Subgroups — #37555832

Order 23571.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21463367	C₃	1	1	yes	maximal, characteristic, complemented
2	#21463365	C₃	1	1	yes	maximal, characteristic, complemented
3	#21463352	C₃	1	1	yes	maximal, characteristic, complemented
4	#732×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
5	#14579757	—	3	1	no	—
6	C₃²⋊(C₉₇⋊C₃)	—	3	1	no	—
7	C₃×C₉₇⋊C₉	—	3	1	no	—
8	H(3,𝔽₃)×C₉₇	—	3	1	no	—
9	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
10	C₃²×C₉₇	—	9	1	no	—
11	C₃²×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
12	C₃×C₉₇⋊C₃	—	9	1	no	—
13	C₉×C₉₇	—	3	1	no	—
14	C₉₇⋊C₉	—	9	1	no	—
15	C₉₇⋊C₉	—	9	1	no	—
16	C₃×C₉₇	—	3	1	no	—
17	C₃×C₉₇	—	27	1	no	—
18	C₃×C₉₇	#732	1	1	yes	characteristic
19	C₉₇⋊C₃	—	27	1	no	—
20	#6881	—	97	1	no	maximal, Sylow
21	C₉₇	#6881	1	1	yes	characteristic, complemented, Sylow
22	#733	—	97	1	no	—
23	#732	—	97	1	no	—
24	#732	C₉₇⋊C₃	1	1	yes	characteristic, complemented
25	C₉⋊C₉	—	97	1	no	—
26	3₋¹⁺²	—	291	1	no	—
27	H(3,𝔽₃)	—	3	1	no	—
28	H(3,𝔽₃)	—	291	1	no	—
29	C₃×C₉	—	291	1	no	—
30	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
31	C₃²	—	9	1	no	—
32	C₃²	—	873	1	no	—
33	C₃²	C₃²⋊(C₉₇⋊C₃)	1	1	yes	characteristic
34	C₉	—	3	1	no	—
35	C₉	—	873	1	no	—
36	C₉	—	873	1	no	—
37	C₃	—	3	1	no	—
38	C₃	—	27	1	no	—
39	C₃	—	2619	1	no	—
40	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.