Subgroups — C₂²×C₉²×C₄₇ #72193243

Order 15228.

230 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉²×C₄₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₃×C₉×C₄₇	C₃	1	4	yes	maximal
3	C₂×C₃×C₉×C₄₇	C₂×C₃	1	12	yes	—
4	C₉²×C₄₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
5	C₂²×C₃²×C₄₇	C₃²	1	1	yes	characteristic
6	C₂²×C₉×C₄₇	C₉	1	12	yes	direct product factor
7	C₃×C₉×C₄₇	C₂²×C₃	1	4	yes	—
8	C₂×C₃²×C₄₇	C₂×C₃²	1	3	yes	—
9	C₂×C₉×C₄₇	C₂×C₉	1	36	yes	direct product factor
10	C₂²×C₃×C₄₇	C₃×C₉	1	4	yes	—
11	C₃²×C₄₇	C₂²×C₃²	1	1	yes	characteristic
12	C₉×C₄₇	C₂²×C₉	1	12	yes	direct product factor
13	C₂²×C₉²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₃×C₄₇	C₂×C₃×C₉	1	12	yes	—
15	C₂²×C₄₇	C₉²	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₉²	C₂×C₄₇	1	3	yes	direct product factor
17	C₃×C₄₇	C₂²×C₃×C₉	1	4	yes	—
18	C₂²×C₃×C₉	C₃×C₄₇	1	4	yes	—
19	C₂×C₄₇	C₂×C₉²	1	3	yes	direct product factor
20	C₉²	C₂²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×C₃×C₉	C₂×C₃×C₄₇	1	12	yes	—
22	C₄₇	C₂²×C₉²	1	1	yes	characteristic, direct product factor, Sylow
23	C₂²×C₃²	C₃²×C₄₇	1	1	yes	characteristic
24	C₂²×C₉	C₉×C₄₇	1	12	yes	direct product factor
25	C₃×C₉	C₂²×C₃×C₄₇	1	4	yes	—
26	C₂×C₃²	C₂×C₃²×C₄₇	1	3	yes	—
27	C₂×C₉	C₂×C₉×C₄₇	1	36	yes	direct product factor
28	C₂²×C₃	C₃×C₉×C₄₇	1	4	yes	—
29	C₃²	C₂²×C₃²×C₄₇	1	1	yes	characteristic
30	C₉	C₂²×C₉×C₄₇	1	12	yes	direct product factor
31	C₂×C₃	C₂×C₃×C₉×C₄₇	1	12	yes	—
32	C₂²	C₉²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₂²×C₃×C₉×C₄₇	1	4	yes	—
34	C₂	C₂×C₉²×C₄₇	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃²	C₂²×C₃²×C₄₇
socle, prime radical	C₂²×C₃²×C₄₇	C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₉²×C₄₇	C₂	direct (N × H)
4. C₉²×C₄₇	C₂²	direct (N × H)
6. C₂²×C₉×C₄₇	C₉	direct (N × H)
9. C₂×C₉×C₄₇	C₂×C₉	direct (N × H)
12. C₉×C₄₇	C₂²×C₉	direct (N × H)
13. C₂²×C₉²	C₄₇	direct (N × H)
15. C₂²×C₄₇	C₉²	direct (N × H)
16. C₂×C₉²	C₂×C₄₇	direct (N × H)
19. C₂×C₄₇	C₂×C₉²	direct (N × H)
20. C₉²	C₂²×C₄₇	direct (N × H)
22. C₄₇	C₂²×C₉²	direct (N × H)
24. C₂²×C₉	C₉×C₄₇	direct (N × H)
27. C₂×C₉	C₂×C₉×C₄₇	direct (N × H)
30. C₉	C₂²×C₉×C₄₇	direct (N × H)
32. C₂²	C₉²×C₄₇	direct (N × H)
34. C₂	C₂×C₉²×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₉²×C₄₇	2
C₂²×C₃×C₉×C₄₇	3
C₂²×C₉²	47

Subgroups — C22×C92×C47 #72193243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₉²×C₄₇ #72193243