Subgroups — #28407621

Order 14464.

98 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	#20299688	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×#90673	C₂	1	1	yes	maximal, characteristic
4	#16813717	—	2	1	no	—
5	C₄⋊#11744762	—	2	1	no	—
6	Q₈×#90673	—	2	1	no	—
7	#16813691	C₄	1	1	yes	characteristic
8	#16813685	—	2	1	no	—
9	C₈×#90673	C₂²	1	1	yes	characteristic
10	Q₁₆×D₁₁₃	C₄	1	1	yes	characteristic
11	C₂×#11744762	—	4	1	no	—
12	#14268659	—	2	2	no	—
13	#14268655	D₄	1	1	yes	characteristic
14	C₄⋊#90673	—	2	1	no	—
15	C₄⋊#90673	—	4	1	no	—
16	C₄×#90673	—	4	1	no	—
17	C₄×#90673	D₄	1	1	yes	characteristic
18	Q₈×D₁₁₃	—	2	1	no	—
19	Dic₄₅₂	C₈	1	1	yes	characteristic, complemented
20	#14268637	—	2	1	no	—
21	C₈×D₁₁₃	C₂×C₄	1	1	yes	characteristic
22	Q₁₆×C₁₁₃	C₈	1	1	yes	characteristic, complemented
23	C₂×#90673	—	4	1	no	—
24	C₂×#90673	D₈	1	1	yes	characteristic
25	C₂×#90673	SD₁₆	1	1	yes	characteristic
26	#11744762	—	8	1	no	—
27	Q₈×C₁₁₃	—	2	1	no	—
28	C₄×D₁₁₃	—	4	1	no	—
29	C₄×D₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	Dic₂₂₆	—	2	1	no	—
31	Dic₂₂₆	—	4	1	no	—
32	#11744753	—	2	1	no	—
33	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
34	#11744751	M₁₆	1	1	yes	characteristic
35	C₂×D₁₁₃	#102	1	1	yes	characteristic
36	#90673	—	2	1	no	—
37	#90673	—	8	1	no	—
38	#90673	SD₃₂	1	1	yes	characteristic
39	#90673	Q₃₂	1	1	yes	characteristic
40	C₄×C₁₁₃	—	4	1	no	—
41	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
42	Dic₁₁₃	—	4	1	no	—
43	Dic₁₁₃	#104	1	1	yes	characteristic
44	C₂×C₁₁₃	D₄⋊C₈	1	1	yes	characteristic
45	D₁₁₃	#358	1	1	yes	characteristic
46	D₁₁₃	#359	1	1	yes	characteristic
47	#1332	—	113	1	no	maximal, Sylow
48	C₁₁₃	#1332	1	1	yes	characteristic, complemented, Sylow
49	C₄×Q₁₆	—	113	1	no	—
50	C₄×C₁₆	—	113	1	no	—
51	#335	—	113	1	no	—
52	C₂×Q₁₆	—	113	1	no	—
53	C₄×Q₈	—	226	1	no	—
54	C₂×C₁₆	—	226	1	no	—
55	#107	—	113	1	no	—
56	C₄⋊C₈	—	226	1	no	—
57	#103	—	226	1	no	—
58	C₄×C₈	—	113	1	no	—
59	C₂×Q₈	—	226	1	no	—
60	Q₁₆	—	113	1	no	—
61	Q₁₆	—	226	1	no	—
62	Q₁₆	#11744762	1	1	yes	characteristic, complemented
63	C₂×C₈	—	113	1	no	—
64	C₂×C₈	—	113	1	no	—
65	C₂×C₈	—	452	1	no	—
66	C₄⋊C₄	—	452	1	no	—
67	C₄⋊C₄	—	226	1	no	—
68	C₄²	—	113	1	no	—
69	C₄²	—	452	1	no	—
70	C₁₆	—	226	2	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	452	1	no	—
73	Q₈	—	226	1	no	—
74	C₂×C₄	—	113	1	no	—
75	C₂×C₄	—	113	1	no	—
76	C₂×C₄	—	113	1	no	—
77	C₂×C₄	—	452	1	no	—
78	C₂×C₄	—	452	1	no	—
79	C₈	—	113	1	no	—
80	C₈	—	904	1	no	—
81	C₈	—	226	1	no	—
82	C₈	C₂×#11744762	1	1	yes	characteristic
83	C₂²	—	113	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	113	1	no	—
86	C₄	—	113	1	no	—
87	C₄	—	113	1	no	—
88	C₄	—	904	1	no	—
89	C₄	—	452	1	no	—
90	C₄	—	226	1	no	—
91	C₄	C₂²⋊#11744762	1	1	yes	characteristic
92	C₂	—	113	1	no	—
93	C₂	—	113	1	no	—
94	C₂	D₄⋊#11744762	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄⋊#11744762
commutator	C₈×C₁₁₃	C₂×C₈
Frattini	C₈	C₂×#11744762
Fitting	Q₁₆×C₁₁₃	C₈
socle	C₂×C₁₁₃	D₄⋊C₈
prime radical	C₂×D₁₁₃	#102
cosocle	C₈×#90673	C₂²
hypercenter	Q₁₆	#11744762
hypocenter	C₁₁₃	#1332
LCS	G ▷ C₈×C₁₁₃ ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
19. Dic₄₅₂	C₈	semidirect
22. Q₁₆×C₁₁₃	C₈	semidirect
48. C₁₁₃	#1332	semidirect
62. Q₁₆	#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
#20299688	2
Q₁₆×#90673	2
#1332	113