Subgroups — C₃⋊D₃×D₈₂₃ #44444229

Order 29628.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₈₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×C₈₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₄₆₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×D₈₂₃	—	3	4	no	maximal
5	C₃²×C₈₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₂₄₆₉	—	3	4	no	—
7	C₃×D₈₂₃	D₃	1	4	yes	complemented
8	D₃×C₈₂₃	—	3	4	no	—
9	C₂×D₈₂₃	—	9	1	no	Hall
10	C₃×C₈₂₃	C₂×D₃	1	4	yes	complemented
11	C₂×C₈₂₃	—	9	1	no	—
12	D₈₂₃	—	9	1	no	—
13	D₈₂₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
14	C₈₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃⋊D₃	—	823	1	no	maximal, Hall
16	C₂×C₃²	—	823	1	no	—
17	C₃⋊D₃	—	823	1	no	—
18	C₃⋊D₃	D₈₂₃	1	1	yes	characteristic, direct product factor
19	C₂×D₃	—	2469	4	no	—
20	C₃²	C₂×D₈₂₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₃	—	823	4	no	—
22	D₃	—	3	4	no	—
23	D₃	—	2469	4	no	—
24	C₂²	—	7407	1	no	Sylow
25	C₃	D₃×D₈₂₃	1	4	yes	complemented
26	C₂	—	9	1	no	—
27	C₂	—	823	1	no	—
28	C₂	—	7407	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₈₂₃	C₂²
LCS	G ▷ C₃²×C₈₂₃
UCS	C₁

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

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