Subgroups — #21447689

Order 7808.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₄₈₈	C₂	1	1	yes	maximal, characteristic
2	#16839856	C₂	1	2	yes	maximal
3	#16839565	C₂	1	2	yes	maximal
4	#16839537	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#367	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₂₄₄	C₂²	1	2	yes	—
7	#14519742	—	2	2	no	—
8	Dic₄₈₈	C₄	1	4	yes	complemented
9	C₂×#11758185	C₂²	1	1	yes	characteristic
10	#14519700	—	2	2	no	—
11	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	#107×C₆₁	C₂²	1	2	yes	—
14	C₂×Dic₁₂₂	—	2	2	no	—
15	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
16	C₄⋊C₄×C₆₁	—	2	2	no	—
17	#11758196	—	4	2	no	—
18	C₄×Dic₆₁	—	4	2	no	—
19	C₄×Dic₆₁	D₄	1	1	yes	characteristic
20	C₂×#92418	D₄	1	1	yes	characteristic
21	Dic₂₄₄	—	2	2	no	—
22	Dic₂₄₄	C₂×C₄	1	4	yes	—
23	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
24	#11758185	—	2	1	no	—
25	C₂×C₄×C₆₁	—	4	2	no	—
26	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	4	2	no	—
28	C₂×Dic₆₁	D₈	1	2	yes	—
29	Dic₁₂₂	—	2	4	no	—
30	Dic₁₂₂	—	4	2	no	—
31	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₆₁	#41	1	1	yes	characteristic
33	#92418	—	2	1	no	—
34	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
35	C₄×C₆₁	—	8	2	no	—
36	C₄×C₆₁	C₄×D₄	1	1	yes	characteristic
37	C₄×C₆₁	#135	1	1	yes	characteristic
38	Dic₆₁	—	2	2	no	—
39	Dic₆₁	—	4	4	no	—
40	#2176	—	61	1	no	maximal, Sylow
41	C₂×C₆₁	C₄×D₈	1	1	yes	characteristic
42	C₂×C₆₁	#510	1	2	yes	—
43	C₂×Q₃₂	—	61	1	no	—
44	C₄×Q₁₆	—	61	2	no	—
45	#367	D₆₁	1	1	yes	characteristic
46	#358	—	61	2	no	—
47	#346	—	61	1	no	—
48	C₆₁	#2176	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	—	61	2	no	—
50	C₄×Q₈	—	122	2	no	—
51	Q₃₂	—	61	4	no	—
52	C₂×C₁₆	—	61	1	no	—
53	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
54	#107	C₂×D₆₁	1	2	yes	—
55	#103	—	122	2	no	—
56	C₄×C₈	—	61	1	no	—
57	C₂×Q₈	—	122	2	no	—
58	Q₁₆	—	61	4	no	—
59	Q₁₆	—	122	2	no	—
60	C₂×C₈	—	61	1	no	—
61	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	244	2	no	—
64	C₄²	—	61	1	no	—
65	C₄²	—	244	2	no	—
66	C₁₆	—	122	1	no	—
67	C₁₆	C₄×D₆₁	1	2	yes	—
68	Q₈	—	122	4	no	—
69	Q₈	—	244	2	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	61	2	no	—
72	C₂×C₄	—	244	2	no	—
73	C₂×C₄	D₄×D₆₁	1	1	yes	characteristic
74	C₈	—	122	1	no	—
75	C₈	C₂×C₄×D₆₁	1	1	yes	characteristic
76	C₈	#11758226	1	1	yes	characteristic
77	C₂²	D₈×D₆₁	1	1	yes	characteristic
78	C₄	—	8	2	no	—
79	C₄	—	122	2	no	—
80	C₄	—	244	4	no	—
81	C₄	#14519739	1	1	yes	characteristic
82	C₄	#14519800	1	1	yes	characteristic
83	C₂	#16839844	1	1	yes	characteristic
84	C₂	#16840201	1	2	yes	—

	subgroup	G/H
center	C₂²	D₈×D₆₁
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#367	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#367	D₆₁
hypocenter	C₆₁	#2176
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

Complements

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

N	H ≅ G/N	type
8. Dic₄₈₈	C₄	semidirect
48. C₆₁	#2176	semidirect