Subgroups — C₄₇×#6899 #26037708

Order 11421.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₄₇	C₃	1	1	yes	maximal, characteristic
2	C₄₇×C₉⋊C₉	C₃	1	6	yes	maximal, complemented
3	C₄₇×C₉⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₄₇×C₃²⋊C₉	C₃	1	3	yes	maximal
5	C₉²×C₄₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₄₇	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₄₇	—	3	3	no	—
8	C₃×C₉×C₄₇	C₃²	1	3	yes	—
9	C₃×C₉×C₄₇	C₃²	1	6	yes	—
10	C₃×C₉×C₄₇	C₃²	1	2	yes	—
11	C₃×C₉×C₄₇	C₃²	1	1	yes	characteristic
12	C₃²×C₄₇	—	3	1	no	—
13	C₃²×C₄₇	—	3	3	no	—
14	C₃²×C₄₇	C₃³	1	1	yes	characteristic
15	C₉×C₄₇	—	3	2	no	—
16	C₉×C₄₇	—	3	3	no	—
17	C₉×C₄₇	—	3	6	no	—
18	C₉×C₄₇	3₋¹⁺²	1	3	yes	—
19	#6899	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₃×C₄₇	—	9	1	no	—
21	C₃×C₄₇	C₃×3₋¹⁺²	1	1	yes	characteristic
22	C₃×C₄₇	#737	1	3	yes	—
23	C₃×3₋¹⁺²	C₃×C₄₇	1	1	yes	characteristic
24	C₉⋊C₉	C₃×C₄₇	1	6	yes	complemented
25	C₉⋊C₉	C₃×C₄₇	1	2	yes	complemented
26	C₃²⋊C₉	C₃×C₄₇	1	3	yes	—
27	C₉²	C₃×C₄₇	1	1	yes	characteristic, complemented
28	C₄₇	#6899	1	1	yes	characteristic, direct product factor, Sylow
29	C₃³	C₃²×C₄₇	1	1	yes	characteristic
30	3₋¹⁺²	—	3	3	no	—
31	C₃×C₉	C₃²×C₄₇	1	3	yes	—
32	C₃×C₉	C₃²×C₄₇	1	6	yes	—
33	C₃×C₉	C₃²×C₄₇	1	2	yes	—
34	C₃×C₉	C₃²×C₄₇	1	1	yes	characteristic
35	C₃²	—	3	1	no	—
36	C₃²	—	3	3	no	—
37	C₃²	C₃³×C₄₇	1	1	yes	characteristic
38	C₉	—	3	2	no	—
39	C₉	—	3	3	no	—
40	C₉	—	3	6	no	—
41	C₉	3₋¹⁺²×C₄₇	1	3	yes	—
42	C₃	—	9	1	no	—
43	C₃	C₃×3₋¹⁺²×C₄₇	1	1	yes	characteristic
44	C₃	C₄₇×#737	1	3	yes	—

	subgroup	G/H
center, socle	C₃²×C₄₇	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₄₇
prime radical	C₃³×C₄₇	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×C₉⋊C₉	C₃	semidirect
3. C₄₇×C₉⋊C₉	C₃	semidirect
5. C₉²×C₄₇	C₃	semidirect
19. #6899	C₄₇	direct (N × H)
24. C₉⋊C₉	C₃×C₄₇	semidirect
25. C₉⋊C₉	C₃×C₄₇	semidirect
27. C₉²	C₃×C₄₇	semidirect
28. C₄₇	#6899	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×3₋¹⁺²×C₄₇	3
C₄₇×C₉⋊C₉	3
C₄₇×C₃²⋊C₉	3
C₉²×C₄₇	3
#6899	47

Subgroups — C47×#6899 #26037708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#6899 #26037708