Subgroups — #20298899

Order 7232.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813614	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₄₅₂	C₂	1	1	yes	maximal, characteristic
3	#16813556	C₂	1	1	yes	maximal, characteristic, complemented
4	#16813554	C₂	1	1	yes	maximal, characteristic, complemented
5	#16813544	C₂	1	1	yes	maximal, characteristic
6	#16813544	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₄₅₂	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₁₃	—	2	1	no	—
10	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
13	#14268626	—	2	1	no	—
14	#14268626	—	2	1	no	—
15	#14268624	—	2	1	no	—
16	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₄²×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₁₁₃	—	2	1	no	—
20	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₁₃	—	2	1	no	—
24	C₂×Dic₁₁₃	—	2	1	no	—
25	C₂×Dic₁₁₃	—	2	1	no	—
26	D₄₅₂	—	2	1	no	—
27	D₄₅₂	Q₈	1	2	yes	—
28	C₄×D₁₁₃	—	4	2	no	—
29	C₈×C₁₁₃	—	2	1	no	—
30	C₈×C₁₁₃	—	2	1	no	—
31	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
32	C₂×D₁₁₃	—	2	2	no	—
33	C₂×D₁₁₃	—	4	1	no	—
34	C₂×D₁₁₃	—	4	1	no	—
35	C₄×C₁₁₃	—	2	1	no	—
36	C₄×C₁₁₃	—	2	1	no	—
37	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
38	C₄×C₁₁₃	#41	1	1	yes	characteristic
39	Dic₁₁₃	—	4	1	no	—
40	Dic₁₁₃	—	4	1	no	—
41	Dic₁₁₃	—	4	1	no	—
42	C₂×C₁₁₃	C₂²⋊Q₈	1	1	yes	characteristic
43	C₂×C₁₁₃	#135	1	1	yes	characteristic
44	C₂×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
45	D₁₁₃	—	4	2	no	—
46	C₁₁₃	#478	1	1	yes	characteristic, complemented, Sylow
47	#478	—	113	1	no	maximal, Sylow
48	#125	—	113	1	no	—
49	C₄×D₄	—	113	1	no	—
50	#107	—	113	1	no	—
51	#106	—	113	1	no	—
52	C₄⋊C₈	D₁₁₃	1	1	yes	characteristic, complemented
53	#102	—	113	1	no	—
54	#102	—	113	1	no	—
55	C₂×D₄	—	113	1	no	—
56	C₂²×C₄	—	226	1	no	—
57	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
58	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
59	C₄⋊C₄	—	113	1	no	—
60	C₄⋊C₄	—	113	1	no	—
61	C₄⋊C₄	—	113	1	no	—
62	C₄⋊C₄	—	226	1	no	—
63	C₄⋊C₄	—	226	1	no	—
64	C₂²⋊C₄	—	226	1	no	—
65	C₄²	C₂×D₁₁₃	1	1	yes	characteristic
66	C₂³	—	226	1	no	—
67	D₄	—	113	2	no	—
68	D₄	—	226	1	no	—
69	C₂×C₄	—	452	2	no	—
70	C₂×C₄	—	226	1	no	—
71	C₂×C₄	—	226	1	no	—
72	C₂×C₄	—	226	1	no	—
73	C₂×C₄	D₄₅₂	1	1	yes	characteristic
74	C₂×C₄	D₄₅₂	1	1	yes	characteristic
75	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	2	1	no	—
78	C₂²	—	452	1	no	—
79	C₂²	—	452	1	no	—
80	C₂²	—	226	2	no	—
81	C₂²	C₂×D₄₅₂	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	452	1	no	—
85	C₄	—	452	1	no	—
86	C₄	—	452	1	no	—
87	C₄	Q₈×D₁₁₃	1	1	yes	characteristic
88	C₄	#14268646	1	1	yes	characteristic
89	C₂	—	452	2	no	—
90	C₂	#16813602	1	1	yes	characteristic
91	C₂	#16813644	1	1	yes	characteristic
92	C₂	#16813650	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄₅₂
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₄⋊C₈×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	C₄⋊C₈	D₁₁₃
hypocenter	C₁₁₃	#478
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. #16813614	C₂	semidirect
3. #16813556	C₂	semidirect
4. #16813554	C₂	semidirect
7. C₄⋊C₈×C₁₁₃	C₂	semidirect
46. C₁₁₃	#478	semidirect
52. C₄⋊C₈	D₁₁₃	semidirect