Subgroups — #28407627

Order 14464.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299702	C₂	1	1	yes	maximal, characteristic, complemented
2	#20299682	C₂	1	1	yes	maximal, characteristic, complemented
3	#20299642	C₂	1	1	yes	maximal, characteristic
4	#16813719	—	2	1	no	—
5	C₄×#11744762	—	2	1	no	—
6	#16813710	—	2	1	no	—
7	#16813693	C₄	1	1	yes	characteristic
8	#16813687	—	2	1	no	—
9	C₈×#90673	C₂²	1	1	yes	characteristic
10	#16813645	C₄	1	1	yes	characteristic
11	C₂×#11744762	—	2	2	no	—
12	#14268659	—	4	1	no	—
13	#14268657	—	2	1	no	—
14	#14268657	—	4	1	no	—
15	#14268655	—	4	1	no	—
16	#14268655	D₄	1	1	yes	characteristic
17	C₄×#90673	D₄	1	1	yes	characteristic
18	#14268648	—	2	1	no	—
19	#14268634	—	2	1	no	—
20	D₉₀₄	C₈	1	1	yes	characteristic, complemented
21	C₈×D₁₁₃	C₂×C₄	1	1	yes	characteristic
22	Q₁₆×C₁₁₃	C₈	1	1	yes	characteristic, complemented
23	C₂×#90673	—	2	1	no	—
24	#11744762	—	4	2	no	—
25	Q₈×C₁₁₃	—	2	1	no	—
26	D₄₅₂	—	2	1	no	—
27	D₄₅₂	—	4	1	no	—
28	C₄×D₁₁₃	—	4	1	no	—
29	C₄×D₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	#11744753	—	4	1	no	—
31	#11744753	D₈	1	1	yes	characteristic
32	#11744753	SD₁₆	1	1	yes	characteristic
33	C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
34	#11744751	M₁₆	1	1	yes	characteristic
35	C₂×D₁₁₃	—	4	1	no	—
36	C₂×D₁₁₃	#104	1	1	yes	characteristic
37	#90673	—	2	2	no	—
38	C₄×C₁₁₃	—	4	1	no	—
39	C₄×C₁₁₃	C₂²⋊C₈	1	1	yes	characteristic
40	Dic₁₁₃	#102	1	1	yes	characteristic
41	C₂×C₁₁₃	D₄⋊C₈	1	1	yes	characteristic
42	D₁₁₃	—	2	1	no	—
43	D₁₁₃	—	8	1	no	—
44	#1336	—	113	1	no	maximal, Sylow
45	C₁₁₃	#1336	1	1	yes	characteristic, complemented, Sylow
46	#443	—	113	1	no	—
47	#364	—	113	1	no	—
48	#322	—	113	1	no	—
49	#135	—	113	1	no	—
50	#131	—	226	1	no	—
51	M₃₂	—	226	1	no	—
52	#108	—	113	1	no	—
53	#104	—	226	1	no	—
54	C₄×C₈	—	113	1	no	—
55	C₄×C₈	—	226	1	no	—
56	#41	—	226	1	no	—
57	Q₁₆	#11744762	1	1	yes	characteristic, complemented
58	SD₁₆	—	226	1	no	—
59	D₈	—	113	1	no	—
60	M₁₆	—	452	1	no	—
61	M₁₆	—	226	1	no	—
62	C₂×C₈	—	113	1	no	—
63	C₂×C₈	—	113	1	no	—
64	C₂×C₈	—	452	1	no	—
65	C₂×C₈	—	226	2	no	—
66	C₄²	—	113	1	no	—
67	C₁₆	—	452	1	no	—
68	Q₈	—	2	1	no	—
69	D₄	—	452	1	no	—
70	D₄	—	226	1	no	—
71	C₂×C₄	—	113	1	no	—
72	C₂×C₄	—	452	1	no	—
73	C₂×C₄	—	226	1	no	—
74	C₈	—	113	1	no	—
75	C₈	—	113	1	no	—
76	C₈	—	113	1	no	—
77	C₈	—	452	1	no	—
78	C₈	—	452	2	no	—
79	C₈	C₂×#11744762	1	1	yes	characteristic
80	C₂²	—	113	1	no	—
81	C₂²	—	452	1	no	—
82	C₄	—	4	1	no	—
83	C₄	—	113	1	no	—
84	C₄	—	226	2	no	—
85	C₄	C₂²⋊#11744762	1	1	yes	characteristic
86	C₂	—	904	1	no	—
87	C₂	—	226	1	no	—
88	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	#16813645	C₄
cosocle	C₈×#90673	C₂²
hypercenter	Q₁₆	#11744762
hypocenter	C₁₁₃	#1336
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
1. #20299702	C₂	semidirect
2. #20299682	C₂	semidirect
20. D₉₀₄	C₈	semidirect
22. Q₁₆×C₁₁₃	C₈	semidirect
45. C₁₁₃	#1336	semidirect
57. Q₁₆	#11744762	semidirect

Maximal subgroups

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

subgroup	index
#20299702	2
#20299682	2
#20299642	2
#1336	113