Subgroups — C₃×#22547865 #37562027

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, complemented, Hall
2	#22547865	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₄₃×D₃₁	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	complemented
6	C₄₃×D₃₁	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	C₃×D₃₁⋊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	—	93	1	no	—
13	C₂×C₄₃⋊C₃	—	31	3	no	—
14	C₃×D₃₁	C₄₃⋊C₃	1	1	yes	characteristic, complemented
15	D₃₁⋊C₃	—	43	3	no	—
16	C₃×C₄₃	D₃₁⋊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	—	93	1	no	Hall
21	D₃₁	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
22	C₄₃	C₃×D₃₁⋊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	—	93	1	no	—
28	C₃	—	1333	3	no	—
29	C₃	#22547865	1	1	yes	characteristic, direct product factor
30	C₂	—	93	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	#22547865
commutator, cosocle, hypocenter	C₃₁×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₃₁×C₄₃	C₂×C₃
LCS	G ▷ C₃₁×C₄₃
UCS	C₁ ◁ C₃

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

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