Subgroups — C₂×C₃⁴×C₁₂₁ #72197296

Order 19602.

1272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₁₂₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃³×C₁₂₁	C₃	1	40	yes	maximal, direct product factor
3	C₃³×C₁₂₁	C₂×C₃	1	40	yes	direct product factor
4	C₂×C₃²×C₁₂₁	C₃²	1	130	yes	direct product factor
5	C₂×C₃⁴×C₁₁	C₁₁	1	1	yes	maximal, characteristic
6	C₃²×C₁₂₁	C₂×C₃²	1	130	yes	direct product factor
7	C₃⁴×C₁₁	C₂×C₁₁	1	1	yes	characteristic
8	C₂×C₃×C₁₂₁	C₃³	1	40	yes	direct product factor
9	C₂×C₃³×C₁₁	C₃×C₁₁	1	40	yes	—
10	C₃×C₁₂₁	C₂×C₃³	1	40	yes	direct product factor
11	C₃³×C₁₁	C₂×C₃×C₁₁	1	40	yes	—
12	C₂×C₁₂₁	C₃⁴	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃²×C₁₁	C₃²×C₁₁	1	130	yes	—
14	C₂×C₃⁴	C₁₂₁	1	1	yes	characteristic, direct product factor, Hall
15	C₁₂₁	C₂×C₃⁴	1	1	yes	characteristic, direct product factor, Sylow
16	C₃²×C₁₁	C₂×C₃²×C₁₁	1	130	yes	—
17	C₃⁴	C₂×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃×C₁₁	C₃³×C₁₁	1	40	yes	—
19	C₂×C₃³	C₃×C₁₂₁	1	40	yes	direct product factor
20	C₃×C₁₁	C₂×C₃³×C₁₁	1	40	yes	—
21	C₃³	C₂×C₃×C₁₂₁	1	40	yes	direct product factor
22	C₂×C₁₁	C₃⁴×C₁₁	1	1	yes	characteristic
23	C₂×C₃²	C₃²×C₁₂₁	1	130	yes	direct product factor
24	C₁₁	C₂×C₃⁴×C₁₁	1	1	yes	characteristic
25	C₃²	C₂×C₃²×C₁₂₁	1	130	yes	direct product factor
26	C₂×C₃	C₃³×C₁₂₁	1	40	yes	direct product factor
27	C₃	C₂×C₃³×C₁₂₁	1	40	yes	direct product factor
28	C₂	C₃⁴×C₁₂₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₁	C₂×C₃⁴×C₁₁
socle, prime radical	C₂×C₃⁴×C₁₁	C₁₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃⁴×C₁₂₁	C₂	direct (N × H)
2. C₂×C₃³×C₁₂₁	C₃	direct (N × H)
3. C₃³×C₁₂₁	C₂×C₃	direct (N × H)
4. C₂×C₃²×C₁₂₁	C₃²	direct (N × H)
6. C₃²×C₁₂₁	C₂×C₃²	direct (N × H)
8. C₂×C₃×C₁₂₁	C₃³	direct (N × H)
10. C₃×C₁₂₁	C₂×C₃³	direct (N × H)
12. C₂×C₁₂₁	C₃⁴	direct (N × H)
14. C₂×C₃⁴	C₁₂₁	direct (N × H)
15. C₁₂₁	C₂×C₃⁴	direct (N × H)
17. C₃⁴	C₂×C₁₂₁	direct (N × H)
19. C₂×C₃³	C₃×C₁₂₁	direct (N × H)
21. C₃³	C₂×C₃×C₁₂₁	direct (N × H)
23. C₂×C₃²	C₃²×C₁₂₁	direct (N × H)
25. C₃²	C₂×C₃²×C₁₂₁	direct (N × H)
26. C₂×C₃	C₃³×C₁₂₁	direct (N × H)
27. C₃	C₂×C₃³×C₁₂₁	direct (N × H)
28. C₂	C₃⁴×C₁₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃⁴×C₁₂₁	2
C₂×C₃³×C₁₂₁	3
C₂×C₃⁴×C₁₁	11

Subgroups — C2×C34×C121 #72197296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⁴×C₁₂₁ #72197296