Subgroups — #21447704

Order 7808.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840194	C₂	1	1	yes	maximal, characteristic
2	#16839878	C₂	1	2	yes	maximal, complemented
3	#16839568	C₂	1	2	yes	maximal, complemented
4	#16839537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#368	C₂	1	1	yes	maximal, characteristic, complemented
6	#14519799	C₂²	1	2	yes	—
7	#14519785	—	2	2	no	—
8	Dic₄₈₈	C₄	1	1	yes	characteristic, complemented
9	#14519722	C₄	1	2	yes	complemented
10	D₉₇₆	C₄	1	1	yes	characteristic, complemented
11	C₂×#11758185	C₂²	1	1	yes	characteristic
12	#14519703	—	2	2	no	—
13	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	#108×C₆₁	C₂²	1	2	yes	—
16	#11758222	—	2	2	no	—
17	M₁₆×C₆₁	—	2	2	no	—
18	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
19	C₄×Dic₆₁	D₄	1	1	yes	characteristic
20	C₂×#92418	D₄	1	1	yes	characteristic
21	Dic₂₄₄	C₂×C₄	1	2	yes	—
22	D₄₈₈	C₂×C₄	1	2	yes	—
23	#11758190	—	2	2	no	—
24	#11758189	—	4	2	no	—
25	C₈×D₆₁	—	4	2	no	—
26	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
28	#11758185	—	2	1	no	—
29	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂²⋊D₆₁	—	4	2	no	—
31	C₂×Dic₆₁	—	2	1	no	—
32	D₂₄₄	—	2	2	no	—
33	C₄×D₆₁	—	4	2	no	—
34	Dic₁₂₂	—	2	2	no	—
35	C₈×C₆₁	—	4	2	no	—
36	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₆₁	#41	1	1	yes	characteristic
38	#92418	D₈	1	2	yes	—
39	C₂²×C₆₁	#135	1	1	yes	characteristic
40	C₂×D₆₁	—	4	2	no	—
41	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
42	C₄×C₆₁	C₂×D₈	1	1	yes	characteristic
43	Dic₆₁	—	4	1	no	—
44	Dic₆₁	—	4	2	no	—
45	#2179	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	—	2	1	no	—
47	C₂×C₆₁	C₄×D₈	1	1	yes	characteristic
48	D₆₁	—	8	2	no	—
49	#508	—	61	1	no	—
50	#443	—	61	2	no	—
51	#368	D₆₁	1	1	yes	characteristic, complemented
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	—	61	1	no	—
60	C₂×C₁₆	—	61	1	no	—
61	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
62	#108	C₂×D₆₁	1	2	yes	—
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	—	61	2	no	—
69	M₁₆	—	2	2	no	—
70	M₁₆	—	244	2	no	—
71	C₂×C₈	—	61	1	no	—
72	C₂×C₈	—	244	2	no	—
73	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
74	C₄²	—	61	1	no	—
75	C₁₆	—	122	1	no	—
76	C₁₆	C₄×D₆₁	1	1	yes	characteristic
77	C₁₆	C₄×D₆₁	1	1	yes	characteristic
78	Q₈	—	122	2	no	—
79	D₄	—	122	2	no	—
80	D₄	—	244	2	no	—
81	C₂×C₄	—	122	1	no	—
82	C₂×C₄	—	244	2	no	—
83	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
84	C₈	—	4	2	no	—
85	C₈	—	61	2	no	—
86	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
87	C₈	#11758226	1	1	yes	characteristic
88	C₂²	—	244	2	no	—
89	C₂²	#14519800	1	1	yes	characteristic
90	C₄	—	244	1	no	—
91	C₄	—	244	2	no	—
92	C₄	#14519739	1	1	yes	characteristic
93	C₄	D₈×D₆₁	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	488	2	no	—
96	C₂	#16839844	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₈×D₆₁
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#368	C₂
socle	C₂×C₆₁	C₄×D₈
hypercenter	#368	D₆₁
hypocenter	C₆₁	#2179
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #368

Complements

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

N	H ≅ G/N	type
2. #16839878	C₂	semidirect
3. #16839568	C₂	semidirect
4. #16839537	C₂	semidirect
5. C₆₁×#368	C₂	semidirect
8. Dic₄₈₈	C₄	semidirect
9. #14519722	C₄	semidirect
10. D₉₇₆	C₄	semidirect
51. #368	D₆₁	semidirect
54. C₆₁	#2179	semidirect