Subgroups — #37555811

Order 23571.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉₇⋊C₂₇	C₃	1	3	yes	maximal
2	C₉²×C₉₇	C₃	1	1	yes	maximal, characteristic
3	C₉₇⋊C₂₇	—	3	3	no	—
4	C₃×C₉×C₉₇	C₉	1	2	yes	—
5	C₃×C₉×C₉₇	C₉	1	1	yes	characteristic
6	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
7	C₃²×C₉₇	C₃×C₉	1	1	yes	characteristic
8	C₉×C₉₇	—	3	2	no	—
9	C₉×C₉₇	C₂₇	1	3	yes	complemented
10	C₉×C₉₇	3₋¹⁺²	1	3	yes	—
11	C₃×C₉₇	C₉⋊C₉	1	1	yes	characteristic
12	C₃×C₉₇	C₃×C₂₇	1	1	yes	characteristic
13	C₃×C₉₇	C₂₇⋊C₃	1	2	yes	—
14	C₉⋊C₂₇	—	97	1	no	maximal, Sylow
15	C₉₇	C₉⋊C₂₇	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₂₇	—	97	3	no	—
17	C₉²	C₉₇⋊C₃	1	1	yes	characteristic
18	C₃×C₉	C₉₇⋊C₉	1	2	yes	—
19	C₃×C₉	C₉₇⋊C₉	1	1	yes	characteristic
20	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
21	C₂₇	—	291	3	no	—
22	C₃²	C₃×C₉₇⋊C₉	1	1	yes	characteristic
23	C₉	—	3	2	no	—
24	C₉	C₉₇⋊C₂₇	1	3	yes	complemented
25	C₉	#14579755	1	3	yes	—
26	C₃	#21463352	1	1	yes	characteristic
27	C₃	C₃×C₉₇⋊C₂₇	1	1	yes	characteristic
28	C₃	#21463357	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.