Subgroups — #28407847

Order 14464.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299728	C₂	1	2	yes	maximal, complemented
2	C₂×#16813718	C₂	1	1	yes	maximal, characteristic
3	#16813721	—	2	2	no	—
4	#16813718	—	2	2	no	—
5	C₂×#14268659	C₄	1	1	yes	characteristic
6	C₂×#14268659	C₂²	1	1	yes	characteristic
7	C₂²×#11744753	C₄	1	1	yes	characteristic
8	#14268659	—	2	1	no	—
9	#14268659	D₄	1	2	yes	—
10	C₂×#11744753	—	2	1	no	—
11	C₂×#11744753	—	2	1	no	—
12	C₂×#11744753	C₈	1	1	yes	characteristic
13	C₂×#11744753	C₂×C₄	1	1	yes	characteristic
14	C₂²×Dic₁₁₃	C₈	1	1	yes	characteristic
15	C₂³×C₁₁₃	C₁₆	1	1	yes	characteristic
16	C₂×Dic₁₁₃	—	2	1	no	—
17	C₂×Dic₁₁₃	—	2	1	no	—
18	C₂×Dic₁₁₃	C₁₆	1	1	yes	characteristic
19	C₂×Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
20	#11744753	—	2	1	no	—
21	#11744753	C₂²⋊C₄	1	1	yes	characteristic
22	#11744753	M₁₆	1	1	yes	characteristic
23	C₂²×C₁₁₃	—	2	1	no	—
24	C₂²×C₁₁₃	—	4	1	no	—
25	C₂²×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
26	Dic₁₁₃	—	2	1	no	—
27	Dic₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
28	Dic₁₁₃	M₃₂	1	1	yes	characteristic
29	C₂×C₁₁₃	—	2	1	no	—
30	C₂×C₁₁₃	—	4	1	no	—
31	C₂×C₁₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
32	#1400	—	113	1	no	maximal, Sylow
33	C₁₁₃	#1400	1	1	yes	characteristic, complemented, Sylow
34	C₂×M₃₂	—	113	1	no	—
35	M₆₄	—	113	2	no	—
36	C₂²×C₈	—	113	1	no	—
37	M₃₂	—	226	2	no	—
38	C₂×C₁₆	—	113	1	no	—
39	C₂×C₁₆	—	113	1	no	—
40	C₃₂	—	226	2	no	—
41	C₂²×C₄	—	113	1	no	—
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	113	1	no	—
44	C₂×C₈	—	226	1	no	—
45	C₂×C₈	—	226	1	no	—
46	C₁₆	—	113	2	no	—
47	C₁₆	—	226	1	no	—
48	C₂³	#14268661	1	1	yes	characteristic
49	C₂×C₄	—	113	1	no	—
50	C₂×C₄	—	113	1	no	—
51	C₂×C₄	—	226	1	no	—
52	C₂×C₄	—	226	1	no	—
53	C₈	—	113	1	no	—
54	C₈	—	113	1	no	—
55	C₈	—	226	1	no	—
56	C₂²	—	2	1	no	—
57	C₂²	—	4	1	no	—
58	C₂²	C₂×#14268661	1	1	yes	characteristic
59	C₄	—	113	1	no	—
60	C₄	—	113	1	no	—
61	C₄	—	226	1	no	—
62	C₂	—	2	1	no	—
63	C₂	—	4	1	no	—
64	C₂	C₂²⋊#14268661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#14268661
commutator	C₂²×C₁₁₃	C₂×C₁₆
Frattini	C₂²	C₂×#14268661
Fitting, prime radical	C₂³×C₁₁₃	C₁₆
socle	C₂×C₁₁₃	C₂²⋊C₁₆
cosocle	C₂×#14268659	C₂²
hypercenter	C₂³	#14268661
hypocenter	C₁₁₃	#1400
LCS	G ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. #20299728	C₂	semidirect
33. C₁₁₃	#1400	semidirect

Maximal subgroups

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

subgroup	index
#20299728	2
C₂×#16813718	2
#1400	113