Subgroups — C₂⁸×C₁₁² #72207752

Order 30976.

5840786 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₁₁²	C₂	1	255	yes	maximal, direct product factor
2	C₂⁶×C₁₁²	C₂²	1	10795	yes	direct product factor
3	C₂⁵×C₁₁²	C₂³	1	97155	yes	direct product factor
4	C₂⁸×C₁₁	C₁₁	1	12	yes	maximal, direct product factor
5	C₂⁴×C₁₁²	C₂⁴	1	200787	yes	direct product factor
6	C₂⁷×C₁₁	C₂×C₁₁	1	3060	yes	direct product factor
7	C₂³×C₁₁²	C₂⁵	1	97155	yes	direct product factor
8	C₂⁶×C₁₁	C₂²×C₁₁	1	129540	yes	direct product factor
9	C₂²×C₁₁²	C₂⁶	1	10795	yes	direct product factor
10	C₂⁵×C₁₁	C₂³×C₁₁	1	1165860	yes	direct product factor
11	C₂⁸	C₁₁²	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₁₁²	C₂⁷	1	255	yes	direct product factor
13	C₂⁴×C₁₁	C₂⁴×C₁₁	1	2409444	yes	direct product factor
14	C₂⁷	C₂×C₁₁²	1	255	yes	direct product factor
15	C₁₁²	C₂⁸	1	1	yes	characteristic, direct product factor, Sylow
16	C₂³×C₁₁	C₂⁵×C₁₁	1	1165860	yes	direct product factor
17	C₂⁶	C₂²×C₁₁²	1	10795	yes	direct product factor
18	C₂²×C₁₁	C₂⁶×C₁₁	1	129540	yes	direct product factor
19	C₂⁵	C₂³×C₁₁²	1	97155	yes	direct product factor
20	C₂×C₁₁	C₂⁷×C₁₁	1	3060	yes	direct product factor
21	C₂⁴	C₂⁴×C₁₁²	1	200787	yes	direct product factor
22	C₁₁	C₂⁸×C₁₁	1	12	yes	direct product factor
23	C₂³	C₂⁵×C₁₁²	1	97155	yes	direct product factor
24	C₂²	C₂⁶×C₁₁²	1	10795	yes	direct product factor
25	C₂	C₂⁷×C₁₁²	1	255	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. C₂⁷×C₁₁²	C₂	direct (N × H)
2. C₂⁶×C₁₁²	C₂²	direct (N × H)
3. C₂⁵×C₁₁²	C₂³	direct (N × H)
4. C₂⁸×C₁₁	C₁₁	direct (N × H)
5. C₂⁴×C₁₁²	C₂⁴	direct (N × H)
6. C₂⁷×C₁₁	C₂×C₁₁	direct (N × H)
7. C₂³×C₁₁²	C₂⁵	direct (N × H)
8. C₂⁶×C₁₁	C₂²×C₁₁	direct (N × H)
9. C₂²×C₁₁²	C₂⁶	direct (N × H)
10. C₂⁵×C₁₁	C₂³×C₁₁	direct (N × H)
11. C₂⁸	C₁₁²	direct (N × H)
12. C₂×C₁₁²	C₂⁷	direct (N × H)
13. C₂⁴×C₁₁	C₂⁴×C₁₁	direct (N × H)
14. C₂⁷	C₂×C₁₁²	direct (N × H)
15. C₁₁²	C₂⁸	direct (N × H)
16. C₂³×C₁₁	C₂⁵×C₁₁	direct (N × H)
17. C₂⁶	C₂²×C₁₁²	direct (N × H)
18. C₂²×C₁₁	C₂⁶×C₁₁	direct (N × H)
19. C₂⁵	C₂³×C₁₁²	direct (N × H)
20. C₂×C₁₁	C₂⁷×C₁₁	direct (N × H)
21. C₂⁴	C₂⁴×C₁₁²	direct (N × H)
22. C₁₁	C₂⁸×C₁₁	direct (N × H)
23. C₂³	C₂⁵×C₁₁²	direct (N × H)
24. C₂²	C₂⁶×C₁₁²	direct (N × H)
25. C₂	C₂⁷×C₁₁²	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁷×C₁₁²	2
C₂⁸×C₁₁	11

Subgroups — C28×C112 #72207752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁸×C₁₁² #72207752