Subgroups — #11765621

Order 1134.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10588037	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃⋊D₆₃	C₃	1	1	yes	maximal, characteristic, complemented
3	#67369	—	3	1	no	maximal
4	C₃×C₇×C₉	C₂×C₃	1	1	yes	characteristic, complemented
5	C₇⋊H(3,𝔽₃)	D₃	1	1	yes	characteristic
6	#4430	—	2	1	no	—
7	#4177	—	7	1	no	maximal, Hall
8	C₃⋊D₂₁	—	3	1	no	—
9	C₃⋊AGL(1,𝔽₇)	—	9	1	no	—
10	D₆₃	—	9	1	no	—
11	#731	—	7	1	no	Sylow
12	C₃²×C₇	C₃×D₃	1	1	yes	characteristic
13	C₃×ΓL(1,𝔽₈)	—	3	1	no	—
14	C₇×C₉	—	3	1	no	—
15	C₇⋊C₉	—	6	1	no	—
16	C₃⋊D₉	—	7	1	no	—
17	(C₃⋊D₃)⋊C₃	—	21	1	no	—
18	D₂₁	—	9	1	no	—
19	D₂₁	—	27	1	no	—
20	AGL(1,𝔽₇)	—	27	1	no	—
21	3₋¹⁺²	—	14	1	no	—
22	H(3,𝔽₃)	—	7	1	no	—
23	C₃×C₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
24	C₃×C₇	—	3	1	no	—
25	C₃×C₇	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
26	ΓL(1,𝔽₈)	—	9	1	no	—
27	C₃⋊D₃	—	21	1	no	—
28	C₃×D₃	—	63	1	no	—
29	D₉	—	63	1	no	—
30	D₇	—	27	1	no	Hall
31	C₃²	—	21	1	no	—
32	C₃²	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic
33	C₉	—	3	1	no	—
34	C₉	—	42	1	no	—
35	C₇	#4177	1	1	yes	characteristic, complemented, Sylow
36	C₂×C₃	—	189	1	no	—
37	D₃	—	63	1	no	—
38	D₃	—	189	1	no	—
39	C₃	—	3	1	no	—
40	C₃	—	63	1	no	—
41	C₃	#67369	1	1	yes	characteristic
42	C₂	—	189	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₃×C₇×C₉	C₂×C₃
Frattini	C₃²	C₃⋊AGL(1,𝔽₇)
socle	C₃×C₇	(C₃⋊D₃)⋊C₃
LCS	G ▷ C₃×C₇×C₉
UCS	C₁

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

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