Subgroups — #20298959

Order 7232.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813621	C₂	1	1	yes	maximal, characteristic, complemented
2	#16813611	C₂	1	1	yes	maximal, characteristic
3	#16813546	C₂	1	1	yes	maximal, characteristic, complemented
4	#16813544	C₂	1	1	yes	maximal, characteristic
5	#16813542	C₂	1	1	yes	maximal, characteristic
6	#16813532	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₂₆	—	2	1	no	—
9	C₂×D₄₅₂	C₂²	1	1	yes	characteristic
10	C₂×#11744751	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
12	#14268626	—	2	1	no	—
13	#14268624	—	2	1	no	—
14	#14268624	—	2	1	no	—
15	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₂²×D₁₁₃	—	2	1	no	—
20	Q₈×C₁₁₃	—	2	1	no	—
21	Q₈×C₁₁₃	—	2	1	no	—
22	C₂×C₄×C₁₁₃	—	2	1	no	—
23	C₂×C₄×C₁₁₃	—	2	1	no	—
24	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₁₃	—	2	1	no	—
26	C₂×Dic₁₁₃	D₄	1	1	yes	characteristic
27	C₂×Dic₁₁₃	D₄	1	1	yes	characteristic
28	D₄₅₂	—	2	1	no	—
29	D₄₅₂	—	2	1	no	—
30	Dic₂₂₆	—	4	2	no	—
31	C₈×C₁₁₃	—	2	1	no	—
32	#11744751	—	2	1	no	—
33	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₁₃	—	4	1	no	—
35	C₂×D₁₁₃	—	4	1	no	—
36	C₂×D₁₁₃	—	4	1	no	—
37	C₄×C₁₁₃	—	4	1	no	—
38	C₄×C₁₁₃	—	4	1	no	—
39	C₄×C₁₁₃	#41	1	1	yes	characteristic
40	C₄×C₁₁₃	#41	1	1	yes	characteristic
41	Dic₁₁₃	—	2	1	no	—
42	Dic₁₁₃	—	2	1	no	—
43	Dic₁₁₃	—	4	1	no	—
44	C₂×C₁₁₃	#124	1	1	yes	characteristic
45	C₂×C₁₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₁₁₃	#137	1	1	yes	characteristic
47	D₁₁₃	—	8	1	no	—
48	C₁₁₃	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	113	1	no	maximal, Sylow
50	C₄⋊Q₈	—	113	1	no	—
51	#124	—	113	1	no	—
52	#103	—	113	1	no	—
53	#103	D₁₁₃	1	1	yes	characteristic, complemented
54	#102	—	113	1	no	—
55	#102	—	113	1	no	—
56	#97	—	113	1	no	—
57	C₂×Q₈	—	226	1	no	—
58	C₂×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
59	C₂×D₄	—	113	1	no	—
60	C₂×C₈	—	113	1	no	—
61	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
62	C₄⋊C₄	—	113	1	no	—
63	C₄⋊C₄	—	226	1	no	—
64	C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
65	C₂²⋊C₄	—	226	1	no	—
66	C₂²⋊C₄	—	226	1	no	—
67	C₄²	—	113	1	no	—
68	C₂³	—	226	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	452	2	no	—
72	D₄	—	226	1	no	—
73	D₄	—	226	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	113	1	no	—
77	C₂×C₄	—	113	1	no	—
78	C₂×C₄	—	226	1	no	—
79	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	226	1	no	—
82	C₂²	—	452	1	no	—
83	C₂²	—	452	1	no	—
84	C₂²	—	452	1	no	—
85	C₂²	D₄×D₁₁₃	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	452	1	no	—
89	C₄	—	226	1	no	—
90	C₄	—	226	1	no	—
91	C₄	#14268646	1	1	yes	characteristic
92	C₄	#14268647	1	1	yes	characteristic
93	C₂	—	904	1	no	—
94	C₂	#16813608	1	1	yes	characteristic
95	C₂	#16813649	1	1	yes	characteristic
96	C₂	#16813654	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₁₃
commutator	C₂×C₄×C₁₁₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	#103×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	#103	D₁₁₃
hypocenter	C₁₁₃	#489
LCS	G ▷ C₂×C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #16813621	C₂	semidirect
3. #16813546	C₂	semidirect
6. #16813532	C₂	semidirect
7. #103×C₁₁₃	C₂	semidirect
48. C₁₁₃	#489	semidirect
53. #103	D₁₁₃	semidirect