Subgroups — #28407589

Order 14464.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299691	C₂	1	1	yes	maximal, characteristic
2	C₈×#11744762	C₂	1	1	yes	maximal, characteristic
3	C₁₆×#90673	C₂	1	1	yes	maximal, characteristic
4	#16813717	C₄	1	2	yes	—
5	C₄×#11744762	C₄	1	2	yes	—
6	#16813695	C₄	1	1	yes	characteristic
7	C₈×#90673	C₂²	1	1	yes	characteristic
8	C₁₆×D₁₁₃	C₄	1	1	yes	characteristic
9	C₂×#11744762	C₈	1	4	yes	—
10	#14268659	C₈	1	4	yes	complemented
11	#14268655	C₂×C₄	1	1	yes	characteristic
12	C₄×#90673	C₂×C₄	1	1	yes	characteristic
13	#14268650	C₈	1	2	yes	complemented
14	C₈×D₁₁₃	C₂×C₄	1	1	yes	characteristic
15	#14268622	C₈	1	1	yes	characteristic, complemented
16	C₁₆×C₁₁₃	C₈	1	1	yes	characteristic, complemented
17	C₂×#90673	C₂×C₈	1	2	yes	—
18	#11744762	—	2	4	no	—
19	C₄×D₁₁₃	C₄²	1	1	yes	characteristic
20	#11744753	C₂×C₈	1	2	yes	—
21	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
22	#11744751	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₁₃	C₄×C₈	1	1	yes	characteristic
24	#90673	M₃₂	1	4	yes	—
25	C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
26	Dic₁₁₃	C₄×C₈	1	1	yes	characteristic
27	C₂×C₁₁₃	C₈²	1	1	yes	characteristic
28	D₁₁₃	#346	1	2	yes	—
29	#1311	—	113	1	no	maximal, Sylow
30	C₁₁₃	#1311	1	1	yes	characteristic, complemented, Sylow
31	C₄×C₁₆	—	113	1	no	—
32	C₄×C₁₆	—	113	1	no	—
33	C₈²	—	113	1	no	—
34	C₂×C₁₆	—	113	1	no	—
35	C₂×C₁₆	—	113	2	no	—
36	C₂×C₁₆	—	113	1	no	—
37	C₄×C₈	—	113	1	no	—
38	C₄×C₈	—	113	2	no	—
39	C₂×C₈	—	113	1	no	—
40	C₂×C₈	—	113	1	no	—
41	C₂×C₈	—	113	4	no	—
42	C₄²	—	113	1	no	—
43	C₁₆	—	113	2	no	—
44	C₁₆	—	113	4	no	—
45	C₁₆	—	113	1	no	—
46	C₁₆	#11744762	1	1	yes	characteristic, complemented
47	C₂×C₄	—	113	2	no	—
48	C₂×C₄	—	113	1	no	—
49	C₈	—	113	2	no	—
50	C₈	—	113	1	no	—
51	C₈	—	226	4	no	—
52	C₈	C₂×#11744762	1	1	yes	characteristic
53	C₂²	—	113	1	no	—
54	C₄	—	113	4	no	—
55	C₄	—	113	1	no	—
56	C₄	C₄×#11744762	1	1	yes	characteristic
57	C₂	—	113	2	no	—
58	C₂	C₈×#11744762	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×#11744762
commutator, socle	C₂×C₁₁₃	C₈²
Fitting	C₁₆×C₁₁₃	C₈
prime radical	C₂×D₁₁₃	C₄×C₈
cosocle	C₈×#90673	C₂²
hypercenter	C₁₆	#11744762
hypocenter	C₁₁₃	#1311
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₈ ◁ C₁₆

Complements

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

N	H ≅ G/N	type
10. #14268659	C₈	semidirect
13. #14268650	C₈	semidirect
15. #14268622	C₈	semidirect
16. C₁₆×C₁₁₃	C₈	semidirect
30. C₁₁₃	#1311	semidirect
46. C₁₆	#11744762	semidirect

Maximal subgroups

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

subgroup	index
#20299691	2
C₈×#11744762	2
C₁₆×#90673	2
#1311	113