Subgroups — #44534495

Order 31347.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#733×C₄₃⋊C₃	C₃	1	3	yes	maximal
2	#23782780	C₃	1	1	yes	maximal, characteristic
3	#23782754	C₃	1	2	yes	maximal, complemented
4	#23782753	C₃	1	3	yes	maximal, complemented
5	#23782752	C₃	1	3	yes	maximal, complemented
6	C₄₃×#6880	C₃	1	1	yes	maximal, characteristic, complemented
7	3₋¹⁺²×C₄₃⋊C₃	—	3	3	no	—
8	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	#16812515	C₃²	1	6	yes	—
10	#16812514	—	3	6	no	—
11	(C₄₃⋊C₉)⋊C₉	—	3	2	no	—
12	(C₃×C₄₃⋊C₃)⋊C₉	—	3	1	no	—
13	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
14	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
15	C₄₃×#733	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	#11923957	—	9	3	no	—
20	#11923956	—	9	3	no	—
21	C₃×C₄₃⋊C₉	—	3	1	no	—
22	C₃×C₄₃⋊C₉	—	3	1	no	—
23	C₃×C₄₃⋊C₉	H(3,𝔽₃)	1	2	yes	—
24	C₉×C₄₃⋊C₃	—	3	3	no	—
25	C₉×C₄₃⋊C₃	—	9	3	no	—
26	3₋¹⁺²×C₄₃	—	3	3	no	—
27	C₃×C₉×C₄₃	—	3	1	no	—
28	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
29	#10624840	—	43	1	no	maximal, Sylow
30	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₄₃⋊C₃	—	9	1	no	—
32	C₃×C₄₃⋊C₃	#732	1	3	yes	—
33	C₉×C₄₃	—	3	1	no	—
34	C₉×C₄₃	—	9	1	no	—
35	C₉×C₄₃	—	9	3	no	—
36	C₄₃⋊C₉	—	3	2	no	—
37	C₄₃⋊C₉	—	9	1	no	—
38	C₄₃⋊C₉	—	9	1	no	—
39	C₄₃⋊C₉	—	9	6	no	—
40	C₃×#733	—	43	3	no	—
41	#6887	—	43	1	no	—
42	#6880	—	43	3	no	—
43	#6880	—	43	3	no	—
44	#6880	—	43	2	no	—
45	#6880	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	C₃×C₄₃	—	3	1	no	—
47	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
48	C₄₃⋊C₃	—	3	3	no	—
49	C₃×3₋¹⁺²	—	129	3	no	—
50	C₃²×C₉	—	43	1	no	—
51	#733	—	43	6	no	—
52	#733	—	129	6	no	—
53	#733	C₃×C₄₃⋊C₃	1	3	yes	—
54	C₉⋊C₉	—	129	2	no	—
55	C₃²⋊C₉	—	129	1	no	—
56	C₉²	—	43	1	no	—
57	C₉²	—	43	1	no	—
58	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
59	C₄₃	#10624840	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	43	1	no	—
61	3₋¹⁺²	—	3	3	no	—
62	3₋¹⁺²	—	129	6	no	—
63	3₋¹⁺²	—	387	3	no	—
64	3₋¹⁺²	—	387	3	no	—
65	C₃×C₉	—	3	1	no	—
66	C₃×C₉	—	43	2	no	—
67	C₃×C₉	—	129	3	no	—
68	C₃×C₉	—	129	1	no	—
69	C₃×C₉	—	129	1	no	—
70	C₃×C₉	—	387	3	no	—
71	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
72	C₃²	—	43	3	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	—	9	3	no	—
78	C₉	—	129	2	no	—
79	C₉	—	387	1	no	—
80	C₉	—	387	1	no	—
81	C₉	—	387	6	no	—
82	C₃	—	3	1	no	—
83	C₃	—	129	3	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×#6880	C₃
socle	C₃×C₄₃	C₃×#732
prime radical	C₃²×C₄₃⋊C₃	H(3,𝔽₃)
hypercenter	#6880	C₄₃⋊C₃
hypocenter	C₄₃	#10624840
LCS	G ▷ C₃×C₉×C₄₃ ▷ C₃²×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃×C₉ ◁ #6880

Complements

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

N	H ≅ G/N	type
3. #23782754	C₃	semidirect
4. #23782753	C₃	semidirect
5. #23782752	C₃	semidirect
6. C₄₃×#6880	C₃	semidirect
45. #6880	C₄₃⋊C₃	semidirect
59. C₄₃	#10624840	semidirect

Maximal subgroups

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

subgroup	index
#733×C₄₃⋊C₃	3
#23782780	3
#23782754	3
#23782753	3
#23782752	3
C₄₃×#6880	3
#10624840	43