Subgroups — C₂×#16813696 #20299653

Order 7232.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813696	C₂	1	4	yes	maximal, direct product factor
2	C₂×#14268650	C₂	1	2	yes	maximal, complemented
3	C₂²×#11744751	C₂	1	1	yes	maximal, characteristic
4	#14268650	C₂²	1	4	yes	complemented
5	C₂×#11744751	C₄	1	2	yes	—
6	C₂×#11744751	C₄	1	1	yes	characteristic
7	C₂×#11744751	C₂²	1	1	yes	characteristic
8	C₂×#11744751	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₁₃	C₄	1	1	yes	characteristic
10	C₂³×C₁₁₃	C₈	1	1	yes	characteristic
11	C₂×C₄×C₁₁₃	C₈	1	2	yes	—
12	C₂×C₄×C₁₁₃	C₈	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
15	#11744751	C₂×C₄	1	1	yes	characteristic
16	#11744751	C₂×C₄	1	2	yes	—
17	#11744751	C₂³	1	1	yes	characteristic
18	C₂²×C₁₁₃	—	2	2	no	—
19	C₂²×C₁₁₃	C₂×C₈	1	2	yes	—
20	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
21	C₄×C₁₁₃	C₂×C₈	1	2	yes	—
22	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₁₁₃	—	2	2	no	—
25	C₂×C₁₁₃	M₃₂	1	2	yes	complemented
26	C₂×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
27	C₁₁₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×M₃₂	—	113	1	no	maximal, Sylow
29	C₂²×C₈	—	113	1	no	—
30	M₃₂	—	113	4	no	—
31	C₂×C₁₆	—	113	2	no	—
32	C₂²×C₄	#90673	1	1	yes	characteristic
33	C₂×C₈	—	113	2	no	—
34	C₂×C₈	—	113	2	no	—
35	C₂×C₈	—	113	1	no	—
36	C₂×C₈	—	113	1	no	—
37	C₁₆	—	113	4	no	—
38	C₂³	#11744753	1	1	yes	characteristic
39	C₂×C₄	#11744753	1	1	yes	characteristic
40	C₂×C₄	#11744753	1	2	yes	—
41	C₂×C₄	C₂×#90673	1	2	yes	—
42	C₂×C₄	C₂×#90673	1	1	yes	characteristic
43	C₈	—	113	1	no	—
44	C₈	—	113	2	no	—
45	C₈	—	113	1	no	—
46	C₂²	—	2	2	no	—
47	C₂²	C₂×#11744753	1	2	yes	—
48	C₂²	C₂×#11744753	1	1	yes	characteristic
49	C₄	C₂×#11744753	1	2	yes	—
50	C₄	C₂×#11744753	1	1	yes	characteristic
51	C₄	C₂²×#90673	1	1	yes	characteristic
52	C₂	—	2	2	no	—
53	C₂	#16813696	1	2	yes	direct product factor
54	C₂	C₂²×#11744753	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#90673
commutator	C₂×C₁₁₃	C₂²×C₈
Frattini	C₄	C₂²×#90673
Fitting	C₂²×C₄×C₁₁₃	C₄
socle	C₂²×C₁₁₃	C₂×C₈
hypercenter	C₂²×C₄	#90673
hypocenter	C₁₁₃	C₂×M₃₂
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. #16813696	C₂	direct (N × H)
2. C₂×#14268650	C₂	semidirect
4. #14268650	C₂²	semidirect
25. C₂×C₁₁₃	M₃₂	semidirect
27. C₁₁₃	C₂×M₃₂	semidirect
53. C₂	#16813696	direct (N × H)

Subgroups — C2×#16813696 #20299653

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813696 #20299653