Subgroups — C₃×#21463367 #37555949

Order 23571.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14579757	C₃	1	3	yes	maximal
2	#21463367	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
4	#14579757	—	3	6	no	—
5	#14579757	C₃²	1	9	yes	—
6	C₃×C₉₇⋊C₉	—	3	3	no	—
7	C₃³×C₉₇	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₉₇	—	3	2	no	—
9	C₃×C₉×C₉₇	—	3	1	no	—
10	C₃×C₉×C₉₇	C₃²	1	3	yes	—
11	C₃²×C₉₇	—	3	3	no	—
12	C₃²×C₉₇	H(3,𝔽₃)	1	2	yes	—
13	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
14	C₃²×C₉₇	C₃³	1	1	yes	characteristic
15	C₉×C₉₇	—	3	3	no	—
16	C₉₇⋊C₉	—	3	9	no	—
17	C₃×C₉₇	—	3	2	no	—
18	C₃×C₉₇	—	3	1	no	—
19	C₃×C₉₇	#733	1	3	yes	complemented
20	C₃×C₉₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×#733	—	97	1	no	maximal, Sylow
22	C₉₇	C₃×#733	1	1	yes	characteristic, complemented, Sylow
23	C₃×3₋¹⁺²	—	97	3	no	—
24	C₃²×C₉	C₉₇⋊C₃	1	1	yes	characteristic
25	#733	—	97	9	no	—
26	C₃³	C₃×C₉₇⋊C₃	1	1	yes	characteristic
27	3₋¹⁺²	—	291	6	no	—
28	3₋¹⁺²	—	97	9	no	—
29	C₃×C₉	—	3	2	no	—
30	C₃×C₉	—	3	1	no	—
31	C₃×C₉	—	291	3	no	—
32	C₃×C₉	C₃×C₉₇⋊C₃	1	3	yes	—
33	C₃²	—	3	3	no	—
34	C₃²	C₃²⋊(C₉₇⋊C₃)	1	2	yes	—
35	C₃²	C₃²⋊(C₉₇⋊C₃)	1	1	yes	characteristic
36	C₃²	C₃²×C₉₇⋊C₃	1	1	yes	characteristic
37	C₉	—	3	3	no	—
38	C₉	—	291	9	no	—
39	C₃	—	3	2	no	—
40	C₃	—	3	1	no	—
41	C₃	#21463367	1	3	yes	direct product factor
42	C₃	C₃×C₃²⋊(C₉₇⋊C₃)	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.