Subgroups — #44534284

Order 31347.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782798	C₃	1	2	yes	maximal
2	C₃×C₃²⋊(C₄₃⋊C₉)	C₃	1	1	yes	maximal, characteristic
3	#23782715	C₃	1	9	yes	maximal, complemented
4	C₃×C₄₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
5	C₃×#11923958	—	3	2	no	—
6	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
7	C₃²⋊(C₄₃⋊C₉)	—	3	2	no	—
8	C₃²⋊(C₄₃⋊C₉)	—	3	1	no	—
9	C₃²⋊(C₄₃⋊C₉)	—	3	4	no	—
10	C₃²⋊(C₄₃⋊C₉)	C₃²	1	6	yes	—
11	C₃⁴×C₄₃	C₃²	1	1	yes	characteristic
12	C₃²×C₉×C₄₃	—	3	1	no	—
13	C₄₃×C₃²⋊C₉	—	3	2	no	—
14	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
15	#11923958	—	9	6	no	—
16	C₃×C₄₃⋊C₉	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	6	no	—
18	C₃×C₄₃⋊C₉	—	3	9	no	—
19	C₃³×C₄₃	—	3	3	no	—
20	C₃³×C₄₃	—	3	3	no	—
21	C₃³×C₄₃	—	9	2	no	—
22	C₃³×C₄₃	H(3,𝔽₃)	1	2	yes	—
23	C₃³×C₄₃	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃³×C₄₃	C₃³	1	1	yes	characteristic
25	C₃×C₉×C₄₃	—	3	3	no	—
26	C₃×C₉×C₄₃	—	9	3	no	—
27	#10624806	—	43	1	no	maximal, Sylow
28	C₃²×C₄₃	—	3	2	no	—
29	C₃²×C₄₃	—	3	2	no	—
30	C₃²×C₄₃	—	3	1	no	—
31	C₃²×C₄₃	—	3	1	no	—
32	C₃²×C₄₃	—	3	4	no	—
33	C₃²×C₄₃	—	3	2	no	—
34	C₃²×C₄₃	—	3	2	no	—
35	C₃²×C₄₃	—	9	9	no	—
36	C₃²×C₄₃	#732	1	3	yes	—
37	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
38	C₃²×C₄₃	#737	1	3	yes	—
39	C₉×C₄₃	—	9	3	no	—
40	C₄₃⋊C₉	—	9	3	no	—
41	C₄₃⋊C₉	—	9	6	no	—
42	#6891	—	43	2	no	—
43	C₃×C₃²⋊C₉	—	43	1	no	—
44	C₃×C₃²⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
45	#6868	—	43	9	no	—
46	C₃×C₄₃	—	3	3	no	—
47	C₃×C₄₃	—	3	3	no	—
48	C₃×C₄₃	—	9	2	no	—
49	C₃×C₄₃	#6893	1	1	yes	characteristic
50	C₃×C₄₃	C₃×#732	1	1	yes	characteristic
51	C₃×C₄₃	#6912	1	2	yes	—
52	C₃⁴	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃×3₋¹⁺²	—	129	2	no	—
54	C₃²×C₉	—	3	1	no	—
55	C₃²×C₉	—	43	3	no	—
56	C₃²⋊C₉	—	3	2	no	—
57	C₃²⋊C₉	—	43	6	no	—
58	C₃²⋊C₉	—	129	2	no	—
59	C₃²⋊C₉	—	129	1	no	—
60	C₃²⋊C₉	—	129	4	no	—
61	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
62	C₄₃	#10624806	1	1	yes	characteristic, complemented, Sylow
63	C₃³	—	3	3	no	—
64	C₃³	—	3	3	no	—
65	C₃³	—	9	2	no	—
66	C₃³	C₃²⋊(C₄₃⋊C₃)	1	2	yes	—
67	C₃³	C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
68	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
69	3₋¹⁺²	—	387	6	no	—
70	C₃×C₉	—	3	3	no	—
71	C₃×C₉	—	9	3	no	—
72	C₃×C₉	—	129	6	no	—
73	C₃×C₉	—	129	3	no	—
74	C₃×C₉	—	129	9	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	2	no	—
78	C₃²	—	3	2	no	—
79	C₃²	—	3	2	no	—
80	C₃²	—	3	2	no	—
81	C₃²	—	3	4	no	—
82	C₃²	—	9	9	no	—
83	C₃²	#16812512	1	3	yes	—
84	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
85	C₃²	#16812525	1	3	yes	—
86	C₉	—	9	3	no	—
87	C₉	—	387	3	no	—
88	C₉	—	387	6	no	—
89	C₃	—	3	3	no	—
90	C₃	—	3	3	no	—
91	C₃	—	9	2	no	—
92	C₃	#23782808	1	1	yes	characteristic
93	C₃	C₃×#16812512	1	1	yes	characteristic
94	C₃	#23782895	1	2	yes	—

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₃×C₄₃×C₃²⋊C₉	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃⁴×C₄₃	C₃²
hypercenter	C₃×C₃²⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624806
LCS	G ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃⁴ ◁ C₃×C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. #23782715	C₃	semidirect
62. C₄₃	#10624806	semidirect

Maximal subgroups

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

subgroup	index
#23782798	3
C₃×C₃²⋊(C₄₃⋊C₉)	3
#23782715	3
C₃×C₄₃×C₃²⋊C₉	3
#10624806	43