Subgroups — #28407605

Order 14464.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299697	C₂	1	2	yes	maximal, complemented
2	#20299572	C₂	1	1	yes	maximal, characteristic
3	#16813718	—	2	2	no	—
4	C₂×#14268657	C₂²	1	1	yes	characteristic
5	C₂×#14268655	C₄	1	1	yes	characteristic
6	C₂²⋊#11744753	—	2	2	no	—
7	C₂×#14268646	C₄	1	1	yes	characteristic
8	#14268659	—	4	2	no	—
9	#14268657	—	4	1	no	—
10	#14268655	—	4	1	no	—
11	C₂×#11744753	—	2	1	no	—
12	C₂×#11744753	D₄	1	2	yes	—
13	#14268646	—	4	1	no	—
14	#14268646	—	4	1	no	—
15	C₂×Dic₂₂₆	C₈	1	1	yes	characteristic
16	C₂×C₂²⋊D₁₁₃	—	2	1	no	—
17	C₂²×Dic₁₁₃	—	2	1	no	—
18	C₂×C₄×D₁₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×D₄×C₁₁₃	C₈	1	1	yes	characteristic
20	C₂³×C₁₁₃	—	2	1	no	—
21	C₂²×D₁₁₃	M₁₆	1	1	yes	characteristic
22	D₄×C₁₁₃	—	4	1	no	—
23	C₂×C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
24	C₂²⋊D₁₁₃	—	4	2	no	—
25	C₂×Dic₁₁₃	—	2	1	no	—
26	C₂×Dic₁₁₃	—	4	1	no	—
27	C₂×Dic₁₁₃	—	4	1	no	—
28	C₂×Dic₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₄×D₁₁₃	—	2	1	no	—
30	C₄×D₁₁₃	—	2	1	no	—
31	Dic₂₂₆	—	4	1	no	—
32	#11744753	—	2	2	no	—
33	#11744753	—	4	1	no	—
34	C₂²×C₁₁₃	—	4	2	no	—
35	C₂²×C₁₁₃	—	4	1	no	—
36	C₂²×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₁₁₃	—	2	1	no	—
38	C₂×D₁₁₃	—	4	1	no	—
39	C₄×C₁₁₃	—	2	1	no	—
40	Dic₁₁₃	—	4	1	no	—
41	Dic₁₁₃	#99	1	1	yes	characteristic
42	Dic₁₁₃	#100	1	1	yes	characteristic
43	C₂×C₁₁₃	—	2	1	no	—
44	C₂×C₁₁₃	—	8	1	no	—
45	C₂×C₁₁₃	#323	1	1	yes	characteristic
46	D₁₁₃	—	4	1	no	—
47	#1321	—	113	1	no	maximal, Sylow
48	C₁₁₃	#1321	1	1	yes	characteristic, complemented, Sylow
49	#408	—	113	1	no	—
50	#349	—	113	2	no	—
51	C₂×#41	—	113	1	no	—
52	C₂×M₁₆	—	113	1	no	—
53	C₂²×C₈	—	113	1	no	—
54	M₃₂	—	226	2	no	—
55	C₂²⋊C₈	—	226	2	no	—
56	#41	—	452	1	no	—
57	#41	—	452	1	no	—
58	C₂×Q₈	—	113	1	no	—
59	C₂×D₄	—	226	1	no	—
60	C₂×D₄	#11744762	1	1	yes	characteristic
61	C₂²×C₄	—	113	1	no	—
62	C₂²×C₄	—	226	1	no	—
63	M₁₆	—	452	1	no	—
64	C₂×C₈	—	113	2	no	—
65	C₂×C₈	—	452	1	no	—
66	C₂×C₈	—	226	1	no	—
67	C₁₆	—	452	2	no	—
68	C₂³	—	2	1	no	—
69	C₂³	—	113	1	no	—
70	Q₈	—	452	1	no	—
71	D₄	—	4	1	no	—
72	D₄	—	452	2	no	—
73	C₂×C₄	—	113	1	no	—
74	C₂×C₄	—	452	1	no	—
75	C₂×C₄	—	452	1	no	—
76	C₂×C₄	—	226	1	no	—
77	C₂×C₄	—	226	1	no	—
78	C₂×C₄	—	226	1	no	—
79	C₂×C₄	C₂×#11744762	1	1	yes	characteristic
80	C₈	—	452	1	no	—
81	C₈	—	226	2	no	—
82	C₂²	—	4	2	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	452	1	no	—
85	C₂²	—	226	1	no	—
86	C₂²	C₂²⋊#11744762	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	113	1	no	—
89	C₄	—	113	1	no	—
90	C₄	—	452	1	no	—
91	C₂	—	2	1	no	—
92	C₂	—	8	1	no	—
93	C₂	—	452	1	no	—
94	C₂	#20299683	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20299683
commutator	C₂×C₄×C₁₁₃	C₂×C₈
Frattini	C₂×C₄	C₂×#11744762
Fitting	C₂×D₄×C₁₁₃	C₈
socle	C₂×C₁₁₃	#323
prime radical	C₂×#14268646	C₄
cosocle	C₂×#14268657	C₂²
hypercenter	C₂×D₄	#11744762
hypocenter	C₁₁₃	#1321
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂²×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
1. #20299697	C₂	semidirect
48. C₁₁₃	#1321	semidirect

Maximal subgroups

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

subgroup	index
#20299697	2
#20299572	2
#1321	113