Subgroups — #37555899

Order 23571.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₉₇⋊C₉)⋊C₉	C₃	1	9	yes	maximal, complemented
2	C₃²⋊(C₉₇⋊C₉)	C₃	1	3	yes	maximal
3	C₃²×C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉₇⋊C₉	C₃²	1	9	yes	—
5	C₃³×C₉₇	C₃²	1	1	yes	characteristic
6	C₃×C₉×C₉₇	—	3	3	no	—
7	C₃×C₉×C₉₇	C₃²	1	3	yes	—
8	C₃²×C₉₇	—	3	3	no	—
9	C₃²×C₉₇	3₋¹⁺²	1	3	yes	—
10	C₃²×C₉₇	C₃³	1	1	yes	characteristic
11	C₉×C₉₇	—	3	3	no	—
12	C₉₇⋊C₉	—	3	9	no	—
13	C₃×C₉₇	—	3	3	no	—
14	C₃×C₉₇	C₃×3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉₇	#737	1	3	yes	—
16	#6895	—	97	1	no	maximal, Sylow
17	C₉₇	#6895	1	1	yes	characteristic, complemented, Sylow
18	C₃²×C₉	C₉₇⋊C₃	1	1	yes	characteristic
19	C₉⋊C₉	—	97	9	no	—
20	C₃²⋊C₉	—	97	3	no	—
21	C₃³	C₃×C₉₇⋊C₃	1	1	yes	characteristic
22	C₃×C₉	—	3	3	no	—
23	C₃×C₉	—	97	9	no	—
24	C₃×C₉	C₃×C₉₇⋊C₃	1	3	yes	—
25	C₃²	—	3	3	no	—
26	C₃²	#14579757	1	3	yes	—
27	C₃²	C₃²×C₉₇⋊C₃	1	1	yes	characteristic
28	C₉	—	3	3	no	—
29	C₉	—	291	9	no	—
30	C₃	—	3	3	no	—
31	C₃	C₃×#14579757	1	1	yes	characteristic
32	C₃	#21463377	1	3	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. (C₉₇⋊C₉)⋊C₉	C₃	semidirect
17. C₉₇	#6895	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.