Subgroups — #44532401

Order 31347.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×(C₄₃⋊C₉)⋊C₉	C₃	1	3	yes	maximal
2	C₄₃⋊#6855	C₃	1	3	yes	maximal
3	C₄₃⋊#6855	C₃	1	3	yes	maximal
4	C₄₃⋊#6855	C₃	1	3	yes	maximal
5	C₃×C₄₃×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
6	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
7	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
8	C₃²×C₄₃⋊C₉	C₃²	1	3	yes	—
9	(C₄₃⋊C₉)⋊C₉	—	3	9	no	—
10	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₉⋊C₉	—	3	3	no	—
13	C₃×C₄₃⋊C₉	—	3	3	no	—
14	C₃×C₄₃⋊C₉	—	3	3	no	—
15	C₃×C₄₃⋊C₉	—	3	3	no	—
16	C₃×C₄₃⋊C₉	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	3	no	—
18	C₃×C₄₃⋊C₉	—	3	6	no	—
19	C₃×C₄₃⋊C₉	—	3	3	no	—
20	C₃×C₄₃⋊C₉	—	3	3	no	—
21	C₃×C₄₃⋊C₉	—	3	6	no	—
22	C₃×C₄₃⋊C₉	3₋¹⁺²	1	9	yes	—
23	C₃³×C₄₃	C₃³	1	1	yes	characteristic
24	C₃×C₉×C₄₃	—	3	3	no	—
25	C₃×C₉×C₄₃	—	3	3	no	—
26	C₃×C₉×C₄₃	—	3	3	no	—
27	C₃×C₉×C₄₃	—	3	3	no	—
28	C₃×C₉×C₄₃	—	3	3	no	—
29	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
30	#10624575	—	43	1	no	maximal, Sylow
31	C₃²×C₄₃	C₃×3₋¹⁺²	1	3	yes	—
32	C₃²×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
33	C₃²×C₄₃	#737	1	3	yes	—
34	C₃²×C₄₃	#737	1	3	yes	—
35	C₃²×C₄₃	#737	1	3	yes	—
36	C₉×C₄₃	—	3	3	no	—
37	C₉×C₄₃	—	9	3	no	—
38	C₄₃⋊C₉	—	3	9	no	—
39	C₄₃⋊C₉	—	9	3	no	—
40	C₄₃⋊C₉	—	9	3	no	—
41	C₃×C₉⋊C₉	—	43	3	no	—
42	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
43	#6855	—	43	3	no	—
44	#6855	—	43	3	no	—
45	#6855	—	43	3	no	—
46	C₃×C₄₃	#6894	1	3	yes	—
47	C₃×C₄₃	#6895	1	1	yes	characteristic
48	C₃×C₄₃	#6896	1	3	yes	—
49	C₃×C₄₃	#6897	1	3	yes	—
50	C₃×C₄₃	#6899	1	3	yes	—
51	C₃²×C₉	—	43	3	no	—
52	C₃²×C₉	—	43	3	no	—
53	C₃²×C₉	—	43	3	no	—
54	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
55	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
56	C₉⋊C₉	—	3	3	no	—
57	C₉⋊C₉	—	129	9	no	—
58	C₄₃	#10624575	1	1	yes	characteristic, complemented, Sylow
59	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
60	C₃×C₉	—	3	3	no	—
61	C₃×C₉	—	3	3	no	—
62	C₃×C₉	—	3	3	no	—
63	C₃×C₉	—	3	3	no	—
64	C₃×C₉	—	3	3	no	—
65	C₃×C₉	—	43	9	no	—
66	C₃×C₉	—	129	3	no	—
67	C₃×C₉	—	129	3	no	—
68	C₃×C₉	—	129	3	no	—
69	C₃×C₉	—	129	3	no	—
70	C₃×C₉	—	129	3	no	—
71	C₃×C₉	—	129	3	no	—
72	C₃×C₉	—	129	6	no	—
73	C₃×C₉	—	129	3	no	—
74	C₃×C₉	—	129	6	no	—
75	C₃×C₉	#11923958	1	3	yes	—
76	C₃²	3₋¹⁺²×C₄₃⋊C₃	1	3	yes	—
77	C₃²	C₃×#11923958	1	1	yes	characteristic
78	C₃²	#16812525	1	3	yes	—
79	C₃²	#16812526	1	3	yes	—
80	C₃²	#16812526	1	3	yes	—
81	C₉	—	3	3	no	—
82	C₉	—	9	3	no	—
83	C₉	—	129	9	no	—
84	C₉	—	387	3	no	—
85	C₉	—	387	3	no	—
86	C₃	#23782813	1	3	yes	—
87	C₃	#23782822	1	1	yes	characteristic
88	C₃	#23782824	1	3	yes	—
89	C₃	#23782833	1	3	yes	—
90	C₃	#23782841	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, prime radical, cosocle	C₃³×C₄₃	C₃³
Fitting	C₃×C₄₃×C₉⋊C₉	C₃
hypercenter	C₃×C₉⋊C₉	C₄₃⋊C₃
hypocenter	C₄₃	#10624575
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ C₃×C₉⋊C₉

Complements

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

N	H ≅ G/N	type
58. C₄₃	#10624575	semidirect

Maximal subgroups

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

subgroup	index
C₃×(C₄₃⋊C₉)⋊C₉	3
C₄₃⋊#6855	3
C₃×C₄₃×C₉⋊C₉	3
#10624575	43