Subgroups — #28388644

Order 14464.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14268622	C₂	1	2	yes	maximal
2	C₈²×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14268622	—	2	2	no	—
4	C₄×C₈×C₁₁₃	C₄	1	1	yes	characteristic
5	C₄×C₈×C₁₁₃	C₄	1	1	yes	characteristic
6	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
7	#14268622	—	4	2	no	—
8	C₂×C₈×C₁₁₃	—	2	1	no	—
9	C₂×C₈×C₁₁₃	C₈	1	1	yes	characteristic
10	C₂×C₈×C₁₁₃	C₈	1	1	yes	characteristic
11	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
12	C₂×C₈×C₁₁₃	Q₈	1	1	yes	characteristic
13	C₄²×C₁₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	M₁₆	1	1	yes	characteristic
17	C₈×C₁₁₃	—	2	2	no	—
18	C₈×C₁₁₃	—	2	1	no	—
19	C₈×C₁₁₃	—	2	1	no	—
20	C₈×C₁₁₃	C₁₆	1	2	yes	complemented
21	C₈×C₁₁₃	D₈	1	1	yes	characteristic
22	C₈×C₁₁₃	Q₁₆	1	1	yes	characteristic
23	C₂²×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
24	C₄×C₁₁₃	—	2	1	no	—
25	C₄×C₁₁₃	#107	1	1	yes	characteristic
26	C₄×C₁₁₃	#108	1	1	yes	characteristic
27	C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
28	C₄×C₁₁₃	M₃₂	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	D₁₁₃	1	1	yes	characteristic
36	C₂×C₁₆	—	226	2	no	—
37	C₄×C₈	Dic₁₁₃	1	1	yes	characteristic
38	C₄×C₈	Dic₁₁₃	1	1	yes	characteristic
39	C₄×C₈	C₂×D₁₁₃	1	1	yes	characteristic
40	C₂×C₈	—	2	1	no	—
41	C₂×C₈	#11744751	1	1	yes	characteristic
42	C₂×C₈	#11744751	1	1	yes	characteristic
43	C₂×C₈	Dic₂₂₆	1	1	yes	characteristic
44	C₂×C₈	D₄₅₂	1	1	yes	characteristic
45	C₄²	C₂×Dic₁₁₃	1	1	yes	characteristic
46	C₁₆	—	452	2	no	—
47	C₂×C₄	C₄⋊Dic₁₁₃	1	1	yes	characteristic
48	C₂×C₄	C₂×#11744751	1	1	yes	characteristic
49	C₂×C₄	#14268631	1	1	yes	characteristic
50	C₈	—	2	2	no	—
51	C₈	—	2	1	no	—
52	C₈	—	2	1	no	—
53	C₈	#14268622	1	2	yes	complemented
54	C₈	D₉₀₄	1	1	yes	characteristic
55	C₈	Dic₄₅₂	1	1	yes	characteristic
56	C₂²	C₄⋊#11744751	1	1	yes	characteristic
57	C₄	—	2	1	no	—
58	C₄	#16813556	1	1	yes	characteristic
59	C₄	#16813558	1	1	yes	characteristic
60	C₄	C₂×#14268622	1	1	yes	characteristic
61	C₄	#16813562	1	1	yes	characteristic
62	C₂	#20298351	1	1	yes	characteristic
63	C₂	C₄⋊#14268622	1	1	yes	characteristic
64	C₂	#20298419	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄₅₂
commutator	C₄×C₁₁₃	C₂×C₁₆
Frattini	C₄×C₈	C₂×D₁₁₃
Fitting	C₈²×C₁₁₃	C₂
socle, prime radical	C₂²×C₁₁₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₁₃	C₂²
hypercenter	C₈²	D₁₁₃
hypocenter	C₁₁₃	#1370
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
20. C₈×C₁₁₃	C₁₆	semidirect
33. C₁₁₃	#1370	semidirect
53. C₈	#14268622	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#14268622	2
C₈²×C₁₁₃	2
#1370	113