Subgroups — C₄₃⋊#11725071 #49181595

Order 37926.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#89205	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₉₀₃	—	3	1	no	maximal
3	C₃×C₇²×C₄₃	D₃	1	1	yes	characteristic
4	C₇×D₃₀₁	—	9	1	no	Hall
5	C₄₃×C₇⋊C₉	—	14	1	no	—
6	C₇²×C₄₃	D₉	1	1	yes	characteristic, complemented, Hall
7	D₉₀₃	—	3	1	no	—
8	C₇×D₁₂₉	—	21	1	no	—
9	C₃×C₇×C₄₃	—	2	1	no	—
10	C₃×C₇×C₄₃	—	3	1	no	—
11	C₃×C₇×C₄₃	—	3	1	no	—
12	#11725071	—	43	1	no	maximal, Hall
13	D₃₈₇	—	49	1	no	maximal, Hall
14	D₃₀₁	—	9	1	no	—
15	C₇×D₄₃	—	63	1	no	—
16	#89205	D₄₃	1	1	yes	characteristic, complemented, Hall
17	C₉×C₄₃	—	49	1	no	Hall
18	C₇×C₄₃	—	2	1	no	—
19	C₇×C₄₃	—	3	1	no	—
20	C₇×C₄₃	—	3	1	no	—
21	C₇×D₂₁	—	129	1	no	—
22	D₁₂₉	—	21	1	no	—
23	C₃×C₇²	D₁₂₉	1	1	yes	characteristic
24	C₃×C₄₃	#64418	1	1	yes	characteristic
25	C₇×D₇	—	387	1	no	Hall
26	D₄₃	—	63	1	no	Hall
27	C₇⋊C₉	—	14	1	no	—
28	C₇²	D₃₈₇	1	1	yes	characteristic, complemented, Sylow
29	C₄₃	#11725071	1	1	yes	characteristic, complemented, Sylow
30	D₂₁	—	129	1	no	—
31	D₃×C₇	—	903	1	no	—
32	C₃×C₇	—	2	1	no	—
33	C₃×C₇	—	3	1	no	—
34	C₃×C₇	—	3	1	no	—
35	D₉	—	2107	1	no	Hall
36	C₂×C₇	—	2709	1	no	—
37	D₇	—	387	1	no	—
38	C₉	—	49	1	no	Sylow
39	C₇	—	2	1	no	—
40	C₇	—	3	1	no	—
41	C₇	—	3	1	no	—
42	D₃	—	903	1	no	—
43	C₃	C₄₃⋊#64418	1	1	yes	characteristic
44	C₂	—	2709	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₄₃×#89205	C₂
Frattini	C₃	C₄₃⋊#64418
Fitting, socle	C₃×C₇²×C₄₃	D₃
LCS	G ▷ C₄₃×#89205
UCS	C₁

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.