Finite Group Databasebeta

← C₂²×C₁₁²×C₇₁ #46805372

Subgroups — C₂²×C₁₁²×C₇₁ #46805372

Order 34364.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁²×C₇₁	C₂	1	3	yes	maximal, direct product factor
2	C₁₁²×C₇₁	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₁×C₇₁	C₁₁	1	12	yes	maximal, direct product factor
4	C₂×C₁₁×C₇₁	C₂×C₁₁	1	36	yes	direct product factor
5	C₁₁×C₇₁	C₂²×C₁₁	1	12	yes	direct product factor
6	C₂²×C₁₁²	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₇₁	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₁₁²	C₂×C₇₁	1	3	yes	direct product factor
9	C₂×C₇₁	C₂×C₁₁²	1	3	yes	direct product factor
10	C₁₁²	C₂²×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₇₁	C₂²×C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₁₁	C₁₁×C₇₁	1	12	yes	direct product factor
13	C₂×C₁₁	C₂×C₁₁×C₇₁	1	36	yes	direct product factor
14	C₁₁	C₂²×C₁₁×C₇₁	1	12	yes	direct product factor
15	C₂²	C₁₁²×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂	C₂×C₁₁²×C₇₁	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁²×C₇₁	C₂	direct (N × H)
2. C₁₁²×C₇₁	C₂²	direct (N × H)
3. C₂²×C₁₁×C₇₁	C₁₁	direct (N × H)
4. C₂×C₁₁×C₇₁	C₂×C₁₁	direct (N × H)
5. C₁₁×C₇₁	C₂²×C₁₁	direct (N × H)
6. C₂²×C₁₁²	C₇₁	direct (N × H)
7. C₂²×C₇₁	C₁₁²	direct (N × H)
8. C₂×C₁₁²	C₂×C₇₁	direct (N × H)
9. C₂×C₇₁	C₂×C₁₁²	direct (N × H)
10. C₁₁²	C₂²×C₇₁	direct (N × H)
11. C₇₁	C₂²×C₁₁²	direct (N × H)
12. C₂²×C₁₁	C₁₁×C₇₁	direct (N × H)
13. C₂×C₁₁	C₂×C₁₁×C₇₁	direct (N × H)
14. C₁₁	C₂²×C₁₁×C₇₁	direct (N × H)
15. C₂²	C₁₁²×C₇₁	direct (N × H)
16. C₂	C₂×C₁₁²×C₇₁	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×C₁₁²×C₇₁	2
C₂²×C₁₁×C₇₁	11
C₂²×C₁₁²	71