Subgroups — #44532234

Order 31347.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄₃⋊C₉	C₃	1	4	yes	maximal
2	C₄₃⋊#6855	C₃	1	8	yes	maximal
3	C₄₃×#6855	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₄₃⋊C₉	C₃²	1	8	yes	—
5	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
6	C₉×C₄₃⋊C₉	C₉	1	36	yes	complemented
7	C₃²×C₉×C₄₃	C₃²	1	4	yes	—
8	C₃×C₄₃⋊C₉	—	3	24	no	—
9	C₃×C₄₃⋊C₉	C₃×C₉	1	24	yes	—
10	C₃×C₄₃⋊C₉	C₃×C₉	1	12	yes	—
11	C₃³×C₄₃	C₃³	1	1	yes	characteristic
12	C₃×C₉×C₄₃	—	3	4	no	—
13	C₃×C₉×C₄₃	—	3	8	no	—
14	C₃×C₉×C₄₃	C₃×C₉	1	12	yes	—
15	#10624544	—	43	1	no	maximal, Sylow
16	C₃²×C₄₃	C₃²×C₉	1	4	yes	—
17	C₃²×C₄₃	#737	1	1	yes	characteristic
18	C₃²×C₄₃	#737	1	8	yes	—
19	C₉×C₄₃	—	3	12	no	—
20	C₄₃⋊C₉	—	3	24	no	—
21	C₄₃⋊C₉	C₉²	1	9	yes	—
22	C₃×C₉²	—	43	4	no	—
23	#6855	—	43	8	no	—
24	#6855	C₄₃⋊C₃	1	1	yes	characteristic
25	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
26	C₃×C₄₃	#6887	1	4	yes	—
27	C₃×C₄₃	#6887	1	8	yes	—
28	C₃²×C₉	—	43	1	no	—
29	C₃²×C₉	—	43	8	no	—
30	C₃²×C₉	C₃×C₄₃⋊C₃	1	4	yes	—
31	C₉²	—	43	36	no	—
32	C₄₃	#10624544	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
34	C₃×C₉	—	3	4	no	—
35	C₃×C₉	—	3	8	no	—
36	C₃×C₉	—	43	12	no	—
37	C₃×C₉	—	43	24	no	—
38	C₃×C₉	—	129	24	no	—
39	C₃×C₉	C₉×C₄₃⋊C₃	1	12	yes	—
40	C₃²	C₃×C₉×C₄₃⋊C₃	1	4	yes	—
41	C₃²	#16812524	1	1	yes	characteristic
42	C₃²	#16812526	1	8	yes	—
43	C₉	—	3	12	no	—
44	C₉	—	43	9	no	—
45	C₉	—	129	24	no	—
46	C₃	C₉²×C₄₃⋊C₃	1	1	yes	characteristic
47	C₃	#23782779	1	4	yes	—
48	C₃	#23782781	1	8	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₉²
Fitting	C₄₃×#6855	C₃
socle, prime radical, cosocle	C₃³×C₄₃	C₃³
hypercenter	#6855	C₄₃⋊C₃
hypocenter	C₄₃	#10624544
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ #6855

Complements

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

N	H ≅ G/N	type
6. C₉×C₄₃⋊C₉	C₉	semidirect
32. C₄₃	#10624544	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₄₃⋊C₉	3
C₄₃⋊#6855	3
C₄₃×#6855	3
#10624544	43