Subgroups — C₃×C₄₁⋊(D₄₃⋊C₃) #44540625

Order 31734.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄₁×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₁⋊(D₄₃⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×D₁₇₆₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄₁×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
5	C₄₁×C₄₃⋊C₃	C₂×C₃	1	3	yes	complemented
6	D₁₇₆₃	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₄₁×C₄₃	C₂×C₃²	1	1	yes	characteristic, complemented, Hall
8	C₃×D₄₃⋊C₃	—	41	1	no	maximal, Hall
9	C₃²×D₄₁	—	43	1	no	maximal, Hall
10	C₃×C₄₃⋊C₃	D₄₁	1	1	yes	characteristic, complemented, Hall
11	C₃²×C₄₁	—	43	1	no	Hall
12	C₃×D₄₃	—	41	1	no	—
13	D₄₃⋊C₃	—	41	3	no	—
14	C₃×D₄₁	—	43	3	no	—
15	C₃×D₄₁	—	43	1	no	—
16	C₃×C₄₃	C₃×D₄₁	1	1	yes	characteristic, complemented
17	C₄₃⋊C₃	C₃×D₄₁	1	3	yes	complemented
18	C₃×C₄₁	—	43	3	no	—
19	C₃×C₄₁	D₄₃⋊C₃	1	1	yes	characteristic, complemented
20	D₄₃	—	41	1	no	Hall
21	D₄₁	—	43	1	no	Hall
22	C₄₃	C₃²×D₄₁	1	1	yes	characteristic, complemented, Sylow
23	C₄₁	C₃×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃²	—	1763	1	no	Hall
25	C₃²	—	43	1	no	Sylow
26	C₂×C₃	—	1763	3	no	—
27	C₂×C₃	—	1763	1	no	—
28	C₃	—	43	3	no	—
29	C₃	C₄₁⋊(D₄₃⋊C₃)	1	1	yes	characteristic, direct product factor
30	C₂	—	1763	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	C₄₁⋊(D₄₃⋊C₃)
commutator, cosocle, hypocenter	C₄₁×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₄₁×C₄₃	C₂×C₃
LCS	G ▷ C₄₁×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.