Subgroups — C₂⁴×Dic₁₂₂ #21460614

Order 7808.

6264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₁₂₂	C₂	1	60	yes	maximal, direct product factor
2	C₂⁴×Dic₆₁	C₂	1	2	yes	maximal
3	C₂⁴×C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₁₂₂	C₂²	1	560	yes	direct product factor
5	C₂³×Dic₆₁	C₂²	1	60	yes	—
6	C₂⁵×C₆₁	C₂²	1	1	yes	characteristic
7	C₂³×C₄×C₆₁	C₂²	1	30	yes	—
8	C₂⁴×C₆₁	Q₈	1	16	yes	complemented
9	C₂⁴×C₆₁	C₂³	1	15	yes	—
10	C₂²×C₄×C₆₁	C₂³	1	140	yes	—
11	C₂²×Dic₆₁	C₂³	1	280	yes	—
12	C₂×Dic₁₂₂	C₂³	1	960	yes	direct product factor
13	C₂³×C₆₁	C₂×Q₈	1	120	yes	complemented
14	C₂³×C₆₁	C₂⁴	1	35	yes	—
15	C₂×C₄×C₆₁	C₂⁴	1	120	yes	—
16	C₂×Dic₆₁	C₂⁴	1	240	yes	—
17	Dic₁₂₂	C₂⁴	1	256	yes	direct product factor
18	C₂²×C₆₁	C₂²×Q₈	1	140	yes	complemented
19	C₂²×C₆₁	C₂⁵	1	15	yes	—
20	C₄×C₆₁	C₂⁵	1	16	yes	—
21	Dic₆₁	C₂⁵	1	32	yes	—
22	C₂⁴×Q₈	—	61	1	no	maximal, Sylow
23	C₂×C₆₁	C₂³×Q₈	1	30	yes	complemented
24	C₂×C₆₁	C₂⁶	1	1	yes	characteristic
25	C₂³×Q₈	—	61	60	no	—
26	C₂⁴×C₄	—	61	2	no	—
27	C₂⁴×C₄	D₆₁	1	1	yes	characteristic
28	C₆₁	C₂⁴×Q₈	1	1	yes	characteristic, complemented, Sylow
29	C₂⁵	C₂×D₆₁	1	1	yes	characteristic
30	C₂²×Q₈	—	61	560	no	—
31	C₂³×C₄	—	61	60	no	—
32	C₂³×C₄	C₂×D₆₁	1	30	yes	—
33	C₂⁴	Dic₁₂₂	1	16	yes	direct product factor
34	C₂⁴	C₂²×D₆₁	1	15	yes	—
35	C₂×Q₈	—	61	960	no	—
36	C₂²×C₄	—	61	280	no	—
37	C₂²×C₄	C₂²×D₆₁	1	140	yes	—
38	C₂³	C₂×Dic₁₂₂	1	120	yes	direct product factor
39	C₂³	C₂³×D₆₁	1	35	yes	—
40	Q₈	—	61	256	no	—
41	C₂×C₄	—	61	240	no	—
42	C₂×C₄	C₂³×D₆₁	1	120	yes	—
43	C₂²	C₂²×Dic₁₂₂	1	140	yes	direct product factor
44	C₂²	C₂⁴×D₆₁	1	15	yes	—
45	C₄	—	61	32	no	—
46	C₄	C₂⁴×D₆₁	1	16	yes	—
47	C₂	C₂³×Dic₁₂₂	1	30	yes	direct product factor
48	C₂	C₂⁵×D₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₆₁
commutator	C₂×C₆₁	C₂⁶
Frattini	C₂	C₂⁵×D₆₁
Fitting	C₂⁴×C₄×C₆₁	C₂
socle	C₂⁵×C₆₁	C₂²
hypercenter	C₂⁴×C₄	D₆₁
hypocenter	C₆₁	C₂⁴×Q₈
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×Dic₁₂₂	C₂	direct (N × H)
4. C₂²×Dic₁₂₂	C₂²	direct (N × H)
8. C₂⁴×C₆₁	Q₈	semidirect
12. C₂×Dic₁₂₂	C₂³	direct (N × H)
13. C₂³×C₆₁	C₂×Q₈	semidirect
17. Dic₁₂₂	C₂⁴	direct (N × H)
18. C₂²×C₆₁	C₂²×Q₈	semidirect
23. C₂×C₆₁	C₂³×Q₈	semidirect
28. C₆₁	C₂⁴×Q₈	semidirect
33. C₂⁴	Dic₁₂₂	direct (N × H)
38. C₂³	C₂×Dic₁₂₂	direct (N × H)
43. C₂²	C₂²×Dic₁₂₂	direct (N × H)
47. C₂	C₂³×Dic₁₂₂	direct (N × H)

Subgroups — C24×Dic122 #21460614

Conjugacy classes of subgroups

Complements

Subgroups — C₂⁴×Dic₁₂₂ #21460614