Subgroups — #37555813

Order 23571.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21463357	C₃	1	2	yes	maximal
2	#21463351	C₃	1	1	yes	maximal, characteristic
3	C₂₇⋊C₃×C₉₇	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉₇⋊C₉	—	3	1	no	—
5	C₉₇⋊C₂₇	—	3	2	no	—
6	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
7	C₂₇×C₉₇	C₉	1	3	yes	complemented
8	C₃²×C₉₇	3₋¹⁺²	1	1	yes	characteristic
9	C₉×C₉₇	C₃×C₉	1	1	yes	characteristic
10	C₉×C₉₇	3₋¹⁺²	1	2	yes	—
11	C₉₇⋊C₉	—	9	1	no	—
12	C₃×C₉₇	—	3	1	no	—
13	C₃×C₉₇	C₉⋊C₉	1	1	yes	characteristic
14	#6875	—	97	1	no	maximal, Sylow
15	C₉₇	#6875	1	1	yes	characteristic, complemented, Sylow
16	C₂₇⋊C₃	—	97	2	no	—
17	C₂₇⋊C₃	C₉₇⋊C₃	1	1	yes	characteristic
18	C₉⋊C₉	—	97	1	no	—
19	C₃×C₉	—	291	1	no	—
20	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
21	C₂₇	—	291	2	no	—
22	C₂₇	C₉₇⋊C₉	1	3	yes	complemented
23	C₃²	#14579756	1	1	yes	characteristic
24	C₉	—	873	1	no	—
25	C₉	C₃×C₉₇⋊C₉	1	1	yes	characteristic
26	C₉	#14579756	1	2	yes	—
27	C₃	—	3	1	no	—
28	C₃	#21463351	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.