Subgroups — C₂×#16840240 #21459010

Order 7808.

1488 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840240	C₂	1	16	yes	maximal, direct product factor
2	C₂×Q₈×Dic₆₁	C₂	1	8	yes	maximal, complemented
3	C₂×#14519736	C₂	1	6	yes	maximal
4	C₂³×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
5	Q₈×Dic₆₁	C₂²	1	64	yes	complemented
6	#14519736	C₂²	1	48	yes	—
7	C₂×C₄⋊Dic₆₁	C₂²	1	12	yes	—
8	C₂×C₂²⋊Dic₆₁	C₂²	1	4	yes	—
9	C₂×C₄×Dic₆₁	C₂²	1	12	yes	—
10	C₂²×Q₈×C₆₁	C₄	1	16	yes	complemented
11	C₂²×Q₈×C₆₁	C₂²	1	4	yes	—
12	C₂²×Q₈×C₆₁	C₂²	1	8	yes	—
13	C₂³×C₄×C₆₁	C₂²	1	3	yes	—
14	C₂⁴×C₆₁	C₂³	1	1	yes	characteristic
15	C₂×Q₈×C₆₁	C₂×C₄	1	32	yes	—
16	C₂×Q₈×C₆₁	C₂×C₄	1	64	yes	complemented
17	C₂×Q₈×C₆₁	C₂³	1	16	yes	—
18	C₂²×C₄×C₆₁	C₂×C₄	1	24	yes	—
19	C₂²×C₄×C₆₁	C₂³	1	6	yes	—
20	C₂²×C₄×C₆₁	C₂³	1	12	yes	—
21	C₂²×Dic₆₁	C₂³	1	8	yes	—
22	C₂²⋊Dic₆₁	C₂³	1	16	yes	—
23	C₄⋊Dic₆₁	C₂³	1	48	yes	—
24	C₄×Dic₆₁	C₂³	1	48	yes	—
25	C₂³×C₆₁	—	2	4	no	—
26	C₂³×C₆₁	C₂²×C₄	1	4	yes	—
27	C₂³×C₆₁	C₂⁴	1	2	yes	—
28	C₂³×C₆₁	C₂⁴	1	1	yes	characteristic
29	Q₈×C₆₁	C₂²×C₄	1	64	yes	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	24	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	48	yes	—
32	C₂×C₄×C₆₁	C₂⁴	1	12	yes	—
33	C₂×Dic₆₁	—	2	16	no	—
34	C₂×Dic₆₁	C₂⁴	1	16	yes	—
35	C₂²×C₆₁	—	2	8	no	—
36	C₂²×C₆₁	—	2	4	no	—
37	C₂²×C₆₁	C₂³×C₄	1	4	yes	—
38	C₂²×C₆₁	C₂³×C₄	1	2	yes	—
39	C₂²×C₆₁	2₋¹⁺⁴	1	4	yes	—
40	C₂²×C₆₁	C₂⁵	1	1	yes	characteristic
41	C₄×C₆₁	C₂³×C₄	1	24	yes	—
42	Dic₆₁	—	2	16	no	—
43	C₂×#519	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	—	2	4	no	—
45	C₂×C₆₁	#519	1	4	yes	complemented
46	C₂×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
47	C₂×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
48	C₂³×Q₈	D₆₁	1	1	yes	characteristic
49	#519	—	61	16	no	—
50	C₂×C₄×Q₈	—	61	8	no	—
51	C₂×#117	—	61	6	no	—
52	C₆₁	C₂×#519	1	1	yes	characteristic, complemented, Sylow
53	C₂²×Q₈	Dic₆₁	1	16	yes	complemented
54	C₂²×Q₈	C₂×D₆₁	1	4	yes	—
55	C₂²×Q₈	C₂×D₆₁	1	8	yes	—
56	C₂³×C₄	C₂×D₆₁	1	3	yes	—
57	C₄×Q₈	—	61	64	no	—
58	#117	—	61	48	no	—
59	C₂×C₄⋊C₄	—	61	12	no	—
60	C₂×C₂²⋊C₄	—	61	4	no	—
61	C₂×C₄²	—	61	12	no	—
62	C₂⁴	C₂²×D₆₁	1	1	yes	characteristic
63	C₂×Q₈	C₂×Dic₆₁	1	32	yes	—
64	C₂×Q₈	C₂×Dic₆₁	1	64	yes	complemented
65	C₂×Q₈	C₂²×D₆₁	1	16	yes	—
66	C₂²×C₄	—	61	8	no	—
67	C₂²×C₄	C₂×Dic₆₁	1	24	yes	—
68	C₂²×C₄	C₂²×D₆₁	1	12	yes	—
69	C₂²×C₄	C₂²×D₆₁	1	6	yes	—
70	C₄⋊C₄	—	61	48	no	—
71	C₂²⋊C₄	—	61	16	no	—
72	C₄²	—	61	48	no	—
73	C₂³	—	2	4	no	—
74	C₂³	C₂²×Dic₆₁	1	4	yes	—
75	C₂³	C₂³×D₆₁	1	2	yes	—
76	C₂³	C₂³×D₆₁	1	1	yes	characteristic
77	Q₈	C₂²×Dic₆₁	1	64	yes	—
78	C₂×C₄	—	61	16	no	—
79	C₂×C₄	—	122	16	no	—
80	C₂×C₄	C₂²×Dic₆₁	1	24	yes	—
81	C₂×C₄	C₂²×Dic₆₁	1	48	yes	—
82	C₂×C₄	C₂³×D₆₁	1	12	yes	—
83	C₂²	—	2	8	no	—
84	C₂²	—	2	4	no	—
85	C₂²	C₂³×Dic₆₁	1	4	yes	—
86	C₂²	C₂³×Dic₆₁	1	2	yes	—
87	C₂²	#14519825	1	4	yes	—
88	C₂²	C₂⁴×D₆₁	1	1	yes	characteristic
89	C₄	—	122	16	no	—
90	C₄	C₂³×Dic₆₁	1	24	yes	—
91	C₂	—	2	4	no	—
92	C₂	#16840240	1	4	yes	direct product factor
93	C₂	C₂⁴×Dic₆₁	1	1	yes	characteristic
94	C₂	C₂×#14519825	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₆₁
commutator	C₂×C₆₁	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₆₁
Fitting	C₂³×Q₈×C₆₁	C₂
socle	C₂³×C₆₁	C₂⁴
hypercenter	C₂³×Q₈	D₆₁
hypocenter	C₆₁	C₂×#519
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
1. #16840240	C₂	direct (N × H)
2. C₂×Q₈×Dic₆₁	C₂	semidirect
5. Q₈×Dic₆₁	C₂²	semidirect
10. C₂²×Q₈×C₆₁	C₄	semidirect
16. C₂×Q₈×C₆₁	C₂×C₄	semidirect
45. C₂×C₆₁	#519	semidirect
52. C₆₁	C₂×#519	semidirect
53. C₂²×Q₈	Dic₆₁	semidirect
64. C₂×Q₈	C₂×Dic₆₁	semidirect
92. C₂	#16840240	direct (N × H)

Subgroups — C2×#16840240 #21459010

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16840240 #21459010