Subgroups — D₃²×C₇×C₉₇ #37567967

Order 24444.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₃×C₇×C₉₇	C₂	1	2	yes	maximal, complemented
2	C₇×C₃⋊D₃×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃×C₇×C₉₇	—	3	2	no	maximal
4	C₃²×C₇×C₉₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃×C₇×C₉₇	—	3	2	no	—
6	D₃×C₇×C₉₇	—	6	1	no	—
7	D₃×C₇×C₉₇	D₃	1	2	yes	direct product factor
8	C₂×C₃×C₇×C₉₇	—	3	2	no	—
9	D₃²×C₉₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₇×C₉₇	—	9	1	no	Hall
11	C₃×C₇×C₉₇	—	2	1	no	—
12	C₃×C₇×C₉₇	C₂×D₃	1	2	yes	complemented
13	C₃⋊D₃×C₉₇	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×D₃×C₉₇	C₂×C₇	1	2	yes	complemented
15	C₂×C₇×C₉₇	—	3	2	no	—
16	C₂×C₇×C₉₇	—	9	1	no	—
17	C₂×D₃×C₉₇	—	3	2	no	—
18	C₃²×C₉₇	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
19	C₇×C₉₇	D₃²	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₉₇	—	3	2	no	—
21	D₃×C₉₇	—	3	2	no	—
22	D₃×C₉₇	—	6	1	no	—
23	D₃×C₉₇	D₃×C₇	1	2	yes	direct product factor
24	C₂²×C₉₇	—	9	1	no	Hall
25	C₃×C₉₇	—	2	1	no	—
26	C₃×C₉₇	C₂×D₃×C₇	1	2	yes	complemented
27	D₃²×C₇	C₉₇	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₉₇	—	3	2	no	—
29	C₂×C₉₇	—	9	1	no	—
30	C₇×C₃⋊D₃	C₂×C₉₇	1	1	yes	characteristic, complemented
31	C₃×D₃×C₇	C₂×C₉₇	1	2	yes	complemented
32	C₉₇	D₃²×C₇	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×D₃×C₇	—	3	2	no	—
34	C₃²×C₇	C₂²×C₉₇	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₇	—	3	2	no	—
36	D₃×C₇	—	3	2	no	—
37	D₃×C₇	—	6	1	no	—
38	D₃×C₇	D₃×C₉₇	1	2	yes	direct product factor
39	D₃²	C₇×C₉₇	1	1	yes	characteristic, direct product factor, Hall
40	C₂²×C₇	—	9	1	no	Hall
41	C₃×C₇	—	2	1	no	—
42	C₃×C₇	C₂×D₃×C₉₇	1	2	yes	complemented
43	C₃⋊D₃	C₂×C₇×C₉₇	1	1	yes	characteristic, complemented
44	C₃×D₃	C₂×C₇×C₉₇	1	2	yes	complemented
45	C₂×C₇	—	3	2	no	—
46	C₂×C₇	—	9	1	no	—
47	C₂×D₃	—	3	2	no	—
48	C₃²	C₂²×C₇×C₉₇	1	1	yes	characteristic, complemented, Sylow
49	C₇	D₃²×C₉₇	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×C₃	—	3	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	D₃×C₇×C₉₇	1	2	yes	direct product factor
54	C₂²	—	9	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	C₂×D₃×C₇×C₉₇	1	2	yes	complemented
57	C₂	—	3	2	no	—
58	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₉₇	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₇×C₉₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₉₇	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₇×C₉₇

Complements

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

N	H ≅ G/N	type
1. C₃×D₃×C₇×C₉₇	C₂	semidirect
2. C₇×C₃⋊D₃×C₉₇	C₂	semidirect
4. C₃²×C₇×C₉₇	C₂²	semidirect
7. D₃×C₇×C₉₇	D₃	direct (N × H)
9. D₃²×C₉₇	C₇	direct (N × H)
12. C₃×C₇×C₉₇	C₂×D₃	semidirect
13. C₃⋊D₃×C₉₇	C₂×C₇	semidirect
14. C₃×D₃×C₉₇	C₂×C₇	semidirect
18. C₃²×C₉₇	C₂²×C₇	semidirect
19. C₇×C₉₇	D₃²	direct (N × H)
23. D₃×C₉₇	D₃×C₇	direct (N × H)
26. C₃×C₉₇	C₂×D₃×C₇	semidirect
27. D₃²×C₇	C₉₇	direct (N × H)
30. C₇×C₃⋊D₃	C₂×C₉₇	semidirect
31. C₃×D₃×C₇	C₂×C₉₇	semidirect
32. C₉₇	D₃²×C₇	direct (N × H)
34. C₃²×C₇	C₂²×C₉₇	semidirect
38. D₃×C₇	D₃×C₉₇	direct (N × H)
39. D₃²	C₇×C₉₇	direct (N × H)
42. C₃×C₇	C₂×D₃×C₉₇	semidirect
43. C₃⋊D₃	C₂×C₇×C₉₇	semidirect
44. C₃×D₃	C₂×C₇×C₉₇	semidirect
48. C₃²	C₂²×C₇×C₉₇	semidirect
49. C₇	D₃²×C₉₇	direct (N × H)
53. D₃	D₃×C₇×C₉₇	direct (N × H)
56. C₃	C₂×D₃×C₇×C₉₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₃×C₇×C₉₇	2
C₇×C₃⋊D₃×C₉₇	2
C₂×D₃×C₇×C₉₇	3
D₃²×C₉₇	7
D₃²×C₇	97

Subgroups — D32×C7×C97 #37567967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃²×C₇×C₉₇ #37567967