Subgroups — #44534494

Order 31347.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812513	C₃	1	3	yes	maximal, complemented
2	#23782751	C₃	1	9	yes	maximal, complemented
3	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
5	#16812513	—	3	6	no	—
6	#16812513	C₃²	1	9	yes	complemented
7	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
8	C₄₃×C₉⋊C₉	—	3	2	no	—
9	C₄₃×C₃²⋊C₉	—	3	1	no	—
10	C₉²×C₄₃	C₃²	1	3	yes	complemented
11	C₃²×C₄₃⋊C₃	—	9	3	no	—
12	C₃²⋊(C₄₃⋊C₃)	—	3	9	no	—
13	C₃²⋊(C₄₃⋊C₃)	—	9	6	no	—
14	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
15	C₃×C₉×C₄₃	—	3	3	no	—
16	C₃×C₉×C₄₃	—	3	3	no	—
17	C₃×C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
18	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
19	#10624839	—	43	1	no	maximal, Sylow
20	C₃²×C₄₃	—	9	1	no	—
21	C₃²×C₄₃	#732	1	3	yes	—
22	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×C₄₃⋊C₃	—	9	9	no	—
24	C₃×C₄₃⋊C₃	—	27	9	no	—
25	C₉×C₄₃	—	3	2	no	—
26	C₉×C₄₃	—	3	1	no	—
27	C₉×C₄₃	—	9	3	no	—
28	C₃×#732	—	43	3	no	—
29	#6887	C₄₃⋊C₃	1	1	yes	characteristic, complemented
30	#6879	—	43	9	no	—
31	C₃×C₄₃	—	3	1	no	—
32	C₃×C₄₃	—	3	3	no	—
33	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
34	C₄₃⋊C₃	—	27	9	no	—
35	C₃×H(3,𝔽₃)	—	129	3	no	—
36	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
37	#732	—	43	9	no	—
38	#732	—	129	6	no	—
39	C₉⋊C₉	—	3	2	no	—
40	C₃²⋊C₉	—	3	1	no	—
41	C₉²	C₃×C₄₃⋊C₃	1	3	yes	complemented
42	C₄₃	#10624839	1	1	yes	characteristic, complemented, Sylow
43	C₃³	—	387	3	no	—
44	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
45	H(3,𝔽₃)	—	129	9	no	—
46	H(3,𝔽₃)	—	387	6	no	—
47	C₃×C₉	—	3	3	no	—
48	C₃×C₉	—	3	3	no	—
49	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
50	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
51	C₃²	—	9	1	no	—
52	C₃²	—	387	9	no	—
53	C₃²	—	1161	9	no	—
54	C₃²	#16812513	1	3	yes	—
55	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
56	C₉	—	3	2	no	—
57	C₉	—	3	1	no	—
58	C₉	—	9	3	no	—
59	C₃	—	3	1	no	—
60	C₃	—	3	3	no	—
61	C₃	—	1161	9	no	—
62	C₃	C₃×#16812513	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×#16812513
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃×C₄₃	C₃×#732
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624839
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. C₃×#16812513	C₃	semidirect
2. #23782751	C₃	semidirect
3. C₄₃×#6887	C₃	semidirect
6. #16812513	C₃²	semidirect
10. C₉²×C₄₃	C₃²	semidirect
29. #6887	C₄₃⋊C₃	semidirect
41. C₉²	C₃×C₄₃⋊C₃	semidirect
42. C₄₃	#10624839	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812513	3
#23782751	3
C₄₃×#6887	3
#10624839	43