Subgroups — C₉₇×#6899 #37555739

Order 23571.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×3₋¹⁺²×C₉₇	C₃	1	1	yes	maximal, characteristic
2	C₉⋊C₉×C₉₇	C₃	1	6	yes	maximal, complemented
3	C₉⋊C₉×C₉₇	C₃	1	2	yes	maximal, complemented
4	C₃²⋊C₉×C₉₇	C₃	1	3	yes	maximal
5	C₉²×C₉₇	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃³×C₉₇	C₃²	1	1	yes	characteristic
7	3₋¹⁺²×C₉₇	—	3	3	no	—
8	C₃×C₉×C₉₇	C₃²	1	3	yes	—
9	C₃×C₉×C₉₇	C₃²	1	6	yes	—
10	C₃×C₉×C₉₇	C₃²	1	2	yes	—
11	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
12	C₃²×C₉₇	—	3	1	no	—
13	C₃²×C₉₇	—	3	3	no	—
14	C₃²×C₉₇	C₃³	1	1	yes	characteristic
15	C₉×C₉₇	—	3	2	no	—
16	C₉×C₉₇	—	3	3	no	—
17	C₉×C₉₇	—	3	6	no	—
18	C₉×C₉₇	3₋¹⁺²	1	3	yes	—
19	C₃×C₉₇	—	9	1	no	—
20	C₃×C₉₇	C₃×3₋¹⁺²	1	1	yes	characteristic
21	C₃×C₉₇	#737	1	3	yes	—
22	#6899	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₉₇	#6899	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×3₋¹⁺²	C₃×C₉₇	1	1	yes	characteristic
25	C₉⋊C₉	C₃×C₉₇	1	6	yes	complemented
26	C₉⋊C₉	C₃×C₉₇	1	2	yes	complemented
27	C₃²⋊C₉	C₃×C₉₇	1	3	yes	—
28	C₉²	C₃×C₉₇	1	1	yes	characteristic, complemented
29	C₃³	C₃²×C₉₇	1	1	yes	characteristic
30	3₋¹⁺²	—	3	3	no	—
31	C₃×C₉	C₃²×C₉₇	1	3	yes	—
32	C₃×C₉	C₃²×C₉₇	1	6	yes	—
33	C₃×C₉	C₃²×C₉₇	1	2	yes	—
34	C₃×C₉	C₃²×C₉₇	1	1	yes	characteristic
35	C₃²	—	3	1	no	—
36	C₃²	—	3	3	no	—
37	C₃²	C₃³×C₉₇	1	1	yes	characteristic
38	C₉	—	3	2	no	—
39	C₉	—	3	3	no	—
40	C₉	—	3	6	no	—
41	C₉	3₋¹⁺²×C₉₇	1	3	yes	—
42	C₃	—	9	1	no	—
43	C₃	C₃×3₋¹⁺²×C₉₇	1	1	yes	characteristic
44	C₃	#737×C₉₇	1	3	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

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₉⋊C₉×C₉₇	C₃	semidirect
3. C₉⋊C₉×C₉₇	C₃	semidirect
5. C₉²×C₉₇	C₃	semidirect
22. #6899	C₉₇	direct (N × H)
23. C₉₇	#6899	direct (N × H)
25. C₉⋊C₉	C₃×C₉₇	semidirect
26. C₉⋊C₉	C₃×C₉₇	semidirect
28. C₉²	C₃×C₉₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×3₋¹⁺²×C₉₇	3
C₉⋊C₉×C₉₇	3
C₃²⋊C₉×C₉₇	3
C₉²×C₉₇	3
#6899	97

Subgroups — C97×#6899 #37555739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉₇×#6899 #37555739