Subgroups — #44532411

Order 31347.

254 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812500	C₃	1	1	yes	maximal, characteristic
2	C₄₃⋊#6855	C₃	1	3	yes	maximal
3	C₄₃⋊#6855	C₃	1	6	yes	maximal
4	C₄₃⋊#6855	C₃	1	2	yes	maximal
5	C₄₃×#6855	C₃	1	1	yes	maximal, characteristic
6	C₃²×C₄₃⋊C₉	C₃²	1	6	yes	—
7	C₃²×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
8	C₃²×C₄₃⋊C₉	C₃²	1	2	yes	—
9	#16812500	—	3	3	no	—
10	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₃×C₄₃⋊C₉	—	3	1	no	—
13	C₃×C₄₃⋊C₉	—	3	2	no	—
14	C₃×C₄₃⋊C₉	—	3	6	no	—
15	C₃×C₄₃⋊C₉	—	3	6	no	—
16	C₃×C₄₃⋊C₉	—	3	12	no	—
17	C₃×C₄₃⋊C₉	—	3	3	no	—
18	C₃×C₄₃⋊C₉	—	3	6	no	—
19	C₃³×C₄₃	C₃³	1	1	yes	characteristic
20	C₃×C₉×C₄₃	—	3	2	no	—
21	C₃×C₉×C₄₃	—	3	1	no	—
22	C₃×C₉×C₄₃	—	3	3	no	—
23	C₃×C₉×C₄₃	—	3	3	no	—
24	C₃×C₉×C₄₃	—	3	6	no	—
25	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
26	#10624576	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃²×C₄₃	#737	1	2	yes	—
29	C₃²×C₄₃	#737	1	1	yes	characteristic
30	C₃²×C₄₃	#737	1	3	yes	—
31	C₃²×C₄₃	#737	1	6	yes	—
32	C₉×C₄₃	—	3	3	no	—
33	C₉×C₄₃	—	9	3	no	—
34	C₄₃⋊C₉	—	9	6	no	—
35	C₄₃⋊C₉	—	9	1	no	—
36	C₄₃⋊C₉	—	9	2	no	—
37	C₃×C₉⋊C₉	—	43	1	no	—
38	#6855	—	43	2	no	—
39	#6855	—	43	3	no	—
40	#6855	—	43	6	no	—
41	#6855	C₄₃⋊C₃	1	1	yes	characteristic
42	C₃×C₄₃	#6895	1	1	yes	characteristic
43	C₃×C₄₃	#6897	1	6	yes	—
44	C₃×C₄₃	#6898	1	3	yes	—
45	C₃×C₄₃	#6899	1	1	yes	characteristic
46	C₃×C₄₃	#6899	1	2	yes	—
47	C₃²×C₉	—	43	6	no	—
48	C₃²×C₉	—	43	1	no	—
49	C₃²×C₉	—	43	2	no	—
50	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
51	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
52	C₉⋊C₉	—	129	3	no	—
53	C₄₃	#10624576	1	1	yes	characteristic, complemented, Sylow
54	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
55	C₃×C₉	—	3	1	no	—
56	C₃×C₉	—	3	2	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	—	3	3	no	—
59	C₃×C₉	—	3	6	no	—
60	C₃×C₉	—	129	1	no	—
61	C₃×C₉	—	129	2	no	—
62	C₃×C₉	—	129	6	no	—
63	C₃×C₉	—	129	3	no	—
64	C₃×C₉	—	129	6	no	—
65	C₃×C₉	—	129	12	no	—
66	C₃×C₉	—	129	6	no	—
67	C₃×C₉	#11923956	1	3	yes	—
68	C₃²	C₃×#11923956	1	1	yes	characteristic
69	C₃²	#16812524	1	1	yes	characteristic
70	C₃²	#16812525	1	3	yes	—
71	C₃²	#16812526	1	2	yes	—
72	C₃²	#16812526	1	6	yes	—
73	C₉	—	3	3	no	—
74	C₉	—	9	3	no	—
75	C₉	—	387	6	no	—
76	C₉	—	387	1	no	—
77	C₉	—	387	2	no	—
78	C₃	#23782819	1	1	yes	characteristic
79	C₃	#23782832	1	6	yes	—
80	C₃	#23782834	1	3	yes	—
81	C₃	#23782839	1	1	yes	characteristic
82	C₃	#23782844	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃³	C₃²×C₄₃⋊C₃
commutator, socle, prime radical, cosocle	C₃³×C₄₃	C₃³
Fitting	C₄₃×#6855	C₃
hypercenter	#6855	C₄₃⋊C₃
hypocenter	C₄₃	#10624576
LCS	G ▷ C₃³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃³ ◁ #6855

Complements

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

N	H ≅ G/N	type
53. C₄₃	#10624576	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812500	3
C₄₃⋊#6855	3
C₄₃×#6855	3
#10624576	43