Subgroups — C₂×#16839590 #21447599

Order 7808.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519711	C₂	1	2	yes	maximal
2	#16839590	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₆₁	—	2	2	no	—
5	#14519711	—	2	2	no	—
6	#14519711	C₂²	1	4	yes	—
7	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₆₁	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
10	C₂²×C₄×C₆₁	D₄	1	1	yes	characteristic
11	C₂²×Dic₆₁	—	4	2	no	—
12	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	Q₈	1	2	yes	—
15	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
16	C₄⋊Dic₆₁	—	2	4	no	—
17	C₄⋊Dic₆₁	—	4	2	no	—
18	C₁₆×C₆₁	C₂×C₄	1	4	yes	complemented
19	C₂³×C₆₁	D₈	1	1	yes	characteristic
20	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₆₁	Q₁₆	1	2	yes	—
23	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₆₁	—	4	4	no	—
25	C₂×Dic₆₁	—	8	4	no	—
26	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
27	C₈×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₆₁	#107	1	2	yes	—
30	C₂²×C₆₁	SD₃₂	1	4	yes	—
31	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₆₁	#107	1	2	yes	—
33	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
35	Dic₆₁	—	8	4	no	—
36	C₂×#367	—	61	1	no	maximal, Sylow
37	C₂×C₆₁	#367	1	4	yes	complemented
38	C₂×C₆₁	C₂×#107	1	1	yes	characteristic
39	C₂×C₆₁	C₂×SD₃₂	1	2	yes	—
40	C₂²×C₁₆	D₆₁	1	1	yes	characteristic
41	C₂×#107	—	61	2	no	—
42	#367	—	61	4	no	—
43	C₆₁	C₂×#367	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
45	C₂×C₄⋊C₄	—	122	2	no	—
46	C₂×C₁₆	Dic₆₁	1	4	yes	complemented
47	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
48	#107	—	61	4	no	—
49	#107	—	122	2	no	—
50	C₂²×C₄	—	244	2	no	—
51	C₂²×C₄	D₂₄₄	1	1	yes	characteristic
52	C₂×C₈	Dic₁₂₂	1	2	yes	—
53	C₂×C₈	D₂₄₄	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
55	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
56	C₄⋊C₄	—	122	4	no	—
57	C₄⋊C₄	—	244	2	no	—
58	C₁₆	C₂×Dic₆₁	1	4	yes	complemented
59	C₂³	D₄₈₈	1	1	yes	characteristic
60	C₂×C₄	—	488	4	no	—
61	C₂×C₄	—	244	4	no	—
62	C₂×C₄	D₄₈₈	1	1	yes	characteristic
63	C₂×C₄	Dic₂₄₄	1	2	yes	—
64	C₂×C₄	C₄⋊Dic₆₁	1	2	yes	—
65	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
66	C₈	C₄⋊Dic₆₁	1	2	yes	—
67	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
68	C₈	C₂²×Dic₆₁	1	1	yes	characteristic
69	C₂²	#14519711	1	2	yes	—
70	C₂²	#14519722	1	4	yes	—
71	C₂²	C₂×D₄₈₈	1	1	yes	characteristic
72	C₄	—	488	4	no	—
73	C₄	#14519711	1	2	yes	—
74	C₄	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
75	C₄	C₂×Dic₂₄₄	1	1	yes	characteristic
76	C₂	#16839590	1	4	yes	direct product factor
77	C₂	C₂×#14519711	1	1	yes	characteristic
78	C₂	C₂×#14519722	1	2	yes	—

	subgroup	G/H
center	C₂³	D₄₈₈
commutator	C₈×C₆₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₂²×C₁₆×C₆₁	C₂
socle	C₂³×C₆₁	D₈
hypercenter	C₂²×C₁₆	D₆₁
hypocenter	C₆₁	C₂×#367
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ 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	direct (N × H)
8. C₂×C₁₆×C₆₁	C₄	semidirect
18. C₁₆×C₆₁	C₂×C₄	semidirect
37. C₂×C₆₁	#367	semidirect
43. C₆₁	C₂×#367	semidirect
46. C₂×C₁₆	Dic₆₁	semidirect
58. C₁₆	C₂×Dic₆₁	semidirect
76. C₂	#16839590	direct (N × H)

Subgroups — C2×#16839590 #21447599

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839590 #21447599