Subgroups — C₂₇⋊C₃×C₃₁⋊C₃ #21419366

Order 7533.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₃₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#14578892	C₃	1	2	yes	maximal, complemented
3	#14578891	C₃	1	3	yes	maximal, complemented
4	#14578890	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₃₁⋊C₃	C₃	1	3	yes	maximal, complemented
6	C₃₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₃₁⋊C₃	C₉	1	1	yes	characteristic
8	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
9	C₃×C₃₁⋊C₉	C₉	1	2	yes	—
10	C₉×C₃₁⋊C₃	C₉	1	2	yes	—
11	C₉×C₃₁⋊C₃	C₉	1	2	yes	—
12	C₉×C₃₁⋊C₃	C₉	1	2	yes	—
13	C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
14	C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
15	C₉×C₃₁⋊C₃	C₃²	1	1	yes	characteristic
16	C₂₇×C₃₁	C₃²	1	3	yes	complemented
17	C₃₁⋊C₂₇	C₃²	1	6	yes	complemented
18	C₃²×C₃₁	C₃×C₉	1	1	yes	characteristic
19	C₃×C₃₁⋊C₃	—	3	3	no	—
20	C₃×C₃₁⋊C₃	C₃×C₉	1	1	yes	characteristic
21	C₃×C₃₁⋊C₃	C₃×C₉	1	1	yes	characteristic
22	C₃×C₃₁⋊C₃	C₃×C₉	1	1	yes	characteristic
23	C₉×C₃₁	C₃×C₉	1	2	yes	—
24	C₉×C₃₁	C₃³	1	1	yes	characteristic
25	C₃₁⋊C₉	C₃×C₉	1	2	yes	—
26	C₃₁⋊C₉	C₃×C₉	1	2	yes	—
27	C₃₁⋊C₉	C₃×C₉	1	2	yes	—
28	C₃×C₂₇⋊C₃	—	31	1	no	maximal, Sylow
29	C₃×C₃₁	—	3	1	no	—
30	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
31	C₃₁⋊C₃	—	3	1	no	—
32	C₃₁⋊C₃	—	3	1	no	—
33	C₃₁⋊C₃	C₂₇⋊C₃	1	3	yes	direct product factor
34	C₃²×C₉	—	31	1	no	—
35	C₂₇⋊C₃	—	31	2	no	—
36	C₂₇⋊C₃	—	31	3	no	—
37	C₂₇⋊C₃	—	31	3	no	—
38	C₂₇⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
39	C₃×C₂₇	—	31	3	no	—
40	C₃₁	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	31	1	no	—
42	C₃×C₉	—	31	2	no	—
43	C₃×C₉	—	31	2	no	—
44	C₃×C₉	—	31	2	no	—
45	C₃×C₉	—	31	2	no	—
46	C₃×C₉	—	31	1	no	—
47	C₃×C₉	—	31	1	no	—
48	C₃×C₉	—	31	1	no	—
49	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
50	C₂₇	—	31	6	no	—
51	C₂₇	C₃×C₃₁⋊C₃	1	3	yes	complemented
52	C₃²	—	31	1	no	—
53	C₃²	—	31	1	no	—
54	C₃²	—	31	1	no	—
55	C₃²	—	93	3	no	—
56	C₃²	C₉×C₃₁⋊C₃	1	1	yes	characteristic
57	C₉	—	31	2	no	—
58	C₉	—	31	2	no	—
59	C₉	—	31	2	no	—
60	C₉	C₉×C₃₁⋊C₃	1	2	yes	—
61	C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
62	C₃	—	3	1	no	—
63	C₃	—	31	3	no	—
64	C₃	—	93	1	no	—
65	C₃	—	93	1	no	—
66	C₃	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₉	C₃²×C₃₁⋊C₃
commutator, socle	C₃×C₃₁	C₃²×C₉
Fitting	C₃₁×C₂₇⋊C₃	C₃
hypercenter	C₂₇⋊C₃	C₃₁⋊C₃
hypocenter	C₃₁	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₉ ◁ C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
2. #14578892	C₃	semidirect
3. #14578891	C₃	semidirect
4. #14578890	C₃	semidirect
5. C₂₇×C₃₁⋊C₃	C₃	semidirect
6. C₃₁×C₂₇⋊C₃	C₃	semidirect
16. C₂₇×C₃₁	C₃²	semidirect
17. C₃₁⋊C₂₇	C₃²	semidirect
33. C₃₁⋊C₃	C₂₇⋊C₃	direct (N × H)
38. C₂₇⋊C₃	C₃₁⋊C₃	direct (N × H)
40. C₃₁	C₃×C₂₇⋊C₃	semidirect
51. C₂₇	C₃×C₃₁⋊C₃	semidirect

Subgroups — C27⋊C3×C31⋊C3 #21419366

Conjugacy classes of subgroups

Complements

Subgroups — C₂₇⋊C₃×C₃₁⋊C₃ #21419366