Subgroups — #28407849

Order 14464.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299729	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299727	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299719	C₂	1	1	yes	maximal, characteristic
4	#16813721	—	2	1	no	—
5	#16813721	—	2	1	no	—
6	#16813719	C₄	1	1	yes	characteristic
7	#16813718	—	2	1	no	—
8	#16813717	C₂²	1	1	yes	characteristic
9	C₂×#14268659	—	2	1	no	—
10	#16813709	C₄	1	1	yes	characteristic
11	#14268659	—	2	1	no	—
12	#14268659	D₄	1	1	yes	characteristic
13	#14268659	D₄	1	1	yes	characteristic
14	#14268657	C₈	1	1	yes	characteristic
15	#14268656	—	2	1	no	—
16	#14268655	C₂×C₄	1	1	yes	characteristic
17	C₂×#11744753	—	2	1	no	—
18	#14268646	C₈	1	1	yes	characteristic
19	D₄×C₁₁₃	C₁₆	1	1	yes	characteristic
20	C₂²⋊D₁₁₃	—	2	1	no	—
21	C₂×Dic₁₁₃	—	2	1	no	—
22	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
23	Dic₂₂₆	C₁₆	1	1	yes	characteristic
24	#11744753	—	2	1	no	—
25	#11744753	C₂²⋊C₄	1	1	yes	characteristic
26	#11744753	M₁₆	1	1	yes	characteristic
27	C₂²×C₁₁₃	—	2	1	no	—
28	C₂×D₁₁₃	M₃₂	1	1	yes	characteristic
29	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
30	Dic₁₁₃	—	2	1	no	—
31	Dic₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
32	C₂×C₁₁₃	—	4	1	no	—
33	C₂×C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
34	D₁₁₃	—	2	1	no	—
35	#1401	—	113	1	no	maximal, Sylow
36	C₁₁₃	#1401	1	1	yes	characteristic, complemented, Sylow
37	#504	—	113	1	no	—
38	M₆₄	—	113	1	no	—
39	C₂×C₃₂	—	113	1	no	—
40	#131	—	113	1	no	—
41	M₃₂	—	113	1	no	—
42	M₃₂	—	226	1	no	—
43	C₂×C₁₆	—	113	1	no	—
44	C₂×C₁₆	—	226	1	no	—
45	C₃₂	—	226	1	no	—
46	C₃₂	—	226	1	no	—
47	#41	—	113	1	no	—
48	M₁₆	—	113	1	no	—
49	M₁₆	—	226	1	no	—
50	C₂×C₈	—	113	1	no	—
51	C₂×C₈	—	226	1	no	—
52	C₁₆	—	113	1	no	—
53	C₁₆	—	113	1	no	—
54	C₁₆	—	226	1	no	—
55	Q₈	—	113	1	no	—
56	D₄	—	226	1	no	—
57	D₄	#14268661	1	1	yes	characteristic
58	C₂×C₄	—	113	1	no	—
59	C₂×C₄	—	226	1	no	—
60	C₈	—	113	1	no	—
61	C₈	—	113	1	no	—
62	C₈	—	226	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	113	1	no	—
65	C₄	—	113	1	no	—
66	C₄	—	226	1	no	—
67	C₄	C₂×#14268661	1	1	yes	characteristic
68	C₂	—	4	1	no	—
69	C₂	—	226	1	no	—
70	C₂	C₂²⋊#14268661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#14268661
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₄	C₂×#14268661
Fitting	D₄×C₁₁₃	C₁₆
socle	C₂×C₁₁₃	C₂²⋊C₁₆
prime radical	#14268646	C₈
cosocle	#16813717	C₂²
hypercenter	D₄	#14268661
hypocenter	C₁₁₃	#1401
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #20299729	C₂	semidirect
2. #20299727	C₂	semidirect
36. C₁₁₃	#1401	semidirect

Maximal subgroups

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

subgroup	index
#20299729	2
#20299727	2
#20299719	2
#1401	113