Subgroups — #20298690

Order 7232.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268637	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
3	#16813587	C₂	1	1	yes	maximal, characteristic
4	#16813555	C₂	1	1	yes	maximal, characteristic
5	#16813547	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₁₁₃	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₂₆	C₂²	1	1	yes	characteristic
9	#14268637	C₄	1	4	yes	complemented
10	C₂×#11744751	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₁₃	—	2	1	no	—
12	C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
13	#14268626	—	2	1	no	—
14	C₄×Dic₁₁₃	—	2	1	no	—
15	C₄×Dic₁₁₃	—	2	1	no	—
16	C₄×Dic₁₁₃	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
20	Q₈×C₁₁₃	—	2	1	no	—
21	Q₈×C₁₁₃	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
27	C₂×Dic₁₁₃	D₄	1	1	yes	characteristic
28	C₂×Dic₁₁₃	D₄	1	1	yes	characteristic
29	Dic₂₂₆	—	2	1	no	—
30	Dic₂₂₆	C₂×C₄	1	2	yes	—
31	C₈×C₁₁₃	—	2	1	no	—
32	#11744751	C₂×C₄	1	2	yes	—
33	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₁₃	—	2	2	no	—
35	C₄×C₁₁₃	—	4	1	no	—
36	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₁₁₃	#41	1	1	yes	characteristic
38	Dic₁₁₃	—	2	2	no	—
39	Dic₁₁₃	—	2	1	no	—
40	Dic₁₁₃	—	4	1	no	—
41	Dic₁₁₃	Q₁₆	1	2	yes	complemented
42	C₂×C₁₁₃	C₄×D₄	1	1	yes	characteristic
43	C₂×C₁₁₃	C₂×Q₁₆	1	1	yes	characteristic
44	C₂×C₁₁₃	#135	1	1	yes	characteristic
45	C₁₁₃	C₄×Q₁₆	1	1	yes	characteristic, complemented, Sylow
46	C₄×Q₁₆	—	113	1	no	maximal, Sylow
47	C₂×Q₁₆	—	113	1	no	—
48	C₄×Q₈	—	113	1	no	—
49	C₄×Q₈	—	113	1	no	—
50	#107	—	113	1	no	—
51	#103	—	113	1	no	—
52	#103	D₁₁₃	1	1	yes	characteristic
53	C₄×C₈	—	113	1	no	—
54	C₂×Q₈	—	113	1	no	—
55	C₂×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
56	Q₁₆	—	113	4	no	—
57	C₂×C₈	—	113	1	no	—
58	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
59	C₄⋊C₄	—	113	1	no	—
60	C₄⋊C₄	—	226	1	no	—
61	C₄⋊C₄	—	226	1	no	—
62	C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
63	C₄²	—	113	1	no	—
64	C₄²	—	226	1	no	—
65	C₄²	—	226	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	113	2	no	—
68	Q₈	—	226	1	no	—
69	Q₈	C₄×D₁₁₃	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	113	1	no	—
73	C₂×C₄	—	113	1	no	—
74	C₂×C₄	—	226	1	no	—
75	C₂×C₄	—	226	1	no	—
76	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	113	2	no	—
79	C₂²	D₄×D₁₁₃	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	113	2	no	—
83	C₄	—	452	1	no	—
84	C₄	—	226	2	no	—
85	C₄	—	226	1	no	—
86	C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
87	C₄	#14268646	1	1	yes	characteristic
88	C₂	#16813582	1	1	yes	characteristic
89	C₂	Q₁₆×D₁₁₃	1	1	yes	characteristic
90	C₂	#16813643	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₁₃
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	#103×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	#103	D₁₁₃
hypocenter	C₁₁₃	C₄×Q₁₆
LCS	G ▷ 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
9. #14268637	C₄	semidirect
41. Dic₁₁₃	Q₁₆	semidirect
45. C₁₁₃	C₄×Q₁₆	semidirect