Subgroups — #37555923

Order 23571.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14579756	C₃	1	4	yes	maximal
2	#21463351	C₃	1	8	yes	maximal, complemented
3	C₉²×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₉₇⋊C₃	C₃²	1	1	yes	characteristic
5	#14579756	—	3	12	no	—
6	C₃×C₉₇⋊C₉	C₃²	1	8	yes	—
7	C₃×C₉×C₉₇	C₃²	1	4	yes	—
8	C₃²×C₉₇	C₃³	1	1	yes	characteristic
9	C₃×C₉₇⋊C₃	—	3	4	no	—
10	C₉×C₉₇	3₋¹⁺²	1	12	yes	complemented
11	C₉₇⋊C₉	—	3	8	no	—
12	C₃×C₉₇	C₃×3₋¹⁺²	1	4	yes	—
13	C₉₇⋊C₃	—	9	1	no	—
14	#6900	—	97	1	no	maximal, Sylow
15	C₉₇	#6900	1	1	yes	characteristic, complemented, Sylow
16	C₃×3₋¹⁺²	—	97	4	no	—
17	C₉⋊C₉	—	97	8	no	—
18	C₉²	C₉₇⋊C₃	1	1	yes	characteristic, complemented
19	C₃³	—	97	1	no	—
20	3₋¹⁺²	—	291	12	no	—
21	C₃×C₉	—	97	8	no	—
22	C₃×C₉	C₃×C₉₇⋊C₃	1	4	yes	—
23	C₃²	—	291	4	no	—
24	C₃²	C₃²×C₉₇⋊C₃	1	1	yes	characteristic
25	C₉	—	291	8	no	—
26	C₉	#14579756	1	12	yes	complemented
27	C₃	—	873	1	no	—
28	C₃	C₃×#14579756	1	4	yes	—

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.