Subgroups — #44533168

Order 31347.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782797	C₃	1	2	yes	maximal
2	#23782795	C₃	1	2	yes	maximal
3	#23782699	C₃	1	4	yes	maximal, complemented
4	#23782698	C₃	1	4	yes	maximal, complemented
5	C₄₃×#6860	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
7	C₃×#11923958	C₃²	1	4	yes	—
8	C₃×#11923957	—	3	2	no	—
9	C₃²⋊(C₄₃⋊C₉)	C₃²	1	4	yes	—
10	(C₃×C₄₃⋊C₃)⋊C₉	—	3	4	no	—
11	(C₃×C₄₃⋊C₃)⋊C₉	—	3	2	no	—
12	(C₃×C₄₃⋊C₃)⋊C₉	—	3	4	no	—
13	C₃×3₋¹⁺²×C₄₃	C₃²	1	2	yes	—
14	C₄₃×C₃²⋊C₉	C₃²	1	2	yes	—
15	C₃²×C₄₃⋊C₃	—	9	2	no	—
16	C₃²×C₄₃⋊C₃	—	9	2	no	—
17	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	2	yes	—
18	C₃²×C₄₃⋊C₃	H(3,𝔽₃)	1	1	yes	characteristic
19	#11923958	—	9	4	no	—
20	#11923957	—	9	6	no	—
21	C₃×C₄₃⋊C₉	—	3	4	no	—
22	C₃×C₄₃⋊C₉	—	3	4	no	—
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	3₋¹⁺²×C₄₃	—	9	2	no	—
25	C₃×C₉×C₄₃	—	3	2	no	—
26	C₃×C₉×C₄₃	—	3	2	no	—
27	#10624662	—	43	1	no	maximal, Sylow
28	C₃²×C₄₃	—	3	2	no	—
29	C₃²×C₄₃	—	3	2	no	—
30	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₃×C₄₃⋊C₃	—	3	4	no	—
32	C₃×C₄₃⋊C₃	—	3	2	no	—
33	C₃×C₄₃⋊C₃	—	3	2	no	—
34	C₃×C₄₃⋊C₃	—	3	4	no	—
35	C₃×C₄₃⋊C₃	—	9	9	no	—
36	C₉×C₄₃	—	9	2	no	—
37	C₉×C₄₃	—	9	2	no	—
38	C₄₃⋊C₉	—	9	4	no	—
39	C₄₃⋊C₉	—	9	4	no	—
40	#6891	—	43	2	no	—
41	#6891	—	43	2	no	—
42	#6860	—	43	4	no	—
43	#6860	—	43	4	no	—
44	#6860	C₄₃⋊C₃	1	1	yes	characteristic, complemented
45	C₃×C₄₃	—	9	1	no	—
46	C₃×C₄₃	#6909	1	2	yes	—
47	C₃×C₄₃	#6912	1	2	yes	—
48	C₄₃⋊C₃	—	9	1	no	—
49	C₄₃⋊C₃	—	9	2	no	—
50	C₃⁴	—	43	1	no	—
51	C₃×3₋¹⁺²	—	43	4	no	—
52	C₃×3₋¹⁺²	—	129	2	no	—
53	C₃×3₋¹⁺²	C₃×C₄₃⋊C₃	1	2	yes	—
54	C₃²⋊C₉	—	43	4	no	—
55	C₃²⋊C₉	—	129	4	no	—
56	C₃²⋊C₉	—	129	2	no	—
57	C₃²⋊C₉	—	129	4	no	—
58	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	2	yes	—
59	C₄₃	#10624662	1	1	yes	characteristic, complemented, Sylow
60	C₃³	—	43	2	no	—
61	C₃³	—	43	1	no	—
62	C₃³	—	387	2	no	—
63	C₃³	—	387	2	no	—
64	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
65	3₋¹⁺²	—	9	2	no	—
66	3₋¹⁺²	—	387	6	no	—
67	3₋¹⁺²	—	387	4	no	—
68	C₃×C₉	—	3	2	no	—
69	C₃×C₉	—	3	2	no	—
70	C₃×C₉	—	129	4	no	—
71	C₃×C₉	—	129	4	no	—
72	C₃²	—	3	2	no	—
73	C₃²	—	3	2	no	—
74	C₃²	—	129	2	no	—
75	C₃²	—	129	4	no	—
76	C₃²	—	129	4	no	—
77	C₃²	—	129	2	no	—
78	C₃²	—	387	9	no	—
79	C₃²	H(3,𝔽₃)×C₄₃⋊C₃	1	1	yes	characteristic
80	C₉	—	9	2	no	—
81	C₉	—	9	2	no	—
82	C₉	—	387	4	no	—
83	C₉	—	387	4	no	—
84	C₃	—	9	1	no	—
85	C₃	—	387	1	no	—
86	C₃	—	387	2	no	—
87	C₃	#23782880	1	2	yes	—
88	C₃	#23782893	1	2	yes	—

	subgroup	G/H
center	C₃²	H(3,𝔽₃)×C₄₃⋊C₃
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6860	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃³×C₄₃⋊C₃	C₃²
hypercenter	#6860	C₄₃⋊C₃
hypocenter	C₄₃	#10624662
LCS	G ▷ C₃³×C₄₃ ▷ C₃²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ #6860

Complements

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

N	H ≅ G/N	type
3. #23782699	C₃	semidirect
4. #23782698	C₃	semidirect
5. C₄₃×#6860	C₃	semidirect
44. #6860	C₄₃⋊C₃	semidirect
59. C₄₃	#10624662	semidirect

Maximal subgroups

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

subgroup	index
#23782797	3
#23782795	3
#23782699	3
#23782698	3
C₄₃×#6860	3
#10624662	43