Subgroups — C₃×C₁₁×C₇₂₉ #72201331

Order 24057.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₁×C₂₄₃	C₃	1	1	yes	maximal, characteristic
2	C₁₁×C₇₂₉	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₁₁×C₈₁	C₉	1	1	yes	characteristic
4	C₁₁×C₂₄₃	C₉	1	2	yes	—
5	C₁₁×C₂₄₃	C₃²	1	1	yes	characteristic
6	C₃×C₇₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₃×C₁₁×C₂₇	C₂₇	1	1	yes	characteristic
8	C₁₁×C₈₁	C₂₇	1	2	yes	—
9	C₁₁×C₈₁	C₃×C₉	1	1	yes	characteristic
10	C₃×C₂₄₃	C₃×C₁₁	1	1	yes	characteristic
11	C₇₂₉	C₃×C₁₁	1	3	yes	direct product factor
12	C₃×C₉×C₁₁	C₈₁	1	1	yes	characteristic
13	C₁₁×C₂₇	C₈₁	1	2	yes	—
14	C₁₁×C₂₇	C₃×C₂₇	1	1	yes	characteristic
15	C₃×C₈₁	C₉×C₁₁	1	1	yes	characteristic
16	C₂₄₃	C₉×C₁₁	1	2	yes	—
17	C₂₄₃	C₃²×C₁₁	1	1	yes	characteristic
18	C₃²×C₁₁	C₂₄₃	1	1	yes	characteristic
19	C₉×C₁₁	C₂₄₃	1	2	yes	—
20	C₉×C₁₁	C₃×C₈₁	1	1	yes	characteristic
21	C₃×C₂₇	C₁₁×C₂₇	1	1	yes	characteristic
22	C₈₁	C₁₁×C₂₇	1	2	yes	—
23	C₈₁	C₃×C₉×C₁₁	1	1	yes	characteristic
24	C₃×C₁₁	C₇₂₉	1	3	yes	direct product factor
25	C₃×C₁₁	C₃×C₂₄₃	1	1	yes	characteristic
26	C₃×C₉	C₁₁×C₈₁	1	1	yes	characteristic
27	C₂₇	C₁₁×C₈₁	1	2	yes	—
28	C₂₇	C₃×C₁₁×C₂₇	1	1	yes	characteristic
29	C₁₁	C₃×C₇₂₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₃²	C₁₁×C₂₄₃	1	1	yes	characteristic
31	C₉	C₁₁×C₂₄₃	1	2	yes	—
32	C₉	C₃×C₁₁×C₈₁	1	1	yes	characteristic
33	C₃	C₁₁×C₇₂₉	1	3	yes	direct product factor
34	C₃	C₃×C₁₁×C₂₄₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₄₃	C₃²×C₁₁
socle, prime radical	C₃²×C₁₁	C₂₄₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×C₇₂₉	C₃	direct (N × H)
6. C₃×C₇₂₉	C₁₁	direct (N × H)
11. C₇₂₉	C₃×C₁₁	direct (N × H)
24. C₃×C₁₁	C₇₂₉	direct (N × H)
29. C₁₁	C₃×C₇₂₉	direct (N × H)
33. C₃	C₁₁×C₇₂₉	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×C₁₁×C₂₄₃	3
C₁₁×C₇₂₉	3
C₃×C₇₂₉	11

Subgroups — C3×C11×C729 #72201331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₁×C₇₂₉ #72201331