Subgroups — C₂×D₃×C₈₂₃⋊C₃ #44444222

Order 29628.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₈₂₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₈₂₃⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₈₂₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₈₂₃⋊C₃	—	3	1	no	maximal
5	C₃×C₈₂₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₈₂₃	C₂×C₃	1	1	yes	characteristic, complemented
7	D₃×C₈₂₃	C₂×C₃	1	2	yes	complemented
8	C₂×C₈₂₃⋊C₃	—	2	1	no	—
9	C₂×C₈₂₃⋊C₃	—	3	2	no	—
10	C₂×C₈₂₃⋊C₃	D₃	1	1	yes	characteristic, direct product factor
11	C₂²×C₈₂₃	—	3	1	no	Hall
12	C₃×C₈₂₃	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₈₂₃⋊C₃	—	2	1	no	—
14	C₈₂₃⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×C₈₂₃	—	3	2	no	—
16	C₂×C₈₂₃	C₃×D₃	1	1	yes	characteristic, complemented
17	C₈₂₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×D₃	—	823	1	no	maximal, Hall
19	C₂×C₃²	—	823	1	no	—
20	C₃×D₃	—	823	2	no	—
21	C₂²×C₃	—	2469	1	no	—
22	C₂×D₃	C₈₂₃⋊C₃	1	1	yes	characteristic, direct product factor
23	C₃²	—	823	1	no	Sylow
24	C₂×C₃	—	823	1	no	—
25	C₂×C₃	—	1646	1	no	—
26	C₂×C₃	—	2469	2	no	—
27	C₂×C₃	C₂×C₈₂₃⋊C₃	1	1	yes	characteristic, complemented
28	D₃	C₂×C₈₂₃⋊C₃	1	2	yes	direct product factor
29	C₂²	—	3	1	no	Sylow
30	C₃	—	823	1	no	—
31	C₃	—	1646	1	no	—
32	C₃	C₂²×C₈₂₃⋊C₃	1	1	yes	characteristic, complemented
33	C₂	—	3	2	no	—
34	C₂	D₃×C₈₂₃⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₃×C₈₂₃⋊C₃
commutator, cosocle, hypocenter	C₃×C₈₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₈₂₃	C₂×C₃
LCS	G ▷ C₃×C₈₂₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₈₂₃⋊C₃	C₂	semidirect
2. D₃×C₈₂₃⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₈₂₃	C₃	semidirect
5. C₃×C₈₂₃⋊C₃	C₂²	semidirect
6. C₂×C₃×C₈₂₃	C₂×C₃	semidirect
7. D₃×C₈₂₃	C₂×C₃	semidirect
10. C₂×C₈₂₃⋊C₃	D₃	direct (N × H)
12. C₃×C₈₂₃	C₂²×C₃	semidirect
14. C₈₂₃⋊C₃	C₂×D₃	direct (N × H)
16. C₂×C₈₂₃	C₃×D₃	semidirect
17. C₈₂₃	C₂×C₃×D₃	semidirect
22. C₂×D₃	C₈₂₃⋊C₃	direct (N × H)
27. C₂×C₃	C₂×C₈₂₃⋊C₃	semidirect
28. D₃	C₂×C₈₂₃⋊C₃	direct (N × H)
32. C₃	C₂²×C₈₂₃⋊C₃	semidirect
34. C₂	D₃×C₈₂₃⋊C₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₈₂₃⋊C₃	2
D₃×C₈₂₃⋊C₃	2
C₂×D₃×C₈₂₃	3
C₂²×C₈₂₃⋊C₃	3
C₂×C₃×D₃	823

Subgroups — C2×D3×C823⋊C3 #44444222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₃×C₈₂₃⋊C₃ #44444222