Subgroups — #28407853

Order 14464.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299729	C₂	1	2	yes	maximal
2	#20299691	C₂	1	1	yes	maximal, characteristic
3	#16813721	—	2	2	no	—
4	#16813717	C₄	1	1	yes	characteristic
5	#16813717	C₂²	1	1	yes	characteristic
6	C₈×#90673	C₄	1	1	yes	characteristic
7	#14268659	—	2	1	no	—
8	#14268659	D₄	1	1	yes	characteristic
9	#14268659	Q₈	1	1	yes	characteristic
10	#14268655	C₂×C₄	1	1	yes	characteristic
11	C₄×#90673	C₈	1	1	yes	characteristic
12	C₈×D₁₁₃	C₈	1	1	yes	characteristic
13	C₂×#90673	—	2	1	no	—
14	C₄×D₁₁₃	C₂×C₈	1	1	yes	characteristic
15	#11744753	C₄⋊C₄	1	1	yes	characteristic
16	#11744753	M₁₆	1	1	yes	characteristic
17	C₈×C₁₁₃	C₁₆	1	1	yes	characteristic
18	#11744751	C₁₆	1	1	yes	characteristic
19	C₂×D₁₁₃	M₃₂	1	1	yes	characteristic
20	#90673	—	2	2	no	—
21	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
22	Dic₁₁₃	C₄⋊C₈	1	1	yes	characteristic
23	C₂×C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic
24	D₁₁₃	—	2	1	no	—
25	#1422	—	113	1	no	maximal, Sylow
26	C₁₁₃	#1422	1	1	yes	characteristic, complemented, Sylow
27	M₆₄	—	113	2	no	—
28	C₄×C₁₆	—	113	1	no	—
29	C₂×C₁₆	—	113	1	no	—
30	C₂×C₁₆	—	113	1	no	—
31	C₄×C₈	—	113	1	no	—
32	C₃₂	—	226	2	no	—
33	C₂×C₈	—	113	1	no	—
34	C₂×C₈	—	113	1	no	—
35	C₄²	—	113	1	no	—
36	C₁₆	—	113	1	no	—
37	C₁₆	—	113	1	no	—
38	C₁₆	—	226	1	no	—
39	C₂×C₄	—	113	1	no	—
40	C₂×C₄	—	226	1	no	—
41	C₈	—	113	1	no	—
42	C₈	—	113	1	no	—
43	C₈	—	113	1	no	—
44	C₈	#14268661	1	1	yes	characteristic
45	C₂²	—	113	1	no	—
46	C₄	—	113	1	no	—
47	C₄	—	226	2	no	—
48	C₄	C₂×#14268661	1	1	yes	characteristic
49	C₂	—	226	1	no	—
50	C₂	C₄⋊#14268661	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₄⋊#14268661
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₄	C₂×#14268661
Fitting	C₈×C₁₁₃	C₁₆
socle	C₂×C₁₁₃	C₄⋊C₁₆
prime radical	C₂×D₁₁₃	M₃₂
cosocle	#16813717	C₂²
hypercenter	C₈	#14268661
hypocenter	C₁₁₃	#1422
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
26. C₁₁₃	#1422	semidirect

Maximal subgroups

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

subgroup	index
#20299729	2
#20299691	2
#1422	113