Subgroups — C₇⋊(C₉⋊#89137) #42117374

Order 27468.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×D₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#89137)	—	3	1	no	maximal
3	C₇×C₉×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₇×D₁₀₉	D₃	1	1	yes	characteristic
5	C₉⋊#89137	—	7	1	no	maximal, Hall
6	C₇⋊#89137	—	9	1	no	Hall
7	C₃×C₇×C₁₀₉	Dic₃	1	1	yes	characteristic
8	C₉×D₁₀₉	D₇	1	1	yes	characteristic
9	C₇×D₁₀₉	D₉	1	1	yes	characteristic
10	C₃⋊#89137	—	21	1	no	—
11	C₉×C₁₀₉	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₇×C₁₀₉	Dic₉	1	1	yes	characteristic, complemented, Hall
13	C₃×D₁₀₉	D₂₁	1	1	yes	characteristic
14	#89137	—	63	1	no	Hall
15	C₃×C₁₀₉	Dic₂₁	1	1	yes	characteristic
16	Dic₆₃	—	109	1	no	maximal, Hall
17	D₁₀₉	D₆₃	1	1	yes	characteristic
18	C₂×C₇×C₉	—	109	1	no	—
19	C₁₀₉	Dic₆₃	1	1	yes	characteristic, complemented, Sylow
20	Dic₂₁	—	327	1	no	—
21	C₇×C₉	#89137	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇	—	109	1	no	—
23	Dic₉	—	763	1	no	Hall
24	Dic₇	—	981	1	no	Hall
25	C₃×C₇	C₃⋊#89137	1	1	yes	characteristic
26	C₂×C₉	—	109	1	no	—
27	C₂×C₇	—	109	1	no	—
28	Dic₃	—	2289	1	no	—
29	C₉	C₇⋊#89137	1	1	yes	characteristic, complemented, Sylow
30	C₇	C₉⋊#89137	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	109	1	no	—
32	C₄	—	6867	1	no	Sylow
33	C₃	C₃⋊(C₇⋊#89137)	1	1	yes	characteristic
34	C₂	—	109	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₇×C₉×C₁₀₉	C₄
Frattini	C₃	C₃⋊(C₇⋊#89137)
socle	C₃×C₇×C₁₀₉	Dic₃
prime radical	C₃×C₇×D₁₀₉	D₃
cosocle	C₇×C₉×D₁₀₉	C₂
LCS	G ▷ C₇×C₉×C₁₀₉
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.