Subgroups — C₂×C₉×C₁₇×C₈₁ #72202074

Order 24786.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₇×C₂₇	C₃	1	1	yes	maximal, characteristic
2	C₂×C₃×C₁₇×C₈₁	C₃	1	3	yes	maximal
3	C₂×C₉²×C₁₇	C₉	1	1	yes	characteristic
4	C₂×C₃×C₁₇×C₂₇	C₉	1	2	yes	—
5	C₂×C₃×C₁₇×C₂₇	C₃²	1	1	yes	characteristic
6	C₂×C₁₇×C₈₁	C₉	1	9	yes	direct product factor
7	C₉×C₁₇×C₈₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₃×C₁₇×C₈₁	C₂×C₃	1	3	yes	—
9	C₉×C₁₇×C₂₇	C₂×C₃	1	1	yes	characteristic
10	C₂×C₉×C₈₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₁₇×C₂₇	C₂×C₉	1	2	yes	—
12	C₃×C₁₇×C₂₇	C₂×C₃²	1	1	yes	characteristic
13	C₉²×C₁₇	C₂×C₉	1	1	yes	characteristic
14	C₁₇×C₈₁	C₂×C₉	1	9	yes	direct product factor
15	C₂×C₃×C₉×C₁₇	C₂₇	1	3	yes	—
16	C₂×C₃×C₉×C₁₇	C₃×C₉	1	1	yes	characteristic
17	C₂×C₁₇×C₂₇	C₂₇	1	6	yes	—
18	C₂×C₁₇×C₂₇	C₃×C₉	1	3	yes	—
19	C₉×C₈₁	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₈₁	C₃×C₁₇	1	3	yes	—
21	C₂×C₉×C₂₇	C₃×C₁₇	1	1	yes	characteristic
22	C₃×C₉×C₁₇	C₂×C₂₇	1	3	yes	—
23	C₃×C₉×C₁₇	C₂×C₃×C₉	1	1	yes	characteristic
24	C₁₇×C₂₇	C₂×C₂₇	1	6	yes	—
25	C₁₇×C₂₇	C₂×C₃×C₉	1	3	yes	—
26	C₂×C₃²×C₁₇	C₃×C₂₇	1	1	yes	characteristic
27	C₂×C₉×C₁₇	C₈₁	1	9	yes	direct product factor
28	C₂×C₉×C₁₇	C₉²	1	1	yes	characteristic
29	C₂×C₉×C₁₇	C₃×C₂₇	1	2	yes	—
30	C₃×C₈₁	C₂×C₃×C₁₇	1	3	yes	—
31	C₉×C₂₇	C₂×C₃×C₁₇	1	1	yes	characteristic
32	C₂×C₃×C₂₇	C₉×C₁₇	1	2	yes	—
33	C₂×C₃×C₂₇	C₃²×C₁₇	1	1	yes	characteristic
34	C₂×C₉²	C₉×C₁₇	1	1	yes	characteristic
35	C₂×C₈₁	C₉×C₁₇	1	9	yes	direct product factor
36	C₃²×C₁₇	C₂×C₃×C₂₇	1	1	yes	characteristic
37	C₉×C₁₇	C₂×C₈₁	1	9	yes	direct product factor
38	C₉×C₁₇	C₂×C₉²	1	1	yes	characteristic
39	C₉×C₁₇	C₂×C₃×C₂₇	1	2	yes	—
40	C₂×C₃×C₁₇	C₉×C₂₇	1	1	yes	characteristic
41	C₂×C₃×C₁₇	C₃×C₈₁	1	3	yes	—
42	C₃×C₂₇	C₂×C₉×C₁₇	1	2	yes	—
43	C₃×C₂₇	C₂×C₃²×C₁₇	1	1	yes	characteristic
44	C₉²	C₂×C₉×C₁₇	1	1	yes	characteristic
45	C₈₁	C₂×C₉×C₁₇	1	9	yes	direct product factor
46	C₂×C₃×C₉	C₁₇×C₂₇	1	3	yes	—
47	C₂×C₃×C₉	C₃×C₉×C₁₇	1	1	yes	characteristic
48	C₂×C₂₇	C₁₇×C₂₇	1	6	yes	—
49	C₂×C₂₇	C₃×C₉×C₁₇	1	3	yes	—
50	C₃×C₁₇	C₂×C₉×C₂₇	1	1	yes	characteristic
51	C₃×C₁₇	C₂×C₃×C₈₁	1	3	yes	—
52	C₂×C₁₇	C₉×C₈₁	1	1	yes	characteristic, direct product factor, Hall
53	C₃×C₉	C₂×C₁₇×C₂₇	1	3	yes	—
54	C₃×C₉	C₂×C₃×C₉×C₁₇	1	1	yes	characteristic
55	C₂₇	C₂×C₁₇×C₂₇	1	6	yes	—
56	C₂₇	C₂×C₃×C₉×C₁₇	1	3	yes	—
57	C₂×C₃²	C₃×C₁₇×C₂₇	1	1	yes	characteristic
58	C₂×C₉	C₁₇×C₈₁	1	9	yes	direct product factor
59	C₂×C₉	C₉²×C₁₇	1	1	yes	characteristic
60	C₂×C₉	C₃×C₁₇×C₂₇	1	2	yes	—
61	C₁₇	C₂×C₉×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
62	C₃²	C₂×C₃×C₁₇×C₂₇	1	1	yes	characteristic
63	C₉	C₂×C₁₇×C₈₁	1	9	yes	direct product factor
64	C₉	C₂×C₃×C₁₇×C₂₇	1	2	yes	—
65	C₉	C₂×C₉²×C₁₇	1	1	yes	characteristic
66	C₂×C₃	C₉×C₁₇×C₂₇	1	1	yes	characteristic
67	C₂×C₃	C₃×C₁₇×C₈₁	1	3	yes	—
68	C₃	C₂×C₃×C₁₇×C₈₁	1	3	yes	—
69	C₃	C₂×C₉×C₁₇×C₂₇	1	1	yes	characteristic
70	C₂	C₉×C₁₇×C₈₁	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₂₇	C₂×C₃²×C₁₇
socle, prime radical	C₂×C₃²×C₁₇	C₃×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₇×C₈₁	C₉	direct (N × H)
7. C₉×C₁₇×C₈₁	C₂	direct (N × H)
10. C₂×C₉×C₈₁	C₁₇	direct (N × H)
14. C₁₇×C₈₁	C₂×C₉	direct (N × H)
19. C₉×C₈₁	C₂×C₁₇	direct (N × H)
27. C₂×C₉×C₁₇	C₈₁	direct (N × H)
35. C₂×C₈₁	C₉×C₁₇	direct (N × H)
37. C₉×C₁₇	C₂×C₈₁	direct (N × H)
45. C₈₁	C₂×C₉×C₁₇	direct (N × H)
52. C₂×C₁₇	C₉×C₈₁	direct (N × H)
58. C₂×C₉	C₁₇×C₈₁	direct (N × H)
61. C₁₇	C₂×C₉×C₈₁	direct (N × H)
63. C₉	C₂×C₁₇×C₈₁	direct (N × H)
70. C₂	C₉×C₁₇×C₈₁	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×C₉×C₁₇×C₂₇	3
C₂×C₃×C₁₇×C₈₁	3
C₉×C₁₇×C₈₁	2
C₂×C₉×C₈₁	17

Subgroups — C2×C9×C17×C81 #72202074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×C₁₇×C₈₁ #72202074