Subgroups — C₂×C₇×C₉²×C₁₁ #72190816

Order 12474.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉²×C₁₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇×C₉×C₁₁	C₃	1	4	yes	maximal
3	C₃×C₇×C₉×C₁₁	C₂×C₃	1	4	yes	—
4	C₂×C₉²×C₁₁	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃²×C₇×C₁₁	C₃²	1	1	yes	characteristic
6	C₂×C₇×C₉×C₁₁	C₉	1	12	yes	direct product factor
7	C₂×C₇×C₉²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₉²×C₁₁	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
9	C₃²×C₇×C₁₁	C₂×C₃²	1	1	yes	characteristic
10	C₇×C₉×C₁₁	C₂×C₉	1	12	yes	direct product factor
11	C₂×C₃×C₉×C₁₁	C₃×C₇	1	4	yes	—
12	C₇×C₉²	C₂×C₁₁	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇×C₁₁	C₃×C₉	1	4	yes	—
14	C₂×C₃×C₇×C₉	C₃×C₁₁	1	4	yes	—
15	C₃×C₉×C₁₁	C₂×C₃×C₇	1	4	yes	—
16	C₃×C₇×C₁₁	C₂×C₃×C₉	1	4	yes	—
17	C₂×C₃²×C₁₁	C₃²×C₇	1	1	yes	characteristic
18	C₂×C₉×C₁₁	C₇×C₉	1	12	yes	direct product factor
19	C₃×C₇×C₉	C₂×C₃×C₁₁	1	4	yes	—
20	C₂×C₉²	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₇×C₁₁	C₉²	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₃²×C₇	C₃²×C₁₁	1	1	yes	characteristic
23	C₂×C₇×C₉	C₉×C₁₁	1	12	yes	direct product factor
24	C₃²×C₁₁	C₂×C₃²×C₇	1	1	yes	characteristic
25	C₉×C₁₁	C₂×C₇×C₉	1	12	yes	direct product factor
26	C₉²	C₂×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₇×C₁₁	C₂×C₉²	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₁₁	C₃×C₇×C₉	1	4	yes	—
29	C₃²×C₇	C₂×C₃²×C₁₁	1	1	yes	characteristic
30	C₇×C₉	C₂×C₉×C₁₁	1	12	yes	direct product factor
31	C₂×C₃×C₉	C₃×C₇×C₁₁	1	4	yes	—
32	C₂×C₃×C₇	C₃×C₉×C₁₁	1	4	yes	—
33	C₃×C₁₁	C₂×C₃×C₇×C₉	1	4	yes	—
34	C₃×C₉	C₂×C₃×C₇×C₁₁	1	4	yes	—
35	C₂×C₁₁	C₇×C₉²	1	1	yes	characteristic, direct product factor, Hall
36	C₃×C₇	C₂×C₃×C₉×C₁₁	1	4	yes	—
37	C₂×C₃²	C₃²×C₇×C₁₁	1	1	yes	characteristic
38	C₂×C₉	C₇×C₉×C₁₁	1	12	yes	direct product factor
39	C₂×C₇	C₉²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
40	C₁₁	C₂×C₇×C₉²	1	1	yes	characteristic, direct product factor, Sylow
41	C₃²	C₂×C₃²×C₇×C₁₁	1	1	yes	characteristic
42	C₉	C₂×C₇×C₉×C₁₁	1	12	yes	direct product factor
43	C₇	C₂×C₉²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×C₃	C₃×C₇×C₉×C₁₁	1	4	yes	—
45	C₃	C₂×C₃×C₇×C₉×C₁₁	1	4	yes	—
46	C₂	C₇×C₉²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₂×C₃²×C₇×C₁₁
socle, prime radical	C₂×C₃²×C₇×C₁₁	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₉²×C₁₁	C₂	direct (N × H)
4. C₂×C₉²×C₁₁	C₇	direct (N × H)
6. C₂×C₇×C₉×C₁₁	C₉	direct (N × H)
7. C₂×C₇×C₉²	C₁₁	direct (N × H)
8. C₉²×C₁₁	C₂×C₇	direct (N × H)
10. C₇×C₉×C₁₁	C₂×C₉	direct (N × H)
12. C₇×C₉²	C₂×C₁₁	direct (N × H)
18. C₂×C₉×C₁₁	C₇×C₉	direct (N × H)
20. C₂×C₉²	C₇×C₁₁	direct (N × H)
21. C₂×C₇×C₁₁	C₉²	direct (N × H)
23. C₂×C₇×C₉	C₉×C₁₁	direct (N × H)
25. C₉×C₁₁	C₂×C₇×C₉	direct (N × H)
26. C₉²	C₂×C₇×C₁₁	direct (N × H)
27. C₇×C₁₁	C₂×C₉²	direct (N × H)
30. C₇×C₉	C₂×C₉×C₁₁	direct (N × H)
35. C₂×C₁₁	C₇×C₉²	direct (N × H)
38. C₂×C₉	C₇×C₉×C₁₁	direct (N × H)
39. C₂×C₇	C₉²×C₁₁	direct (N × H)
40. C₁₁	C₂×C₇×C₉²	direct (N × H)
42. C₉	C₂×C₇×C₉×C₁₁	direct (N × H)
43. C₇	C₂×C₉²×C₁₁	direct (N × H)
46. C₂	C₇×C₉²×C₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₉²×C₁₁	2
C₂×C₃×C₇×C₉×C₁₁	3
C₂×C₉²×C₁₁	7
C₂×C₇×C₉²	11

Subgroups — C2×C7×C92×C11 #72190816

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₉²×C₁₁ #72190816