Subgroups — C₂×C₁₇×C₂₇² #72202075

Order 24786.

304 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₁₇×C₂₇	C₃	1	4	yes	maximal
2	C₂×C₉²×C₁₇	C₃²	1	1	yes	characteristic
3	C₂×C₃×C₁₇×C₂₇	C₉	1	12	yes	—
4	C₁₇×C₂₇²	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₉×C₁₇×C₂₇	C₂×C₃	1	4	yes	—
6	C₂×C₂₇²	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃×C₁₇×C₂₇	C₂×C₉	1	12	yes	—
8	C₉²×C₁₇	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₃×C₉×C₁₇	C₃×C₉	1	4	yes	—
10	C₂×C₁₇×C₂₇	C₂₇	1	36	yes	direct product factor
11	C₂₇²	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₉×C₂₇	C₃×C₁₇	1	4	yes	—
13	C₃×C₉×C₁₇	C₂×C₃×C₉	1	4	yes	—
14	C₁₇×C₂₇	C₂×C₂₇	1	36	yes	direct product factor
15	C₂×C₃²×C₁₇	C₉²	1	1	yes	characteristic
16	C₂×C₉×C₁₇	C₃×C₂₇	1	12	yes	—
17	C₉×C₂₇	C₂×C₃×C₁₇	1	4	yes	—
18	C₂×C₃×C₂₇	C₉×C₁₇	1	12	yes	—
19	C₂×C₉²	C₃²×C₁₇	1	1	yes	characteristic
20	C₃²×C₁₇	C₂×C₉²	1	1	yes	characteristic
21	C₉×C₁₇	C₂×C₃×C₂₇	1	12	yes	—
22	C₂×C₃×C₁₇	C₉×C₂₇	1	4	yes	—
23	C₃×C₂₇	C₂×C₉×C₁₇	1	12	yes	—
24	C₉²	C₂×C₃²×C₁₇	1	1	yes	characteristic
25	C₂×C₃×C₉	C₃×C₉×C₁₇	1	4	yes	—
26	C₂×C₂₇	C₁₇×C₂₇	1	36	yes	direct product factor
27	C₃×C₁₇	C₂×C₉×C₂₇	1	4	yes	—
28	C₂×C₁₇	C₂₇²	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₉	C₂×C₃×C₉×C₁₇	1	4	yes	—
30	C₂₇	C₂×C₁₇×C₂₇	1	36	yes	direct product factor
31	C₂×C₃²	C₉²×C₁₇	1	1	yes	characteristic
32	C₂×C₉	C₃×C₁₇×C₂₇	1	12	yes	—
33	C₁₇	C₂×C₂₇²	1	1	yes	characteristic, direct product factor, Sylow
34	C₃²	C₂×C₉²×C₁₇	1	1	yes	characteristic
35	C₉	C₂×C₃×C₁₇×C₂₇	1	12	yes	—
36	C₂×C₃	C₉×C₁₇×C₂₇	1	4	yes	—
37	C₃	C₂×C₉×C₁₇×C₂₇	1	4	yes	—
38	C₂	C₁₇×C₂₇²	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉²	C₂×C₃²×C₁₇
socle, prime radical	C₂×C₃²×C₁₇	C₉²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₇×C₂₇²	C₂	direct (N × H)
6. C₂×C₂₇²	C₁₇	direct (N × H)
10. C₂×C₁₇×C₂₇	C₂₇	direct (N × H)
11. C₂₇²	C₂×C₁₇	direct (N × H)
14. C₁₇×C₂₇	C₂×C₂₇	direct (N × H)
26. C₂×C₂₇	C₁₇×C₂₇	direct (N × H)
28. C₂×C₁₇	C₂₇²	direct (N × H)
30. C₂₇	C₂×C₁₇×C₂₇	direct (N × H)
33. C₁₇	C₂×C₂₇²	direct (N × H)
38. C₂	C₁₇×C₂₇²	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
C₁₇×C₂₇²	2
C₂×C₂₇²	17

Subgroups — C2×C17×C272 #72202075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×C₂₇² #72202075