Subgroups — #44534492

Order 31347.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#732×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
2	#23782780	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782751	C₃	1	2	yes	maximal, complemented
4	#23782750	C₃	1	6	yes	maximal, complemented
5	C₄₃×#6879	C₃	1	1	yes	maximal, characteristic, complemented
6	H(3,𝔽₃)×C₄₃⋊C₃	—	3	3	no	—
7	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
8	#16812513	C₃²	1	6	yes	complemented
9	#16812512	—	3	6	no	—
10	(C₄₃⋊C₉)⋊C₉	—	3	2	no	—
11	(C₃×C₄₃⋊C₃)⋊C₉	—	3	1	no	—
12	C₉×C₄₃⋊C₉	C₃²	1	2	yes	complemented
13	C₄₃×#732	C₃²	1	3	yes	complemented
14	C₉²×C₄₃	C₃²	1	1	yes	characteristic, complemented
15	C₃²×C₄₃⋊C₃	—	9	3	no	—
16	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
17	C₃²⋊(C₄₃⋊C₃)	—	3	6	no	—
18	C₃²⋊(C₄₃⋊C₃)	—	9	6	no	—
19	C₃×C₄₃⋊C₉	—	3	2	no	—
20	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	2	yes	—
21	C₉×C₄₃⋊C₃	—	3	3	no	—
22	H(3,𝔽₃)×C₄₃	—	3	3	no	—
23	C₃×C₉×C₄₃	—	3	1	no	—
24	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
25	#10624839	—	43	1	no	maximal, Sylow
26	C₃²×C₄₃	—	9	3	no	—
27	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
28	C₃×C₄₃⋊C₃	—	9	1	no	—
29	C₃×C₄₃⋊C₃	—	9	6	no	—
30	C₃×C₄₃⋊C₃	—	27	9	no	—
31	C₃×C₄₃⋊C₃	#732	1	3	yes	—
32	C₉×C₄₃	—	3	1	no	—
33	C₉×C₄₃	—	9	1	no	—
34	C₄₃⋊C₉	—	3	2	no	—
35	C₄₃⋊C₉	—	9	2	no	—
36	C₃×#732	—	43	3	no	—
37	#6887	—	43	1	no	—
38	#6879	—	43	6	no	—
39	#6879	—	43	2	no	—
40	#6879	C₄₃⋊C₃	1	1	yes	characteristic, complemented
41	C₃×C₄₃	—	3	1	no	—
42	C₃×C₄₃	—	27	3	no	—
43	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
44	C₄₃⋊C₃	—	3	3	no	—
45	C₄₃⋊C₃	—	27	6	no	—
46	C₃×H(3,𝔽₃)	—	129	3	no	—
47	C₃²×C₉	—	43	1	no	—
48	#732	—	43	6	no	—
49	#732	—	129	6	no	—
50	#732	C₃×C₄₃⋊C₃	1	3	yes	complemented
51	C₉⋊C₉	—	129	2	no	—
52	C₃²⋊C₉	—	129	1	no	—
53	C₉²	—	43	2	no	—
54	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic, complemented
55	C₄₃	#10624839	1	1	yes	characteristic, complemented, Sylow
56	C₃³	—	43	1	no	—
57	C₃³	—	387	3	no	—
58	H(3,𝔽₃)	—	3	3	no	—
59	H(3,𝔽₃)	—	129	6	no	—
60	H(3,𝔽₃)	—	387	6	no	—
61	C₃×C₉	—	3	1	no	—
62	C₃×C₉	—	43	2	no	—
63	C₃×C₉	—	129	3	no	—
64	C₃×C₉	—	129	2	no	—
65	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
66	C₃²	—	9	3	no	—
67	C₃²	—	43	3	no	—
68	C₃²	—	387	1	no	—
69	C₃²	—	387	6	no	—
70	C₃²	—	1161	9	no	—
71	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
72	C₉	—	3	1	no	—
73	C₉	—	9	1	no	—
74	C₉	—	129	2	no	—
75	C₉	—	387	2	no	—
76	C₃	—	3	1	no	—
77	C₃	—	27	3	no	—
78	C₃	—	129	3	no	—
79	C₃	—	1161	6	no	—
80	C₃	#732×C₄₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#732×C₄₃⋊C₃
commutator, cosocle	C₃×C₉×C₄₃	C₃³
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6879	C₃
socle	C₃×C₄₃	C₃×#732
hypercenter	#6879	C₄₃⋊C₃
hypocenter	C₄₃	#10624839
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ #6879

Complements

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

N	H ≅ G/N	type
1. #732×C₄₃⋊C₃	C₃	semidirect
2. #23782780	C₃	semidirect
3. #23782751	C₃	semidirect
4. #23782750	C₃	semidirect
5. C₄₃×#6879	C₃	semidirect
8. #16812513	C₃²	semidirect
12. C₉×C₄₃⋊C₉	C₃²	semidirect
13. C₄₃×#732	C₃²	semidirect
14. C₉²×C₄₃	C₃²	semidirect
40. #6879	C₄₃⋊C₃	semidirect
50. #732	C₃×C₄₃⋊C₃	semidirect
54. C₉²	C₃×C₄₃⋊C₃	semidirect
55. C₄₃	#10624839	semidirect

Maximal subgroups

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

subgroup	index
#732×C₄₃⋊C₃	3
#23782780	3
#23782751	3
#23782750	3
C₄₃×#6879	3
#10624839	43