Subgroups — C₉₇×#6897 #37555737

Order 23571.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉⋊C₉×C₉₇	C₃	1	8	yes	maximal, complemented
2	C₃²⋊C₉×C₉₇	C₃	1	4	yes	maximal
3	C₉²×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃³×C₉₇	C₃²	1	1	yes	characteristic
5	C₃×C₉×C₉₇	C₃²	1	4	yes	—
6	C₃×C₉×C₉₇	C₃²	1	8	yes	—
7	C₃²×C₉₇	—	3	4	no	—
8	C₃²×C₉₇	C₃³	1	1	yes	characteristic
9	C₉×C₉₇	—	3	4	no	—
10	C₉×C₉₇	—	3	8	no	—
11	C₃×C₉₇	—	9	1	no	—
12	C₃×C₉₇	#737	1	4	yes	—
13	#6897	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
14	C₉₇	#6897	1	1	yes	characteristic, direct product factor, Sylow
15	C₉⋊C₉	C₃×C₉₇	1	8	yes	complemented
16	C₃²⋊C₉	C₃×C₉₇	1	4	yes	—
17	C₉²	C₃×C₉₇	1	1	yes	characteristic, complemented
18	C₃³	C₃²×C₉₇	1	1	yes	characteristic
19	C₃×C₉	C₃²×C₉₇	1	4	yes	—
20	C₃×C₉	C₃²×C₉₇	1	8	yes	—
21	C₃²	—	3	4	no	—
22	C₃²	C₃³×C₉₇	1	1	yes	characteristic
23	C₉	—	3	4	no	—
24	C₉	—	3	8	no	—
25	C₃	—	9	1	no	—
26	C₃	#737×C₉₇	1	4	yes	—

	subgroup	G/H
center, socle	C₃²×C₉₇	C₃³
commutator, Frattini, cosocle	C₃²	C₃³×C₉₇
prime radical	C₃³×C₉₇	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₃²×C₉₇ ◁ G

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.