Subgroups — C₂×(C₃⋊D₃)⋊D₂₃ #13110292

Order 1656.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₆₉	C₂	1	2	yes	maximal, complemented
3	(C₃⋊D₃)⋊D₂₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₃×D₂₃	—	3	2	no	maximal
5	C₂×C₃²×C₂₃	C₂²	1	1	yes	characteristic, complemented
6	C₃⋊D₃×C₂₃	C₂²	1	2	yes	complemented
7	C₃×D₆₉	C₂²	1	4	yes	complemented
8	C₂×D₆₉	D₃	1	2	yes	complemented
9	C₂×D₃×C₂₃	—	3	2	no	—
10	C₂×D₃×C₂₃	—	6	1	no	—
11	C₂×C₃×D₂₃	—	3	2	no	—
12	D₃×D₂₃	—	3	8	no	—
13	C₃²×C₂₃	C₂³	1	1	yes	characteristic, complemented, Hall
14	C₂²×D₂₃	—	9	1	no	Hall
15	C₂×C₃×C₂₃	—	2	1	no	—
16	C₂×C₃×C₂₃	C₂×D₃	1	2	yes	complemented
17	D₆₉	C₂×D₃	1	4	yes	complemented
18	C₃×D₂₃	—	3	4	no	—
19	D₃×C₂₃	—	3	4	no	—
20	D₃×C₂₃	—	6	2	no	—
21	C₂²×C₂₃	—	9	1	no	—
22	C₂×D₂₃	—	3	2	no	—
23	C₂×D₂₃	—	9	4	no	—
24	C₂×D₃²	—	23	1	no	maximal, Hall
25	C₃×C₂₃	—	2	1	no	—
26	C₃×C₂₃	C₂²×D₃	1	2	yes	complemented
27	C₂×C₂₃	—	9	2	no	—
28	C₂×C₂₃	D₃²	1	1	yes	characteristic, complemented
29	D₂₃	—	3	4	no	—
30	C₂×C₃⋊D₃	D₂₃	1	1	yes	characteristic, complemented
31	C₂×C₃×D₃	—	23	2	no	—
32	D₃²	—	23	4	no	—
33	C₂²×D₃	—	69	2	no	—
34	C₂₃	C₂×D₃²	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃²	C₂×D₂₃	1	1	yes	characteristic, complemented
36	C₃⋊D₃	C₂×D₂₃	1	2	yes	complemented
37	C₃×D₃	—	23	4	no	—
38	C₂²×C₃	—	69	2	no	—
39	C₂×D₃	—	3	2	no	—
40	C₂×D₃	—	6	1	no	—
41	C₂×D₃	—	23	2	no	—
42	C₂×D₃	—	69	8	no	—
43	C₃²	C₂²×D₂₃	1	1	yes	characteristic, complemented, Sylow
44	C₂³	—	207	1	no	Sylow
45	C₂×C₃	—	2	1	no	—
46	C₂×C₃	—	69	4	no	—
47	C₂×C₃	D₃×D₂₃	1	2	yes	complemented
48	D₃	—	3	4	no	—
49	D₃	—	6	2	no	—
50	D₃	—	23	4	no	—
51	C₂²	—	9	1	no	—
52	C₂²	—	69	2	no	—
53	C₂²	—	207	4	no	—
54	C₃	—	2	1	no	—
55	C₃	C₂×D₃×D₂₃	1	2	yes	complemented
56	C₂	—	9	2	no	—
57	C₂	—	69	4	no	—
58	C₂	(C₃⋊D₃)⋊D₂₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₃⋊D₃)⋊D₂₃
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₂₃	C₂²
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊D₃×C₂₃	C₂	semidirect
2. C₂×C₃×D₆₉	C₂	semidirect
3. (C₃⋊D₃)⋊D₂₃	C₂	direct (N × H)
5. C₂×C₃²×C₂₃	C₂²	semidirect
6. C₃⋊D₃×C₂₃	C₂²	semidirect
7. C₃×D₆₉	C₂²	semidirect
8. C₂×D₆₉	D₃	semidirect
13. C₃²×C₂₃	C₂³	semidirect
16. C₂×C₃×C₂₃	C₂×D₃	semidirect
17. D₆₉	C₂×D₃	semidirect
26. C₃×C₂₃	C₂²×D₃	semidirect
28. C₂×C₂₃	D₃²	semidirect
30. C₂×C₃⋊D₃	D₂₃	semidirect
34. C₂₃	C₂×D₃²	semidirect
35. C₂×C₃²	C₂×D₂₃	semidirect
36. C₃⋊D₃	C₂×D₂₃	semidirect
43. C₃²	C₂²×D₂₃	semidirect
47. C₂×C₃	D₃×D₂₃	semidirect
55. C₃	C₂×D₃×D₂₃	semidirect
58. C₂	(C₃⋊D₃)⋊D₂₃	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⋊D₃×C₂₃	2
C₂×C₃×D₆₉	2
(C₃⋊D₃)⋊D₂₃	2
C₂×D₃×D₂₃	3
C₂×D₃²	23

Subgroups — C2×(C3⋊D3)⋊D23 #13110292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×(C₃⋊D₃)⋊D₂₃ #13110292