Subgroups — #28407730

Order 14464.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813717	C₂	1	2	yes	maximal
2	#20299692	C₂	1	4	yes	maximal, complemented
3	C₄×#14268655	C₂	1	1	yes	maximal, characteristic
4	#16813717	C₄	1	8	yes	complemented
5	C₂×#14268659	C₂²	1	4	yes	—
6	C₂×#14268655	C₄	1	1	yes	characteristic
7	C₂×#14268655	C₂²	1	1	yes	characteristic
8	C₄×#11744753	C₄	1	2	yes	—
9	C₄×#11744753	C₂²	1	2	yes	—
10	C₄²×D₁₁₃	C₄	1	1	yes	characteristic
11	#14268659	C₂×C₄	1	8	yes	complemented
12	#14268655	C₈	1	4	yes	—
13	#14268655	C₂×C₄	1	4	yes	—
14	C₂×#11744753	C₂×C₄	1	1	yes	characteristic
15	C₂×#11744753	C₂×C₄	1	2	yes	—
16	C₂×#11744753	C₂³	1	1	yes	characteristic
17	C₂×C₄×D₁₁₃	C₈	1	2	yes	—
18	C₂×C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₁₃	C₈	1	1	yes	characteristic
20	C₄×Dic₁₁₃	C₂×C₄	1	2	yes	—
21	C₄²×C₁₁₃	C₈	1	1	yes	characteristic
22	C₂²×D₁₁₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₁₃	C₂×C₈	1	2	yes	—
24	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×Dic₁₁₃	C₂×C₈	1	2	yes	—
26	C₂×Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
27	C₄×D₁₁₃	—	2	4	no	—
28	C₄×D₁₁₃	C₄²	1	2	yes	—
29	C₄×D₁₁₃	C₂×C₈	1	2	yes	—
30	#11744753	C₄²	1	2	yes	—
31	#11744753	C₂×C₈	1	4	yes	—
32	#11744753	C₂²×C₄	1	2	yes	—
33	C₂²×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
34	C₂×D₁₁₃	C₄×C₈	1	2	yes	—
35	C₂×D₁₁₃	M₃₂	1	4	yes	—
36	C₄×C₁₁₃	—	2	2	no	—
37	C₄×C₁₁₃	C₄×C₈	1	2	yes	—
38	Dic₁₁₃	—	2	2	no	—
39	Dic₁₁₃	C₂×C₄²	1	1	yes	characteristic
40	Dic₁₁₃	C₂²×C₈	1	1	yes	characteristic
41	C₂×C₁₁₃	C₂×C₄×C₈	1	1	yes	characteristic
42	C₂×C₁₁₃	C₂×M₃₂	1	2	yes	—
43	D₁₁₃	#346	1	4	yes	complemented
44	C₂×#346	—	113	1	no	maximal, Sylow
45	C₁₁₃	C₂×#346	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₁₆	—	113	2	no	—
47	C₂×C₄×C₈	—	113	1	no	—
48	#346	—	113	4	no	—
49	C₂²×C₈	—	113	1	no	—
50	C₂²×C₈	—	113	1	no	—
51	C₂×C₄²	—	113	1	no	—
52	C₂×C₁₆	—	113	4	no	—
53	C₂×C₁₆	—	113	8	no	—
54	C₄×C₈	—	113	2	no	—
55	C₄×C₈	—	113	2	no	—
56	C₂²×C₄	—	113	1	no	—
57	C₂²×C₄	—	113	2	no	—
58	C₂×C₈	—	113	1	no	—
59	C₂×C₈	—	113	1	no	—
60	C₂×C₈	—	113	2	no	—
61	C₂×C₈	—	113	4	no	—
62	C₂×C₈	—	113	4	no	—
63	C₄²	—	113	2	no	—
64	C₄²	—	113	1	no	—
65	C₄²	#11744762	1	1	yes	characteristic
66	C₁₆	—	113	8	no	—
67	C₂³	—	113	1	no	—
68	C₂×C₄	—	113	1	no	—
69	C₂×C₄	—	113	2	no	—
70	C₂×C₄	—	113	2	no	—
71	C₂×C₄	—	113	2	no	—
72	C₂×C₄	—	226	4	no	—
73	C₂×C₄	C₂×#11744762	1	2	yes	—
74	C₂×C₄	C₂×#11744762	1	1	yes	characteristic
75	C₈	—	113	2	no	—
76	C₈	—	113	2	no	—
77	C₈	—	113	4	no	—
78	C₂²	—	113	2	no	—
79	C₂²	—	113	4	no	—
80	C₂²	C₂²×#11744762	1	1	yes	characteristic
81	C₄	—	2	2	no	—
82	C₄	—	113	1	no	—
83	C₄	—	113	1	no	—
84	C₄	—	226	2	no	—
85	C₄	C₄×#11744762	1	2	yes	—
86	C₂	—	113	4	no	—
87	C₂	C₂×C₄×#11744762	1	1	yes	characteristic
88	C₂	#20299717	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#11744762
commutator	C₂×C₁₁₃	C₂×C₄×C₈
Frattini	C₂²	C₂²×#11744762
Fitting	C₄²×C₁₁₃	C₈
socle	C₂²×C₁₁₃	C₂²×C₈
prime radical	C₂²×D₁₁₃	C₂×C₈
cosocle	C₂×#11744753	C₂³
hypercenter	C₄²	#11744762
hypocenter	C₁₁₃	C₂×#346
LCS	G ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. #20299692	C₂	semidirect
4. #16813717	C₄	semidirect
11. #14268659	C₂×C₄	semidirect
43. D₁₁₃	#346	semidirect
45. C₁₁₃	C₂×#346	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16813717	2
#20299692	2
C₄×#14268655	2
C₂×#346	113