Subgroups — C₂×C₇×C₂₇×C₄₉ #72196330

Order 18522.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₇×C₄₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₉×C₄₉	C₃	1	1	yes	maximal, characteristic
3	C₇×C₉×C₄₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₇²×C₂₇	C₇	1	1	yes	maximal, characteristic
5	C₂×C₂₇×C₄₉	C₇	1	7	yes	maximal, direct product factor
6	C₂×C₃×C₇×C₄₉	C₉	1	1	yes	characteristic
7	C₇²×C₂₇	C₂×C₇	1	1	yes	characteristic
8	C₂₇×C₄₉	C₂×C₇	1	7	yes	direct product factor
9	C₃×C₇×C₄₉	C₂×C₉	1	1	yes	characteristic
10	C₂×C₇²×C₉	C₃×C₇	1	1	yes	characteristic
11	C₂×C₉×C₄₉	C₃×C₇	1	7	yes	—
12	C₂×C₇×C₄₉	C₂₇	1	1	yes	characteristic, direct product factor, Hall
13	C₇²×C₉	C₂×C₃×C₇	1	1	yes	characteristic
14	C₉×C₄₉	C₂×C₃×C₇	1	7	yes	—
15	C₂×C₇×C₂₇	C₄₉	1	7	yes	direct product factor
16	C₂×C₇×C₂₇	C₇²	1	1	yes	characteristic
17	C₇×C₄₉	C₂×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×C₇²	C₇×C₉	1	1	yes	characteristic
19	C₂×C₃×C₄₉	C₇×C₉	1	7	yes	—
20	C₇×C₂₇	C₂×C₄₉	1	7	yes	direct product factor
21	C₇×C₂₇	C₂×C₇²	1	1	yes	characteristic
22	C₃×C₇²	C₂×C₇×C₉	1	1	yes	characteristic
23	C₃×C₄₉	C₂×C₇×C₉	1	7	yes	—
24	C₂×C₇×C₉	C₃×C₄₉	1	7	yes	—
25	C₂×C₇×C₉	C₃×C₇²	1	1	yes	characteristic
26	C₂×C₇²	C₇×C₂₇	1	1	yes	characteristic
27	C₂×C₄₉	C₇×C₂₇	1	7	yes	direct product factor
28	C₇×C₉	C₂×C₃×C₄₉	1	7	yes	—
29	C₇×C₉	C₂×C₃×C₇²	1	1	yes	characteristic
30	C₂×C₂₇	C₇×C₄₉	1	1	yes	characteristic, direct product factor, Hall
31	C₇²	C₂×C₇×C₂₇	1	1	yes	characteristic
32	C₄₉	C₂×C₇×C₂₇	1	7	yes	direct product factor
33	C₂×C₃×C₇	C₉×C₄₉	1	7	yes	—
34	C₂×C₃×C₇	C₇²×C₉	1	1	yes	characteristic
35	C₂₇	C₂×C₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₇	C₂×C₉×C₄₉	1	7	yes	—
37	C₃×C₇	C₂×C₇²×C₉	1	1	yes	characteristic
38	C₂×C₉	C₃×C₇×C₄₉	1	1	yes	characteristic
39	C₂×C₇	C₂₇×C₄₉	1	7	yes	direct product factor
40	C₂×C₇	C₇²×C₂₇	1	1	yes	characteristic
41	C₉	C₂×C₃×C₇×C₄₉	1	1	yes	characteristic
42	C₇	C₂×C₂₇×C₄₉	1	7	yes	direct product factor
43	C₇	C₂×C₇²×C₂₇	1	1	yes	characteristic
44	C₂×C₃	C₇×C₉×C₄₉	1	1	yes	characteristic
45	C₃	C₂×C₇×C₉×C₄₉	1	1	yes	characteristic
46	C₂	C₇×C₂₇×C₄₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇×C₉	C₂×C₃×C₇²
socle, prime radical	C₂×C₃×C₇²	C₇×C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₇×C₄₉	C₂	direct (N × H)
5. C₂×C₂₇×C₄₉	C₇	direct (N × H)
8. C₂₇×C₄₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₄₉	C₂₇	direct (N × H)
15. C₂×C₇×C₂₇	C₄₉	direct (N × H)
17. C₇×C₄₉	C₂×C₂₇	direct (N × H)
20. C₇×C₂₇	C₂×C₄₉	direct (N × H)
27. C₂×C₄₉	C₇×C₂₇	direct (N × H)
30. C₂×C₂₇	C₇×C₄₉	direct (N × H)
32. C₄₉	C₂×C₇×C₂₇	direct (N × H)
35. C₂₇	C₂×C₇×C₄₉	direct (N × H)
39. C₂×C₇	C₂₇×C₄₉	direct (N × H)
42. C₇	C₂×C₂₇×C₄₉	direct (N × H)
46. C₂	C₇×C₂₇×C₄₉	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×C₂₇×C₄₉	2
C₂×C₇×C₉×C₄₉	3
C₂×C₇²×C₂₇	7
C₂×C₂₇×C₄₉	7

Subgroups — C2×C7×C27×C49 #72196330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂₇×C₄₉ #72196330