Subgroups — #28407634

Order 14464.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299687	C₂	1	2	yes	maximal
2	#20299485	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11744762	—	2	2	no	—
4	#16813695	C₄	1	1	yes	characteristic
5	C₈×#90673	C₂²	1	1	yes	characteristic
6	C₁₆×D₁₁₃	C₄	1	1	yes	characteristic
7	C₂×#11744762	—	4	2	no	—
8	#14268655	Q₈	1	1	yes	characteristic
9	C₄×#90673	D₄	1	1	yes	characteristic
10	#14268650	—	2	1	no	—
11	C₈×D₁₁₃	C₂×C₄	1	1	yes	characteristic
12	#14268622	C₈	1	1	yes	characteristic, complemented
13	C₁₆×C₁₁₃	C₈	1	1	yes	characteristic, complemented
14	C₂×#90673	SD₁₆	1	2	yes	—
15	#11744762	—	8	2	no	—
16	C₄×D₁₁₃	C₄⋊C₄	1	1	yes	characteristic
17	#11744753	—	2	1	no	—
18	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
19	#11744751	M₁₆	1	1	yes	characteristic
20	C₂×D₁₁₃	#106	1	1	yes	characteristic
21	#90673	—	2	2	no	—
22	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
23	Dic₁₁₃	#108	1	1	yes	characteristic
24	C₂×C₁₁₃	#334	1	1	yes	characteristic
25	D₁₁₃	#365	1	2	yes	—
26	#1368	—	113	1	no	maximal, Sylow
27	C₁₁₃	#1368	1	1	yes	characteristic, complemented, Sylow
28	#346	—	113	1	no	—
29	#334	—	113	2	no	—
30	C₂×C₁₆	—	113	1	no	—
31	C₂×C₁₆	—	113	1	no	—
32	C₄⋊C₈	—	226	2	no	—
33	C₄×C₈	—	113	1	no	—
34	C₂×C₈	—	113	1	no	—
35	C₂×C₈	—	113	1	no	—
36	C₂×C₈	—	452	2	no	—
37	C₄²	—	113	1	no	—
38	C₁₆	—	113	1	no	—
39	C₁₆	—	226	1	no	—
40	C₁₆	#11744762	1	1	yes	characteristic, complemented
41	C₂×C₄	—	113	1	no	—
42	C₂×C₄	—	113	2	no	—
43	C₈	—	113	1	no	—
44	C₈	—	904	2	no	—
45	C₈	—	226	1	no	—
46	C₈	C₂×#11744762	1	1	yes	characteristic
47	C₂²	—	113	1	no	—
48	C₄	—	113	1	no	—
49	C₄	—	226	2	no	—
50	C₄	C₄⋊#11744762	1	1	yes	characteristic
51	C₂	—	113	2	no	—
52	C₂	#20299687	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299687
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₈	C₂×#11744762
Fitting	C₁₆×C₁₁₃	C₈
socle	C₂×C₁₁₃	#334
prime radical	C₂×D₁₁₃	#106
cosocle	C₈×#90673	C₂²
hypercenter	C₁₆	#11744762
hypocenter	C₁₁₃	#1368
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
12. #14268622	C₈	semidirect
13. C₁₆×C₁₁₃	C₈	semidirect
27. C₁₁₃	#1368	semidirect
40. C₁₆	#11744762	semidirect

Maximal subgroups

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

subgroup	index
#20299687	2
#20299485	2
#1368	113