Subgroups — #28407639

Order 14464.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14268659	C₂	1	2	yes	maximal
2	C₈×#11744753	C₂	1	1	yes	maximal, characteristic
3	C₂×#14268659	—	2	2	no	—
4	C₄×#11744753	C₄	1	1	yes	characteristic
5	C₄×#11744753	C₂²	1	1	yes	characteristic
6	C₈×Dic₁₁₃	C₄	1	1	yes	characteristic
7	#14268659	—	4	2	no	—
8	C₂×#11744753	—	2	1	no	—
9	C₂×#11744753	D₄	1	1	yes	characteristic
10	C₂×#11744753	Q₈	1	1	yes	characteristic
11	C₂×#11744751	C₈	1	1	yes	characteristic
12	C₄×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₁₃	C₈	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
15	C₂×Dic₁₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₂×Dic₁₁₃	M₁₆	1	1	yes	characteristic
17	#11744753	—	2	2	no	—
18	#11744753	—	2	1	no	—
19	#11744753	D₈	1	1	yes	characteristic
20	#11744753	Q₁₆	1	1	yes	characteristic
21	C₈×C₁₁₃	—	2	1	no	—
22	#11744751	C₁₆	1	2	yes	complemented
23	C₂²×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
25	C₄×C₁₁₃	M₃₂	1	1	yes	characteristic
26	Dic₁₁₃	—	2	1	no	—
27	Dic₁₁₃	#107	1	1	yes	characteristic
28	Dic₁₁₃	#108	1	1	yes	characteristic
29	C₂×C₁₁₃	#335	1	1	yes	characteristic
30	C₂×C₁₁₃	C₄⋊C₁₆	1	1	yes	characteristic
31	C₂×C₁₁₃	#364	1	1	yes	characteristic
32	#1370	—	113	1	no	maximal, Sylow
33	C₁₁₃	#1370	1	1	yes	characteristic, complemented, Sylow
34	C₄⋊C₁₆	—	113	2	no	—
35	C₈²	—	113	1	no	—
36	C₂×C₁₆	—	226	2	no	—
37	C₄×C₈	—	113	1	no	—
38	C₄×C₈	—	113	1	no	—
39	C₄×C₈	—	113	1	no	—
40	C₂×C₈	—	113	1	no	—
41	C₂×C₈	—	113	1	no	—
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	226	1	no	—
44	C₂×C₈	#11744762	1	1	yes	characteristic
45	C₄²	—	113	1	no	—
46	C₁₆	—	452	2	no	—
47	C₂×C₄	—	113	1	no	—
48	C₂×C₄	—	113	1	no	—
49	C₂×C₄	C₂×#11744762	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	—	113	1	no	—
52	C₈	—	113	1	no	—
53	C₈	—	113	2	no	—
54	C₈	—	226	1	no	—
55	C₈	—	226	2	no	—
56	C₂²	C₄⋊#11744762	1	1	yes	characteristic
57	C₄	—	113	1	no	—
58	C₄	—	113	1	no	—
59	C₄	—	226	1	no	—
60	C₄	#16813717	1	1	yes	characteristic
61	C₄	#16813718	1	1	yes	characteristic
62	C₂	#20299688	1	1	yes	characteristic
63	C₂	#20299701	1	1	yes	characteristic
64	C₂	#20299702	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#11744762
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₂×C₄	C₂×#11744762
Fitting	C₂×C₈×C₁₁₃	C₈
socle, prime radical	C₂²×C₁₁₃	C₄⋊C₈
cosocle	C₄×#11744753	C₂²
hypercenter	C₂×C₈	#11744762
hypocenter	C₁₁₃	#1370
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
22. #11744751	C₁₆	semidirect
33. C₁₁₃	#1370	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14268659	2
C₈×#11744753	2
#1370	113