Subgroups — #20299695

Order 7232.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268659	C₂	1	2	yes	maximal, complemented
2	C₂×#14268655	C₂	1	1	yes	maximal, characteristic
3	#14268659	—	2	2	no	—
4	#14268655	—	2	2	no	—
5	C₂×#11744753	C₄	1	1	yes	characteristic
6	C₂×#11744753	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₁₁₃	C₄	1	1	yes	characteristic
8	C₂²×D₁₁₃	C₈	1	1	yes	characteristic
9	C₂×C₄×C₁₁₃	C₈	1	1	yes	characteristic
10	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
11	C₄×D₁₁₃	—	2	1	no	—
12	C₄×D₁₁₃	—	2	1	no	—
13	#11744753	—	2	1	no	—
14	#11744753	D₄	1	2	yes	—
15	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	C₂×D₁₁₃	—	2	1	no	—
17	C₂×D₁₁₃	—	2	1	no	—
18	C₂×D₁₁₃	C₁₆	1	2	yes	complemented
19	C₄×C₁₁₃	—	2	1	no	—
20	Dic₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	Dic₁₁₃	M₁₆	1	1	yes	characteristic
22	C₂×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
23	C₂×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
24	C₂×C₁₁₃	M₃₂	1	1	yes	characteristic
25	D₁₁₃	—	2	2	no	—
26	C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	113	1	no	maximal, Sylow
28	C₂²×C₈	—	113	1	no	—
29	C₂×C₁₆	—	113	2	no	—
30	C₂²×C₄	—	113	1	no	—
31	C₂×C₈	—	113	1	no	—
32	C₂×C₈	—	113	1	no	—
33	C₂×C₈	—	226	2	no	—
34	C₁₆	—	226	2	no	—
35	C₂³	—	113	1	no	—
36	C₂×C₄	—	113	1	no	—
37	C₂×C₄	—	226	1	no	—
38	C₂×C₄	—	226	1	no	—
39	C₂×C₄	#11744762	1	1	yes	characteristic
40	C₈	—	113	2	no	—
41	C₈	—	226	1	no	—
42	C₂²	—	113	2	no	—
43	C₂²	—	226	1	no	—
44	C₂²	—	226	1	no	—
45	C₂²	C₂×#11744762	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	—	113	1	no	—
48	C₄	—	113	1	no	—
49	C₂	—	226	2	no	—
50	C₂	C₂²⋊#11744762	1	1	yes	characteristic
51	C₂	#16813717	1	1	yes	characteristic
52	C₂	#16813719	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#11744762
commutator	C₂×C₁₁₃	C₂×C₁₆
Fitting	C₂×C₄×C₁₁₃	C₈
socle	C₂²×C₁₁₃	C₂×C₈
hypercenter	C₂×C₄	#11744762
hypocenter	C₁₁₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#14268659	C₂	semidirect
18. C₂×D₁₁₃	C₁₆	semidirect
26. C₁₁₃	C₂²⋊C₁₆	semidirect