Subgroups — #28407852

Order 14464.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813721	C₂	1	2	yes	maximal
2	C₄×#14268659	C₂	1	1	yes	maximal, characteristic
3	#16813721	—	2	2	no	—
4	C₂×#14268659	C₄	1	1	yes	characteristic
5	C₂×#14268659	C₂²	1	1	yes	characteristic
6	C₄×#11744753	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	C₂×#11744753	C₈	1	1	yes	characteristic
11	C₂×#11744753	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₁₁₃	C₈	1	1	yes	characteristic
13	C₂×C₄×C₁₁₃	C₁₆	1	1	yes	characteristic
14	C₂×Dic₁₁₃	C₁₆	1	1	yes	characteristic
15	C₂×Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
16	#11744753	—	2	1	no	—
17	#11744753	C₄⋊C₄	1	1	yes	characteristic
18	#11744753	M₁₆	1	1	yes	characteristic
19	C₂²×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
20	C₄×C₁₁₃	—	2	1	no	—
21	Dic₁₁₃	C₃₂	1	2	yes	complemented
22	Dic₁₁₃	C₄⋊C₈	1	1	yes	characteristic
23	Dic₁₁₃	M₃₂	1	1	yes	characteristic
24	C₂×C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic
25	C₂×C₁₁₃	C₂×C₃₂	1	1	yes	characteristic
26	C₂×C₁₁₃	M₆₄	1	1	yes	characteristic
27	C₄⋊C₃₂	—	113	1	no	maximal, Sylow
28	C₁₁₃	C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃₂	—	113	2	no	—
30	C₄×C₁₆	—	113	1	no	—
31	C₂×C₁₆	—	113	1	no	—
32	C₂×C₁₆	—	113	1	no	—
33	C₄×C₈	—	113	1	no	—
34	C₃₂	—	226	2	no	—
35	C₂×C₈	—	113	1	no	—
36	C₂×C₈	—	113	1	no	—
37	C₄²	—	113	1	no	—
38	C₁₆	—	113	1	no	—
39	C₁₆	—	113	1	no	—
40	C₁₆	—	226	1	no	—
41	C₂×C₄	—	113	1	no	—
42	C₂×C₄	—	113	1	no	—
43	C₂×C₄	#14268661	1	1	yes	characteristic
44	C₈	—	113	1	no	—
45	C₈	—	113	1	no	—
46	C₈	—	226	1	no	—
47	C₂²	C₂×#14268661	1	1	yes	characteristic
48	C₄	—	2	1	no	—
49	C₄	—	113	1	no	—
50	C₄	—	113	1	no	—
51	C₄	—	113	2	no	—
52	C₂	C₄⋊#14268661	1	1	yes	characteristic
53	C₂	#20299727	1	1	yes	characteristic
54	C₂	#20299728	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×#14268661
commutator	C₂×C₁₁₃	C₂×C₃₂
Fitting	C₂×C₄×C₁₁₃	C₁₆
socle, prime radical	C₂²×C₁₁₃	C₂×C₁₆
cosocle	C₂×#14268659	C₂²
hypercenter	C₂×C₄	#14268661
hypocenter	C₁₁₃	C₄⋊C₃₂
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
21. Dic₁₁₃	C₃₂	semidirect
28. C₁₁₃	C₄⋊C₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813721	2
C₄×#14268659	2
C₄⋊C₃₂	113