Subgroups — #37555912

Order 23571.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₉₇⋊C₉)⋊C₉	C₃	1	8	yes	maximal, complemented
2	(C₃×C₉₇⋊C₃)⋊C₉	C₃	1	4	yes	maximal
3	C₉²×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₉₇⋊C₃	C₃²	1	1	yes	characteristic
5	C₃×C₉₇⋊C₉	C₃²	1	8	yes	—
6	C₃×C₉×C₉₇	C₃²	1	4	yes	—
7	C₃²×C₉₇	C₃³	1	1	yes	characteristic
8	C₃×C₉₇⋊C₃	—	3	4	no	—
9	C₉×C₉₇	—	3	4	no	—
10	C₉₇⋊C₉	—	3	8	no	—
11	C₃×C₉₇	#737	1	4	yes	—
12	C₉₇⋊C₃	—	9	1	no	—
13	#6898	—	97	1	no	maximal, Sylow
14	C₉₇	#6898	1	1	yes	characteristic, complemented, Sylow
15	C₉⋊C₉	—	97	8	no	—
16	C₃²⋊C₉	—	97	4	no	—
17	C₉²	C₉₇⋊C₃	1	1	yes	characteristic, complemented
18	C₃³	—	97	1	no	—
19	C₃×C₉	—	97	8	no	—
20	C₃×C₉	C₃×C₉₇⋊C₃	1	4	yes	—
21	C₃²	—	291	4	no	—
22	C₃²	C₃²×C₉₇⋊C₃	1	1	yes	characteristic
23	C₉	—	3	4	no	—
24	C₉	—	291	8	no	—
25	C₃	—	873	1	no	—
26	C₃	#21463377	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.