Subgroups — #44565451

Order 32157.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24924308	C₃	1	1	yes	maximal, characteristic, complemented
2	#24924307	C₃	1	3	yes	maximal, complemented
3	#24924306	C₃	1	3	yes	maximal, complemented
4	C₃²⋊(C₃₉₇⋊C₃)	C₃	1	1	yes	maximal, characteristic
5	C₃×#16813208	C₃	1	1	yes	maximal, characteristic, complemented
6	C₉×C₃₉₇⋊C₃	C₃	1	3	yes	maximal, complemented
7	3₋¹⁺²×C₃₉₇	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₃₉₇	C₃²	1	1	yes	characteristic
9	C₃×C₃₉₇⋊C₃	C₃²	1	3	yes	—
10	C₉×C₃₉₇	C₃²	1	3	yes	—
11	#16813208	C₃²	1	1	yes	characteristic
12	#16813208	C₃²	1	3	yes	—
13	#16813208	C₃²	1	1	yes	characteristic
14	#16813208	C₃²	1	1	yes	characteristic
15	C₃×C₃₉₇	—	3	1	no	—
16	C₃×C₃₉₇	C₃³	1	1	yes	characteristic
17	C₃₉₇⋊C₃	—	3	3	no	—
18	C₃₉₇	#737	1	1	yes	characteristic, complemented, Sylow
19	#737	—	397	1	no	maximal, Sylow
20	3₋¹⁺²	—	397	1	no	—
21	3₋¹⁺²	—	397	3	no	—
22	3₋¹⁺²	—	397	3	no	—
23	3₋¹⁺²	C₃₉₇⋊C₃	1	1	yes	characteristic, complemented
24	H(3,𝔽₃)	—	397	1	no	—
25	C₃×C₉	—	397	1	no	—
26	C₃×C₉	—	397	3	no	—
27	C₃²	—	397	3	no	—
28	C₃²	C₃×C₃₉₇⋊C₃	1	1	yes	characteristic
29	C₉	—	397	1	no	—
30	C₉	—	397	1	no	—
31	C₉	—	397	1	no	—
32	C₉	—	397	3	no	—
33	C₉	C₃×C₃₉₇⋊C₃	1	3	yes	—
34	C₃	—	3	1	no	—
35	C₃	—	1191	3	no	—
36	C₃	C₃²×C₃₉₇⋊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.