Subgroups — C₃×C₄₉×C₈₁ #72190332

Order 11907.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₇×C₄₉	C₃	1	1	yes	maximal, characteristic
2	C₄₉×C₈₁	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₇×C₈₁	C₇	1	1	yes	maximal, characteristic
4	C₃×C₉×C₄₉	C₉	1	1	yes	characteristic
5	C₂₇×C₄₉	C₉	1	2	yes	—
6	C₂₇×C₄₉	C₃²	1	1	yes	characteristic
7	C₃×C₇×C₂₇	C₃×C₇	1	1	yes	characteristic
8	C₇×C₈₁	C₃×C₇	1	3	yes	—
9	C₃²×C₄₉	C₂₇	1	1	yes	characteristic
10	C₉×C₄₉	C₂₇	1	2	yes	—
11	C₉×C₄₉	C₃×C₉	1	1	yes	characteristic
12	C₃×C₈₁	C₄₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₇×C₉	C₇×C₉	1	1	yes	characteristic
14	C₇×C₂₇	C₇×C₉	1	2	yes	—
15	C₇×C₂₇	C₃²×C₇	1	1	yes	characteristic
16	C₃×C₄₉	C₈₁	1	3	yes	direct product factor
17	C₃×C₄₉	C₃×C₂₇	1	1	yes	characteristic
18	C₃×C₂₇	C₃×C₄₉	1	1	yes	characteristic
19	C₈₁	C₃×C₄₉	1	3	yes	direct product factor
20	C₃²×C₇	C₇×C₂₇	1	1	yes	characteristic
21	C₇×C₉	C₇×C₂₇	1	2	yes	—
22	C₇×C₉	C₃×C₇×C₉	1	1	yes	characteristic
23	C₄₉	C₃×C₈₁	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×C₉	C₉×C₄₉	1	1	yes	characteristic
25	C₂₇	C₉×C₄₉	1	2	yes	—
26	C₂₇	C₃²×C₄₉	1	1	yes	characteristic
27	C₃×C₇	C₇×C₈₁	1	3	yes	—
28	C₃×C₇	C₃×C₇×C₂₇	1	1	yes	characteristic
29	C₃²	C₂₇×C₄₉	1	1	yes	characteristic
30	C₉	C₂₇×C₄₉	1	2	yes	—
31	C₉	C₃×C₉×C₄₉	1	1	yes	characteristic
32	C₇	C₃×C₇×C₈₁	1	1	yes	characteristic
33	C₃	C₄₉×C₈₁	1	3	yes	direct product factor
34	C₃	C₃×C₂₇×C₄₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₇×C₂₇	C₃²×C₇
socle, prime radical	C₃²×C₇	C₇×C₂₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₉×C₈₁	C₃	direct (N × H)
12. C₃×C₈₁	C₄₉	direct (N × H)
16. C₃×C₄₉	C₈₁	direct (N × H)
19. C₈₁	C₃×C₄₉	direct (N × H)
23. C₄₉	C₃×C₈₁	direct (N × H)
33. C₃	C₄₉×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
C₃×C₂₇×C₄₉	3
C₄₉×C₈₁	3
C₃×C₇×C₈₁	7

Subgroups — C3×C49×C81 #72190332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄₉×C₈₁ #72190332