Subgroups — C₂₇⋊C₃×C₄₃⋊C₃ #23782852

Order 10449.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄₃⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#16812505	C₃	1	2	yes	maximal, complemented
3	#16812504	C₃	1	3	yes	maximal, complemented
4	#16812503	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₄₃⋊C₃	C₃	1	3	yes	maximal, complemented
6	C₄₃×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₄₃⋊C₃	C₉	1	1	yes	characteristic
8	C₃×C₄₃⋊C₉	C₉	1	2	yes	—
9	C₉×C₄₃⋊C₃	C₉	1	2	yes	—
10	C₉×C₄₃⋊C₃	C₉	1	2	yes	—
11	C₉×C₄₃⋊C₃	C₉	1	2	yes	—
12	C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
13	C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
14	C₉×C₄₃⋊C₃	C₃²	1	1	yes	characteristic
15	C₄₃⋊C₂₇	C₃²	1	6	yes	complemented
16	C₃×C₉×C₄₃	C₃²	1	1	yes	characteristic
17	C₂₇×C₄₃	C₃²	1	3	yes	complemented
18	C₃²×C₄₃	C₃×C₉	1	1	yes	characteristic
19	C₃×C₄₃⋊C₃	—	3	3	no	—
20	C₃×C₄₃⋊C₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₄₃⋊C₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₄₃⋊C₃	C₃×C₉	1	1	yes	characteristic
23	C₉×C₄₃	C₃×C₉	1	2	yes	—
24	C₉×C₄₃	C₃³	1	1	yes	characteristic
25	C₄₃⋊C₉	C₃×C₉	1	2	yes	—
26	C₄₃⋊C₉	C₃×C₉	1	2	yes	—
27	C₄₃⋊C₉	C₃×C₉	1	2	yes	—
28	C₃×C₂₇⋊C₃	—	43	1	no	maximal, Sylow
29	C₃×C₄₃	—	3	1	no	—
30	C₃×C₄₃	C₃²×C₉	1	1	yes	characteristic
31	C₄₃⋊C₃	—	3	1	no	—
32	C₄₃⋊C₃	—	3	1	no	—
33	C₄₃⋊C₃	C₂₇⋊C₃	1	3	yes	direct product factor
34	C₃²×C₉	—	43	1	no	—
35	C₂₇⋊C₃	—	43	2	no	—
36	C₂₇⋊C₃	—	43	3	no	—
37	C₂₇⋊C₃	—	43	3	no	—
38	C₂₇⋊C₃	C₄₃⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃×C₂₇	—	43	3	no	—
40	C₄₃	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	43	1	no	—
42	C₃×C₉	—	43	2	no	—
43	C₃×C₉	—	43	2	no	—
44	C₃×C₉	—	43	2	no	—
45	C₃×C₉	—	43	2	no	—
46	C₃×C₉	—	43	1	no	—
47	C₃×C₉	—	43	1	no	—
48	C₃×C₉	—	43	1	no	—
49	C₃×C₉	C₃×C₄₃⋊C₃	1	1	yes	characteristic
50	C₂₇	—	43	6	no	—
51	C₂₇	C₃×C₄₃⋊C₃	1	3	yes	complemented
52	C₃²	—	43	1	no	—
53	C₃²	—	43	1	no	—
54	C₃²	—	43	1	no	—
55	C₃²	—	129	3	no	—
56	C₃²	C₉×C₄₃⋊C₃	1	1	yes	characteristic
57	C₉	—	43	2	no	—
58	C₉	—	43	2	no	—
59	C₉	—	43	2	no	—
60	C₉	C₉×C₄₃⋊C₃	1	2	yes	—
61	C₉	C₃²×C₄₃⋊C₃	1	1	yes	characteristic
62	C₃	—	3	1	no	—
63	C₃	—	43	3	no	—
64	C₃	—	129	1	no	—
65	C₃	—	129	1	no	—
66	C₃	C₃×C₉×C₄₃⋊C₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #16812505	C₃	semidirect
3. #16812504	C₃	semidirect
4. #16812503	C₃	semidirect
5. C₂₇×C₄₃⋊C₃	C₃	semidirect
6. C₄₃×C₂₇⋊C₃	C₃	semidirect
15. C₄₃⋊C₂₇	C₃²	semidirect
17. C₂₇×C₄₃	C₃²	semidirect
33. C₄₃⋊C₃	C₂₇⋊C₃	direct (N × H)
38. C₂₇⋊C₃	C₄₃⋊C₃	direct (N × H)
40. C₄₃	C₃×C₂₇⋊C₃	semidirect
51. C₂₇	C₃×C₄₃⋊C₃	semidirect

Subgroups — C27⋊C3×C43⋊C3 #23782852

Conjugacy classes of subgroups

Complements

Subgroups — C₂₇⋊C₃×C₄₃⋊C₃ #23782852