Subgroups — C₉₇×#6873 #37555713

Order 23571.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#737×C₉₇	C₃	1	1	yes	maximal, characteristic
2	C₂₇⋊C₃×C₉₇	C₃	1	2	yes	maximal, complemented
3	C₃×C₂₇×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₉₇	—	3	2	no	—
5	3₋¹⁺²×C₉₇	C₉	1	2	yes	—
6	H(3,𝔽₃)×C₉₇	C₉	1	1	yes	characteristic
7	C₃×C₉×C₉₇	—	3	1	no	—
8	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
9	C₂₇×C₉₇	—	3	1	no	—
10	C₂₇×C₉₇	—	3	2	no	—
11	C₃²×C₉₇	—	3	1	no	—
12	C₃²×C₉₇	C₃×C₉	1	1	yes	characteristic
13	C₉×C₉₇	—	3	2	no	—
14	C₉×C₉₇	H(3,𝔽₃)	1	1	yes	characteristic
15	C₉×C₉₇	3₋¹⁺²	1	2	yes	—
16	C₃×C₉₇	—	3	1	no	—
17	C₃×C₉₇	—	9	1	no	—
18	C₃×C₉₇	C₃²⋊C₉	1	1	yes	characteristic
19	#6873	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₉₇	#6873	1	1	yes	characteristic, direct product factor, Sylow
21	#737	C₃×C₉₇	1	1	yes	characteristic
22	C₂₇⋊C₃	C₃×C₉₇	1	2	yes	complemented
23	C₃×C₂₇	C₃×C₉₇	1	1	yes	characteristic, complemented
24	3₋¹⁺²	—	3	2	no	—
25	3₋¹⁺²	C₉×C₉₇	1	2	yes	—
26	H(3,𝔽₃)	C₉×C₉₇	1	1	yes	characteristic
27	C₃×C₉	—	3	1	no	—
28	C₃×C₉	C₃²×C₉₇	1	1	yes	characteristic
29	C₂₇	—	3	1	no	—
30	C₂₇	—	3	2	no	—
31	C₃²	—	3	1	no	—
32	C₃²	C₃×C₉×C₉₇	1	1	yes	characteristic
33	C₉	—	3	2	no	—
34	C₉	H(3,𝔽₃)×C₉₇	1	1	yes	characteristic
35	C₉	3₋¹⁺²×C₉₇	1	2	yes	—
36	C₃	—	3	1	no	—
37	C₃	—	9	1	no	—
38	C₃	C₃²⋊C₉×C₉₇	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.