Subgroups — #44533354

Order 31347.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812505	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
3	#23782782	C₃	1	1	yes	maximal, characteristic
4	#23782707	C₃	1	3	yes	maximal, complemented
5	#23782706	C₃	1	3	yes	maximal, complemented
6	C₂₇×C₄₃⋊C₉	C₃	1	3	yes	maximal, complemented
7	C₃×C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
8	#16812505	C₉	1	9	yes	complemented
9	C₃×C₄₃⋊C₂₇	C₉	1	9	yes	complemented
10	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
11	C₃×C₄₃⋊C₂₇	C₃²	1	3	yes	—
12	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
13	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
14	#16812500	C₉	1	3	yes	—
15	#16812499	C₉	1	3	yes	—
16	C₃²⋊(C₄₃⋊C₉)	C₉	1	3	yes	—
17	C₉×C₄₃⋊C₉	C₃²	1	3	yes	—
18	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
19	C₄₃×C₂₇⋊C₃	C₉	1	9	yes	complemented
20	C₃×C₂₇×C₄₃	C₃²	1	3	yes	—
21	C₃×C₄₃⋊C₉	C₃×C₉	1	9	yes	—
22	C₄₃⋊C₂₇	C₃×C₉	1	3	yes	—
23	C₄₃⋊C₂₇	C₃×C₉	1	3	yes	—
24	C₄₃⋊C₂₇	C₃×C₉	1	3	yes	—
25	C₄₃⋊C₂₇	C₃×C₉	1	9	yes	—
26	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
27	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
28	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
29	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
30	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
31	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
32	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
33	C₂₇×C₄₃	C₃×C₉	1	9	yes	—
34	#10624681	—	43	1	no	maximal, Sylow
35	C₃²×C₄₃	—	3	3	no	—
36	C₃²×C₄₃	C₉²	1	3	yes	—
37	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
38	C₉×C₄₃	C₉²	1	3	yes	—
39	C₉×C₄₃	C₉²	1	3	yes	—
40	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
41	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
42	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
43	C₄₃⋊C₉	—	3	9	no	—
44	C₃×C₂₇⋊C₃	—	43	1	no	—
45	C₃×C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic
46	C₃²×C₂₇	—	43	1	no	—
47	#6887	—	43	1	no	—
48	#6864	—	43	3	no	—
49	#6864	—	43	3	no	—
50	C₉×C₂₇	—	43	3	no	—
51	C₃×C₄₃	—	3	3	no	—
52	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
53	C₃×C₄₃	#6903	1	3	yes	—
54	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
55	C₂₇⋊C₃	—	43	9	no	—
56	C₂₇⋊C₃	C₄₃⋊C₉	1	9	yes	complemented
57	C₃×C₂₇	—	43	9	no	—
58	C₃×C₂₇	—	43	1	no	—
59	C₃×C₂₇	—	43	3	no	—
60	C₃×C₂₇	—	43	1	no	—
61	C₃×C₂₇	—	43	1	no	—
62	C₃×C₂₇	C₃×C₄₃⋊C₃	1	3	yes	—
63	C₉⋊C₉	—	43	3	no	—
64	C₉⋊C₉	—	43	3	no	—
65	C₃²⋊C₉	—	43	3	no	—
66	C₉²	—	43	3	no	—
67	C₄₃	#10624681	1	1	yes	characteristic, complemented, Sylow
68	C₃³	C₉×C₄₃⋊C₃	1	1	yes	characteristic
69	C₃×C₉	—	43	9	no	—
70	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
71	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
72	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
73	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
74	C₃×C₉	C₃×C₄₃⋊C₉	1	3	yes	—
75	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
76	C₂₇	—	43	3	no	—
77	C₂₇	—	43	3	no	—
78	C₂₇	—	43	3	no	—
79	C₂₇	—	43	9	no	—
80	C₂₇	C₃×C₄₃⋊C₉	1	9	yes	—
81	C₃²	—	3	3	no	—
82	C₃²	C₉×C₄₃⋊C₉	1	3	yes	—
83	C₃²	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
84	C₉	—	129	9	no	—
85	C₉	C₉×C₄₃⋊C₉	1	3	yes	—
86	C₉	C₉×C₄₃⋊C₉	1	3	yes	—
87	C₉	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
88	C₉	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
89	C₉	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
90	C₃	—	3	3	no	—
91	C₃	C₃×C₉×C₄₃⋊C₉	1	1	yes	characteristic
92	C₃	#23782858	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₉²
Fitting	C₃×C₄₃×C₂₇⋊C₃	C₃
socle	C₃²×C₄₃	C₃²×C₉
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₄₃⋊C₃
hypocenter	C₄₃	#10624681
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
4. #23782707	C₃	semidirect
5. #23782706	C₃	semidirect
6. C₂₇×C₄₃⋊C₉	C₃	semidirect
8. #16812505	C₉	semidirect
9. C₃×C₄₃⋊C₂₇	C₉	semidirect
19. C₄₃×C₂₇⋊C₃	C₉	semidirect
56. C₂₇⋊C₃	C₄₃⋊C₉	semidirect
67. C₄₃	#10624681	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812505	3
C₃²×C₄₃⋊C₂₇	3
#23782782	3
#23782707	3
#23782706	3
C₂₇×C₄₃⋊C₉	3
C₃×C₄₃×C₂₇⋊C₃	3
#10624681	43