Subgroups — #37555834

Order 23571.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21463367	C₃	1	1	yes	maximal, characteristic, complemented
2	#21463365	C₃	1	2	yes	maximal, complemented
3	C₉⋊C₉×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	#14579757	—	3	1	no	—
5	C₃²⋊(C₉₇⋊C₃)	—	3	2	no	—
6	C₃×C₉×C₉₇	—	3	1	no	—
7	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
8	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₃×C₉₇⋊C₃	—	9	2	no	—
10	C₉×C₉₇	—	3	1	no	—
11	C₉×C₉₇	—	9	1	no	—
12	C₉₇⋊C₉	—	9	1	no	—
13	C₃×C₉₇	—	3	1	no	—
14	C₃×C₉₇	#732	1	1	yes	characteristic
15	C₉₇⋊C₃	—	27	2	no	—
16	#6881	—	97	1	no	maximal, Sylow
17	C₉₇	#6881	1	1	yes	characteristic, complemented, Sylow
18	#733	—	97	1	no	—
19	#732	—	97	2	no	—
20	C₉⋊C₉	C₉₇⋊C₃	1	1	yes	characteristic, complemented
21	3₋¹⁺²	—	291	1	no	—
22	H(3,𝔽₃)	—	291	2	no	—
23	C₃×C₉	—	3	1	no	—
24	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
25	C₃²	—	873	2	no	—
26	C₃²	C₃²⋊(C₉₇⋊C₃)	1	1	yes	characteristic
27	C₉	—	3	1	no	—
28	C₉	—	9	1	no	—
29	C₉	—	873	1	no	—
30	C₃	—	3	1	no	—
31	C₃	—	2619	2	no	—
32	C₃	#21463365	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.