Subgroups — #44533351

Order 31347.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812505	C₃	1	2	yes	maximal
2	#23782782	C₃	1	1	yes	maximal, characteristic
3	#23782707	C₃	1	3	yes	maximal, complemented
4	#23782706	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₄₃⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃²×C₂₇×C₄₃	C₃	1	1	yes	maximal, characteristic
7	#16812505	C₉	1	18	yes	complemented
8	C₃×C₄₃⋊C₂₇	C₃²	1	6	yes	—
9	#16812500	C₉	1	3	yes	—
10	#16812499	C₉	1	3	yes	—
11	C₃²⋊(C₄₃⋊C₉)	C₉	1	3	yes	—
12	C₉×C₄₃⋊C₉	C₃²	1	3	yes	—
13	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
14	C₃×C₂₇×C₄₃	C₉	1	9	yes	complemented
15	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
16	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
17	C₃×C₂₇×C₄₃	C₃²	1	1	yes	characteristic
18	C₃×C₄₃⋊C₉	C₃×C₉	1	9	yes	—
19	C₄₃⋊C₂₇	C₃×C₉	1	18	yes	—
20	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₉×C₄₃	C₃×C₉	1	1	yes	characteristic
23	C₃×C₉×C₄₃	C₃×C₉	1	6	yes	—
24	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
25	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
26	C₂₇×C₄₃	C₃×C₉	1	3	yes	—
27	C₂₇×C₄₃	C₃×C₉	1	3	yes	—
28	C₂₇×C₄₃	C₃×C₉	1	3	yes	—
29	#10624681	—	43	1	no	maximal, Sylow
30	C₃²×C₄₃	—	3	3	no	—
31	C₃²×C₄₃	C₉²	1	3	yes	—
32	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
33	C₉×C₄₃	C₉²	1	3	yes	—
34	C₉×C₄₃	C₉²	1	3	yes	—
35	C₉×C₄₃	C₃²×C₉	1	2	yes	—
36	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
37	C₄₃⋊C₉	—	3	9	no	—
38	C₃×C₂₇⋊C₃	—	43	2	no	—
39	C₃²×C₂₇	C₄₃⋊C₃	1	1	yes	characteristic
40	#6887	—	43	1	no	—
41	#6864	—	43	3	no	—
42	#6864	—	43	3	no	—
43	C₉×C₂₇	—	43	3	no	—
44	C₃×C₄₃	—	3	3	no	—
45	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
46	C₃×C₄₃	#6903	1	3	yes	—
47	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
48	C₂₇⋊C₃	—	43	18	no	—
49	C₃×C₂₇	—	43	6	no	—
50	C₃×C₂₇	C₄₃⋊C₉	1	9	yes	complemented
51	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
52	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	C₃×C₂₇	C₃×C₄₃⋊C₃	1	1	yes	characteristic
54	C₉⋊C₉	—	43	3	no	—
55	C₉⋊C₉	—	43	3	no	—
56	C₃²⋊C₉	—	43	3	no	—
57	C₉²	—	43	3	no	—
58	C₄₃	#10624681	1	1	yes	characteristic, complemented, Sylow
59	C₃³	C₉×C₄₃⋊C₃	1	1	yes	characteristic
60	C₃×C₉	—	43	9	no	—
61	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
62	C₃×C₉	C₉×C₄₃⋊C₃	1	1	yes	characteristic
63	C₃×C₉	C₉×C₄₃⋊C₃	1	6	yes	—
64	C₃×C₉	C₃×C₄₃⋊C₉	1	3	yes	—
65	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
66	C₂₇	—	43	18	no	—
67	C₂₇	C₃×C₄₃⋊C₉	1	3	yes	—
68	C₂₇	C₃×C₄₃⋊C₉	1	3	yes	—
69	C₂₇	C₃×C₄₃⋊C₉	1	3	yes	—
70	C₃²	—	3	3	no	—
71	C₃²	C₉×C₄₃⋊C₉	1	3	yes	—
72	C₃²	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
73	C₉	—	129	9	no	—
74	C₉	C₉×C₄₃⋊C₉	1	3	yes	—
75	C₉	C₉×C₄₃⋊C₉	1	3	yes	—
76	C₉	C₃×C₉×C₄₃⋊C₃	1	2	yes	—
77	C₉	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
78	C₃	—	3	3	no	—
79	C₃	C₃×C₉×C₄₃⋊C₉	1	1	yes	characteristic
80	C₃	#23782856	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
3. #23782707	C₃	semidirect
4. #23782706	C₃	semidirect
5. C₂₇×C₄₃⋊C₉	C₃	semidirect
7. #16812505	C₉	semidirect
14. C₃×C₂₇×C₄₃	C₉	semidirect
50. C₃×C₂₇	C₄₃⋊C₉	semidirect
58. 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
#23782782	3
#23782707	3
#23782706	3
C₂₇×C₄₃⋊C₉	3
C₃²×C₂₇×C₄₃	3
#10624681	43