Subgroups — C₂³×C₃×C₈ #5895

Order 192.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₈	C₂	1	14	yes	maximal, direct product factor
3	C₂³×C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
4	C₂⁴×C₃	C₄	1	1	yes	characteristic
5	C₂²×C₃×C₄	C₄	1	7	yes	—
6	C₂²×C₃×C₄	C₂²	1	7	yes	—
7	C₂×C₃×C₈	C₂²	1	28	yes	direct product factor
8	C₂³×C₄	C₂×C₃	1	1	yes	characteristic
9	C₂²×C₈	C₂×C₃	1	14	yes	direct product factor
10	C₂³×C₃	C₈	1	8	yes	direct product factor
11	C₂³×C₃	C₂×C₄	1	7	yes	—
12	C₂×C₃×C₄	C₂×C₄	1	21	yes	—
13	C₂×C₃×C₄	C₂³	1	7	yes	—
14	C₃×C₈	C₂³	1	8	yes	direct product factor
15	C₂⁴	C₃×C₄	1	1	yes	characteristic
16	C₂²×C₄	C₃×C₄	1	7	yes	—
17	C₂²×C₄	C₂²×C₃	1	7	yes	—
18	C₂×C₈	C₂²×C₃	1	28	yes	direct product factor
19	C₂²×C₃	C₂×C₈	1	28	yes	direct product factor
20	C₂²×C₃	C₂²×C₄	1	7	yes	—
21	C₃×C₄	C₂²×C₄	1	7	yes	—
22	C₃×C₄	C₂⁴	1	1	yes	characteristic
23	C₂³	C₃×C₈	1	8	yes	direct product factor
24	C₂³	C₂×C₃×C₄	1	7	yes	—
25	C₂×C₄	C₂×C₃×C₄	1	21	yes	—
26	C₂×C₄	C₂³×C₃	1	7	yes	—
27	C₈	C₂³×C₃	1	8	yes	direct product factor
28	C₂×C₃	C₂²×C₈	1	14	yes	direct product factor
29	C₂×C₃	C₂³×C₄	1	1	yes	characteristic
30	C₂²	C₂×C₃×C₈	1	28	yes	direct product factor
31	C₂²	C₂²×C₃×C₄	1	7	yes	—
32	C₄	C₂²×C₃×C₄	1	7	yes	—
33	C₄	C₂⁴×C₃	1	1	yes	characteristic
34	C₃	C₂³×C₈	1	1	yes	characteristic, direct product factor, Sylow
35	C₂	C₂²×C₃×C₈	1	14	yes	direct product factor
36	C₂	C₂³×C₃×C₄	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₈	C₂	direct (N × H)
3. C₂³×C₈	C₃	direct (N × H)
7. C₂×C₃×C₈	C₂²	direct (N × H)
9. C₂²×C₈	C₂×C₃	direct (N × H)
10. C₂³×C₃	C₈	direct (N × H)
14. C₃×C₈	C₂³	direct (N × H)
18. C₂×C₈	C₂²×C₃	direct (N × H)
19. C₂²×C₃	C₂×C₈	direct (N × H)
23. C₂³	C₃×C₈	direct (N × H)
27. C₈	C₂³×C₃	direct (N × H)
28. C₂×C₃	C₂²×C₈	direct (N × H)
30. C₂²	C₂×C₃×C₈	direct (N × H)
34. C₃	C₂³×C₈	direct (N × H)
35. C₂	C₂²×C₃×C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂²×C₃×C₈	2
C₂³×C₈	3

Subgroups — C23×C3×C8 #5895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₈ #5895