Subgroups — C₂×#16839630 #21448209

Order 7808.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839630	C₂	1	8	yes	maximal, direct product factor
2	C₂×#14519684	C₂	1	6	yes	maximal
3	C₂²×C₄²×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₆₁	C₂²	1	4	yes	—
5	#14519684	C₂²	1	24	yes	—
6	C₂³×C₄×C₆₁	C₂²	1	3	yes	—
7	C₂×C₄²×C₆₁	C₄	1	8	yes	complemented
8	C₂×C₄²×C₆₁	C₂²	1	4	yes	—
9	C₂⁴×C₆₁	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₆₁	—	2	12	no	—
11	C₂²×C₄×C₆₁	C₂×C₄	1	12	yes	—
12	C₂²×C₄×C₆₁	C₂³	1	6	yes	—
13	C₂²×Dic₆₁	—	2	24	no	—
14	C₂²×Dic₆₁	C₂³	1	8	yes	—
15	C₄²×C₆₁	C₂×C₄	1	16	yes	complemented
16	C₂³×C₆₁	C₂²×C₄	1	2	yes	—
17	C₂³×C₆₁	#41	1	12	yes	—
18	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₆₁	—	2	24	no	—
20	C₂×C₄×C₆₁	—	2	12	no	—
21	C₂×C₄×C₆₁	C₂²×C₄	1	12	yes	—
22	C₂×Dic₆₁	—	2	24	no	—
23	C₂×Dic₆₁	—	4	16	no	—
24	C₂²×C₆₁	#117	1	12	yes	—
25	C₂²×C₆₁	#126	1	16	yes	—
26	C₂²×C₆₁	C₂³×C₄	1	1	yes	characteristic
27	C₂²×C₆₁	C₂×#41	1	6	yes	—
28	C₄×C₆₁	—	2	12	no	—
29	Dic₆₁	—	4	8	no	—
30	C₂×#383	—	61	1	no	maximal, Sylow
31	C₂×C₆₁	#383	1	8	yes	complemented
32	C₂×C₆₁	C₂×#117	1	3	yes	—
33	C₂×C₆₁	C₂×#126	1	4	yes	—
34	C₂²×C₄²	D₆₁	1	1	yes	characteristic
35	#383	—	61	8	no	—
36	C₂×#95	—	61	6	no	—
37	C₆₁	C₂×#383	1	1	yes	characteristic, complemented, Sylow
38	C₂³×C₄	—	61	4	no	—
39	C₂³×C₄	C₂×D₆₁	1	3	yes	—
40	C₂×C₄²	Dic₆₁	1	8	yes	complemented
41	C₂×C₄²	C₂×D₆₁	1	4	yes	—
42	#95	—	61	24	no	—
43	C₂⁴	C₂²×D₆₁	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	61	8	no	—
46	C₂²×C₄	—	122	24	no	—
47	C₂²×C₄	C₂×Dic₆₁	1	12	yes	—
48	C₂²×C₄	C₂²×D₆₁	1	6	yes	—
49	C₄²	C₂×Dic₆₁	1	16	yes	complemented
50	C₂³	#11758222	1	12	yes	—
51	C₂³	C₂²×Dic₆₁	1	2	yes	—
52	C₂³	C₂³×D₆₁	1	1	yes	characteristic
53	C₂×C₄	—	2	12	no	—
54	C₂×C₄	—	2	24	no	—
55	C₂×C₄	—	122	24	no	—
56	C₂×C₄	—	244	16	no	—
57	C₂×C₄	C₂²×Dic₆₁	1	12	yes	—
58	C₂²	#14519736	1	12	yes	—
59	C₂²	#14519771	1	16	yes	—
60	C₂²	C₂³×Dic₆₁	1	1	yes	characteristic
61	C₂²	C₂×#11758222	1	6	yes	—
62	C₄	—	2	12	no	—
63	C₄	—	244	8	no	—
64	C₂	#16839630	1	8	yes	direct product factor
65	C₂	C₂×#14519736	1	3	yes	—
66	C₂	C₂×#14519771	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₆₁
commutator	C₂²×C₆₁	C₂³×C₄
Frattini	C₂³	C₂³×D₆₁
Fitting	C₂²×C₄²×C₆₁	C₂
socle	C₂⁴×C₆₁	C₂³
hypercenter	C₂²×C₄²	D₆₁
hypocenter	C₆₁	C₂×#383
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #16839630	C₂	direct (N × H)
7. C₂×C₄²×C₆₁	C₄	semidirect
15. C₄²×C₆₁	C₂×C₄	semidirect
31. C₂×C₆₁	#383	semidirect
37. C₆₁	C₂×#383	semidirect
40. C₂×C₄²	Dic₆₁	semidirect
49. C₄²	C₂×Dic₆₁	semidirect
64. C₂	#16839630	direct (N × H)

Subgroups — C2×#16839630 #21448209

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16839630 #21448209