Subgroups — #44533348

Order 31347.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#16812504	C₃	1	3	yes	maximal
2	C₉²×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
3	#23782708	C₃	1	2	yes	maximal, complemented
4	#23782706	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₄₃⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₄₃×#6864	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×C₄₃⋊C₃	C₉	1	3	yes	—
8	C₃×C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
9	#16812504	C₉	1	27	yes	complemented
10	C₃×C₄₃⋊C₂₇	C₃²	1	6	yes	—
11	C₉×C₄₃⋊C₉	C₉	1	6	yes	—
12	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
13	C₉×C₄₃⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₂₇×C₄₃	C₃²	1	3	yes	—
15	C₉²×C₄₃	C₃²	1	1	yes	characteristic
16	C₃²×C₄₃⋊C₃	C₃×C₉	1	1	yes	characteristic
17	C₃×C₄₃⋊C₉	C₃×C₉	1	3	yes	—
18	C₃×C₄₃⋊C₉	C₃×C₉	1	2	yes	—
19	C₃×C₄₃⋊C₉	C₃×C₉	1	3	yes	—
20	C₉×C₄₃⋊C₃	—	3	9	no	—
21	C₉×C₄₃⋊C₃	C₃×C₉	1	9	yes	—
22	C₄₃⋊C₂₇	C₃×C₉	1	18	yes	complemented
23	C₃×C₉×C₄₃	C₃×C₉	1	3	yes	—
24	C₃×C₉×C₄₃	C₃³	1	1	yes	characteristic
25	C₂₇×C₄₃	C₃×C₉	1	9	yes	complemented
26	C₉×C₂₇⋊C₃	—	43	1	no	maximal, Sylow
27	C₃²×C₄₃	C₃²×C₉	1	1	yes	characteristic
28	C₃×C₄₃⋊C₃	—	3	3	no	—
29	C₃×C₄₃⋊C₃	C₉²	1	3	yes	—
30	C₉×C₄₃	—	3	3	no	—
31	C₉×C₄₃	C₃²×C₉	1	3	yes	—
32	C₄₃⋊C₉	—	3	3	no	—
33	C₄₃⋊C₉	C₉²	1	6	yes	—
34	C₄₃⋊C₉	C₂₇⋊C₃	1	9	yes	complemented
35	C₃×C₂₇⋊C₃	—	43	3	no	—
36	C₃×C₉²	—	43	1	no	—
37	#6864	—	43	3	no	—
38	#6864	—	43	2	no	—
39	#6864	C₄₃⋊C₃	1	1	yes	characteristic, complemented
40	C₉×C₂₇	—	43	3	no	—
41	C₃×C₄₃	C₃×C₉²	1	1	yes	characteristic
42	C₃×C₄₃	C₃×C₂₇⋊C₃	1	3	yes	—
43	C₄₃⋊C₃	—	3	3	no	—
44	C₃²×C₉	—	43	1	no	—
45	C₃²×C₉	—	43	3	no	—
46	C₂₇⋊C₃	—	43	27	no	—
47	C₃×C₂₇	—	43	6	no	—
48	C₃×C₂₇	C₃×C₄₃⋊C₃	1	3	yes	—
49	C₉²	—	43	6	no	—
50	C₉²	—	43	1	no	—
51	C₉²	—	43	1	no	—
52	C₉²	C₃×C₄₃⋊C₃	1	1	yes	characteristic
53	C₄₃	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
54	C₃³	—	43	1	no	—
55	C₃×C₉	—	43	2	no	—
56	C₃×C₉	—	43	3	no	—
57	C₃×C₉	—	43	9	no	—
58	C₃×C₉	—	43	3	no	—
59	C₃×C₉	—	129	9	no	—
60	C₃×C₉	C₉×C₄₃⋊C₃	1	3	yes	—
61	C₃×C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
62	C₂₇	—	43	18	no	—
63	C₂₇	C₉×C₄₃⋊C₃	1	9	yes	complemented
64	C₃²	—	43	3	no	—
65	C₃²	—	129	3	no	—
66	C₃²	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic
67	C₉	—	3	3	no	—
68	C₉	—	43	6	no	—
69	C₉	—	43	9	no	—
70	C₉	—	129	3	no	—
71	C₉	C₃×C₉×C₄₃⋊C₃	1	3	yes	—
72	C₃	—	129	3	no	—
73	C₃	C₉²×C₄₃⋊C₃	1	1	yes	characteristic
74	C₃	C₂₇⋊C₃×C₄₃⋊C₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₄₃⋊C₃
commutator	C₃×C₄₃	C₃×C₉²
Fitting	C₄₃×#6864	C₃
socle	C₃²×C₄₃	C₃²×C₉
prime radical	C₃²×C₄₃⋊C₃	C₃×C₉
cosocle	C₃×C₉×C₄₃	C₃³
hypercenter	#6864	C₄₃⋊C₃
hypocenter	C₄₃	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₃×C₉ ◁ #6864

Complements

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

N	H ≅ G/N	type
3. #23782708	C₃	semidirect
4. #23782706	C₃	semidirect
5. C₂₇×C₄₃⋊C₉	C₃	semidirect
6. C₄₃×#6864	C₃	semidirect
9. #16812504	C₉	semidirect
22. C₄₃⋊C₂₇	C₃×C₉	semidirect
25. C₂₇×C₄₃	C₃×C₉	semidirect
34. C₄₃⋊C₉	C₂₇⋊C₃	semidirect
39. #6864	C₄₃⋊C₃	semidirect
53. C₄₃	C₉×C₂₇⋊C₃	semidirect
63. C₂₇	C₉×C₄₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₃×#16812504	3
C₉²×C₄₃⋊C₃	3
#23782708	3
#23782706	3
C₂₇×C₄₃⋊C₉	3
C₄₃×#6864	3
C₉×C₂₇⋊C₃	43