Subgroups — C₉₇×#6868 #37555708

Order 23571.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊C₉×C₉₇	C₃	1	3	yes	maximal
3	C₃³×C₉₇	C₃²	1	1	yes	characteristic
4	C₃×C₉×C₉₇	—	3	1	no	—
5	C₃×C₉×C₉₇	—	3	3	no	—
6	C₃×C₉×C₉₇	—	3	2	no	—
7	C₃×C₉×C₉₇	C₉	1	3	yes	complemented
8	C₃²×C₉₇	—	3	1	no	—
9	C₃²×C₉₇	—	3	2	no	—
10	C₃²×C₉₇	C₃×C₉	1	1	yes	characteristic
11	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃²×C₉₇	3₋¹⁺²	1	2	yes	—
13	C₉×C₉₇	—	3	3	no	—
14	C₉×C₉₇	—	9	3	no	—
15	C₃×C₉₇	—	3	1	no	—
16	C₃×C₉₇	—	3	2	no	—
17	C₃×C₉₇	C₃²⋊C₉	1	1	yes	characteristic
18	C₃×C₉₇	#732	1	1	yes	characteristic
19	C₃×C₉₇	#733	1	2	yes	—
20	#6868	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₉₇	#6868	1	1	yes	characteristic, direct product factor, Sylow
22	C₃²×C₉	C₃×C₉₇	1	1	yes	characteristic
23	C₃²⋊C₉	C₃×C₉₇	1	3	yes	—
24	C₃³	C₃²×C₉₇	1	1	yes	characteristic
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	—	3	2	no	—
27	C₃×C₉	—	3	3	no	—
28	C₃×C₉	C₉×C₉₇	1	3	yes	complemented
29	C₃²	—	3	1	no	—
30	C₃²	—	3	2	no	—
31	C₃²	C₃×C₉×C₉₇	1	1	yes	characteristic
32	C₃²	H(3,𝔽₃)×C₉₇	1	1	yes	characteristic
33	C₃²	3₋¹⁺²×C₉₇	1	2	yes	—
34	C₉	—	3	3	no	—
35	C₉	—	9	3	no	—
36	C₃	—	3	1	no	—
37	C₃	—	3	2	no	—
38	C₃	C₃²⋊C₉×C₉₇	1	1	yes	characteristic
39	C₃	#732×C₉₇	1	1	yes	characteristic
40	C₃	#733×C₉₇	1	2	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.