Subgroups — #11758603⋊C₂₇ #41008267

Order 26973.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11758603	C₃	1	1	yes	maximal, characteristic
2	C₉×#11758603	C₃	1	1	yes	maximal, characteristic
3	C₉×#11758603	C₃	1	1	yes	maximal, characteristic
4	C₂₇×#66524	C₃	1	1	yes	maximal, characteristic
5	C₃×#11758603	C₉	1	3	yes	—
6	C₃×#11758603	C₉	1	3	yes	—
7	C₃×#11758603	C₉	1	3	yes	—
8	C₃×#11758601	C₉	1	1	yes	characteristic
9	C₃×#11758601	C₉	1	1	yes	characteristic
10	C₉×#66524	C₃²	1	1	yes	characteristic
11	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
12	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
13	C₃×#66524	C₃×C₉	1	1	yes	characteristic
14	C₃×#66524	C₃×C₉	1	1	yes	characteristic
15	C₃×#66524	C₃×C₉	1	1	yes	characteristic
16	#11758603	—	3	3	no	—
17	#11758603	—	3	3	no	—
18	#11758603	C₂₇	1	9	yes	complemented
19	C₂₇×C₃₇	—	3	1	no	—
20	#11758601	—	3	1	no	—
21	#11758601	—	3	1	no	—
22	#10624443	—	37	1	no	maximal, Sylow
23	C₃²×C₃₇	C₉²	1	1	yes	characteristic
24	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
25	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
26	C₉×C₃₇	C₂₇⋊C₃	1	1	yes	characteristic
27	#66524	C₃×C₂₇	1	3	yes	—
28	#66524	C₂₇⋊C₃	1	3	yes	—
29	#66524	C₂₇⋊C₃	1	3	yes	—
30	C₉×C₂₇	—	37	1	no	—
31	C₉×C₂₇	—	37	1	no	—
32	C₉×C₂₇	—	37	1	no	—
33	C₉×C₂₇	—	37	1	no	—
34	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
35	C₃×C₃₇	#6864	1	1	yes	characteristic
36	C₃×C₃₇	#6864	1	1	yes	characteristic
37	C₃×C₃₇	#6864	1	1	yes	characteristic
38	C₃×C₂₇	—	37	3	no	—
39	C₃×C₂₇	—	37	3	no	—
40	C₃×C₂₇	—	37	3	no	—
41	C₃×C₂₇	—	37	1	no	—
42	C₃×C₂₇	—	37	1	no	—
43	C₃×C₂₇	#66526	1	1	yes	characteristic
44	C₉²	—	37	1	no	—
45	C₃₇	#10624443	1	1	yes	characteristic, complemented, Sylow
46	C₃×C₉	—	37	1	no	—
47	C₃×C₉	—	37	1	no	—
48	C₃×C₉	—	37	1	no	—
49	C₃×C₉	C₃×#66526	1	1	yes	characteristic
50	C₂₇	—	3	1	no	—
51	C₂₇	—	37	9	no	—
52	C₂₇	—	111	3	no	—
53	C₂₇	—	111	3	no	—
54	C₂₇	—	111	1	no	—
55	C₂₇	—	111	1	no	—
56	C₃²	C₉×#66526	1	1	yes	characteristic
57	C₉	—	37	3	no	—
58	C₉	—	37	3	no	—
59	C₉	—	37	3	no	—
60	C₉	#15688541	1	1	yes	characteristic
61	C₉	#15688542	1	1	yes	characteristic
62	C₉	#15688543	1	1	yes	characteristic
63	C₃	C₂₇×#66526	1	1	yes	characteristic
64	C₃	#22582686	1	1	yes	characteristic
65	C₃	#22582687	1	1	yes	characteristic
66	C₃	#22582688	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃×C₉	C₃×#66526
commutator	C₃×C₃₇	C₉×C₂₇
Fitting	C₃×C₂₇×C₃₇	C₉
socle, prime radical	C₃²×C₃₇	C₉²
cosocle	C₉×#66524	C₃²
hypercenter	C₃×C₂₇	#66526
hypocenter	C₃₇	#10624443
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇

Complements

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

N	H ≅ G/N	type
18. #11758603	C₂₇	semidirect
45. C₃₇	#10624443	semidirect

Maximal subgroups

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

subgroup	index
C₉×#11758603	3
C₂₇×#66524	3
#10624443	37

Subgroups — #11758603⋊C27 #41008267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #11758603⋊C₂₇ #41008267