Subgroups — #44532451

Order 31347.

256 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₃²⋊(C₄₃⋊C₃)	C₃	1	3	yes	maximal, complemented
2	#23782700	C₃	1	3	yes	maximal, complemented
3	#23782696	C₃	1	3	yes	maximal, complemented
4	#23782687	C₃	1	3	yes	maximal, complemented
5	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	3	yes	—
7	C₃×C₉×C₄₃⋊C₃	—	3	3	no	—
8	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
9	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
10	(C₃×C₄₃⋊C₃)⋊C₉	—	3	6	no	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₉⋊C₉	—	3	2	no	—
13	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
14	C₉²×C₄₃	—	3	1	no	—
15	C₃²×C₄₃⋊C₃	—	3	3	no	—
16	C₃²⋊(C₄₃⋊C₃)	—	3	9	no	—
17	C₃×C₄₃⋊C₉	—	3	3	no	—
18	C₃×C₄₃⋊C₉	—	3	3	no	—
19	C₉×C₄₃⋊C₃	—	9	9	no	—
20	C₃³×C₄₃	C₃³	1	1	yes	characteristic
21	C₃×C₉×C₄₃	—	3	3	no	—
22	C₃×C₉×C₄₃	—	3	3	no	—
23	C₃×C₉×C₄₃	H(3,𝔽₃)	1	2	yes	—
24	C₃×C₉×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
25	#10624585	—	43	1	no	maximal, Sylow
26	C₃²×C₄₃	—	3	1	no	—
27	C₃²×C₄₃	—	3	3	no	—
28	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₃×C₄₃⋊C₃	—	3	9	no	—
30	C₃×C₄₃⋊C₃	—	9	3	no	—
31	C₃×C₄₃⋊C₃	—	9	6	no	—
32	C₉×C₄₃	—	3	2	no	—
33	C₉×C₄₃	—	9	3	no	—
34	C₉×C₄₃	#732	1	3	yes	—
35	C₄₃⋊C₉	—	9	3	no	—
36	C₄₃⋊C₉	—	9	3	no	—
37	C₉×H(3,𝔽₃)	—	43	3	no	—
38	#6887	C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	#6861	—	43	3	no	—
40	#6859	—	43	3	no	—
41	#6856	—	43	3	no	—
42	C₃×C₄₃	—	9	1	no	—
43	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
44	C₃×C₄₃	#6908	1	3	yes	—
45	C₄₃⋊C₃	—	9	9	no	—
46	C₃×H(3,𝔽₃)	—	43	3	no	—
47	C₃²×C₉	—	129	3	no	—
48	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
49	C₉⋊C₉	—	3	2	no	—
50	C₃²⋊C₉	—	43	3	no	—
51	C₃²⋊C₉	—	43	3	no	—
52	C₃²⋊C₉	—	129	6	no	—
53	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
54	C₉²	—	3	1	no	—
55	C₄₃	#10624585	1	1	yes	characteristic, complemented, Sylow
56	C₃³	—	129	3	no	—
57	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
58	H(3,𝔽₃)	—	129	9	no	—
59	C₃×C₉	—	3	3	no	—
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	129	3	no	—
62	C₃×C₉	—	129	3	no	—
63	C₃×C₉	—	387	9	no	—
64	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
65	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
66	C₃²	—	3	1	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	129	9	no	—
69	C₃²	—	387	3	no	—
70	C₃²	—	387	6	no	—
71	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
72	C₉	—	3	2	no	—
73	C₉	—	9	3	no	—
74	C₉	—	387	3	no	—
75	C₉	—	387	3	no	—
76	C₉	#16812513	1	3	yes	—
77	C₃	—	9	1	no	—
78	C₃	—	387	9	no	—
79	C₃	C₃×#16812513	1	1	yes	characteristic
80	C₃	#23782874	1	3	yes	—

	subgroup	G/H
center	C₃×C₉	C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6887	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624585
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
1. C₉×C₃²⋊(C₄₃⋊C₃)	C₃	semidirect
2. #23782700	C₃	semidirect
3. #23782696	C₃	semidirect
4. #23782687	C₃	semidirect
5. C₄₃×#6887	C₃	semidirect
38. #6887	C₄₃⋊C₃	semidirect
55. C₄₃	#10624585	semidirect

Maximal subgroups

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

subgroup	index
C₉×C₃²⋊(C₄₃⋊C₃)	3
#23782700	3
#23782696	3
#23782687	3
C₄₃×#6887	3
#10624585	43