Subgroups — #13110221

Order 1656.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃²×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#10587771	—	3	4	no	maximal
5	C₂×C₃²×C₂₃	C₂²	1	1	yes	characteristic
6	C₃⋊D₆₉	—	2	1	no	—
7	C₃²×D₂₃	—	2	1	no	—
8	C₂×D₆₉	—	3	4	no	—
9	C₂×C₃×D₂₃	D₃	1	4	yes	complemented
10	Dic₃×C₂₃	—	3	4	no	—
11	C₃²×C₂₃	D₄	1	1	yes	characteristic, complemented, Hall
12	D₉₂	—	9	1	no	Hall
13	C₂×C₃×C₂₃	C₂×D₃	1	4	yes	—
14	D₆₉	—	6	4	no	—
15	C₃×D₂₃	—	2	4	no	—
16	C₂×D₂₃	—	9	1	no	—
17	C₂×D₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
18	C₄×C₂₃	—	9	1	no	—
19	#638	—	23	1	no	maximal, Hall
20	C₃×C₂₃	#67	1	4	yes	complemented
21	C₂×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic
22	D₂₃	—	2	1	no	—
23	D₂₃	—	18	1	no	—
24	C₂²×C₃²	—	23	1	no	—
25	C₂×C₃⋊D₃	—	23	1	no	—
26	C₃⋊Dic₃	D₂₃	1	1	yes	characteristic, complemented
27	#67	—	69	4	no	—
28	C₂₃	#638	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²	—	46	1	no	—
30	C₂×C₃²	C₂×D₂₃	1	1	yes	characteristic
31	C₃⋊D₃	—	46	1	no	—
32	C₂²×C₃	—	23	4	no	—
33	C₂×D₃	—	69	4	no	—
34	Dic₃	—	3	4	no	—
35	C₃²	D₉₂	1	1	yes	characteristic, complemented, Sylow
36	D₄	—	207	1	no	Sylow
37	C₂×C₃	—	46	4	no	—
38	C₂×C₃	D₃×D₂₃	1	4	yes	—
39	D₃	—	138	4	no	—
40	C₂²	—	23	1	no	—
41	C₂²	—	207	1	no	—
42	C₄	—	9	1	no	—
43	C₃	#10587771	1	4	yes	complemented
44	C₂	—	46	1	no	—
45	C₂	—	414	1	no	—
46	C₂	C₃⋊D₃×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	C₃⋊D₃×D₂₃
commutator, Fitting, socle, cosocle	C₂×C₃²×C₂₃	C₂²
hypocenter	C₃²×C₂₃	D₄
LCS	G ▷ C₂×C₃²×C₂₃ ▷ C₃²×C₂₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊D₆₉	C₂	semidirect
2. C₂×C₃²×D₂₃	C₂	semidirect
3. C₂₃×C₃⋊Dic₃	C₂	semidirect
9. C₂×C₃×D₂₃	D₃	semidirect
11. C₃²×C₂₃	D₄	semidirect
17. C₂×D₂₃	C₃⋊D₃	semidirect
20. C₃×C₂₃	#67	semidirect
26. C₃⋊Dic₃	D₂₃	semidirect
28. C₂₃	#638	semidirect
35. C₃²	D₉₂	semidirect
43. C₃	#10587771	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊D₆₉	2
C₂×C₃²×D₂₃	2
C₂₃×C₃⋊Dic₃	2
#10587771	3
#638	23