Subgroups — C₃×C₂₇×C₃₁⋊C₃ #21419364

Order 7533.

144 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	C₃×C₃₁⋊C₂₇	C₃	1	2	yes	maximal, complemented
3	C₂₇×C₃₁⋊C₃	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₂₇×C₃₁	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₃₁⋊C₃	C₉	1	1	yes	characteristic
6	C₃×C₉×C₃₁	C₃²	1	1	yes	characteristic
7	C₃×C₃₁⋊C₉	C₉	1	2	yes	—
8	C₉×C₃₁⋊C₃	C₉	1	6	yes	—
9	C₉×C₃₁⋊C₃	C₃²	1	3	yes	—
10	C₂₇×C₃₁	C₃²	1	3	yes	complemented
11	C₃₁⋊C₂₇	C₃²	1	6	yes	complemented
12	C₃²×C₃₁	C₃×C₉	1	1	yes	characteristic
13	C₃×C₃₁⋊C₃	C₂₇	1	9	yes	direct product factor
14	C₃×C₃₁⋊C₃	C₃×C₉	1	3	yes	—
15	C₉×C₃₁	C₃×C₉	1	2	yes	—
16	C₉×C₃₁	C₃³	1	1	yes	characteristic
17	C₃₁⋊C₉	C₃×C₉	1	6	yes	—
18	C₃²×C₂₇	—	31	1	no	maximal, Sylow
19	C₃×C₃₁	C₃×C₂₇	1	3	yes	complemented
20	C₃×C₃₁	C₃²×C₉	1	1	yes	characteristic
21	C₃₁⋊C₃	C₃×C₂₇	1	9	yes	direct product factor
22	C₃²×C₉	—	31	1	no	—
23	C₃×C₂₇	—	31	2	no	—
24	C₃×C₂₇	—	31	9	no	—
25	C₃×C₂₇	C₃₁⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃₁	C₃²×C₂₇	1	1	yes	characteristic, complemented, Sylow
27	C₃³	—	31	1	no	—
28	C₃×C₉	—	31	2	no	—
29	C₃×C₉	—	31	6	no	—
30	C₃×C₉	—	31	3	no	—
31	C₃×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₂₇	—	31	6	no	—
33	C₂₇	C₃×C₃₁⋊C₃	1	3	yes	direct product factor
34	C₃²	—	31	9	no	—
35	C₃²	—	31	3	no	—
36	C₃²	C₉×C₃₁⋊C₃	1	1	yes	characteristic
37	C₉	—	31	6	no	—
38	C₉	C₉×C₃₁⋊C₃	1	2	yes	—
39	C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
40	C₃	—	31	9	no	—
41	C₃	C₂₇×C₃₁⋊C₃	1	3	yes	direct product factor
42	C₃	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₃₁⋊C₂₇	C₃	semidirect
3. C₂₇×C₃₁⋊C₃	C₃	direct (N × H)
4. C₃×C₂₇×C₃₁	C₃	semidirect
10. C₂₇×C₃₁	C₃²	semidirect
11. C₃₁⋊C₂₇	C₃²	semidirect
13. C₃×C₃₁⋊C₃	C₂₇	direct (N × H)
19. C₃×C₃₁	C₃×C₂₇	semidirect
21. C₃₁⋊C₃	C₃×C₂₇	direct (N × H)
25. C₃×C₂₇	C₃₁⋊C₃	direct (N × H)
26. C₃₁	C₃²×C₂₇	semidirect
33. C₂₇	C₃×C₃₁⋊C₃	direct (N × H)
41. C₃	C₂₇×C₃₁⋊C₃	direct (N × H)

Subgroups — C3×C27×C31⋊C3 #21419364

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₂₇×C₃₁⋊C₃ #21419364