Subgroups — #44534482

Order 31347.

226 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	C₉²×C₄₃⋊C₃	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	—	3	1	no	—
8	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	#16812515	C₃²	1	6	yes	—
10	#16812509	—	3	3	no	—
11	#16812506	—	3	3	no	—
12	C₉×C₄₃⋊C₉	—	3	1	no	—
13	C₉×C₄₃⋊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	9	no	—
25	C₉×C₄₃⋊C₃	—	3	1	no	—
26	C₉×C₄₃⋊C₃	—	3	2	no	—
27	H(3,𝔽₃)×C₄₃	—	3	3	no	—
28	C₃×C₉×C₄₃	—	3	1	no	—
29	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
30	#10624837	—	43	1	no	maximal, Sylow
31	C₃²×C₄₃	—	9	3	no	—
32	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
33	C₃×C₄₃⋊C₃	—	3	1	no	—
34	C₃×C₄₃⋊C₃	—	3	3	no	—
35	C₉×C₄₃	—	3	3	no	—
36	C₉×C₄₃	—	3	1	no	—
37	C₄₃⋊C₉	—	3	6	no	—
38	C₄₃⋊C₉	—	3	1	no	—
39	C₄₃⋊C₉	—	9	6	no	—
40	C₄₃⋊C₉	#732	1	1	yes	characteristic
41	C₄₃⋊C₉	#732	1	2	yes	—
42	#6908	—	43	3	no	—
43	C₃×C₉²	—	43	1	no	—
44	#6880	—	43	2	no	—
45	#6879	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	#6878	—	43	6	no	—
47	C₃×C₄₃	—	3	1	no	—
48	C₃×C₄₃	—	27	3	no	—
49	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
50	C₄₃⋊C₃	—	3	3	no	—
51	#737	—	129	3	no	—
52	C₃²×C₉	—	43	1	no	—
53	C₃²×C₉	—	129	1	no	—
54	#733	—	43	6	no	—
55	#732	C₃×C₄₃⋊C₃	1	3	yes	—
56	#731	—	129	3	no	—
57	AΣL(1,𝔽₂₇)	—	129	3	no	—
58	C₉²	—	43	2	no	—
59	C₉²	—	129	1	no	—
60	C₉²	—	129	1	no	—
61	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
62	C₄₃	#10624837	1	1	yes	characteristic, complemented, Sylow
63	C₃³	—	43	1	no	—
64	3₋¹⁺²	—	129	6	no	—
65	3₋¹⁺²	—	387	6	no	—
66	H(3,𝔽₃)	—	3	3	no	—
67	C₃×C₉	—	3	1	no	—
68	C₃×C₉	—	43	1	no	—
69	C₃×C₉	—	43	1	no	—
70	C₃×C₉	—	129	1	no	—
71	C₃×C₉	—	129	2	no	—
72	C₃×C₉	—	129	9	no	—
73	C₃×C₉	—	129	2	no	—
74	C₃×C₉	—	387	3	no	—
75	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
76	C₃²	—	9	3	no	—
77	C₃²	—	129	3	no	—
78	C₃²	—	129	1	no	—
79	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
80	C₉	—	3	3	no	—
81	C₉	—	3	1	no	—
82	C₉	—	43	1	no	—
83	C₉	—	43	2	no	—
84	C₉	—	129	6	no	—
85	C₉	—	129	1	no	—
86	C₉	—	387	6	no	—
87	C₃	—	3	1	no	—
88	C₃	—	27	3	no	—
89	C₃	—	129	3	no	—
90	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	#10624837
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. C₉²×C₄₃⋊C₃	C₃	semidirect
3. #23782754	C₃	semidirect
4. #23782745	C₃	semidirect
5. C₄₃×#6879	C₃	semidirect
45. #6879	C₄₃⋊C₃	semidirect
62. C₄₃	#10624837	semidirect

Maximal subgroups

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

subgroup	index
#23782875	3
C₉²×C₄₃⋊C₃	3
#23782754	3
#23782745	3
C₄₃×#6879	3
#10624837	43