Subgroups — C₂²⋊#14268661 #20299724

Order 7232.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268661	C₂	1	2	yes	maximal, complemented
2	C₂²×#11744762	C₂	1	1	yes	maximal, characteristic
3	#14268661	—	2	2	no	—
4	C₂×#11744762	—	2	2	no	—
5	C₂×#11744762	C₄	1	1	yes	characteristic
6	C₂×#11744762	C₂²	1	1	yes	characteristic
7	C₂²×#90673	C₄	1	1	yes	characteristic
8	C₂²×D₁₁₃	C₈	1	1	yes	characteristic
9	C₂×#90673	—	2	1	no	—
10	C₂×#90673	—	2	1	no	—
11	C₂×#90673	C₈	1	1	yes	characteristic
12	C₂×#90673	C₂×C₄	1	1	yes	characteristic
13	#11744762	—	2	1	no	—
14	#11744762	D₄	1	2	yes	—
15	C₂²×C₁₁₃	C₁₆	1	1	yes	characteristic, complemented
16	C₂×D₁₁₃	—	2	1	no	—
17	C₂×D₁₁₃	—	2	1	no	—
18	C₂×D₁₁₃	C₁₆	1	1	yes	characteristic, complemented
19	C₂×D₁₁₃	C₂×C₈	1	1	yes	characteristic
20	#90673	—	2	1	no	—
21	#90673	C₂²⋊C₄	1	1	yes	characteristic
22	#90673	M₁₆	1	1	yes	characteristic
23	C₂×C₁₁₃	—	2	1	no	—
24	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
25	D₁₁₃	—	2	1	no	—
26	D₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
27	D₁₁₃	M₃₂	1	1	yes	characteristic
28	C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²⋊C₁₆	—	113	1	no	maximal, Sylow
30	C₂²×C₈	—	113	1	no	—
31	C₂×C₁₆	—	113	2	no	—
32	C₂²×C₄	—	113	1	no	—
33	C₂×C₈	—	113	1	no	—
34	C₂×C₈	—	113	1	no	—
35	C₂×C₈	—	226	2	no	—
36	C₁₆	—	226	2	no	—
37	C₂³	—	113	1	no	—
38	C₂×C₄	—	113	1	no	—
39	C₂×C₄	—	113	1	no	—
40	C₂×C₄	—	226	1	no	—
41	C₂×C₄	—	226	1	no	—
42	C₈	—	113	2	no	—
43	C₈	—	226	1	no	—
44	C₂²	—	113	1	no	—
45	C₂²	—	113	1	no	—
46	C₂²	—	226	1	no	—
47	C₂²	—	226	1	no	—
48	C₂²	#14268661	1	1	yes	characteristic, complemented
49	C₄	—	113	1	no	—
50	C₄	—	113	1	no	—
51	C₄	—	226	1	no	—
52	C₂	—	2	1	no	—
53	C₂	—	113	1	no	—
54	C₂	—	113	1	no	—
55	C₂	—	226	1	no	—
56	C₂	C₂×#14268661	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#14268661
commutator, socle	C₂×C₁₁₃	C₂×C₁₆
Fitting	C₂²×C₁₁₃	C₁₆
hypercenter	C₂²	#14268661
hypocenter	C₁₁₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#14268661	C₂	semidirect
15. C₂²×C₁₁₃	C₁₆	semidirect
18. C₂×D₁₁₃	C₁₆	semidirect
28. C₁₁₃	C₂²⋊C₁₆	semidirect
48. C₂²	#14268661	semidirect

Subgroups — C22⋊#14268661 #20299724

Conjugacy classes of subgroups

Complements

Subgroups — C₂²⋊#14268661 #20299724