Subgroups — C₂×#14519825 #16840596

Order 3904.

794 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519825	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11758226	C₂	1	4	yes	maximal, complemented
3	C₂×#11758222	C₂	1	6	yes	maximal, complemented
4	C₂×Q₈×D₆₁	C₂	1	4	yes	maximal, complemented
5	C₂²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×Q₈×C₆₁	C₂²	1	4	yes	—
7	C₂×Q₈×C₆₁	C₂²	1	8	yes	complemented
8	C₂²×C₄×C₆₁	C₂²	1	3	yes	—
9	C₂×C₂²⋊D₆₁	C₂²	1	4	yes	—
10	#11758226	C₂²	1	32	yes	complemented
11	Q₈×D₆₁	C₂²	1	32	yes	complemented
12	#11758222	C₂²	1	48	yes	complemented
13	C₂×D₂₄₄	C₂²	1	6	yes	—
14	C₂×C₄×D₆₁	C₂²	1	12	yes	—
15	C₂×Dic₁₂₂	C₂²	1	6	yes	—
16	C₂³×C₆₁	C₂³	1	1	yes	characteristic
17	C₂²×D₆₁	C₂³	1	4	yes	—
18	Q₈×C₆₁	C₂³	1	16	yes	—
19	C₂×C₄×C₆₁	C₂³	1	6	yes	—
20	C₂×C₄×C₆₁	C₂³	1	12	yes	—
21	C₂²⋊D₆₁	C₂³	1	16	yes	—
22	C₂×Dic₆₁	C₂³	1	4	yes	—
23	D₂₄₄	C₂³	1	24	yes	—
24	C₄×D₆₁	C₂³	1	48	yes	—
25	Dic₁₂₂	C₂³	1	24	yes	—
26	C₂²×C₆₁	—	2	2	no	—
27	C₂²×C₆₁	C₂⁴	1	2	yes	—
28	C₂²×C₆₁	C₂⁴	1	1	yes	characteristic
29	C₂×D₆₁	—	2	8	no	—
30	C₂×D₆₁	C₂⁴	1	8	yes	—
31	C₄×C₆₁	C₂⁴	1	12	yes	—
32	Dic₆₁	C₂⁴	1	8	yes	—
33	C₂×C₆₁	—	2	2	no	—
34	C₂×C₆₁	2₋¹⁺⁴	1	2	yes	complemented
35	C₂×C₆₁	C₂⁵	1	1	yes	characteristic
36	D₆₁	—	2	8	no	—
37	C₂×2₋¹⁺⁴	—	61	1	no	maximal, Sylow
38	C₆₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
39	2₋¹⁺⁴	—	61	16	no	—
40	C₂×#41	—	61	4	no	—
41	C₂×#41	—	61	6	no	—
42	C₂²×Q₈	—	61	4	no	—
43	C₂²×Q₈	D₆₁	1	1	yes	characteristic, complemented
44	#41	—	61	32	no	—
45	#41	—	61	48	no	—
46	C₂×Q₈	—	61	32	no	—
47	C₂×Q₈	—	61	6	no	—
48	C₂×Q₈	C₂×D₆₁	1	4	yes	—
49	C₂×Q₈	C₂×D₆₁	1	8	yes	complemented
50	C₂×D₄	—	61	4	no	—
51	C₂×D₄	—	61	6	no	—
52	C₂²×C₄	—	61	12	no	—
53	C₂²×C₄	C₂×D₆₁	1	3	yes	—
54	C₂³	—	61	4	no	—
55	C₂³	C₂²×D₆₁	1	1	yes	characteristic
56	Q₈	—	61	24	no	—
57	Q₈	C₂²×D₆₁	1	16	yes	—
58	D₄	—	61	16	no	—
59	D₄	—	61	24	no	—
60	C₂×C₄	—	61	4	no	—
61	C₂×C₄	—	61	48	no	—
62	C₂×C₄	C₂²×D₆₁	1	12	yes	—
63	C₂×C₄	C₂²×D₆₁	1	6	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	—	61	8	no	—
66	C₂²	—	122	8	no	—
67	C₂²	C₂³×D₆₁	1	2	yes	—
68	C₂²	C₂³×D₆₁	1	1	yes	characteristic
69	C₄	—	61	8	no	—
70	C₄	C₂³×D₆₁	1	12	yes	—
71	C₂	—	2	2	no	—
72	C₂	—	122	8	no	—
73	C₂	#14519825	1	2	yes	direct product factor
74	C₂	C₂⁴×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₆₁
commutator, cosocle	C₂×C₆₁	C₂⁵
Frattini	C₂	C₂⁴×D₆₁
Fitting	C₂²×Q₈×C₆₁	C₂
socle	C₂²×C₆₁	C₂⁴
hypercenter	C₂²×Q₈	D₆₁
hypocenter	C₆₁	C₂×2₋¹⁺⁴
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×Q₈

Complements

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

N	H ≅ G/N	type
1. #14519825	C₂	direct (N × H)
2. C₂×#11758226	C₂	semidirect
3. C₂×#11758222	C₂	semidirect
4. C₂×Q₈×D₆₁	C₂	semidirect
5. C₂²×Q₈×C₆₁	C₂	semidirect
7. C₂×Q₈×C₆₁	C₂²	semidirect
10. #11758226	C₂²	semidirect
11. Q₈×D₆₁	C₂²	semidirect
12. #11758222	C₂²	semidirect
34. C₂×C₆₁	2₋¹⁺⁴	semidirect
38. C₆₁	C₂×2₋¹⁺⁴	semidirect
43. C₂²×Q₈	D₆₁	semidirect
49. C₂×Q₈	C₂×D₆₁	semidirect
73. C₂	#14519825	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#14519825	2
C₂×#11758226	2
C₂×#11758222	2
C₂×Q₈×D₆₁	2
C₂²×Q₈×C₆₁	2
C₂×2₋¹⁺⁴	61

Subgroups — C2×#14519825 #16840596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14519825 #16840596