Subgroups — #44565421

Order 32157.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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