Subgroups — #21462223

Order 7808.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840804	C₂	1	2	yes	maximal, complemented
2	#16840691	C₂	1	1	yes	maximal, characteristic, complemented
3	#16840676	C₂	1	2	yes	maximal, complemented
4	#16840649	C₂	1	1	yes	maximal, characteristic, complemented
5	#16840191	C₂	1	1	yes	maximal, characteristic
6	#14519864	—	2	2	no	—
7	D₆₁⋊C₁₆	C₂²	1	1	yes	characteristic
8	#14519848	C₂²	1	2	yes	—
9	#14519841	—	2	2	no	—
10	C₈×#6923	C₂²	1	1	yes	characteristic
11	#14519796	C₂²	1	2	yes	—
12	Dic₄₈₈	C₄	1	1	yes	characteristic, complemented
13	#14519721	C₄	1	2	yes	complemented
14	C₁₆×D₆₁	C₂²	1	1	yes	characteristic
15	D₁₆×C₆₁	C₄	1	1	yes	characteristic, complemented
16	#11758224	—	2	2	no	—
17	#11758217	—	4	2	no	—
18	C₂×#92420	—	4	2	no	—
19	C₄×#6923	D₄	1	1	yes	characteristic
20	#11758213	—	2	2	no	—
21	D₆₁⋊C₈	D₄	1	1	yes	characteristic
22	D₈×C₆₁	C₂×C₄	1	2	yes	—
23	#11758200	—	2	2	no	—
24	Dic₂₄₄	C₂×C₄	1	2	yes	—
25	C₈×D₆₁	C₂³	1	1	yes	characteristic
26	#11758187	—	2	1	no	—
27	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
28	#11758185	C₂×C₄	1	1	yes	characteristic
29	C₂×#6923	—	2	1	no	—
30	D₄×C₆₁	—	2	2	no	—
31	C₂²⋊D₆₁	—	4	2	no	—
32	C₂×Dic₆₁	—	4	2	no	—
33	C₄×D₆₁	C₂×D₄	1	1	yes	characteristic
34	Dic₁₂₂	—	2	2	no	—
35	#92420	—	4	2	no	—
36	#92420	D₈	1	2	yes	—
37	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
38	#92418	#41	1	1	yes	characteristic
39	C₂²×C₆₁	—	4	2	no	—
40	C₂×D₆₁	#135	1	1	yes	characteristic
41	#6923	—	4	1	no	—
42	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
43	Dic₆₁	—	4	2	no	—
44	Dic₆₁	C₂×D₈	1	1	yes	characteristic
45	#2179	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	—	8	2	no	—
47	C₂×C₆₁	C₄×D₈	1	1	yes	characteristic
48	D₆₁	—	2	1	no	—
49	#508	—	61	1	no	—
50	#443	—	61	2	no	—
51	#368	—	61	1	no	—
52	#359	—	61	2	no	—
53	#346	—	61	1	no	—
54	C₆₁	#2179	1	1	yes	characteristic, complemented, Sylow
55	#135	—	61	2	no	—
56	#131	—	122	2	no	—
57	Q₃₂	—	61	1	no	—
58	SD₃₂	—	61	2	no	—
59	D₁₆	#6923	1	1	yes	characteristic, complemented
60	C₂×C₁₆	—	61	1	no	—
61	C₂×C₁₆	—	61	1	no	—
62	#108	—	61	2	no	—
63	#104	—	122	2	no	—
64	C₄×C₈	—	61	1	no	—
65	#41	—	122	2	no	—
66	Q₁₆	—	61	2	no	—
67	SD₁₆	—	122	2	no	—
68	D₈	C₂×#6923	1	2	yes	—
69	M₁₆	—	122	2	no	—
70	M₁₆	—	244	2	no	—
71	C₂×C₈	—	61	1	no	—
72	C₂×C₈	—	61	1	no	—
73	C₂×C₈	—	244	2	no	—
74	C₄²	—	61	1	no	—
75	C₁₆	—	61	1	no	—
76	C₁₆	—	122	1	no	—
77	C₁₆	C₂×#6923	1	1	yes	characteristic
78	Q₈	—	122	2	no	—
79	D₄	—	2	2	no	—
80	D₄	—	244	2	no	—
81	C₂×C₄	—	61	1	no	—
82	C₂×C₄	—	122	1	no	—
83	C₂×C₄	—	244	2	no	—
84	C₈	—	61	2	no	—
85	C₈	—	61	1	no	—
86	C₈	—	244	2	no	—
87	C₈	C₂²×#6923	1	1	yes	characteristic
88	C₂²	—	4	2	no	—
89	C₂²	—	61	1	no	—
90	C₄	—	61	1	no	—
91	C₄	—	244	1	no	—
92	C₄	—	244	2	no	—
93	C₄	D₄×#6923	1	1	yes	characteristic
94	C₂	—	8	2	no	—
95	C₂	—	122	1	no	—
96	C₂	D₈×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#6923
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₈	C₂²×#6923
Fitting	D₁₆×C₆₁	C₄
socle	C₂×C₆₁	C₄×D₈
hypercenter	D₁₆	#6923
hypocenter	C₆₁	#2179
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #16840804	C₂	semidirect
2. #16840691	C₂	semidirect
3. #16840676	C₂	semidirect
4. #16840649	C₂	semidirect
12. Dic₄₈₈	C₄	semidirect
13. #14519721	C₄	semidirect
15. D₁₆×C₆₁	C₄	semidirect
54. C₆₁	#2179	semidirect
59. D₁₆	#6923	semidirect