Subgroups — C₂³×Dic₂₁₈ #20295850

Order 6976.

850 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₁₈	C₂	1	28	yes	maximal, direct product factor
2	C₂³×Dic₁₀₉	C₂	1	2	yes	maximal
3	C₂³×C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₁₈	C₂²	1	112	yes	direct product factor
5	C₂²×Dic₁₀₉	C₂²	1	28	yes	—
6	C₂⁴×C₁₀₉	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₁₀₉	C₂²	1	14	yes	—
8	C₂³×C₁₀₉	Q₈	1	8	yes	complemented
9	C₂³×C₁₀₉	C₂³	1	7	yes	—
10	C₂×C₄×C₁₀₉	C₂³	1	28	yes	—
11	C₂×Dic₁₀₉	C₂³	1	56	yes	—
12	Dic₂₁₈	C₂³	1	64	yes	direct product factor
13	C₂²×C₁₀₉	C₂×Q₈	1	28	yes	complemented
14	C₂²×C₁₀₉	C₂⁴	1	7	yes	—
15	C₄×C₁₀₉	C₂⁴	1	8	yes	—
16	Dic₁₀₉	C₂⁴	1	16	yes	—
17	C₂×C₁₀₉	C₂²×Q₈	1	14	yes	complemented
18	C₂×C₁₀₉	C₂⁵	1	1	yes	characteristic
19	C₁₀₉	C₂³×Q₈	1	1	yes	characteristic, complemented, Sylow
20	C₂³×Q₈	—	109	1	no	maximal, Sylow
21	C₂²×Q₈	—	109	28	no	—
22	C₂³×C₄	—	109	2	no	—
23	C₂³×C₄	D₁₀₉	1	1	yes	characteristic
24	C₂⁴	C₂×D₁₀₉	1	1	yes	characteristic
25	C₂×Q₈	—	109	112	no	—
26	C₂²×C₄	—	109	28	no	—
27	C₂²×C₄	C₂×D₁₀₉	1	14	yes	—
28	C₂³	Dic₂₁₈	1	8	yes	direct product factor
29	C₂³	C₂²×D₁₀₉	1	7	yes	—
30	Q₈	—	109	64	no	—
31	C₂×C₄	—	109	56	no	—
32	C₂×C₄	C₂²×D₁₀₉	1	28	yes	—
33	C₂²	C₂×Dic₂₁₈	1	28	yes	direct product factor
34	C₂²	C₂³×D₁₀₉	1	7	yes	—
35	C₄	—	109	16	no	—
36	C₄	C₂³×D₁₀₉	1	8	yes	—
37	C₂	C₂²×Dic₂₁₈	1	14	yes	direct product factor
38	C₂	C₂⁴×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₁₀₉
commutator	C₂×C₁₀₉	C₂⁵
Frattini	C₂	C₂⁴×D₁₀₉
Fitting	C₂³×C₄×C₁₀₉	C₂
socle	C₂⁴×C₁₀₉	C₂²
hypercenter	C₂³×C₄	D₁₀₉
hypocenter	C₁₀₉	C₂³×Q₈
LCS	G ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×Dic₂₁₈	C₂	direct (N × H)
4. C₂×Dic₂₁₈	C₂²	direct (N × H)
8. C₂³×C₁₀₉	Q₈	semidirect
12. Dic₂₁₈	C₂³	direct (N × H)
13. C₂²×C₁₀₉	C₂×Q₈	semidirect
17. C₂×C₁₀₉	C₂²×Q₈	semidirect
19. C₁₀₉	C₂³×Q₈	semidirect
28. C₂³	Dic₂₁₈	direct (N × H)
33. C₂²	C₂×Dic₂₁₈	direct (N × H)
37. C₂	C₂²×Dic₂₁₈	direct (N × H)

Subgroups — C23×Dic218 #20295850

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×Dic₂₁₈ #20295850