Subgroups — C₉×#16812503 #44533344

Order 31347.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812503	C₃	1	3	yes	maximal
2	C₉²×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#23782706	C₃	1	6	yes	maximal, complemented
4	C₉×C₄₃⋊C₂₇	C₃	1	2	yes	maximal, complemented
5	C₉×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×C₄₃⋊C₃	C₉	1	3	yes	—
7	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
8	#16812503	C₉	1	27	yes	direct product factor
9	C₃×C₄₃⋊C₂₇	C₃²	1	6	yes	—
10	C₉×C₄₃⋊C₉	C₉	1	6	yes	—
11	C₉×C₄₃⋊C₉	C₃²	1	2	yes	—
12	C₃×C₂₇×C₄₃	C₃²	1	3	yes	—
13	C₉²×C₄₃	C₃²	1	1	yes	characteristic
14	C₃²×C₄₃⋊C₃	C₃×C₉	1	1	yes	characteristic
15	C₃×C₄₃⋊C₉	C₃×C₉	1	6	yes	—
16	C₃×C₄₃⋊C₉	C₃×C₉	1	2	yes	—
17	C₉×C₄₃⋊C₃	—	3	9	no	—
18	C₉×C₄₃⋊C₃	C₃×C₉	1	9	yes	—
19	C₄₃⋊C₂₇	C₃×C₉	1	18	yes	complemented
20	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
21	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
22	C₂₇×C₄₃	C₃×C₉	1	9	yes	complemented
23	C₉×C₂₇⋊C₃	—	43	1	no	maximal, Sylow
24	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
25	C₃×C₄₃⋊C₃	—	3	3	no	—
26	C₃×C₄₃⋊C₃	C₉²	1	3	yes	—
27	C₉×C₄₃	C₂₇⋊C₃	1	9	yes	complemented
28	C₉×C₄₃	C₃²×C₉	1	3	yes	—
29	C₄₃⋊C₉	—	3	6	no	—
30	C₄₃⋊C₉	C₉²	1	6	yes	—
31	C₃×C₂₇⋊C₃	—	43	3	no	—
32	C₃×C₉²	—	43	1	no	—
33	#6864	—	43	6	no	—
34	C₉×C₂₇	—	43	2	no	—
35	C₉×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic, complemented
36	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
37	C₃×C₄₃	C₃×C₂₇⋊C₃	1	3	yes	—
38	C₄₃⋊C₃	—	3	3	no	—
39	C₃²×C₉	—	43	1	no	—
40	C₃²×C₉	—	43	3	no	—
41	C₂₇⋊C₃	—	43	27	no	—
42	C₃×C₂₇	—	43	6	no	—
43	C₃×C₂₇	C₃×C₄₃⋊C₃	1	3	yes	—
44	C₉²	—	43	6	no	—
45	C₉²	—	43	2	no	—
46	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
47	C₄₃	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
48	C₃³	—	43	1	no	—
49	C₃×C₉	—	43	2	no	—
50	C₃×C₉	—	43	9	no	—
51	C₃×C₉	—	43	6	no	—
52	C₃×C₉	—	129	9	no	—
53	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
54	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
55	C₂₇	—	43	18	no	—
56	C₂₇	C₉×C₄₃⋊C₃	1	9	yes	complemented
57	C₃²	—	43	3	no	—
58	C₃²	—	129	3	no	—
59	C₃²	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
60	C₉	—	43	6	no	—
61	C₉	—	129	6	no	—
62	C₉	#16812503	1	9	yes	direct product factor
63	C₉	C₃×C₉×C₄₃⋊C₃	1	3	yes	—
64	C₃	—	129	3	no	—
65	C₃	C₉²×C₄₃⋊C₃	1	1	yes	characteristic
66	C₃	C₃×#16812503	1	3	yes	—

	subgroup	G/H
center	C₉²	C₃×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₉²
Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
Fitting	C₉×C₂₇×C₄₃	C₃
socle	C₃²×C₄₃	C₃²×C₉
prime radical	C₃²×C₄₃⋊C₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₉×C₂₇	C₄₃⋊C₃
hypocenter	C₄₃	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₉² ◁ C₉×C₂₇

Complements

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

N	H ≅ G/N	type
3. #23782706	C₃	semidirect
4. C₉×C₄₃⋊C₂₇	C₃	semidirect
5. C₉×C₂₇×C₄₃	C₃	semidirect
8. #16812503	C₉	direct (N × H)
19. C₄₃⋊C₂₇	C₃×C₉	semidirect
22. C₂₇×C₄₃	C₃×C₉	semidirect
27. C₉×C₄₃	C₂₇⋊C₃	semidirect
35. C₉×C₂₇	C₄₃⋊C₃	semidirect
47. C₄₃	C₉×C₂₇⋊C₃	semidirect
56. C₂₇	C₉×C₄₃⋊C₃	semidirect
62. C₉	#16812503	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#16812503	3
C₉²×C₄₃⋊C₃	3
#23782706	3
C₉×C₄₃⋊C₂₇	3
C₉×C₂₇×C₄₃	3
C₉×C₂₇⋊C₃	43

Subgroups — C9×#16812503 #44533344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#16812503 #44533344