Subgroups — #44532408

Order 31347.

254 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃⋊#6855	C₃	1	9	yes	maximal
2	C₄₃⋊#6855	C₃	1	1	yes	maximal, characteristic
3	C₄₃⋊#6855	C₃	1	1	yes	maximal, characteristic
4	C₄₃⋊#6855	C₃	1	1	yes	maximal, characteristic
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	C₃²×C₉×C₄₃	C₃²	1	3	yes	—
10	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
11	C₄₃×C₉⋊C₉	—	3	3	no	—
12	C₃×C₄₃⋊C₉	—	3	3	no	—
13	C₃×C₄₃⋊C₉	—	3	3	no	—
14	C₃×C₄₃⋊C₉	—	3	9	no	—
15	C₃×C₄₃⋊C₉	—	3	9	no	—
16	C₃×C₄₃⋊C₉	—	3	3	no	—
17	C₃×C₄₃⋊C₉	—	3	9	no	—
18	C₃³×C₄₃	C₃³	1	1	yes	characteristic
19	C₃×C₉×C₄₃	—	3	1	no	—
20	C₃×C₉×C₄₃	—	3	1	no	—
21	C₃×C₉×C₄₃	—	3	1	no	—
22	C₃×C₉×C₄₃	—	3	3	no	—
23	C₃×C₉×C₄₃	—	3	9	no	—
24	C₃×C₉×C₄₃	3₋¹⁺²	1	3	yes	—
25	#10624576	—	43	1	no	maximal, Sylow
26	C₃²×C₄₃	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃²×C₄₃	#737	1	1	yes	characteristic
28	C₃²×C₄₃	#737	1	1	yes	characteristic
29	C₃²×C₄₃	#737	1	1	yes	characteristic
30	C₃²×C₄₃	#737	1	9	yes	—
31	C₉×C₄₃	—	3	3	no	—
32	C₉×C₄₃	—	9	3	no	—
33	C₄₃⋊C₉	—	9	3	no	—
34	C₄₃⋊C₉	—	9	3	no	—
35	C₄₃⋊C₉	—	9	3	no	—
36	C₃×C₉⋊C₉	C₄₃⋊C₃	1	1	yes	characteristic
37	#6855	—	43	9	no	—
38	#6855	—	43	1	no	—
39	#6855	—	43	1	no	—
40	#6855	—	43	1	no	—
41	C₃×C₄₃	#6895	1	1	yes	characteristic
42	C₃×C₄₃	#6897	1	3	yes	—
43	C₃×C₄₃	#6897	1	3	yes	—
44	C₃×C₄₃	#6898	1	3	yes	—
45	C₃×C₄₃	#6899	1	3	yes	—
46	C₃²×C₉	—	43	3	no	—
47	C₃²×C₉	—	43	3	no	—
48	C₃²×C₉	—	43	3	no	—
49	C₃²×C₉	C₃×C₄₃⋊C₃	1	3	yes	—
50	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
51	C₉⋊C₉	—	3	3	no	—
52	C₄₃	#10624576	1	1	yes	characteristic, complemented, Sylow
53	C₃³	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
54	C₃×C₉	—	3	1	no	—
55	C₃×C₉	—	3	1	no	—
56	C₃×C₉	—	3	1	no	—
57	C₃×C₉	—	3	3	no	—
58	C₃×C₉	—	3	9	no	—
59	C₃×C₉	—	129	3	no	—
60	C₃×C₉	—	129	3	no	—
61	C₃×C₉	—	129	3	no	—
62	C₃×C₉	—	129	9	no	—
63	C₃×C₉	—	129	9	no	—
64	C₃×C₉	—	129	9	no	—
65	C₃×C₉	#11923958	1	3	yes	—
66	C₃²	C₃×#11923958	1	1	yes	characteristic
67	C₃²	#16812525	1	1	yes	characteristic
68	C₃²	#16812525	1	1	yes	characteristic
69	C₃²	#16812525	1	1	yes	characteristic
70	C₃²	#16812526	1	9	yes	—
71	C₉	—	3	3	no	—
72	C₉	—	9	3	no	—
73	C₉	—	387	3	no	—
74	C₉	—	387	3	no	—
75	C₉	—	387	3	no	—
76	C₃	#23782822	1	1	yes	characteristic
77	C₃	#23782832	1	3	yes	—
78	C₃	#23782833	1	3	yes	—
79	C₃	#23782836	1	3	yes	—
80	C₃	#23782838	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	#10624576
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
52. C₄₃	#10624576	semidirect

Maximal subgroups

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

subgroup	index
C₄₃⋊#6855	3
C₃×C₄₃×C₉⋊C₉	3
#10624576	43