Subgroups — C₇×C₉×C₃⋊C₈ #13094171

Order 1512.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₇×C₃⋊C₈	C₃	1	1	yes	maximal, characteristic
3	C₇×C₈×C₉	—	3	1	no	maximal
4	C₂×C₃×C₇×C₉	C₄	1	1	yes	characteristic
5	C₃²×C₄×C₇	C₂×C₃	1	1	yes	characteristic
6	C₄×C₇×C₉	—	2	1	no	—
7	C₄×C₇×C₉	D₃	1	1	yes	characteristic
8	C₉×C₃⋊C₈	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₇×C₉	C₈	1	1	yes	characteristic, complemented, Hall
10	C₃×C₇×C₈	—	3	1	no	—
11	C₇×C₃⋊C₈	C₉	1	1	yes	characteristic, direct product factor
12	C₂×C₃²×C₇	C₃×C₄	1	1	yes	characteristic
13	C₂×C₇×C₉	—	2	1	no	—
14	C₂×C₇×C₉	Dic₃	1	1	yes	characteristic
15	C₃×C₄×C₉	C₂×C₇	1	1	yes	characteristic
16	C₃×C₄×C₇	—	2	1	no	—
17	C₃×C₄×C₇	C₂×C₉	1	1	yes	characteristic
18	C₃×C₄×C₇	C₃×D₃	1	1	yes	characteristic
19	C₃×C₃⋊C₈	C₃×C₇	1	1	yes	characteristic
20	C₈×C₉	—	3	1	no	—
21	C₃²×C₇	C₃×C₈	1	1	yes	characteristic
22	C₇×C₉	—	2	1	no	—
23	C₇×C₉	C₃⋊C₈	1	1	yes	characteristic, direct product factor
24	C₇×C₈	—	3	1	no	Hall
25	C₂×C₃×C₉	C₄×C₇	1	1	yes	characteristic
26	C₂×C₃×C₇	—	2	1	no	—
27	C₂×C₃×C₇	C₄×C₉	1	1	yes	characteristic
28	C₂×C₃×C₇	C₃×Dic₃	1	1	yes	characteristic
29	C₃²×C₄	C₂×C₃×C₇	1	1	yes	characteristic
30	C₄×C₉	—	2	1	no	—
31	C₄×C₉	D₃×C₇	1	1	yes	characteristic
32	C₄×C₇	D₃×C₉	1	1	yes	characteristic
33	C₃×C₉	C₇×C₈	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₈	—	3	1	no	—
35	C₃⋊C₈	C₇×C₉	1	1	yes	characteristic, direct product factor
36	C₃×C₇	—	2	1	no	—
37	C₃×C₇	C₈×C₉	1	1	yes	characteristic, complemented
38	C₃×C₇	C₃×C₃⋊C₈	1	1	yes	characteristic
39	C₂×C₃²	C₃×C₄×C₇	1	1	yes	characteristic
40	C₂×C₉	—	2	1	no	—
41	C₂×C₉	C₇×Dic₃	1	1	yes	characteristic
42	C₂×C₇	C₉×Dic₃	1	1	yes	characteristic
43	C₃×C₄	—	2	1	no	—
44	C₃×C₄	C₂×C₇×C₉	1	1	yes	characteristic
45	C₃×C₄	C₃×D₃×C₇	1	1	yes	characteristic
46	C₃²	C₃×C₇×C₈	1	1	yes	characteristic
47	C₉	—	2	1	no	—
48	C₉	C₇×C₃⋊C₈	1	1	yes	characteristic, direct product factor
49	C₈	—	3	1	no	Sylow
50	C₇	C₉×C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	—	2	1	no	—
52	C₂×C₃	C₄×C₇×C₉	1	1	yes	characteristic
53	C₂×C₃	C₃×C₇×Dic₃	1	1	yes	characteristic
54	C₄	D₃×C₇×C₉	1	1	yes	characteristic
55	C₃	—	2	1	no	—
56	C₃	C₇×C₈×C₉	1	1	yes	characteristic, complemented
57	C₃	C₃×C₇×C₃⋊C₈	1	1	yes	characteristic
58	C₂	C₇×C₉×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₇×C₉	D₃
commutator, hypocenter	C₃	C₇×C₈×C₉
Frattini	C₃×C₄	C₃×D₃×C₇
Fitting	C₃×C₄×C₇×C₉	C₂
socle, prime radical	C₂×C₃²×C₇	C₃×C₄
cosocle	C₃²×C₄	C₂×C₃×C₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₄×C₇×C₉

Complements

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

N	H ≅ G/N	type
8. C₉×C₃⋊C₈	C₇	direct (N × H)
9. C₃×C₇×C₉	C₈	semidirect
11. C₇×C₃⋊C₈	C₉	direct (N × H)
23. C₇×C₉	C₃⋊C₈	direct (N × H)
33. C₃×C₉	C₇×C₈	semidirect
35. C₃⋊C₈	C₇×C₉	direct (N × H)
37. C₃×C₇	C₈×C₉	semidirect
48. C₉	C₇×C₃⋊C₈	direct (N × H)
50. C₇	C₉×C₃⋊C₈	direct (N × H)
56. C₃	C₇×C₈×C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₇×C₉	2
C₃×C₇×C₃⋊C₈	3
C₇×C₈×C₉	3
C₉×C₃⋊C₈	7

Subgroups — C7×C9×C3⋊C8 #13094171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₉×C₃⋊C₈ #13094171