Subgroups — #44534503

Order 31347.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782875	C₃	1	3	yes	maximal, complemented
2	#23782780	C₃	1	1	yes	maximal, characteristic, complemented
3	#23782754	C₃	1	2	yes	maximal, complemented
4	#23782745	C₃	1	6	yes	maximal, complemented
5	C₄₃×#6879	C₃	1	1	yes	maximal, characteristic, complemented
6	#16812524	—	3	3	no	—
7	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
8	#16812515	C₃²	1	6	yes	—
9	#16812509	—	3	3	no	—
10	#16812506	—	3	3	no	—
11	(C₄₃⋊C₉)⋊C₉	—	3	1	no	—
12	(C₄₃⋊C₉)⋊C₉	—	3	1	no	—
13	(C₃×C₄₃⋊C₃)⋊C₉	—	3	1	no	—
14	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
15	C₄₃×#732	C₃²	1	3	yes	—
16	C₉²×C₄₃	C₃²	1	1	yes	characteristic
17	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
18	#11923958	—	3	6	no	—
19	#11923958	—	9	6	no	—
20	C₃×C₄₃⋊C₉	—	3	2	no	—
21	C₃×C₄₃⋊C₉	—	9	3	no	—
22	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
24	C₉×C₄₃⋊C₃	—	3	3	no	—
25	H(3,𝔽₃)×C₄₃	—	3	3	no	—
26	C₃×C₉×C₄₃	—	3	1	no	—
27	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
28	#10624841	—	43	1	no	maximal, Sylow
29	C₃²×C₄₃	—	9	3	no	—
30	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₄₃⋊C₃	—	3	1	no	—
32	C₃×C₄₃⋊C₃	—	9	1	no	—
33	C₉×C₄₃	—	3	1	no	—
34	C₉×C₄₃	—	9	1	no	—
35	C₄₃⋊C₉	—	3	1	no	—
36	C₄₃⋊C₉	—	9	2	no	—
37	C₄₃⋊C₉	—	9	6	no	—
38	C₄₃⋊C₉	#732	1	3	yes	—
39	#6908	—	43	3	no	—
40	#6887	—	43	1	no	—
41	#6880	—	43	2	no	—
42	#6879	C₄₃⋊C₃	1	1	yes	characteristic, complemented
43	#6878	—	43	6	no	—
44	C₃×C₄₃	—	3	1	no	—
45	C₃×C₄₃	—	27	3	no	—
46	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
47	C₄₃⋊C₃	—	9	1	no	—
48	#737	—	129	3	no	—
49	C₃²×C₉	—	43	1	no	—
50	#733	—	43	6	no	—
51	#732	C₃×C₄₃⋊C₃	1	3	yes	—
52	#731	—	129	3	no	—
53	AΣL(1,𝔽₂₇)	—	129	3	no	—
54	C₉⋊C₉	—	129	1	no	—
55	C₉⋊C₉	—	129	1	no	—
56	C₃²⋊C₉	—	129	1	no	—
57	C₉²	—	43	2	no	—
58	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
59	C₄₃	#10624841	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	43	1	no	—
61	3₋¹⁺²	—	129	6	no	—
62	3₋¹⁺²	—	387	6	no	—
63	H(3,𝔽₃)	—	3	3	no	—
64	C₃×C₉	—	3	1	no	—
65	C₃×C₉	—	43	1	no	—
66	C₃×C₉	—	43	1	no	—
67	C₃×C₉	—	129	3	no	—
68	C₃×C₉	—	129	2	no	—
69	C₃×C₉	—	387	3	no	—
70	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
71	C₃²	—	9	3	no	—
72	C₃²	—	129	1	no	—
73	C₃²	—	387	1	no	—
74	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
75	C₉	—	3	1	no	—
76	C₉	—	9	1	no	—
77	C₉	—	43	3	no	—
78	C₉	—	129	1	no	—
79	C₉	—	387	2	no	—
80	C₉	—	387	6	no	—
81	C₃	—	3	1	no	—
82	C₃	—	27	3	no	—
83	C₃	—	387	1	no	—
84	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	#10624841
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. #23782875	C₃	semidirect
2. #23782780	C₃	semidirect
3. #23782754	C₃	semidirect
4. #23782745	C₃	semidirect
5. C₄₃×#6879	C₃	semidirect
42. #6879	C₄₃⋊C₃	semidirect
59. C₄₃	#10624841	semidirect

Maximal subgroups

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

subgroup	index
#23782875	3
#23782780	3
#23782754	3
#23782745	3
C₄₃×#6879	3
#10624841	43