Subgroups — C₂×C₈×C₂₃×C₆₁ #72199847

Order 22448.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×C₂₃×C₆₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄×C₂₃×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₂₃×C₆₁	C₄	1	1	yes	characteristic
4	C₄×C₂₃×C₆₁	C₄	1	1	yes	characteristic
5	C₄×C₂₃×C₆₁	C₂²	1	1	yes	characteristic
6	C₂×C₂₃×C₆₁	C₈	1	2	yes	direct product factor
7	C₂×C₂₃×C₆₁	C₂×C₄	1	1	yes	characteristic
8	C₂₃×C₆₁	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₈×C₆₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₄×C₆₁	C₂×C₂₃	1	1	yes	characteristic
11	C₈×C₆₁	C₂×C₂₃	1	2	yes	direct product factor
12	C₂×C₈×C₂₃	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₆₁	C₄×C₂₃	1	1	yes	characteristic
14	C₄×C₆₁	C₄×C₂₃	1	1	yes	characteristic
15	C₄×C₆₁	C₂²×C₂₃	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂×C₆₁	1	1	yes	characteristic
17	C₈×C₂₃	C₂×C₆₁	1	2	yes	direct product factor
18	C₂×C₆₁	C₈×C₂₃	1	2	yes	direct product factor
19	C₂×C₆₁	C₂×C₄×C₂₃	1	1	yes	characteristic
20	C₂²×C₂₃	C₄×C₆₁	1	1	yes	characteristic
21	C₄×C₂₃	C₄×C₆₁	1	1	yes	characteristic
22	C₄×C₂₃	C₂²×C₆₁	1	1	yes	characteristic
23	C₆₁	C₂×C₈×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₂₃	C₈×C₆₁	1	2	yes	direct product factor
25	C₂×C₂₃	C₂×C₄×C₆₁	1	1	yes	characteristic
26	C₂₃	C₂×C₈×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₈	C₂₃×C₆₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₄	C₂×C₂₃×C₆₁	1	1	yes	characteristic
29	C₈	C₂×C₂₃×C₆₁	1	2	yes	direct product factor
30	C₂²	C₄×C₂₃×C₆₁	1	1	yes	characteristic
31	C₄	C₄×C₂₃×C₆₁	1	1	yes	characteristic
32	C₄	C₂²×C₂₃×C₆₁	1	1	yes	characteristic
33	C₂	C₂×C₄×C₂₃×C₆₁	1	1	yes	characteristic
34	C₂	C₈×C₂₃×C₆₁	1	2	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₂₃×C₆₁
socle, prime radical	C₂²×C₂₃×C₆₁	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈×C₂₃×C₆₁	C₂	direct (N × H)
6. C₂×C₂₃×C₆₁	C₈	direct (N × H)
8. C₂₃×C₆₁	C₂×C₈	direct (N × H)
9. C₂×C₈×C₆₁	C₂₃	direct (N × H)
11. C₈×C₆₁	C₂×C₂₃	direct (N × H)
12. C₂×C₈×C₂₃	C₆₁	direct (N × H)
17. C₈×C₂₃	C₂×C₆₁	direct (N × H)
18. C₂×C₆₁	C₈×C₂₃	direct (N × H)
23. C₆₁	C₂×C₈×C₂₃	direct (N × H)
24. C₂×C₂₃	C₈×C₆₁	direct (N × H)
26. C₂₃	C₂×C₈×C₆₁	direct (N × H)
27. C₂×C₈	C₂₃×C₆₁	direct (N × H)
29. C₈	C₂×C₂₃×C₆₁	direct (N × H)
34. C₂	C₈×C₂₃×C₆₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×C₂₃×C₆₁	2
C₂×C₄×C₂₃×C₆₁	2
C₂×C₈×C₆₁	23
C₂×C₈×C₂₃	61

Subgroups — C2×C8×C23×C61 #72199847

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×C₂₃×C₆₁ #72199847