Subgroups — #28405600

Order 14464.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299459	C₂	1	1	yes	maximal, characteristic
2	#20299459	C₂	1	1	yes	maximal, characteristic
3	#20298373	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11744753	—	2	1	no	—
5	C₄⋊#11744753	—	2	1	no	—
6	C₂×#14268622	C₄	1	1	yes	characteristic
7	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
9	C₂×#11744753	—	4	1	no	—
10	C₂×#11744753	—	4	1	no	—
11	C₂×#11744751	Q₈	1	1	yes	characteristic
12	C₄×Dic₁₁₃	D₄	1	1	yes	characteristic
13	#14268622	C₈	1	2	yes	complemented
14	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₁₃	—	2	1	no	—
16	C₂×C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	C₂×Dic₁₁₃	SD₁₆	1	1	yes	characteristic
18	C₂×Dic₁₁₃	SD₁₆	1	1	yes	characteristic
19	#11744753	—	8	1	no	—
20	#11744753	—	8	1	no	—
21	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
22	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
23	#11744751	—	2	1	no	—
24	C₂²×C₁₁₃	#106	1	1	yes	characteristic
25	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₁₁₃	#108	1	1	yes	characteristic
27	Dic₁₁₃	—	2	1	no	—
28	Dic₁₁₃	—	2	1	no	—
29	C₂×C₁₁₃	#334	1	1	yes	characteristic
30	C₂×C₁₁₃	#365	1	1	yes	characteristic
31	C₂×C₁₁₃	#365	1	1	yes	characteristic
32	#1368	—	113	1	no	maximal, Sylow
33	C₁₁₃	#1368	1	1	yes	characteristic, complemented, Sylow
34	#346	—	113	1	no	—
35	#334	—	113	1	no	—
36	#334	—	113	1	no	—
37	C₂×C₁₆	—	113	1	no	—
38	C₂×C₁₆	#90673	1	1	yes	characteristic
39	C₄⋊C₈	—	226	1	no	—
40	C₄⋊C₈	—	226	1	no	—
41	C₄×C₈	—	113	1	no	—
42	C₂×C₈	—	113	1	no	—
43	C₂×C₈	—	452	1	no	—
44	C₂×C₈	—	452	1	no	—
45	C₂×C₈	C₂×#90673	1	1	yes	characteristic
46	C₄²	—	113	1	no	—
47	C₁₆	—	2	1	no	—
48	C₁₆	—	113	2	no	—
49	C₂×C₄	—	113	1	no	—
50	C₂×C₄	—	113	1	no	—
51	C₂×C₄	C₄⋊#90673	1	1	yes	characteristic
52	C₈	—	904	1	no	—
53	C₈	—	904	1	no	—
54	C₈	—	226	1	no	—
55	C₈	#14268655	1	1	yes	characteristic
56	C₈	#14268656	1	1	yes	characteristic
57	C₂²	#16813690	1	1	yes	characteristic
58	C₄	—	226	1	no	—
59	C₄	—	226	1	no	—
60	C₄	#16813689	1	1	yes	characteristic
61	C₄	#16813693	1	1	yes	characteristic
62	C₂	#20299460	1	1	yes	characteristic
63	C₂	#20299522	1	1	yes	characteristic
64	C₂	#20299523	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813690
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#90673
Fitting	C₂×C₁₆×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	#106
cosocle	C₈×Dic₁₁₃	C₂²
hypercenter	C₂×C₁₆	#90673
hypocenter	C₁₁₃	#1368
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. #14268622	C₈	semidirect
33. C₁₁₃	#1368	semidirect

Maximal subgroups

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

subgroup	index
#20299459	2
#20298373	2
#1368	113