Subgroups — C₇×C₉×C₁₁×C₂₇ #72196475

Order 18711.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₂₇	C₃	1	3	yes	maximal
2	C₇×C₉²×C₁₁	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₉×C₁₁	C₉	1	3	yes	—
4	C₃×C₇×C₉×C₁₁	C₃²	1	1	yes	characteristic
5	C₇×C₁₁×C₂₇	C₉	1	9	yes	direct product factor
6	C₉×C₁₁×C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₉×C₂₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₁×C₂₇	C₃×C₇	1	3	yes	—
9	C₉²×C₁₁	C₃×C₇	1	1	yes	characteristic
10	C₃²×C₇×C₁₁	C₃×C₉	1	1	yes	characteristic
11	C₇×C₉×C₁₁	C₂₇	1	9	yes	direct product factor
12	C₇×C₉×C₁₁	C₃×C₉	1	3	yes	—
13	C₃×C₇×C₂₇	C₃×C₁₁	1	3	yes	—
14	C₇×C₉²	C₃×C₁₁	1	1	yes	characteristic
15	C₃×C₉×C₁₁	C₇×C₉	1	3	yes	—
16	C₃×C₉×C₁₁	C₃²×C₇	1	1	yes	characteristic
17	C₁₁×C₂₇	C₇×C₉	1	9	yes	direct product factor
18	C₉×C₂₇	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₇×C₁₁	C₉²	1	1	yes	characteristic
20	C₃×C₇×C₁₁	C₃×C₂₇	1	3	yes	—
21	C₃×C₇×C₉	C₉×C₁₁	1	3	yes	—
22	C₃×C₇×C₉	C₃²×C₁₁	1	1	yes	characteristic
23	C₇×C₂₇	C₉×C₁₁	1	9	yes	direct product factor
24	C₃²×C₁₁	C₃×C₇×C₉	1	1	yes	characteristic
25	C₉×C₁₁	C₇×C₂₇	1	9	yes	direct product factor
26	C₉×C₁₁	C₃×C₇×C₉	1	3	yes	—
27	C₃×C₂₇	C₃×C₇×C₁₁	1	3	yes	—
28	C₉²	C₃×C₇×C₁₁	1	1	yes	characteristic
29	C₇×C₁₁	C₉×C₂₇	1	1	yes	characteristic, direct product factor, Hall
30	C₃²×C₇	C₃×C₉×C₁₁	1	1	yes	characteristic
31	C₇×C₉	C₁₁×C₂₇	1	9	yes	direct product factor
32	C₇×C₉	C₃×C₉×C₁₁	1	3	yes	—
33	C₃×C₁₁	C₇×C₉²	1	1	yes	characteristic
34	C₃×C₁₁	C₃×C₇×C₂₇	1	3	yes	—
35	C₃×C₉	C₇×C₉×C₁₁	1	3	yes	—
36	C₃×C₉	C₃²×C₇×C₁₁	1	1	yes	characteristic
37	C₂₇	C₇×C₉×C₁₁	1	9	yes	direct product factor
38	C₃×C₇	C₉²×C₁₁	1	1	yes	characteristic
39	C₃×C₇	C₃×C₁₁×C₂₇	1	3	yes	—
40	C₁₁	C₇×C₉×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
41	C₃²	C₃×C₇×C₉×C₁₁	1	1	yes	characteristic
42	C₉	C₇×C₁₁×C₂₇	1	9	yes	direct product factor
43	C₉	C₃×C₇×C₉×C₁₁	1	3	yes	—
44	C₇	C₉×C₁₁×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	C₇×C₉²×C₁₁	1	1	yes	characteristic
46	C₃	C₃×C₇×C₁₁×C₂₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₉	C₃²×C₇×C₁₁
socle, prime radical	C₃²×C₇×C₁₁	C₃×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₇×C₁₁×C₂₇	C₉	direct (N × H)
6. C₉×C₁₁×C₂₇	C₇	direct (N × H)
7. C₇×C₉×C₂₇	C₁₁	direct (N × H)
11. C₇×C₉×C₁₁	C₂₇	direct (N × H)
17. C₁₁×C₂₇	C₇×C₉	direct (N × H)
18. C₉×C₂₇	C₇×C₁₁	direct (N × H)
23. C₇×C₂₇	C₉×C₁₁	direct (N × H)
25. C₉×C₁₁	C₇×C₂₇	direct (N × H)
29. C₇×C₁₁	C₉×C₂₇	direct (N × H)
31. C₇×C₉	C₁₁×C₂₇	direct (N × H)
37. C₂₇	C₇×C₉×C₁₁	direct (N × H)
40. C₁₁	C₇×C₉×C₂₇	direct (N × H)
42. C₉	C₇×C₁₁×C₂₇	direct (N × H)
44. C₇	C₉×C₁₁×C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₇×C₁₁×C₂₇	3
C₇×C₉²×C₁₁	3
C₉×C₁₁×C₂₇	7
C₇×C₉×C₂₇	11

Subgroups — C7×C9×C11×C27 #72196475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×C₁₁×C₂₇ #72196475