Subgroups — C₆₁×#6875 #28414976

Order 14823.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₆₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₆₁×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉×C₆₁	—	3	1	no	—
5	C₃×C₉×C₆₁	C₃²	1	1	yes	characteristic
6	C₂₇×C₆₁	—	3	2	no	—
7	C₂₇×C₆₁	C₉	1	3	yes	complemented
8	C₃²×C₆₁	3₋¹⁺²	1	1	yes	characteristic
9	C₉×C₆₁	—	9	1	no	—
10	C₉×C₆₁	C₃×C₉	1	1	yes	characteristic
11	C₉×C₆₁	3₋¹⁺²	1	2	yes	—
12	#6875	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×C₆₁	—	3	1	no	—
14	C₃×C₆₁	C₉⋊C₉	1	1	yes	characteristic
15	C₂₇⋊C₃	C₃×C₆₁	1	2	yes	—
16	C₂₇⋊C₃	C₃×C₆₁	1	1	yes	characteristic
17	C₉⋊C₉	C₃×C₆₁	1	1	yes	characteristic
18	C₆₁	#6875	1	1	yes	characteristic, direct product factor, Sylow
19	C₃×C₉	—	3	1	no	—
20	C₃×C₉	C₃²×C₆₁	1	1	yes	characteristic
21	C₂₇	—	3	2	no	—
22	C₂₇	C₉×C₆₁	1	3	yes	complemented
23	C₃²	3₋¹⁺²×C₆₁	1	1	yes	characteristic
24	C₉	—	9	1	no	—
25	C₉	C₃×C₉×C₆₁	1	1	yes	characteristic
26	C₉	3₋¹⁺²×C₆₁	1	2	yes	—
27	C₃	—	3	1	no	—
28	C₃	C₆₁×C₉⋊C₉	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.