Subgroups — (C₃⋊D₃)⋊(C₂₃⋊D₂₃) #34039970

Order 19044.

572 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₂₃²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃⋊(C₂₃⋊D₂₃)	C₂	1	2	yes	maximal, complemented
3	D₃×C₂₃⋊D₂₃	—	3	2	no	maximal
4	C₃²×C₂₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₃⋊(C₂₃⋊D₂₃)	D₃	1	2	yes	complemented
6	D₃×C₂₃²	—	3	2	no	—
7	D₃×C₂₃²	—	6	1	no	—
8	C₃×C₂₃⋊D₂₃	—	3	2	no	—
9	C₂×C₂₃⋊D₂₃	—	9	1	no	Hall
10	C₃×C₂₃²	—	2	1	no	—
11	C₃×C₂₃²	C₂×D₃	1	2	yes	complemented
12	C₂×C₂₃²	—	9	1	no	—
13	C₂₃⋊D₂₃	—	3	2	no	—
14	(C₃⋊D₃)⋊D₂₃	—	23	24	no	maximal
15	C₂₃²	D₃²	1	1	yes	characteristic, complemented, Sylow
16	C₃⋊D₃×C₂₃	D₂₃	1	24	yes	complemented
17	C₃×D₆₉	—	23	48	no	—
18	D₃×D₂₃	—	69	48	no	—
19	C₃²×C₂₃	C₂×D₂₃	1	24	yes	complemented
20	D₆₉	—	23	48	no	—
21	C₃×D₂₃	—	69	48	no	—
22	D₃×C₂₃	—	3	48	no	—
23	D₃×C₂₃	—	6	24	no	—
24	C₂×D₂₃	—	207	24	no	—
25	C₃×C₂₃	—	2	24	no	—
26	C₃×C₂₃	D₃×D₂₃	1	48	yes	complemented
27	C₂×C₂₃	—	9	24	no	—
28	D₂₃	—	69	48	no	—
29	D₃²	—	529	1	no	Hall
30	C₂₃	(C₃⋊D₃)⋊D₂₃	1	24	yes	complemented
31	C₃⋊D₃	C₂₃⋊D₂₃	1	1	yes	characteristic, complemented
32	C₃×D₃	—	529	2	no	—
33	C₂×D₃	—	1587	2	no	—
34	C₃²	C₂×C₂₃⋊D₂₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	1587	2	no	—
36	D₃	—	3	2	no	—
37	D₃	—	6	1	no	—
38	D₃	—	529	2	no	—
39	C₂²	—	4761	1	no	Sylow
40	C₃	—	2	1	no	—
41	C₃	D₃×C₂₃⋊D₂₃	1	2	yes	complemented
42	C₂	—	9	1	no	—
43	C₂	—	1587	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₃²	C₂²
LCS	G ▷ C₃²×C₂₃²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₃×C₂₃²	C₂	semidirect
2. C₃×C₃⋊(C₂₃⋊D₂₃)	C₂	semidirect
4. C₃²×C₂₃²	C₂²	semidirect
5. C₃⋊(C₂₃⋊D₂₃)	D₃	semidirect
11. C₃×C₂₃²	C₂×D₃	semidirect
15. C₂₃²	D₃²	semidirect
16. C₃⋊D₃×C₂₃	D₂₃	semidirect
19. C₃²×C₂₃	C₂×D₂₃	semidirect
26. C₃×C₂₃	D₃×D₂₃	semidirect
30. C₂₃	(C₃⋊D₃)⋊D₂₃	semidirect
31. C₃⋊D₃	C₂₃⋊D₂₃	semidirect
34. C₃²	C₂×C₂₃⋊D₂₃	semidirect
41. C₃	D₃×C₂₃⋊D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊D₃×C₂₃²	2
C₃×C₃⋊(C₂₃⋊D₂₃)	2
D₃×C₂₃⋊D₂₃	3
(C₃⋊D₃)⋊D₂₃	23

Subgroups — (C3⋊D3)⋊(C23⋊D23) #34039970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₃)⋊(C₂₃⋊D₂₃) #34039970