Subgroups — #21460778

Order 7808.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840651	C₂	1	1	yes	maximal, characteristic, complemented
2	#16840623	C₂	1	1	yes	maximal, characteristic, complemented
3	#16839844	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758187	—	2	1	no	—
5	C₄⋊#92420	—	2	1	no	—
6	C₂×D₄₈₈	C₄	1	1	yes	characteristic
7	#14519739	—	2	1	no	—
8	#14519697	—	2	1	no	—
9	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
10	#107×C₆₁	C₄	1	1	yes	characteristic
11	C₂×D₂₄₄	—	2	1	no	—
12	C₂×C₄×D₆₁	—	4	1	no	—
13	C₂×#92420	—	4	1	no	—
14	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₄⋊C₄×C₆₁	—	2	1	no	—
16	#11758198	—	4	1	no	—
17	C₄×Dic₆₁	D₄	1	1	yes	characteristic
18	C₂×#92418	D₄	1	1	yes	characteristic
19	D₄₈₈	—	2	1	no	—
20	D₄₈₈	C₈	1	2	yes	complemented
21	#11758187	—	2	2	no	—
22	C₂²×D₆₁	—	4	1	no	—
23	C₂×C₄×C₆₁	—	4	1	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×Dic₆₁	D₈	1	1	yes	characteristic
26	C₂×Dic₆₁	SD₁₆	1	1	yes	characteristic
27	D₂₄₄	—	2	2	no	—
28	D₂₄₄	—	4	1	no	—
29	C₄×D₆₁	—	8	2	no	—
30	#92420	—	8	1	no	—
31	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₆₁	M₁₆	1	1	yes	characteristic
33	#92418	—	2	1	no	—
34	C₂²×C₆₁	#102	1	1	yes	characteristic
35	C₂×D₆₁	—	4	2	no	—
36	C₂×D₆₁	—	8	1	no	—
37	C₂×D₆₁	—	8	1	no	—
38	C₄×C₆₁	—	8	1	no	—
39	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
40	C₄×C₆₁	#104	1	1	yes	characteristic
41	Dic₆₁	—	2	1	no	—
42	Dic₆₁	—	2	1	no	—
43	#1333	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₆₁	#360	1	1	yes	characteristic
46	C₂×C₆₁	#361	1	1	yes	characteristic
47	D₆₁	—	8	2	no	—
48	C₄×D₈	—	61	1	no	—
49	#346	—	61	1	no	—
50	#334	—	61	1	no	—
51	C₆₁	#1333	1	1	yes	characteristic, complemented, Sylow
52	C₂×D₈	—	61	1	no	—
53	C₄×D₄	—	122	1	no	—
54	C₂×C₁₆	—	122	1	no	—
55	#107	#6923	1	1	yes	characteristic
56	C₄⋊C₈	—	122	1	no	—
57	#102	—	122	1	no	—
58	C₄×C₈	—	61	1	no	—
59	C₂×D₄	—	122	1	no	—
60	C₂²×C₄	—	244	1	no	—
61	D₈	—	61	2	no	—
62	D₈	—	122	1	no	—
63	C₂×C₈	—	61	1	no	—
64	C₂×C₈	—	244	1	no	—
65	C₂×C₈	C₂×#6923	1	1	yes	characteristic
66	C₄⋊C₄	—	2	1	no	—
67	C₂²⋊C₄	—	244	1	no	—
68	C₄²	—	61	1	no	—
69	C₁₆	—	122	2	no	—
70	C₂³	—	244	1	no	—
71	D₄	—	122	2	no	—
72	D₄	—	244	1	no	—
73	C₂×C₄	—	4	1	no	—
74	C₂×C₄	—	61	1	no	—
75	C₂×C₄	—	61	1	no	—
76	C₂×C₄	—	488	2	no	—
77	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
78	C₈	—	122	1	no	—
79	C₈	—	488	1	no	—
80	C₈	D₆₁⋊C₈	1	1	yes	characteristic
81	C₈	#11758213	1	1	yes	characteristic
82	C₂²	—	488	1	no	—
83	C₂²	—	488	1	no	—
84	C₂²	—	244	2	no	—
85	C₂²	#14519839	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	—	122	1	no	—
88	C₄	—	122	1	no	—
89	C₄	#14519834	1	1	yes	characteristic
90	C₄	#14519842	1	1	yes	characteristic
91	C₂	—	488	2	no	—
92	C₂	#16840610	1	1	yes	characteristic
93	C₂	#16840679	1	1	yes	characteristic
94	C₂	#16840680	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#14519839
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₂×C₈	C₂×#6923
Fitting	#107×C₆₁	C₄
socle	C₂²×C₆₁	#102
hypercenter	#107	#6923
hypocenter	C₆₁	#1333
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
1. #16840651	C₂	semidirect
2. #16840623	C₂	semidirect
20. D₄₈₈	C₈	semidirect
51. C₆₁	#1333	semidirect