—
36	C₂²	—	541	1	no	—
37	C₂²	—	541	1	no	—
38	C₂²	C₂×#14524194	1	1	yes	characteristic
39	C₄	—	2	1	no	—
40	C₄	—	1082	4	no	—
41	C₄	—	1082	1	no	—
42	C₂	—	541	2	no	—
43	C₂	—	541	2	no	—
44	C₂	C₄×#14524194	1	1	yes	characteristic
45	C₂	C₂²⋊#14524194	1	1	yes	characteristic
46	C₂	C₄⋊#14524194	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#14524194
commutator	C₂×C₅₄₁	C₄²
Fitting	C₂×C₄×C₅₄₁	C₄
socle	C₂²×C₅₄₁	C₂×C₄
prime radical, cosocle	C₂²×D₅₄₁	C₂²
hypercenter	C₂×C₄	#14524194
hypocenter	C₅₄₁	#95
LCS	G ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
5. C₂×#14524194	C₄	semidirect
7. C₂×Dic₅₄₁	C₄	semidirect
9. C₂×C₄×C₅₄₁	C₄	semidirect
23. C₅₄₁	#95	semidirect
33. C₂×C₄	#14524194	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14524194	2
C₂×C₄×D₅₄₁	2
#95	541

Subgroups — (C2×#14524194)⋊C4 #31772679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#14524194)⋊C₄ #31772679