Subgroups — C₂³×C₃×C₂₄₃ #72185083

Order 5832.

352 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₂₄₃	C₂	1	7	yes	maximal, direct product factor
2	C₂³×C₃×C₈₁	C₃	1	1	yes	maximal, characteristic
3	C₂³×C₂₄₃	C₃	1	3	yes	maximal, direct product factor
4	C₂×C₃×C₂₄₃	C₂²	1	7	yes	direct product factor
5	C₂²×C₃×C₈₁	C₂×C₃	1	7	yes	—
6	C₂²×C₂₄₃	C₂×C₃	1	21	yes	direct product factor
7	C₃×C₂₄₃	C₂³	1	1	yes	characteristic, direct product factor, Sylow
8	C₂³×C₃×C₂₇	C₉	1	1	yes	characteristic
9	C₂³×C₈₁	C₉	1	2	yes	—
10	C₂³×C₈₁	C₃²	1	1	yes	characteristic
11	C₂×C₃×C₈₁	C₂²×C₃	1	7	yes	—
12	C₂×C₂₄₃	C₂²×C₃	1	21	yes	direct product factor
13	C₂²×C₃×C₂₇	C₂×C₉	1	7	yes	—
14	C₂²×C₈₁	C₂×C₉	1	14	yes	—
15	C₂²×C₈₁	C₂×C₃²	1	7	yes	—
16	C₃×C₈₁	C₂³×C₃	1	1	yes	characteristic
17	C₂₄₃	C₂³×C₃	1	3	yes	direct product factor
18	C₂³×C₃×C₉	C₂₇	1	1	yes	characteristic
19	C₂³×C₂₇	C₂₇	1	2	yes	—
20	C₂³×C₂₇	C₃×C₉	1	1	yes	characteristic
21	C₂×C₃×C₂₇	C₂²×C₉	1	7	yes	—
22	C₂×C₈₁	C₂²×C₉	1	14	yes	—
23	C₂×C₈₁	C₂²×C₃²	1	7	yes	—
24	C₂²×C₃×C₉	C₂×C₂₇	1	7	yes	—
25	C₂²×C₂₇	C₂×C₂₇	1	14	yes	—
26	C₂²×C₂₇	C₂×C₃×C₉	1	7	yes	—
27	C₃×C₂₇	C₂³×C₉	1	1	yes	characteristic
28	C₈₁	C₂³×C₉	1	2	yes	—
29	C₈₁	C₂³×C₃²	1	1	yes	characteristic
30	C₂³×C₃²	C₈₁	1	1	yes	characteristic
31	C₂³×C₉	C₈₁	1	2	yes	—
32	C₂³×C₉	C₃×C₂₇	1	1	yes	characteristic
33	C₂×C₃×C₉	C₂²×C₂₇	1	7	yes	—
34	C₂×C₂₇	C₂²×C₂₇	1	14	yes	—
35	C₂×C₂₇	C₂²×C₃×C₉	1	7	yes	—
36	C₂²×C₃²	C₂×C₈₁	1	7	yes	—
37	C₂²×C₉	C₂×C₈₁	1	14	yes	—
38	C₂²×C₉	C₂×C₃×C₂₇	1	7	yes	—
39	C₃×C₉	C₂³×C₂₇	1	1	yes	characteristic
40	C₂₇	C₂³×C₂₇	1	2	yes	—
41	C₂₇	C₂³×C₃×C₉	1	1	yes	characteristic
42	C₂³×C₃	C₂₄₃	1	3	yes	direct product factor
43	C₂³×C₃	C₃×C₈₁	1	1	yes	characteristic
44	C₂×C₃²	C₂²×C₈₁	1	7	yes	—
45	C₂×C₉	C₂²×C₈₁	1	14	yes	—
46	C₂×C₉	C₂²×C₃×C₂₇	1	7	yes	—
47	C₂²×C₃	C₂×C₂₄₃	1	21	yes	direct product factor
48	C₂²×C₃	C₂×C₃×C₈₁	1	7	yes	—
49	C₃²	C₂³×C₈₁	1	1	yes	characteristic
50	C₉	C₂³×C₈₁	1	2	yes	—
51	C₉	C₂³×C₃×C₂₇	1	1	yes	characteristic
52	C₂³	C₃×C₂₄₃	1	1	yes	characteristic, direct product factor, Sylow
53	C₂×C₃	C₂²×C₂₄₃	1	21	yes	direct product factor
54	C₂×C₃	C₂²×C₃×C₈₁	1	7	yes	—
55	C₂²	C₂×C₃×C₂₄₃	1	7	yes	direct product factor
56	C₃	C₂³×C₂₄₃	1	3	yes	direct product factor
57	C₃	C₂³×C₃×C₈₁	1	1	yes	characteristic
58	C₂	C₂²×C₃×C₂₄₃	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈₁	C₂³×C₃²
socle, prime radical	C₂³×C₃²	C₈₁
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₂₄₃	C₂	direct (N × H)
3. C₂³×C₂₄₃	C₃	direct (N × H)
4. C₂×C₃×C₂₄₃	C₂²	direct (N × H)
6. C₂²×C₂₄₃	C₂×C₃	direct (N × H)
7. C₃×C₂₄₃	C₂³	direct (N × H)
12. C₂×C₂₄₃	C₂²×C₃	direct (N × H)
17. C₂₄₃	C₂³×C₃	direct (N × H)
42. C₂³×C₃	C₂₄₃	direct (N × H)
47. C₂²×C₃	C₂×C₂₄₃	direct (N × H)
52. C₂³	C₃×C₂₄₃	direct (N × H)
53. C₂×C₃	C₂²×C₂₄₃	direct (N × H)
55. C₂²	C₂×C₃×C₂₄₃	direct (N × H)
56. C₃	C₂³×C₂₄₃	direct (N × H)
58. C₂	C₂²×C₃×C₂₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₂₄₃	2
C₂³×C₃×C₈₁	3
C₂³×C₂₄₃	3

Subgroups — C23×C3×C243 #72185083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₃×C₂₄₃ #72185083