Subgroups — C₄×C₉²×C₃₁ #72188708

Order 10044.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉²×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₉×C₃₁	C₃	1	4	yes	maximal
3	C₉²×C₃₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₉×C₃₁	C₂×C₃	1	4	yes	—
5	C₃²×C₄×C₃₁	C₃²	1	1	yes	characteristic
6	C₄×C₉×C₃₁	C₉	1	12	yes	direct product factor
7	C₃×C₉×C₃₁	C₃×C₄	1	4	yes	—
8	C₂×C₃²×C₃₁	C₂×C₃²	1	1	yes	characteristic
9	C₂×C₉×C₃₁	C₂×C₉	1	12	yes	—
10	C₃×C₄×C₃₁	C₃×C₉	1	4	yes	—
11	C₄×C₉²	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃²×C₃₁	C₃²×C₄	1	1	yes	characteristic
13	C₉×C₃₁	C₄×C₉	1	12	yes	direct product factor
14	C₂×C₃×C₃₁	C₂×C₃×C₉	1	4	yes	—
15	C₂×C₉²	C₂×C₃₁	1	1	yes	characteristic
16	C₄×C₃₁	C₉²	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₄×C₉	C₃×C₃₁	1	4	yes	—
18	C₃×C₃₁	C₃×C₄×C₉	1	4	yes	—
19	C₉²	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃₁	C₂×C₉²	1	1	yes	characteristic
21	C₂×C₃×C₉	C₂×C₃×C₃₁	1	4	yes	—
22	C₃²×C₄	C₃²×C₃₁	1	1	yes	characteristic
23	C₄×C₉	C₉×C₃₁	1	12	yes	direct product factor
24	C₃₁	C₄×C₉²	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₉	C₃×C₄×C₃₁	1	4	yes	—
26	C₂×C₃²	C₂×C₃²×C₃₁	1	1	yes	characteristic
27	C₂×C₉	C₂×C₉×C₃₁	1	12	yes	—
28	C₃×C₄	C₃×C₉×C₃₁	1	4	yes	—
29	C₃²	C₃²×C₄×C₃₁	1	1	yes	characteristic
30	C₉	C₄×C₉×C₃₁	1	12	yes	direct product factor
31	C₂×C₃	C₂×C₃×C₉×C₃₁	1	4	yes	—
32	C₄	C₉²×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₉×C₃₁	1	4	yes	—
34	C₂	C₂×C₉²×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃²	C₂×C₃²×C₃₁
socle, prime radical	C₂×C₃²×C₃₁	C₂×C₃²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉²×C₃₁	C₄	direct (N × H)
6. C₄×C₉×C₃₁	C₉	direct (N × H)
11. C₄×C₉²	C₃₁	direct (N × H)
13. C₉×C₃₁	C₄×C₉	direct (N × H)
16. C₄×C₃₁	C₉²	direct (N × H)
19. C₉²	C₄×C₃₁	direct (N × H)
23. C₄×C₉	C₉×C₃₁	direct (N × H)
24. C₃₁	C₄×C₉²	direct (N × H)
30. C₉	C₄×C₉×C₃₁	direct (N × H)
32. C₄	C₉²×C₃₁	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×C₉²×C₃₁	2
C₃×C₄×C₉×C₃₁	3
C₄×C₉²	31

Subgroups — C4×C92×C31 #72188708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉²×C₃₁ #72188708