Subgroups — #44531934

Order 31347.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23782734	C₃	1	1	yes	maximal, characteristic
2	#23782733	C₃	1	1	yes	maximal, characteristic
3	#23782708	C₃	1	1	yes	maximal, characteristic
4	C₄₃×C₉⋊C₂₇	C₃	1	1	yes	maximal, characteristic
5	C₃×C₄₃⋊C₂₇	—	3	1	no	—
6	C₃×C₄₃⋊C₂₇	—	3	1	no	—
7	C₃×C₄₃⋊C₂₇	C₉	1	1	yes	characteristic
8	C₃×C₄₃⋊C₂₇	C₉	1	1	yes	characteristic
9	C₃×C₄₃⋊C₂₇	C₉	1	1	yes	characteristic
10	C₃×C₂₇×C₄₃	—	3	1	no	—
11	C₉²×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃⋊C₂₇	—	3	1	no	—
13	C₄₃⋊C₂₇	—	3	1	no	—
14	C₄₃⋊C₂₇	—	9	1	no	—
15	C₄₃⋊C₂₇	—	9	1	no	—
16	C₄₃⋊C₂₇	C₂₇	1	3	yes	complemented
17	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
19	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
20	C₃×C₉×C₄₃	3₋¹⁺²	1	1	yes	characteristic
21	C₂₇×C₄₃	—	9	1	no	—
22	#10624462	—	43	1	no	maximal, Sylow
23	C₃²×C₄₃	C₉⋊C₉	1	1	yes	characteristic
24	C₉×C₄₃	—	3	1	no	—
25	C₉×C₄₃	—	3	1	no	—
26	C₉×C₄₃	—	3	1	no	—
27	C₉×C₄₃	C₃×C₂₇	1	1	yes	characteristic
28	C₉×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
29	C₉×C₄₃	C₂₇⋊C₃	1	1	yes	characteristic
30	C₉⋊C₂₇	—	43	1	no	—
31	C₉⋊C₂₇	—	43	1	no	—
32	C₉⋊C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
33	#6864	—	43	1	no	—
34	C₃×C₄₃	C₉⋊C₂₇	1	1	yes	characteristic
35	C₃×C₄₃	#6875	1	1	yes	characteristic
36	C₃×C₄₃	#6875	1	1	yes	characteristic
37	C₃×C₄₃	#6875	1	1	yes	characteristic
38	C₃×C₂₇	—	3	1	no	—
39	C₃×C₂₇	—	43	1	no	—
40	C₃×C₂₇	—	43	1	no	—
41	C₃×C₂₇	—	43	1	no	—
42	C₃×C₂₇	—	129	1	no	—
43	C₃×C₂₇	—	129	1	no	—
44	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
45	C₄₃	#10624462	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
47	C₃×C₉	#11923956	1	1	yes	characteristic
48	C₃×C₉	#11923957	1	1	yes	characteristic
49	C₃×C₉	#11923958	1	1	yes	characteristic
50	C₂₇	—	9	1	no	—
51	C₂₇	—	43	3	no	—
52	C₂₇	—	129	1	no	—
53	C₂₇	—	129	1	no	—
54	C₂₇	—	387	1	no	—
55	C₂₇	—	387	1	no	—
56	C₃²	(C₄₃⋊C₉)⋊C₉	1	1	yes	characteristic
57	C₉	—	3	1	no	—
58	C₉	—	3	1	no	—
59	C₉	—	3	1	no	—
60	C₉	C₂₇×C₄₃⋊C₃	1	1	yes	characteristic
61	C₉	#16812503	1	1	yes	characteristic
62	C₉	#16812504	1	1	yes	characteristic
63	C₃	(C₄₃⋊C₉)⋊C₂₇	1	1	yes	characteristic
64	C₃	#23782735	1	1	yes	characteristic
65	C₃	#23782738	1	1	yes	characteristic
66	C₃	#23782739	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	(C₄₃⋊C₉)⋊C₉
commutator	C₉×C₄₃	C₃×C₂₇
Frattini	C₉²	C₃×C₄₃⋊C₃
Fitting	C₄₃×C₉⋊C₂₇	C₃
socle, prime radical	C₃²×C₄₃	C₉⋊C₉
cosocle	C₉²×C₄₃	C₃²
hypercenter	C₉⋊C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	#10624462
LCS	G ▷ C₉×C₄₃ ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃² ◁ C₉² ◁ C₉⋊C₂₇

Complements

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

N	H ≅ G/N	type
16. C₄₃⋊C₂₇	C₂₇	semidirect
45. C₄₃	#10624462	semidirect

Maximal subgroups

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

subgroup	index
#23782734	3
#23782733	3
#23782708	3
C₄₃×C₉⋊C₂₇	3
#10624462	43