Subgroups — #44534358

Order 31347.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782822	C₃	1	1	yes	maximal, characteristic, complemented
2	#23782808	C₃	1	1	yes	maximal, characteristic
3	C₃×#16812500	C₃	1	1	yes	maximal, characteristic, complemented
4	#23782725	C₃	1	3	yes	maximal, complemented
5	#23782722	C₃	1	3	yes	maximal, complemented
6	#23782719	C₃	1	3	yes	maximal
7	C₄₃×#6895	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃×#11923958	C₃²	1	1	yes	characteristic
9	C₃×#11923958	C₃²	1	1	yes	characteristic
10	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²	1	1	yes	characteristic
11	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
12	#16812500	—	3	3	no	—
13	(C₄₃⋊C₉)⋊C₉	—	3	3	no	—
14	C₃²⋊(C₄₃⋊C₉)	C₃²	1	3	yes	—
15	(C₃×C₄₃⋊C₃)⋊C₉	—	3	3	no	—
16	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
17	C₄₃×C₉⋊C₉	—	3	3	no	—
18	C₄₃×C₃²⋊C₉	C₃²	1	3	yes	—
19	C₃²×C₄₃⋊C₃	—	3	1	no	—
20	#11923958	—	3	3	no	—
21	#11923958	—	3	3	no	—
22	C₃²⋊(C₄₃⋊C₃)	—	3	3	no	—
23	C₃×C₄₃⋊C₉	—	3	1	no	—
24	C₃×C₄₃⋊C₉	—	3	1	no	—
25	C₃×C₄₃⋊C₉	—	3	3	no	—
26	C₃×C₄₃⋊C₉	—	3	3	no	—
27	C₃×C₄₃⋊C₉	—	9	3	no	—
28	C₃³×C₄₃	C₃³	1	1	yes	characteristic
29	C₃×C₉×C₄₃	—	3	3	no	—
30	C₃×C₉×C₄₃	—	3	3	no	—
31	C₃×C₉×C₄₃	H(3,𝔽₃)	1	3	yes	—
32	#10624817	—	43	1	no	maximal, Sylow
33	C₃²×C₄₃	—	3	3	no	—
34	C₃²×C₄₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
35	C₃²×C₄₃	#737	1	3	yes	—
36	C₃×C₄₃⋊C₃	—	9	3	no	—
37	C₃×C₄₃⋊C₃	—	9	1	no	—
38	C₉×C₄₃	—	3	3	no	—
39	C₉×C₄₃	—	9	3	no	—
40	C₄₃⋊C₉	—	9	3	no	—
41	C₄₃⋊C₉	—	9	3	no	—
42	C₄₃⋊C₉	—	9	1	no	—
43	C₄₃⋊C₉	—	9	1	no	—
44	#6895	—	43	1	no	—
45	#6895	C₄₃⋊C₃	1	1	yes	characteristic, complemented
46	#6893	—	43	1	no	—
47	C₃×C₉⋊C₉	—	43	1	no	—
48	3₋¹⁺²⋊C₉	—	43	3	no	—
49	3₋¹⁺²⋊C₉	—	43	3	no	—
50	H(3,𝔽₃)⋊C₉	—	43	3	no	—
51	C₃×C₄₃	—	3	3	no	—
52	C₃×C₄₃	#6893	1	1	yes	characteristic
53	C₃×C₄₃	#6913	1	3	yes	—
54	C₄₃⋊C₃	—	27	1	no	—
55	C₃×3₋¹⁺²	—	43	1	no	—
56	C₃×3₋¹⁺²	—	43	1	no	—
57	C₃×H(3,𝔽₃)	—	43	1	no	—
58	C₃²×C₉	—	43	3	no	—
59	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
60	C₉⋊C₉	—	3	3	no	—
61	C₉⋊C₉	—	129	3	no	—
62	C₉⋊C₉	—	129	3	no	—
63	C₃²⋊C₉	—	43	3	no	—
64	C₃²⋊C₉	—	129	3	no	—
65	C₃²⋊C₉	C₃×C₄₃⋊C₃	1	3	yes	—
66	C₄₃	#10624817	1	1	yes	characteristic, complemented, Sylow
67	C₃³	—	129	1	no	—
68	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
69	3₋¹⁺²	—	129	3	no	—
70	3₋¹⁺²	—	129	3	no	—
71	H(3,𝔽₃)	—	129	3	no	—
72	C₃×C₉	—	3	3	no	—
73	C₃×C₉	—	3	3	no	—
74	C₃×C₉	—	129	3	no	—
75	C₃×C₉	—	129	1	no	—
76	C₃×C₉	—	129	1	no	—
77	C₃×C₉	—	129	3	no	—
78	C₃×C₉	—	387	3	no	—
79	C₃×C₉	C₃²⋊(C₄₃⋊C₃)	1	3	yes	—
80	C₃²	—	3	3	no	—
81	C₃²	—	387	1	no	—
82	C₃²	—	387	3	no	—
83	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)	1	1	yes	characteristic
84	C₃²	#16812526	1	3	yes	—
85	C₉	—	3	3	no	—
86	C₉	—	9	3	no	—
87	C₉	—	387	1	no	—
88	C₉	—	387	1	no	—
89	C₉	—	387	3	no	—
90	C₉	—	387	3	no	—
91	C₃	—	3	3	no	—
92	C₃	—	1161	1	no	—
93	C₃	#23782809	1	1	yes	characteristic
94	C₃	#23782900	1	3	yes	—

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₄₃⋊C₃)
commutator, cosocle	C₃³×C₄₃	C₃³
Frattini	C₃³	C₃²×C₄₃⋊C₃
Fitting	C₄₃×#6895	C₃
socle	C₃²×C₄₃	C₃×H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₄₃⋊C₃)	C₃²
hypercenter	#6895	C₄₃⋊C₃
hypocenter	C₄₃	#10624817
LCS	G ▷ C₃³×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ #6895

Complements

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

N	H ≅ G/N	type
1. #23782822	C₃	semidirect
3. C₃×#16812500	C₃	semidirect
4. #23782725	C₃	semidirect
5. #23782722	C₃	semidirect
7. C₄₃×#6895	C₃	semidirect
45. #6895	C₄₃⋊C₃	semidirect
66. C₄₃	#10624817	semidirect

Maximal subgroups

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

subgroup	index
#23782822	3
#23782808	3
C₃×#16812500	3
#23782725	3
#23782722	3
#23782719	3
C₄₃×#6895	3
#10624817	43