Subgroups — C₂³×D₁₁₆ #14271985

Order 1856.

1362 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₂₉	C₂	1	2	yes	maximal, complemented
2	C₂³×C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₁₆	C₂	1	28	yes	maximal, direct product factor
4	C₂⁴×C₂₉	C₂²	1	1	yes	characteristic
5	C₂³×D₂₉	—	2	16	no	—
6	C₂³×D₂₉	C₂²	1	28	yes	complemented
7	C₂²×C₄×C₂₉	C₂²	1	14	yes	complemented
8	C₂×D₁₁₆	C₂²	1	112	yes	direct product factor
9	C₂³×C₂₉	D₄	1	8	yes	complemented
10	C₂³×C₂₉	C₂³	1	7	yes	—
11	C₂²×D₂₉	—	2	112	no	—
12	C₂²×D₂₉	C₂³	1	56	yes	complemented
13	C₂×C₄×C₂₉	C₂³	1	28	yes	complemented
14	D₁₁₆	C₂³	1	64	yes	direct product factor
15	C₂²×C₂₉	C₂×D₄	1	28	yes	complemented
16	C₂²×C₂₉	C₂⁴	1	7	yes	—
17	C₂×D₂₉	—	2	112	no	—
18	C₂×D₂₉	C₂⁴	1	16	yes	complemented
19	C₄×C₂₉	C₂⁴	1	8	yes	complemented
20	C₂³×D₄	—	29	1	no	maximal, Sylow
21	C₂×C₂₉	C₂²×D₄	1	14	yes	complemented
22	C₂×C₂₉	C₂⁵	1	1	yes	characteristic
23	D₂₉	—	2	16	no	—
24	C₂⁵	—	29	2	no	—
25	C₂²×D₄	—	29	28	no	—
26	C₂³×C₄	D₂₉	1	1	yes	characteristic, complemented
27	C₂₉	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
28	C₂⁴	—	29	28	no	—
29	C₂⁴	—	58	16	no	—
30	C₂⁴	C₂×D₂₉	1	1	yes	characteristic
31	C₂×D₄	—	29	112	no	—
32	C₂²×C₄	C₂×D₂₉	1	14	yes	complemented
33	C₂³	—	29	56	no	—
34	C₂³	—	58	112	no	—
35	C₂³	D₁₁₆	1	8	yes	direct product factor
36	C₂³	C₂²×D₂₉	1	7	yes	—
37	D₄	—	29	64	no	—
38	C₂×C₄	C₂²×D₂₉	1	28	yes	complemented
39	C₂²	—	29	16	no	—
40	C₂²	—	58	112	no	—
41	C₂²	C₂×D₁₁₆	1	28	yes	direct product factor
42	C₂²	C₂³×D₂₉	1	7	yes	—
43	C₄	C₂³×D₂₉	1	8	yes	complemented
44	C₂	—	58	16	no	—
45	C₂	C₂²×D₁₁₆	1	14	yes	direct product factor
46	C₂	C₂⁴×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₉
commutator, cosocle	C₂×C₂₉	C₂⁵
Frattini	C₂	C₂⁴×D₂₉
Fitting	C₂³×C₄×C₂₉	C₂
socle	C₂⁴×C₂₉	C₂²
hypercenter	C₂³×C₄	D₂₉
hypocenter	C₂₉	C₂³×D₄
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁴×D₂₉	C₂	semidirect
2. C₂³×C₄×C₂₉	C₂	semidirect
3. C₂²×D₁₁₆	C₂	direct (N × H)
6. C₂³×D₂₉	C₂²	semidirect
7. C₂²×C₄×C₂₉	C₂²	semidirect
8. C₂×D₁₁₆	C₂²	direct (N × H)
9. C₂³×C₂₉	D₄	semidirect
12. C₂²×D₂₉	C₂³	semidirect
13. C₂×C₄×C₂₉	C₂³	semidirect
14. D₁₁₆	C₂³	direct (N × H)
15. C₂²×C₂₉	C₂×D₄	semidirect
18. C₂×D₂₉	C₂⁴	semidirect
19. C₄×C₂₉	C₂⁴	semidirect
21. C₂×C₂₉	C₂²×D₄	semidirect
26. C₂³×C₄	D₂₉	semidirect
27. C₂₉	C₂³×D₄	semidirect
32. C₂²×C₄	C₂×D₂₉	semidirect
35. C₂³	D₁₁₆	direct (N × H)
38. C₂×C₄	C₂²×D₂₉	semidirect
41. C₂²	C₂×D₁₁₆	direct (N × H)
43. C₄	C₂³×D₂₉	semidirect
45. C₂	C₂²×D₁₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₂₉	2
C₂³×C₄×C₂₉	2
C₂²×D₁₁₆	2
C₂³×D₄	29

Subgroups — C23×D116 #14271985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×D₁₁₆ #14271985