Subgroups — #28407870

Order 14464.

106 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	#20299728	C₂	1	2	yes	maximal, complemented
3	#20299727	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813721	C₂	1	2	yes	maximal, complemented
5	#20299719	C₂	1	1	yes	maximal, characteristic
6	#16813721	C₂²	1	1	yes	characteristic
7	#16813721	C₂²	1	2	yes	—
8	#16813721	C₂²	1	1	yes	characteristic
9	#16813719	C₄	1	1	yes	characteristic
10	#16813718	C₄	1	2	yes	—
11	#16813717	C₂²	1	1	yes	characteristic
12	C₂×#14268659	C₂²	1	2	yes	—
13	#16813709	C₄	1	1	yes	characteristic
14	#14268659	C₂×C₄	1	2	yes	—
15	#14268659	C₂×C₄	1	1	yes	characteristic
16	#14268659	C₂³	1	1	yes	characteristic
17	#14268657	C₈	1	1	yes	characteristic
18	#14268656	C₈	1	2	yes	—
19	#14268655	C₂×C₄	1	1	yes	characteristic
20	C₂×#11744753	C₂×C₄	1	2	yes	—
21	#14268646	C₈	1	1	yes	characteristic
22	D₄×C₁₁₃	C₁₆	1	1	yes	characteristic
23	C₂²⋊D₁₁₃	C₁₆	1	2	yes	—
24	C₂×Dic₁₁₃	C₂×C₈	1	2	yes	—
25	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
26	Dic₂₂₆	C₁₆	1	1	yes	characteristic
27	#11744753	C₂×C₈	1	2	yes	—
28	#11744753	C₂×C₈	1	1	yes	characteristic
29	#11744753	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₁₁₃	C₂×C₁₆	1	2	yes	—
31	C₂×D₁₁₃	C₂×C₁₆	1	1	yes	characteristic
32	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
33	Dic₁₁₃	C₂×C₁₆	1	2	yes	—
34	Dic₁₁₃	C₂²×C₈	1	1	yes	characteristic
35	C₂×C₁₁₃	—	2	2	no	—
36	C₂×C₁₁₃	C₂²×C₁₆	1	1	yes	characteristic
37	D₁₁₃	—	2	1	no	—
38	#2258	—	113	1	no	maximal, Sylow
39	C₁₁₃	#2258	1	1	yes	characteristic, complemented, Sylow
40	#504	—	113	1	no	—
41	M₆₄	—	113	2	no	—
42	M₆₄	—	113	1	no	—
43	C₂×C₃₂	—	113	2	no	—
44	C₂×C₃₂	—	113	1	no	—
45	#131	—	113	1	no	—
46	M₃₂	—	113	2	no	—
47	M₃₂	—	113	1	no	—
48	C₂×C₁₆	—	113	2	no	—
49	C₂×C₁₆	—	113	1	no	—
50	C₃₂	—	113	1	no	—
51	C₃₂	—	113	2	no	—
52	C₃₂	—	113	1	no	—
53	#41	—	113	1	no	—
54	M₁₆	—	113	2	no	—
55	M₁₆	—	113	1	no	—
56	C₂×C₈	—	113	2	no	—
57	C₂×C₈	—	113	1	no	—
58	C₁₆	—	113	1	no	—
59	C₁₆	—	113	2	no	—
60	C₁₆	—	113	1	no	—
61	Q₈	—	113	1	no	—
62	D₄	—	113	2	no	—
63	D₄	#14268661	1	1	yes	characteristic
64	C₂×C₄	—	113	2	no	—
65	C₂×C₄	—	113	1	no	—
66	C₈	—	113	1	no	—
67	C₈	—	113	2	no	—
68	C₈	—	113	1	no	—
69	C₂²	—	113	1	no	—
70	C₂²	C₂×#14268661	1	2	yes	—
71	C₄	—	113	1	no	—
72	C₄	—	113	2	no	—
73	C₄	C₂×#14268661	1	1	yes	characteristic
74	C₂	—	2	2	no	—
75	C₂	—	226	1	no	—
76	C₂	C₂²×#14268661	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#14268661
commutator, socle	C₂×C₁₁₃	C₂²×C₁₆
Fitting	D₄×C₁₁₃	C₁₆
prime radical	#14268646	C₈
cosocle	#14268659	C₂³
hypercenter	D₄	#14268661
hypocenter	C₁₁₃	#2258
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #20299729	C₂	semidirect
2. #20299728	C₂	semidirect
3. #20299727	C₂	semidirect
4. C₂×#16813721	C₂	semidirect
39. C₁₁₃	#2258	semidirect

Maximal subgroups

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

subgroup	index
#20299729	2
#20299728	2
#20299727	2
C₂×#16813721	2
#20299719	2
#2258	113