Subgroups — #28405590

Order 14464.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299519	C₂	1	1	yes	maximal, characteristic
2	#20299460	C₂	1	1	yes	maximal, characteristic
3	#20298999	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268650	—	2	1	no	—
5	C₄⋊#11744753	—	2	1	no	—
6	#16813613	—	2	1	no	—
7	#16813556	C₄	1	1	yes	characteristic
8	#16813553	—	2	1	no	—
9	C₈×Dic₁₁₃	C₂²	1	1	yes	characteristic
10	#107×C₁₁₃	C₄	1	1	yes	characteristic
11	C₂×#11744753	—	4	1	no	—
12	#14268650	—	4	1	no	—
13	C₂×#11744751	D₄	1	1	yes	characteristic
14	C₄⋊Dic₁₁₃	—	2	1	no	—
15	C₄⋊Dic₁₁₃	—	4	1	no	—
16	#14268626	—	4	1	no	—
17	C₄×Dic₁₁₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄⋊C₄×C₁₁₃	—	2	1	no	—
20	C₂×C₄×C₁₁₃	—	4	1	no	—
21	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₁₁₃	—	4	1	no	—
23	C₂×Dic₁₁₃	D₈	1	1	yes	characteristic
24	C₂×Dic₁₁₃	SD₁₆	1	1	yes	characteristic
25	#11744753	—	8	1	no	—
26	C₈×C₁₁₃	—	2	1	no	—
27	#11744751	SD₁₆	1	1	yes	characteristic
28	#11744751	Q₁₆	1	1	yes	characteristic
29	C₂²×C₁₁₃	#102	1	1	yes	characteristic
30	C₄×C₁₁₃	—	8	1	no	—
31	C₄×C₁₁₃	#101	1	1	yes	characteristic
32	C₄×C₁₁₃	#103	1	1	yes	characteristic
33	Dic₁₁₃	—	2	1	no	—
34	Dic₁₁₃	—	2	1	no	—
35	Dic₁₁₃	—	8	1	no	—
36	C₂×C₁₁₃	#332	1	1	yes	characteristic
37	C₂×C₁₁₃	#359	1	1	yes	characteristic
38	C₂×C₁₁₃	#360	1	1	yes	characteristic
39	#1363	—	113	1	no	maximal, Sylow
40	C₁₁₃	#1363	1	1	yes	characteristic, complemented, Sylow
41	#499	—	113	1	no	—
42	C₄⋊C₁₆	—	113	1	no	—
43	#334	—	113	1	no	—
44	#125	—	226	1	no	—
45	C₂×C₁₆	—	226	1	no	—
46	#107	—	113	1	no	—
47	#107	#90673	1	1	yes	characteristic
48	#106	—	226	1	no	—
49	C₄⋊C₈	—	226	1	no	—
50	C₄×C₈	—	113	1	no	—
51	C₂×C₈	—	113	1	no	—
52	C₂×C₈	—	452	1	no	—
53	C₂×C₈	C₂×#90673	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	452	1	no	—
56	C₄⋊C₄	—	452	1	no	—
57	C₄⋊C₄	—	226	1	no	—
58	C₄²	—	113	1	no	—
59	C₁₆	—	452	1	no	—
60	C₂×C₄	—	4	1	no	—
61	C₂×C₄	—	113	1	no	—
62	C₂×C₄	—	113	1	no	—
63	C₂×C₄	—	452	1	no	—
64	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
65	C₈	—	2	1	no	—
66	C₈	—	113	1	no	—
67	C₈	—	113	1	no	—
68	C₈	—	904	1	no	—
69	C₂²	#16813684	1	1	yes	characteristic
70	C₄	—	8	1	no	—
71	C₄	—	904	1	no	—
72	C₄	—	226	1	no	—
73	C₄	—	226	1	no	—
74	C₄	#16813683	1	1	yes	characteristic
75	C₄	#16813685	1	1	yes	characteristic
76	C₂	#20299457	1	1	yes	characteristic
77	C₂	#20299512	1	1	yes	characteristic
78	C₂	#20299515	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813684
commutator	C₂×C₈×C₁₁₃	C₂×C₄
Frattini	C₂×C₈	C₂×#90673
Fitting	#107×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	#102
cosocle	C₈×Dic₁₁₃	C₂²
hypercenter	#107	#90673
hypocenter	C₁₁₃	#1363
LCS	G ▷ C₂×C₈×C₁₁₃ ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
40. C₁₁₃	#1363	semidirect

Maximal subgroups

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

subgroup	index
#20299519	2
#20299460	2
#20298999	2
#1363	113