Subgroups — C₂×C₄×C₉×C₃₀₇ #72199587

Order 22104.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₃₀₇	C₃	1	1	yes	maximal, characteristic
2	C₂²×C₉×C₃₀₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₉×C₃₀₇	C₂	1	2	yes	maximal, direct product factor
4	C₂×C₉×C₃₀₇	C₄	1	2	yes	direct product factor
5	C₂×C₉×C₃₀₇	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₃₀₇	C₂×C₃	1	1	yes	characteristic
7	C₃×C₄×C₃₀₇	C₂×C₃	1	2	yes	—
8	C₉×C₃₀₇	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₄×C₃₀₇	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₃₀₇	C₃×C₄	1	2	yes	—
11	C₂×C₃×C₃₀₇	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃₀₇	C₂×C₉	1	1	yes	characteristic
13	C₄×C₃₀₇	C₂×C₉	1	2	yes	direct product factor
14	C₃×C₃₀₇	C₂×C₃×C₄	1	1	yes	characteristic
15	C₂×C₃₀₇	C₄×C₉	1	2	yes	direct product factor
16	C₂×C₃₀₇	C₂²×C₉	1	1	yes	characteristic
17	C₃₀₇	C₂×C₄×C₉	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₄×C₉	C₃₀₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₉	C₂×C₃₀₇	1	1	yes	characteristic
20	C₄×C₉	C₂×C₃₀₇	1	2	yes	direct product factor
21	C₂×C₃×C₄	C₃×C₃₀₇	1	1	yes	characteristic
22	C₂×C₉	C₄×C₃₀₇	1	2	yes	direct product factor
23	C₂×C₉	C₂²×C₃₀₇	1	1	yes	characteristic
24	C₂²×C₃	C₂×C₃×C₃₀₇	1	1	yes	characteristic
25	C₃×C₄	C₂×C₃×C₃₀₇	1	2	yes	—
26	C₉	C₂×C₄×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₄	C₉×C₃₀₇	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	C₃×C₄×C₃₀₇	1	2	yes	—
29	C₂×C₃	C₂²×C₃×C₃₀₇	1	1	yes	characteristic
30	C₂²	C₂×C₉×C₃₀₇	1	1	yes	characteristic
31	C₄	C₂×C₉×C₃₀₇	1	2	yes	direct product factor
32	C₃	C₂×C₃×C₄×C₃₀₇	1	1	yes	characteristic
33	C₂	C₄×C₉×C₃₀₇	1	2	yes	direct product factor
34	C₂	C₂²×C₉×C₃₀₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂²×C₃×C₃₀₇
socle, prime radical	C₂²×C₃×C₃₀₇	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₉×C₃₀₇	C₂	direct (N × H)
4. C₂×C₉×C₃₀₇	C₄	direct (N × H)
8. C₉×C₃₀₇	C₂×C₄	direct (N × H)
9. C₂×C₄×C₃₀₇	C₉	direct (N × H)
13. C₄×C₃₀₇	C₂×C₉	direct (N × H)
15. C₂×C₃₀₇	C₄×C₉	direct (N × H)
17. C₃₀₇	C₂×C₄×C₉	direct (N × H)
18. C₂×C₄×C₉	C₃₀₇	direct (N × H)
20. C₄×C₉	C₂×C₃₀₇	direct (N × H)
22. C₂×C₉	C₄×C₃₀₇	direct (N × H)
26. C₉	C₂×C₄×C₃₀₇	direct (N × H)
27. C₂×C₄	C₉×C₃₀₇	direct (N × H)
31. C₄	C₂×C₉×C₃₀₇	direct (N × H)
33. C₂	C₄×C₉×C₃₀₇	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×C₄×C₃₀₇	3
C₂²×C₉×C₃₀₇	2
C₄×C₉×C₃₀₇	2
C₂×C₄×C₉	307

Subgroups — C2×C4×C9×C307 #72199587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₉×C₃₀₇ #72199587