Subgroups — C₈₁×#66526 #41008341

Order 26973.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₃₇⋊C₃)⋊C₈₁	C₃	1	2	yes	maximal
2	C₂₇×#66526	C₃	1	1	yes	maximal, characteristic
3	C₈₁×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
4	(C₃₇⋊C₃)⋊C₂₇	C₉	1	2	yes	—
5	C₉×#66526	C₉	1	1	yes	characteristic
6	#15688534	C₉	1	6	yes	complemented
7	C₂₇×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
8	#15688500	C₉	1	2	yes	complemented
9	C₃₇×C₈₁	C₉	1	1	yes	characteristic, complemented
10	C₃×#66526	C₂₇	1	3	yes	—
11	C₉×C₃₇⋊C₃	C₃×C₉	1	1	yes	characteristic
12	#11758603	C₂₇	1	6	yes	—
13	C₂₇×C₃₇	C₃×C₉	1	1	yes	characteristic
14	#11758601	C₃×C₉	1	2	yes	—
15	C₉×C₈₁	—	37	1	no	maximal, Sylow
16	C₃×C₃₇⋊C₃	C₃×C₂₇	1	1	yes	characteristic
17	#66526	C₈₁	1	9	yes	direct product factor
18	C₉×C₃₇	C₉²	1	1	yes	characteristic
19	#66524	C₃×C₂₇	1	2	yes	—
20	C₃×C₈₁	—	37	2	no	—
21	C₃×C₈₁	—	37	1	no	—
22	C₉×C₂₇	—	37	1	no	—
23	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
24	C₃₇⋊C₃	C₃×C₈₁	1	3	yes	—
25	C₃×C₂₇	—	37	2	no	—
26	C₃×C₂₇	—	37	1	no	—
27	C₉²	—	37	1	no	—
28	C₈₁	—	37	6	no	—
29	C₈₁	—	37	2	no	—
30	C₈₁	#66526	1	1	yes	characteristic, direct product factor
31	C₃₇	C₉×C₈₁	1	1	yes	characteristic, complemented, Sylow
32	C₃×C₉	—	37	3	no	—
33	C₃×C₉	—	37	1	no	—
34	C₂₇	—	37	6	no	—
35	C₂₇	—	37	2	no	—
36	C₂₇	C₃×#66526	1	1	yes	characteristic
37	C₃²	—	37	1	no	—
38	C₉	—	37	9	no	—
39	C₉	—	37	2	no	—
40	C₉	C₉×#66526	1	1	yes	characteristic
41	C₃	—	37	3	no	—
42	C₃	C₂₇×#66526	1	1	yes	characteristic

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.