Subgroups — C₂×C₃×#16860687 #37562053

Order 23994.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16860687	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×#16860687	C₃	1	3	yes	maximal, direct product factor
3	C₂×C₃×C₃₁×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	#16860687	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃₁×C₄₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₄₃⋊C₃	—	31	1	no	maximal, Hall
9	C₂×C₃×C₃₁⋊C₃	—	43	1	no	maximal, Hall
10	C₃×C₄₃⋊C₃	—	31	1	no	Hall
11	C₃×C₃₁⋊C₃	—	43	1	no	Hall
12	C₂×C₃×C₄₃	C₃₁⋊C₃	1	1	yes	characteristic, complemented
13	C₂×C₄₃⋊C₃	—	31	3	no	—
14	C₂×C₃×C₃₁	C₄₃⋊C₃	1	1	yes	characteristic, complemented
15	C₂×C₃₁⋊C₃	—	43	3	no	—
16	C₃×C₄₃	C₂×C₃₁⋊C₃	1	1	yes	characteristic, complemented
17	C₄₃⋊C₃	—	31	3	no	—
18	C₃×C₃₁	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
19	C₃₁⋊C₃	—	43	3	no	—
20	C₂×C₄₃	C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Hall
21	C₂×C₃₁	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₄₃	C₂×C₃×C₃₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₃₁	C₂×C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²	—	1333	1	no	Hall
25	C₃²	—	1333	1	no	Sylow
26	C₂×C₃	—	1333	3	no	—
27	C₂×C₃	#16860687	1	1	yes	characteristic, direct product factor
28	C₃	—	1333	3	no	—
29	C₃	C₂×#16860687	1	1	yes	characteristic, direct product factor
30	C₂	C₃×#16860687	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₃	#16860687
commutator, cosocle, hypocenter	C₃₁×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₃₁×C₄₃	C₃
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₃×#16860687	C₂	direct (N × H)
2. C₂×#16860687	C₃	direct (N × H)
3. C₂×C₃×C₃₁×C₄₃	C₃	semidirect
4. C₃×C₃₁×C₄₃	C₂×C₃	semidirect
5. #16860687	C₂×C₃	direct (N × H)
6. C₂×C₃₁×C₄₃	C₃²	semidirect
7. C₃₁×C₄₃	C₂×C₃²	semidirect
12. C₂×C₃×C₄₃	C₃₁⋊C₃	semidirect
14. C₂×C₃×C₃₁	C₄₃⋊C₃	semidirect
16. C₃×C₄₃	C₂×C₃₁⋊C₃	semidirect
18. C₃×C₃₁	C₂×C₄₃⋊C₃	semidirect
20. C₂×C₄₃	C₃×C₃₁⋊C₃	semidirect
21. C₂×C₃₁	C₃×C₄₃⋊C₃	semidirect
22. C₄₃	C₂×C₃×C₃₁⋊C₃	semidirect
23. C₃₁	C₂×C₃×C₄₃⋊C₃	semidirect
27. C₂×C₃	#16860687	direct (N × H)
29. C₃	C₂×#16860687	direct (N × H)
30. C₂	C₃×#16860687	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×#16860687	2
C₂×#16860687	3
C₂×C₃×C₃₁×C₄₃	3
C₂×C₃×C₄₃⋊C₃	31
C₂×C₃×C₃₁⋊C₃	43

Subgroups — C2×C3×#16860687 #37562053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#16860687 #37562053