Subgroups — C₃×#15691772⋊C₂ #34039939

Order 19044.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₂₃⋊D₂₃)⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#15691772	C₂	1	2	yes	maximal, complemented
3	C₃×D₂₃²	—	3	1	no	maximal
4	#15691772⋊C₂	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₂₃²⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₂₃⋊D₂₃	D₃	1	1	yes	characteristic, complemented
7	C₃×C₂₃×D₂₃	—	3	2	no	—
8	(C₂₃⋊D₂₃)⋊C₃	—	2	1	no	—
9	(C₂₃⋊D₂₃)⋊C₃	C₂×C₃	1	1	yes	characteristic, complemented
10	#15691772	C₂×C₃	1	2	yes	complemented
11	D₂₃²	—	3	1	no	Hall
12	C₃×C₂₃²	C₂×D₃	1	1	yes	characteristic, complemented
13	C₂₃²⋊C₃	—	2	1	no	—
14	C₂₃²⋊C₃	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₂₃⋊D₂₃	C₃×D₃	1	1	yes	characteristic, complemented
16	C₂₃×D₂₃	—	3	2	no	—
17	C₂₃²	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×D₂₃	—	69	2	no	—
19	C₂×C₃×C₂₃	—	69	2	no	—
20	C₃×D₂₃	—	3	2	no	—
21	C₃×D₂₃	—	69	2	no	—
22	C₃×D₂₃	—	138	3	no	—
23	C₂×D₂₃	—	69	2	no	—
24	C₃×C₂₃	—	3	2	no	—
25	C₃×C₂₃	—	6	3	no	—
26	C₂×C₂₃	—	69	2	no	—
27	D₂₃	—	3	2	no	—
28	D₂₃	—	138	2	no	—
29	D₂₃	—	138	3	no	—
30	C₂×C₃×D₃	—	529	1	no	maximal, Hall
31	C₂₃	—	6	2	no	—
32	C₂₃	—	6	3	no	—
33	C₂×C₃²	—	529	1	no	—
34	C₃×D₃	—	1058	2	no	—
35	C₂²×C₃	—	1587	1	no	—
36	C₂×D₃	—	529	1	no	—
37	C₃²	—	2116	1	no	Sylow
38	C₂×C₃	—	529	1	no	—
39	C₂×C₃	—	529	1	no	—
40	C₂×C₃	—	1058	1	no	—
41	C₂×C₃	—	69	2	no	—
42	D₃	—	1058	2	no	—
43	C₂²	—	1587	1	no	Sylow
44	C₃	—	2116	1	no	—
45	C₃	—	2116	1	no	—
46	C₃	#15691772⋊C₂	1	1	yes	characteristic, direct product factor
47	C₂	—	529	1	no	—
48	C₂	—	69	2	no	—

	subgroup	G/H
center, hypercenter	C₃	#15691772⋊C₂
commutator, cosocle, hypocenter	C₂₃²⋊C₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₂₃²	C₂×D₃
LCS	G ▷ C₂₃²⋊C₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×(C₂₃⋊D₂₃)⋊C₃	C₂	semidirect
2. C₃×#15691772	C₂	semidirect
4. #15691772⋊C₂	C₃	direct (N × H)
5. C₃×C₂₃²⋊C₃	C₂²	semidirect
6. C₃×C₂₃⋊D₂₃	D₃	semidirect
9. (C₂₃⋊D₂₃)⋊C₃	C₂×C₃	semidirect
10. #15691772	C₂×C₃	semidirect
12. C₃×C₂₃²	C₂×D₃	semidirect
14. C₂₃²⋊C₃	C₂²×C₃	semidirect
15. C₂₃⋊D₂₃	C₃×D₃	semidirect
17. C₂₃²	C₂×C₃×D₃	semidirect
46. C₃	#15691772⋊C₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×(C₂₃⋊D₂₃)⋊C₃	2
C₃×#15691772	2
C₃×D₂₃²	3
#15691772⋊C₂	3
C₂×C₃×D₃	529

Subgroups — C3×#15691772⋊C2 #34039939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#15691772⋊C₂ #34039939