Subgroups — C₂×C₃×C₂₇×C₁₄₉ #72201429

Order 24138.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×C₁₄₉	C₃	1	1	yes	maximal, characteristic
2	C₂×C₂₇×C₁₄₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₂₇×C₁₄₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₉×C₁₄₉	C₂×C₃	1	1	yes	characteristic
5	C₂₇×C₁₄₉	C₂×C₃	1	3	yes	direct product factor
6	C₂×C₃²×C₁₄₉	C₉	1	1	yes	characteristic
7	C₂×C₉×C₁₄₉	C₉	1	2	yes	—
8	C₂×C₉×C₁₄₉	C₃²	1	1	yes	characteristic
9	C₃²×C₁₄₉	C₂×C₉	1	1	yes	characteristic
10	C₉×C₁₄₉	C₂×C₉	1	2	yes	—
11	C₉×C₁₄₉	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃×C₁₄₉	C₂₇	1	3	yes	direct product factor
13	C₂×C₃×C₁₄₉	C₃×C₉	1	1	yes	characteristic
14	C₃×C₁₄₉	C₂×C₂₇	1	3	yes	direct product factor
15	C₃×C₁₄₉	C₂×C₃×C₉	1	1	yes	characteristic
16	C₂×C₁₄₉	C₃×C₂₇	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₂₇	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₁₄₉	C₂×C₃×C₂₇	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₂₇	C₂×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃×C₉	C₃×C₁₄₉	1	1	yes	characteristic
21	C₂×C₂₇	C₃×C₁₄₉	1	3	yes	direct product factor
22	C₃×C₉	C₂×C₃×C₁₄₉	1	1	yes	characteristic
23	C₂₇	C₂×C₃×C₁₄₉	1	3	yes	direct product factor
24	C₂×C₃²	C₉×C₁₄₉	1	1	yes	characteristic
25	C₂×C₉	C₉×C₁₄₉	1	2	yes	—
26	C₂×C₉	C₃²×C₁₄₉	1	1	yes	characteristic
27	C₃²	C₂×C₉×C₁₄₉	1	1	yes	characteristic
28	C₉	C₂×C₉×C₁₄₉	1	2	yes	—
29	C₉	C₂×C₃²×C₁₄₉	1	1	yes	characteristic
30	C₂×C₃	C₂₇×C₁₄₉	1	3	yes	direct product factor
31	C₂×C₃	C₃×C₉×C₁₄₉	1	1	yes	characteristic
32	C₃	C₂×C₂₇×C₁₄₉	1	3	yes	direct product factor
33	C₃	C₂×C₃×C₉×C₁₄₉	1	1	yes	characteristic
34	C₂	C₃×C₂₇×C₁₄₉	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₉	C₂×C₃²×C₁₄₉
socle, prime radical	C₂×C₃²×C₁₄₉	C₉
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₇×C₁₄₉	C₃	direct (N × H)
3. C₃×C₂₇×C₁₄₉	C₂	direct (N × H)
5. C₂₇×C₁₄₉	C₂×C₃	direct (N × H)
12. C₂×C₃×C₁₄₉	C₂₇	direct (N × H)
14. C₃×C₁₄₉	C₂×C₂₇	direct (N × H)
16. C₂×C₁₄₉	C₃×C₂₇	direct (N × H)
17. C₂×C₃×C₂₇	C₁₄₉	direct (N × H)
18. C₁₄₉	C₂×C₃×C₂₇	direct (N × H)
19. C₃×C₂₇	C₂×C₁₄₉	direct (N × H)
21. C₂×C₂₇	C₃×C₁₄₉	direct (N × H)
23. C₂₇	C₂×C₃×C₁₄₉	direct (N × H)
30. C₂×C₃	C₂₇×C₁₄₉	direct (N × H)
32. C₃	C₂×C₂₇×C₁₄₉	direct (N × H)
34. C₂	C₃×C₂₇×C₁₄₉	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×C₃×C₉×C₁₄₉	3
C₂×C₂₇×C₁₄₉	3
C₃×C₂₇×C₁₄₉	2
C₂×C₃×C₂₇	149

Subgroups — C2×C3×C27×C149 #72201429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₂₇×C₁₄₉ #72201429