Subgroups — C₄₇×#10624541 #46804182

Order 34263.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#6880	C₃	1	3	yes	maximal
2	C₄₇×#6864	C₃	1	1	yes	maximal, characteristic
3	C₄₇×#733	—	3	3	no	—
4	C₃×C₂₇×C₄₇	—	3	1	no	—
5	C₉²×C₄₇	C₃²	1	1	yes	characteristic
6	3₋¹⁺²×C₄₇	—	9	3	no	—
7	C₃×C₉×C₄₇	—	3	1	no	—
8	C₃×C₉×C₄₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₂₇×C₄₇	—	3	3	no	—
10	#10624541	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃²×C₄₇	#732	1	1	yes	characteristic
12	C₉×C₄₇	—	3	1	no	—
13	C₉×C₄₇	—	9	1	no	—
14	C₉×C₄₇	—	27	3	no	—
15	#6880	C₃×C₄₇	1	3	yes	—
16	#6864	C₃×C₄₇	1	1	yes	characteristic
17	C₃×C₄₇	—	3	1	no	—
18	C₃×C₄₇	#6879	1	1	yes	characteristic
19	#733	—	3	3	no	—
20	C₃×C₂₇	—	3	1	no	—
21	C₉²	C₃²×C₄₇	1	1	yes	characteristic
22	C₄₇	#10624541	1	1	yes	characteristic, direct product factor, Sylow
23	3₋¹⁺²	—	9	3	no	—
24	C₃×C₉	—	3	1	no	—
25	C₃×C₉	H(3,𝔽₃)×C₄₇	1	1	yes	characteristic
26	C₂₇	—	3	3	no	—
27	C₃²	C₄₇×#732	1	1	yes	characteristic
28	C₉	—	3	1	no	—
29	C₉	—	9	1	no	—
30	C₉	—	27	3	no	—
31	C₃	—	3	1	no	—
32	C₃	C₄₇×#6879	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₄₇	#6879
commutator, Frattini, cosocle	C₉²	C₃²×C₄₇
prime radical	C₃²×C₄₇	#732
LCS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄₇ ◁ C₃²×C₄₇ ◁ C₃×C₉×C₄₇ ◁ C₉²×C₄₇ ◁ G

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

N	H ≅ G/N	type
10. #10624541	C₄₇	direct (N × H)
22. C₄₇	#10624541	direct (N × H)

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