Subgroups — #44531972

Order 31347.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782794	C₃	1	1	yes	maximal, characteristic
2	#23782712	C₃	1	2	yes	maximal, complemented
3	C₄₃×#6891	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
5	C₃×C₃²⋊(C₄₃⋊C₃)	—	3	1	no	—
6	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
7	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
8	C₃×3₋¹⁺²×C₄₃	—	3	1	no	—
9	C₄₃×C₃²⋊C₉	—	3	3	no	—
10	C₃²×C₄₃⋊C₃	—	3	3	no	—
11	C₃²⋊(C₄₃⋊C₃)	—	9	9	no	—
12	C₃²⋊(C₄₃⋊C₃)	—	9	1	no	—
13	C₃²⋊(C₄₃⋊C₃)	—	9	2	no	—
14	C₃×C₄₃⋊C₉	—	9	2	no	—
15	C₃³×C₄₃	—	3	1	no	—
16	C₃³×C₄₃	—	3	1	no	—
17	C₃³×C₄₃	—	3	2	no	—
18	C₃³×C₄₃	—	9	3	no	—
19	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
20	3₋¹⁺²×C₄₃	—	9	1	no	—
21	3₋¹⁺²×C₄₃	—	9	2	no	—
22	C₃×C₉×C₄₃	—	3	3	no	—
23	#10624475	—	43	1	no	maximal, Sylow
24	C₃²×C₄₃	—	3	3	no	—
25	C₃²×C₄₃	—	3	3	no	—
26	C₃²×C₄₃	—	9	1	no	—
27	C₃²×C₄₃	—	9	2	no	—
28	C₃²×C₄₃	—	9	2	no	—
29	C₃²×C₄₃	—	9	6	no	—
30	C₃²×C₄₃	—	9	1	no	—
31	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
32	C₃²×C₄₃	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
33	C₃²×C₄₃	#732	1	2	yes	—
34	C₃×C₄₃⋊C₃	—	9	9	no	—
35	C₃×C₄₃⋊C₃	—	9	3	no	—
36	C₉×C₄₃	—	9	3	no	—
37	C₄₃⋊C₉	—	27	2	no	—
38	#6891	C₄₃⋊C₃	1	1	yes	characteristic, complemented
39	C₃²⋊H(3,𝔽₃)	—	43	1	no	—
40	#6866	—	43	2	no	—
41	C₃×C₄₃	—	3	2	no	—
42	C₃×C₄₃	—	3	1	no	—
43	C₃×C₄₃	—	3	1	no	—
44	C₃×C₄₃	—	9	3	no	—
45	C₃×C₄₃	#6856	1	1	yes	characteristic
46	C₄₃⋊C₃	—	27	3	no	—
47	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
48	C₃×3₋¹⁺²	—	3	1	no	—
49	C₃×H(3,𝔽₃)	—	129	3	no	—
50	C₃×H(3,𝔽₃)	—	129	1	no	—
51	C₃²⋊C₉	—	3	3	no	—
52	C₃²⋊C₉	—	129	2	no	—
53	C₄₃	#10624475	1	1	yes	characteristic, complemented, Sylow
54	C₃³	—	3	1	no	—
55	C₃³	—	3	1	no	—
56	C₃³	—	3	2	no	—
57	C₃³	—	9	3	no	—
58	C₃³	—	129	3	no	—
59	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
60	3₋¹⁺²	—	9	1	no	—
61	3₋¹⁺²	—	9	2	no	—
62	H(3,𝔽₃)	—	387	9	no	—
63	H(3,𝔽₃)	—	387	1	no	—
64	H(3,𝔽₃)	—	387	2	no	—
65	C₃×C₉	—	3	3	no	—
66	C₃×C₉	—	387	2	no	—
67	C₃²	—	3	3	no	—
68	C₃²	—	3	3	no	—
69	C₃²	—	9	1	no	—
70	C₃²	—	9	6	no	—
71	C₃²	—	9	2	no	—
72	C₃²	—	9	2	no	—
73	C₃²	—	9	1	no	—
74	C₃²	—	387	9	no	—
75	C₃²	—	387	3	no	—
76	C₃²	#16812506	1	1	yes	characteristic
77	C₃²	#16812507	1	1	yes	characteristic
78	C₃²	#16812512	1	2	yes	—
79	C₉	—	9	3	no	—
80	C₉	—	1161	2	no	—
81	C₃	—	3	2	no	—
82	C₃	—	3	1	no	—
83	C₃	—	3	1	no	—
84	C₃	—	9	3	no	—
85	C₃	—	1161	3	no	—
86	C₃	#23782686	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#23782686
commutator, cosocle	C₃⁴×C₄₃	C₃²
Frattini	C₃⁴	C₃×C₄₃⋊C₃
Fitting	C₄₃×#6891	C₃
socle	C₃×C₄₃	#6856
prime radical	#23782794	C₃
hypercenter	#6891	C₄₃⋊C₃
hypocenter	C₄₃	#10624475
LCS	G ▷ C₃⁴×C₄₃ ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃³ ◁ C₃⁴ ◁ #6891

Complements

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

N	H ≅ G/N	type
2. #23782712	C₃	semidirect
3. C₄₃×#6891	C₃	semidirect
38. #6891	C₄₃⋊C₃	semidirect
53. C₄₃	#10624475	semidirect

Maximal subgroups

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

subgroup	index
#23782794	3
#23782712	3
C₄₃×#6891	3
#10624475	43