Subgroups — #44533352

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	C₃²×C₄₃⋊C₂₇	C₃	1	1	yes	maximal, characteristic
3	#23782708	C₃	1	6	yes	maximal, complemented
4	C₉×C₄₃⋊C₂₇	C₃	1	3	yes	maximal, complemented
5	C₄₃×#6887	C₃	1	1	yes	maximal, characteristic
6	#16812505	C₉	1	18	yes	complemented
7	C₃×C₄₃⋊C₂₇	C₉	1	9	yes	complemented
8	C₃×C₄₃⋊C₂₇	C₃²	1	1	yes	characteristic
9	C₃×C₄₃⋊C₂₇	C₃²	1	6	yes	—
10	C₃×C₄₃⋊C₂₇	C₃²	1	2	yes	—
11	C₃²×C₉×C₄₃	C₃²	1	1	yes	characteristic
12	C₄₃×C₉⋊C₉	C₉	1	6	yes	—
13	C₄₃×C₃²⋊C₉	C₉	1	3	yes	—
14	C₉²×C₄₃	C₃²	1	3	yes	—
15	C₄₃⋊C₂₇	C₃×C₉	1	3	yes	—
16	C₄₃⋊C₂₇	C₃×C₉	1	6	yes	—
17	C₄₃⋊C₂₇	C₃×C₉	1	18	yes	—
18	C₃³×C₄₃	C₃×C₉	1	1	yes	characteristic
19	C₃×C₉×C₄₃	C₃×C₉	1	9	yes	—
20	C₃×C₉×C₄₃	C₃×C₉	1	2	yes	—
21	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
22	C₃×C₉×C₄₃	C₃×C₉	1	6	yes	—
23	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
24	#10624681	—	43	1	no	maximal, Sylow
25	C₃²×C₄₃	—	3	3	no	—
26	C₃²×C₄₃	C₉²	1	3	yes	—
27	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
28	C₉×C₄₃	—	3	9	no	—
29	C₉×C₄₃	C₉²	1	6	yes	—
30	C₉×C₄₃	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₄₃	C₃²×C₉	1	2	yes	—
32	C₃×C₂₇⋊C₃	—	43	2	no	—
33	C₃²×C₂₇	—	43	1	no	—
34	#6887	C₄₃⋊C₃	1	1	yes	characteristic
35	#6864	—	43	6	no	—
36	C₉×C₂₇	—	43	3	no	—
37	C₃×C₄₃	—	3	3	no	—
38	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
39	C₃×C₄₃	#6903	1	3	yes	—
40	C₃²×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
41	C₂₇⋊C₃	—	43	18	no	—
42	C₃×C₂₇	—	43	9	no	—
43	C₃×C₂₇	—	43	1	no	—
44	C₃×C₂₇	—	43	6	no	—
45	C₃×C₂₇	—	43	2	no	—
46	C₉⋊C₉	C₄₃⋊C₉	1	6	yes	—
47	C₃²⋊C₉	C₄₃⋊C₉	1	3	yes	—
48	C₉²	C₃×C₄₃⋊C₃	1	3	yes	—
49	C₄₃	#10624681	1	1	yes	characteristic, complemented, Sylow
50	C₃³	C₃×C₄₃⋊C₉	1	1	yes	characteristic
51	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
52	C₃×C₉	C₉×C₄₃⋊C₃	1	6	yes	—
53	C₃×C₉	C₃×C₄₃⋊C₉	1	9	yes	—
54	C₃×C₉	C₃×C₄₃⋊C₉	1	2	yes	—
55	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
56	C₂₇	—	43	3	no	—
57	C₂₇	—	43	6	no	—
58	C₂₇	—	43	18	no	—
59	C₃²	—	3	3	no	—
60	C₃²	C₉×C₄₃⋊C₉	1	3	yes	—
61	C₃²	C₃²×C₄₃⋊C₉	1	1	yes	characteristic
62	C₉	—	3	9	no	—
63	C₉	C₉×C₄₃⋊C₉	1	6	yes	—
64	C₉	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
65	C₉	C₃×C₉×C₄₃⋊C₃	1	2	yes	—
66	C₃	—	3	3	no	—
67	C₃	C₃×C₉×C₄₃⋊C₉	1	1	yes	characteristic
68	C₃	#23782857	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₉²
Fitting	C₄₃×#6887	C₃
socle	C₃²×C₄₃	C₃²×C₉
prime radical	C₃³×C₄₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	#6887	C₄₃⋊C₃
hypocenter	C₄₃	#10624681
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ #6887

Complements

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

N	H ≅ G/N	type
3. #23782708	C₃	semidirect
4. C₉×C₄₃⋊C₂₇	C₃	semidirect
6. #16812505	C₉	semidirect
7. C₃×C₄₃⋊C₂₇	C₉	semidirect
49. 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
#23782708	3
C₉×C₄₃⋊C₂₇	3
C₄₃×#6887	3
#10624681	43