Subgroups — C₂×C₃×Q₈×C₉ #88759

Order 432.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×Q₈×C₉	C₂	1	4	yes	maximal, direct product factor
2	C₂×C₃×C₄×C₉	C₂	1	3	yes	maximal
3	C₂×C₃²×Q₈	C₃	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₉	C₃	1	3	yes	maximal, direct product factor
5	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
6	C₃×C₄×C₉	C₂²	1	6	yes	—
7	C₃²×Q₈	C₂×C₃	1	4	yes	—
8	C₂×C₃²×C₄	C₂×C₃	1	3	yes	—
9	Q₈×C₉	C₂×C₃	1	12	yes	direct product factor
10	C₂×C₄×C₉	C₂×C₃	1	9	yes	—
11	C₂×C₃×C₉	Q₈	1	2	yes	direct product factor
12	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
13	C₂×C₃×Q₈	C₉	1	3	yes	direct product factor
14	C₂×C₃×Q₈	C₃²	1	1	yes	characteristic
15	C₂²×C₃²	C₂²×C₃	1	1	yes	characteristic
16	C₃²×C₄	C₂²×C₃	1	6	yes	—
17	C₂²×C₉	C₂²×C₃	1	3	yes	—
18	C₄×C₉	C₂²×C₃	1	18	yes	—
19	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, direct product factor, Sylow
20	C₃×Q₈	C₂×C₉	1	12	yes	direct product factor
21	C₃×Q₈	C₂×C₃²	1	4	yes	—
22	C₂×C₃×C₄	C₂×C₉	1	9	yes	—
23	C₂×C₃×C₄	C₂×C₃²	1	3	yes	—
24	C₂×C₃²	C₃×Q₈	1	2	yes	—
25	C₂×C₃²	C₂³×C₃	1	1	yes	characteristic
26	C₂×C₉	C₃×Q₈	1	6	yes	direct product factor
27	C₂×C₉	C₂³×C₃	1	3	yes	—
28	C₂×Q₈	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₃	C₂²×C₉	1	3	yes	—
30	C₂²×C₃	C₂²×C₃²	1	1	yes	characteristic
31	C₃×C₄	C₂²×C₉	1	18	yes	—
32	C₃×C₄	C₂²×C₃²	1	6	yes	—
33	C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
34	C₉	C₂×C₃×Q₈	1	3	yes	direct product factor
35	Q₈	C₂×C₃×C₉	1	4	yes	direct product factor
36	C₂×C₄	C₂×C₃×C₉	1	3	yes	—
37	C₂×C₃	Q₈×C₉	1	6	yes	direct product factor
38	C₂×C₃	C₂³×C₉	1	3	yes	—
39	C₂×C₃	C₃²×Q₈	1	2	yes	—
40	C₂×C₃	C₂³×C₃²	1	1	yes	characteristic
41	C₂²	C₂²×C₃×C₉	1	1	yes	characteristic
42	C₄	C₂²×C₃×C₉	1	6	yes	—
43	C₃	C₂×Q₈×C₉	1	3	yes	direct product factor
44	C₃	C₂×C₃²×Q₈	1	1	yes	characteristic
45	C₂	C₃×Q₈×C₉	1	2	yes	direct product factor
46	C₂	C₂³×C₃×C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₉	C₂²
commutator	C₂	C₂³×C₃×C₉
Frattini, cosocle	C₂×C₃	C₂³×C₃²
socle, prime radical	C₂²×C₃²	C₂²×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×Q₈×C₉	C₂	direct (N × H)
4. C₂×Q₈×C₉	C₃	direct (N × H)
9. Q₈×C₉	C₂×C₃	direct (N × H)
11. C₂×C₃×C₉	Q₈	direct (N × H)
13. C₂×C₃×Q₈	C₉	direct (N × H)
19. C₃×C₉	C₂×Q₈	direct (N × H)
20. C₃×Q₈	C₂×C₉	direct (N × H)
26. C₂×C₉	C₃×Q₈	direct (N × H)
28. C₂×Q₈	C₃×C₉	direct (N × H)
34. C₉	C₂×C₃×Q₈	direct (N × H)
35. Q₈	C₂×C₃×C₉	direct (N × H)
37. C₂×C₃	Q₈×C₉	direct (N × H)
43. C₃	C₂×Q₈×C₉	direct (N × H)
45. C₂	C₃×Q₈×C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×Q₈×C₉	2
C₂×C₃×C₄×C₉	2
C₂×C₃²×Q₈	3
C₂×Q₈×C₉	3

Subgroups — C2×C3×Q8×C9 #88759

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Q₈×C₉ #88759