Subgroups — C₉×#401 #10588955

Order 576.

177 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#95	C₂	1	7	yes	maximal
2	C₃×#401	C₃	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₉	C₂²	1	7	yes	—
4	C₃×#95	C₂×C₃	1	7	yes	—
5	C₂³×C₉	C₂³	1	1	yes	characteristic
6	C₂×C₄×C₉	—	2	21	no	—
7	#401	C₉	1	1	yes	characteristic, direct product factor, Sylow
8	C₂²×C₃×C₄	C₂²×C₃	1	7	yes	—
9	C₂²×C₉	#41	1	7	yes	—
10	C₄×C₉	—	4	7	no	—
11	#95	C₂×C₉	1	7	yes	—
12	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
13	C₂×C₃×C₄	—	2	21	no	—
14	C₂×C₉	#126	1	7	yes	—
15	C₂²×C₄	C₂²×C₉	1	7	yes	—
16	C₂²×C₃	C₃×#41	1	7	yes	—
17	C₃×C₄	—	4	7	no	—
18	C₉	#401	1	1	yes	characteristic, direct product factor, Sylow
19	C₂³	C₂³×C₉	1	1	yes	characteristic
20	C₂×C₄	—	2	21	no	—
21	C₂×C₃	C₃×#126	1	7	yes	—
22	C₂²	C₉×#41	1	7	yes	—
23	C₄	—	4	7	no	—
24	C₃	C₃×#401	1	1	yes	characteristic
25	C₂	C₉×#126	1	7	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂³
commutator	C₂³	C₂³×C₉
Frattini, socle, prime radical, cosocle	C₂³×C₃	C₂³×C₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₉ ◁ G

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

N	H ≅ G/N	type
7. #401	C₉	direct (N × H)
18. C₉	#401	direct (N × H)

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

subgroup	index
C₉×#95	2
C₃×#401	3