Subgroups — C₂×C₇³×C₂₇ #72196331

Order 18522.

928 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇³×C₂₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇³×C₉	C₃	1	1	yes	maximal, characteristic
3	C₇³×C₉	C₂×C₃	1	1	yes	characteristic
4	C₂×C₇²×C₂₇	C₇	1	57	yes	maximal, direct product factor
5	C₂×C₃×C₇³	C₉	1	1	yes	characteristic
6	C₇²×C₂₇	C₂×C₇	1	57	yes	direct product factor
7	C₃×C₇³	C₂×C₉	1	1	yes	characteristic
8	C₂×C₇²×C₉	C₃×C₇	1	57	yes	—
9	C₂×C₇³	C₂₇	1	1	yes	characteristic, direct product factor, Hall
10	C₇²×C₉	C₂×C₃×C₇	1	57	yes	—
11	C₂×C₇×C₂₇	C₇²	1	57	yes	direct product factor
12	C₇³	C₂×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₃×C₇²	C₇×C₉	1	57	yes	—
14	C₇×C₂₇	C₂×C₇²	1	57	yes	direct product factor
15	C₃×C₇²	C₂×C₇×C₉	1	57	yes	—
16	C₂×C₇×C₉	C₃×C₇²	1	57	yes	—
17	C₂×C₇²	C₇×C₂₇	1	57	yes	direct product factor
18	C₇×C₉	C₂×C₃×C₇²	1	57	yes	—
19	C₂×C₂₇	C₇³	1	1	yes	characteristic, direct product factor, Hall
20	C₇²	C₂×C₇×C₂₇	1	57	yes	direct product factor
21	C₂×C₃×C₇	C₇²×C₉	1	57	yes	—
22	C₂₇	C₂×C₇³	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₇	C₂×C₇²×C₉	1	57	yes	—
24	C₂×C₉	C₃×C₇³	1	1	yes	characteristic
25	C₂×C₇	C₇²×C₂₇	1	57	yes	direct product factor
26	C₉	C₂×C₃×C₇³	1	1	yes	characteristic
27	C₇	C₂×C₇²×C₂₇	1	57	yes	direct product factor
28	C₂×C₃	C₇³×C₉	1	1	yes	characteristic
29	C₃	C₂×C₇³×C₉	1	1	yes	characteristic
30	C₂	C₇³×C₂₇	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃×C₇³
socle, prime radical	C₂×C₃×C₇³	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇³×C₂₇	C₂	direct (N × H)
4. C₂×C₇²×C₂₇	C₇	direct (N × H)
6. C₇²×C₂₇	C₂×C₇	direct (N × H)
9. C₂×C₇³	C₂₇	direct (N × H)
11. C₂×C₇×C₂₇	C₇²	direct (N × H)
12. C₇³	C₂×C₂₇	direct (N × H)
14. C₇×C₂₇	C₂×C₇²	direct (N × H)
17. C₂×C₇²	C₇×C₂₇	direct (N × H)
19. C₂×C₂₇	C₇³	direct (N × H)
20. C₇²	C₂×C₇×C₂₇	direct (N × H)
22. C₂₇	C₂×C₇³	direct (N × H)
25. C₂×C₇	C₇²×C₂₇	direct (N × H)
27. C₇	C₂×C₇²×C₂₇	direct (N × H)
30. C₂	C₇³×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
C₇³×C₂₇	2
C₂×C₇³×C₉	3
C₂×C₇²×C₂₇	7

Subgroups — C2×C73×C27 #72196331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇³×C₂₇ #72196331