Subgroups — #37555827

Order 23571.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21463365	C₃	1	2	yes	maximal, complemented
2	C₉×C₉₇⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	#732×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²⋊(C₉₇⋊C₃)	—	3	2	no	—
5	C₃×C₉₇⋊C₉	—	3	1	no	—
6	H(3,𝔽₃)×C₉₇	—	3	1	no	—
7	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
8	C₃²×C₉₇	—	9	1	no	—
9	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃×C₉₇⋊C₃	—	9	2	no	—
11	C₉×C₉₇	—	3	1	no	—
12	C₉₇⋊C₉	—	3	3	no	—
13	C₃×C₉₇	—	3	1	no	—
14	C₃×C₉₇	—	27	1	no	—
15	C₃×C₉₇	#732	1	1	yes	characteristic
16	C₉₇⋊C₃	—	27	2	no	—
17	#6879	—	97	1	no	maximal, Sylow
18	C₉₇	#6879	1	1	yes	characteristic, complemented, Sylow
19	#732	—	97	2	no	—
20	#732	C₉₇⋊C₃	1	1	yes	characteristic, complemented
21	C₉²	—	97	1	no	—
22	H(3,𝔽₃)	—	3	1	no	—
23	H(3,𝔽₃)	—	291	2	no	—
24	C₃×C₉	—	291	1	no	—
25	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
26	C₃²	—	9	1	no	—
27	C₃²	—	873	2	no	—
28	C₃²	C₃²⋊(C₉₇⋊C₃)	1	1	yes	characteristic
29	C₉	—	3	1	no	—
30	C₉	—	291	3	no	—
31	C₃	—	3	1	no	—
32	C₃	—	27	1	no	—
33	C₃	—	2619	2	no	—
34	C₃	#21463364	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.