Subgroups — #21447603

Order 7808.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839800	C₂	1	2	yes	maximal
2	#16839590	C₂	1	2	yes	maximal, complemented
3	#16839588	C₂	1	2	yes	maximal, complemented
4	C₂²×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
5	#14519736	—	2	2	no	—
6	#14519711	C₂²	1	4	yes	—
7	#14519709	—	2	2	no	—
8	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×C₆₁	C₄	1	4	yes	complemented
10	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
13	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	Q₈	1	2	yes	—
16	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
17	C₂²⋊Dic₆₁	—	4	2	no	—
18	C₄⋊Dic₆₁	—	2	4	no	—
19	C₄×Dic₆₁	—	4	2	no	—
20	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
21	C₁₆×C₆₁	C₂×C₄	1	2	yes	—
22	C₂³×C₆₁	D₈	1	1	yes	characteristic
23	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
25	C₂×C₄×C₆₁	Q₁₆	1	2	yes	—
26	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	4	4	no	—
28	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
29	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
31	C₂²×C₆₁	—	2	2	no	—
32	C₂²×C₆₁	#107	1	2	yes	—
33	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
34	C₄×C₆₁	#107	1	2	yes	—
35	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
37	Dic₆₁	—	8	4	no	—
38	#2158	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	—	2	2	no	—
40	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
41	C₂×C₆₁	#508	1	2	yes	—
42	C₂²×C₁₆	D₆₁	1	1	yes	characteristic
43	#427	—	61	2	no	—
44	#367	—	61	2	no	—
45	#366	—	61	2	no	—
46	C₆₁	#2158	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
48	#117	—	122	2	no	—
49	C₂×C₁₆	Dic₆₁	1	4	yes	complemented
50	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
51	C₂×C₁₆	C₂×D₆₁	1	1	yes	characteristic
52	#107	—	61	4	no	—
53	#106	—	122	2	no	—
54	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
55	C₂×C₈	Dic₁₂₂	1	2	yes	—
56	C₂×C₈	D₂₄₄	1	1	yes	characteristic
57	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
58	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
59	C₄⋊C₄	—	122	4	no	—
60	C₂²⋊C₄	—	244	2	no	—
61	C₄²	—	244	2	no	—
62	C₁₆	C₂×Dic₆₁	1	2	yes	—
63	C₁₆	C₂×Dic₆₁	1	2	yes	—
64	C₂³	D₄₈₈	1	1	yes	characteristic
65	C₂×C₄	—	244	4	no	—
66	C₂×C₄	D₄₈₈	1	1	yes	characteristic
67	C₂×C₄	Dic₂₄₄	1	2	yes	—
68	C₂×C₄	C₄⋊Dic₆₁	1	2	yes	—
69	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
70	C₈	C₄⋊Dic₆₁	1	2	yes	—
71	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
72	C₈	C₂²×Dic₆₁	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	#14519711	1	2	yes	—
75	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
76	C₄	—	488	4	no	—
77	C₄	#14519711	1	2	yes	—
78	C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
79	C₄	C₂×Dic₂₄₄	1	1	yes	characteristic
80	C₂	—	2	2	no	—
81	C₂	C₂×#14519711	1	1	yes	characteristic
82	C₂	#16840194	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₄₈₈
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂²×C₁₆×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	C₂²×C₁₆	D₆₁
hypocenter	C₆₁	#2158
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #16839590	C₂	semidirect
3. #16839588	C₂	semidirect
9. C₂×C₁₆×C₆₁	C₄	semidirect
46. C₆₁	#2158	semidirect
49. C₂×C₁₆	Dic₆₁	semidirect