Subgroups — #28407641

Order 14464.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299688	C₂	1	2	yes	maximal
2	C₁₆×#90673	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	D₈	1	1	yes	characteristic
15	C₂×#90673	Q₁₆	1	1	yes	characteristic
16	#11744762	—	8	2	no	—
17	C₄×D₁₁₃	C₄⋊C₄	1	1	yes	characteristic
18	#11744753	—	2	1	no	—
19	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
20	#11744751	M₁₆	1	1	yes	characteristic
21	C₂×D₁₁₃	#107	1	1	yes	characteristic
22	#90673	—	2	1	no	—
23	#90673	SD₃₂	1	2	yes	—
24	C₄×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
25	Dic₁₁₃	#108	1	1	yes	characteristic
26	C₂×C₁₁₃	#335	1	1	yes	characteristic
27	D₁₁₃	#367	1	1	yes	characteristic
28	D₁₁₃	#368	1	1	yes	characteristic
29	#1372	—	113	1	no	maximal, Sylow
30	C₁₁₃	#1372	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₆	—	113	1	no	—
32	#335	—	113	2	no	—
33	C₂×C₁₆	—	113	1	no	—
34	C₂×C₁₆	—	113	1	no	—
35	C₄⋊C₈	—	226	2	no	—
36	C₄×C₈	—	113	1	no	—
37	C₂×C₈	—	113	1	no	—
38	C₂×C₈	—	113	1	no	—
39	C₂×C₈	—	452	2	no	—
40	C₄²	—	113	1	no	—
41	C₁₆	—	113	1	no	—
42	C₁₆	—	226	1	no	—
43	C₁₆	#11744762	1	1	yes	characteristic, complemented
44	C₂×C₄	—	113	1	no	—
45	C₂×C₄	—	113	1	no	—
46	C₂×C₄	—	113	1	no	—
47	C₈	—	113	1	no	—
48	C₈	—	904	2	no	—
49	C₈	—	226	1	no	—
50	C₈	C₂×#11744762	1	1	yes	characteristic
51	C₂²	—	113	1	no	—
52	C₄	—	113	2	no	—
53	C₄	—	113	1	no	—
54	C₄	—	226	1	no	—
55	C₄	C₄⋊#11744762	1	1	yes	characteristic
56	C₂	—	113	1	no	—
57	C₂	—	113	1	no	—
58	C₂	#20299688	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299688
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₈	C₂×#11744762
Fitting	C₁₆×C₁₁₃	C₈
socle	C₂×C₁₁₃	#335
prime radical	C₂×D₁₁₃	#107
cosocle	C₈×#90673	C₂²
hypercenter	C₁₆	#11744762
hypocenter	C₁₁₃	#1372
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
30. C₁₁₃	#1372	semidirect
43. C₁₆	#11744762	semidirect

Maximal subgroups

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

subgroup	index
#20299688	2
C₁₆×#90673	2
#1372	113