Subgroups — C₂×C₁₆×C₁₇×C₂₃ #72190856

Order 12512.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₁₇×C₂₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₄×C₁₇×C₂₃	C₄	1	1	yes	characteristic
4	C₈×C₁₇×C₂₃	C₄	1	1	yes	characteristic
5	C₈×C₁₇×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₁₇×C₂₃	C₈	1	1	yes	characteristic
7	C₄×C₁₇×C₂₃	C₈	1	1	yes	characteristic
8	C₄×C₁₇×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₁₇×C₂₃	C₁₆	1	2	yes	direct product factor
10	C₂×C₁₇×C₂₃	C₂×C₈	1	1	yes	characteristic
11	C₂×C₁₆×C₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₁₆×C₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₁₇×C₂₃	C₂×C₁₆	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₈×C₂₃	C₂×C₁₇	1	1	yes	characteristic
15	C₁₆×C₂₃	C₂×C₁₇	1	2	yes	direct product factor
16	C₂×C₈×C₁₇	C₂×C₂₃	1	1	yes	characteristic
17	C₁₆×C₁₇	C₂×C₂₃	1	2	yes	direct product factor
18	C₂×C₄×C₂₃	C₄×C₁₇	1	1	yes	characteristic
19	C₈×C₂₃	C₄×C₁₇	1	1	yes	characteristic
20	C₈×C₂₃	C₂²×C₁₇	1	1	yes	characteristic
21	C₂×C₄×C₁₇	C₄×C₂₃	1	1	yes	characteristic
22	C₈×C₁₇	C₄×C₂₃	1	1	yes	characteristic
23	C₈×C₁₇	C₂²×C₂₃	1	1	yes	characteristic
24	C₂²×C₂₃	C₈×C₁₇	1	1	yes	characteristic
25	C₄×C₂₃	C₈×C₁₇	1	1	yes	characteristic
26	C₄×C₂₃	C₂×C₄×C₁₇	1	1	yes	characteristic
27	C₂²×C₁₇	C₈×C₂₃	1	1	yes	characteristic
28	C₄×C₁₇	C₈×C₂₃	1	1	yes	characteristic
29	C₄×C₁₇	C₂×C₄×C₂₃	1	1	yes	characteristic
30	C₂×C₂₃	C₁₆×C₁₇	1	2	yes	direct product factor
31	C₂×C₂₃	C₂×C₈×C₁₇	1	1	yes	characteristic
32	C₂×C₁₇	C₁₆×C₂₃	1	2	yes	direct product factor
33	C₂×C₁₇	C₂×C₈×C₂₃	1	1	yes	characteristic
34	C₂×C₁₆	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
35	C₂₃	C₂×C₁₆×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₇	C₂×C₁₆×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
37	C₂×C₈	C₂×C₁₇×C₂₃	1	1	yes	characteristic
38	C₁₆	C₂×C₁₇×C₂₃	1	2	yes	direct product factor
39	C₂×C₄	C₄×C₁₇×C₂₃	1	1	yes	characteristic
40	C₈	C₄×C₁₇×C₂₃	1	1	yes	characteristic
41	C₈	C₂²×C₁₇×C₂₃	1	1	yes	characteristic
42	C₂²	C₈×C₁₇×C₂₃	1	1	yes	characteristic
43	C₄	C₈×C₁₇×C₂₃	1	1	yes	characteristic
44	C₄	C₂×C₄×C₁₇×C₂₃	1	1	yes	characteristic
45	C₂	C₁₆×C₁₇×C₂₃	1	2	yes	direct product factor
46	C₂	C₂×C₈×C₁₇×C₂₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂²×C₁₇×C₂₃
socle, prime radical	C₂²×C₁₇×C₂₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₆×C₁₇×C₂₃	C₂	direct (N × H)
9. C₂×C₁₇×C₂₃	C₁₆	direct (N × H)
11. C₂×C₁₆×C₂₃	C₁₇	direct (N × H)
12. C₂×C₁₆×C₁₇	C₂₃	direct (N × H)
13. C₁₇×C₂₃	C₂×C₁₆	direct (N × H)
15. C₁₆×C₂₃	C₂×C₁₇	direct (N × H)
17. C₁₆×C₁₇	C₂×C₂₃	direct (N × H)
30. C₂×C₂₃	C₁₆×C₁₇	direct (N × H)
32. C₂×C₁₇	C₁₆×C₂₃	direct (N × H)
34. C₂×C₁₆	C₁₇×C₂₃	direct (N × H)
35. C₂₃	C₂×C₁₆×C₁₇	direct (N × H)
36. C₁₇	C₂×C₁₆×C₂₃	direct (N × H)
38. C₁₆	C₂×C₁₇×C₂₃	direct (N × H)
45. C₂	C₁₆×C₁₇×C₂₃	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×C₈×C₁₇×C₂₃	2
C₁₆×C₁₇×C₂₃	2
C₂×C₁₆×C₂₃	17
C₂×C₁₆×C₁₇	23

Subgroups — C2×C16×C17×C23 #72190856

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₆×C₁₇×C₂₃ #72190856