Subgroups — #28405535

Order 14464.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299487	C₂	1	1	yes	maximal, characteristic
2	#20299459	C₂	1	1	yes	maximal, characteristic
3	#20298692	C₂	1	1	yes	maximal, characteristic
4	C₂×#14268650	—	2	1	no	—
5	C₄⋊#11744753	—	2	1	no	—
6	C₂×Dic₄₅₂	C₄	1	1	yes	characteristic
7	#16813587	—	2	1	no	—
8	#16813545	—	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	—	2	2	no	—
13	C₂×Dic₂₂₆	—	2	1	no	—
14	Dic₄₅₂	—	2	1	no	—
15	Dic₄₅₂	C₈	1	2	yes	complemented
16	C₂×#11744751	D₄	1	1	yes	characteristic
17	#14268626	—	4	1	no	—
18	C₄×Dic₁₁₃	—	4	1	no	—
19	C₄×Dic₁₁₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₁₃	—	2	1	no	—
22	C₂×C₄×C₁₁₃	—	4	1	no	—
23	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×Dic₁₁₃	—	4	1	no	—
25	C₂×Dic₁₁₃	D₈	1	1	yes	characteristic
26	C₂×Dic₁₁₃	SD₁₆	1	1	yes	characteristic
27	Dic₂₂₆	—	2	2	no	—
28	Dic₂₂₆	—	4	1	no	—
29	#11744753	—	8	1	no	—
30	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₁₁₃	M₁₆	1	1	yes	characteristic
32	#11744751	—	2	1	no	—
33	C₂²×C₁₁₃	#102	1	1	yes	characteristic
34	C₄×C₁₁₃	—	8	1	no	—
35	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₁₃	#104	1	1	yes	characteristic
37	Dic₁₁₃	—	2	1	no	—
38	Dic₁₁₃	—	2	1	no	—
39	Dic₁₁₃	—	4	2	no	—
40	C₂×C₁₁₃	D₄⋊C₈	1	1	yes	characteristic
41	C₂×C₁₁₃	#360	1	1	yes	characteristic
42	C₂×C₁₁₃	#362	1	1	yes	characteristic
43	#1334	—	113	1	no	maximal, Sylow
44	C₁₁₃	#1334	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₁₆	—	113	1	no	—
46	#346	—	113	1	no	—
47	#334	—	113	1	no	—
48	C₂×Q₁₆	—	113	1	no	—
49	C₄×Q₈	—	226	1	no	—
50	C₂×C₁₆	—	226	1	no	—
51	#107	#90673	1	1	yes	characteristic
52	C₄⋊C₈	—	226	1	no	—
53	#103	—	226	1	no	—
54	C₄×C₈	—	113	1	no	—
55	C₂×Q₈	—	226	1	no	—
56	Q₁₆	—	113	2	no	—
57	Q₁₆	—	226	1	no	—
58	C₂×C₈	—	113	1	no	—
59	C₂×C₈	—	452	1	no	—
60	C₂×C₈	C₂×#90673	1	1	yes	characteristic
61	C₄⋊C₄	—	2	1	no	—
62	C₄⋊C₄	—	452	1	no	—
63	C₄²	—	113	1	no	—
64	C₄²	—	452	1	no	—
65	C₁₆	—	226	2	no	—
66	Q₈	—	452	1	no	—
67	Q₈	—	226	2	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	113	1	no	—
70	C₂×C₄	—	113	1	no	—
71	C₂×C₄	—	452	1	no	—
72	C₂×C₄	C₂²⋊#90673	1	1	yes	characteristic
73	C₈	—	904	1	no	—
74	C₈	—	226	1	no	—
75	C₈	#14268655	1	1	yes	characteristic
76	C₈	#14268657	1	1	yes	characteristic
77	C₂²	#16813684	1	1	yes	characteristic
78	C₄	—	8	1	no	—
79	C₄	—	452	2	no	—
80	C₄	—	226	1	no	—
81	C₄	—	226	1	no	—
82	C₄	#16813679	1	1	yes	characteristic
83	C₄	#16813687	1	1	yes	characteristic
84	C₂	#20299446	1	1	yes	characteristic
85	C₂	#20299514	1	1	yes	characteristic
86	C₂	#20299517	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16813684
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₂×C₈	C₂×#90673
Fitting	#107×C₁₁₃	C₄
socle, prime radical	C₂²×C₁₁₃	#102
cosocle	C₈×Dic₁₁₃	C₂²
hypercenter	#107	#90673
hypocenter	C₁₁₃	#1334
LCS	G ▷ C₈×C₁₁₃ ▷ 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
15. Dic₄₅₂	C₈	semidirect
44. C₁₁₃	#1334	semidirect

Maximal subgroups

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

subgroup	index
#20299487	2
#20299459	2
#20298692	2
#1334	113