Subgroups — C₃³×C₇×D₄ #13094880

Order 1512.

448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³×C₇	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄×C₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇×D₄	C₃	1	13	yes	maximal, direct product factor
4	C₂×C₃³×C₇	—	2	2	no	—
5	C₂×C₃³×C₇	C₂²	1	1	yes	characteristic
6	C₂²×C₃²×C₇	C₂×C₃	1	26	yes	complemented
7	C₃²×C₄×C₇	C₂×C₃	1	13	yes	complemented
8	C₃³×D₄	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃³×C₇	D₄	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₇×D₄	C₃²	1	13	yes	direct product factor
11	C₂×C₃²×C₇	—	2	26	no	—
12	C₂×C₃²×C₇	C₂²×C₃	1	13	yes	—
13	C₂²×C₃³	C₂×C₇	1	2	yes	complemented
14	C₃³×C₄	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂²×C₃×C₇	C₂×C₃²	1	26	yes	complemented
16	C₃×C₄×C₇	C₂×C₃²	1	13	yes	complemented
17	C₃²×D₄	C₃×C₇	1	13	yes	direct product factor
18	C₃²×C₇	C₃×D₄	1	13	yes	direct product factor
19	C₇×D₄	C₃³	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃³	—	2	2	no	—
21	C₂×C₃³	C₂²×C₇	1	1	yes	characteristic
22	C₂×C₃×C₇	—	2	26	no	—
23	C₂×C₃×C₇	C₂²×C₃²	1	13	yes	—
24	C₂²×C₃²	C₂×C₃×C₇	1	26	yes	complemented
25	C₃²×C₄	C₂×C₃×C₇	1	13	yes	complemented
26	C₂²×C₇	C₂×C₃³	1	2	yes	complemented
27	C₄×C₇	C₂×C₃³	1	1	yes	characteristic, complemented
28	C₃³	C₇×D₄	1	1	yes	characteristic, direct product factor, Sylow
29	C₃×D₄	C₃²×C₇	1	13	yes	direct product factor
30	C₃×C₇	C₃²×D₄	1	13	yes	direct product factor
31	C₂×C₃²	—	2	26	no	—
32	C₂×C₃²	C₂²×C₃×C₇	1	13	yes	—
33	C₂×C₇	—	2	2	no	—
34	C₂×C₇	C₂²×C₃³	1	1	yes	characteristic
35	C₂²×C₃	C₂×C₃²×C₇	1	26	yes	complemented
36	C₃×C₄	C₂×C₃²×C₇	1	13	yes	complemented
37	C₃²	C₃×C₇×D₄	1	13	yes	direct product factor
38	D₄	C₃³×C₇	1	1	yes	characteristic, direct product factor, Sylow
39	C₇	C₃³×D₄	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	2	26	no	—
41	C₂×C₃	C₂²×C₃²×C₇	1	13	yes	—
42	C₂²	C₂×C₃³×C₇	1	2	yes	complemented
43	C₄	C₂×C₃³×C₇	1	1	yes	characteristic, complemented
44	C₃	C₃²×C₇×D₄	1	13	yes	direct product factor
45	C₂	—	2	2	no	—
46	C₂	C₂²×C₃³×C₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃³×C₇	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃³×C₇
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃³×C₇	C₂	semidirect
2. C₃³×C₄×C₇	C₂	semidirect
3. C₃²×C₇×D₄	C₃	direct (N × H)
6. C₂²×C₃²×C₇	C₂×C₃	semidirect
7. C₃²×C₄×C₇	C₂×C₃	semidirect
8. C₃³×D₄	C₇	direct (N × H)
9. C₃³×C₇	D₄	direct (N × H)
10. C₃×C₇×D₄	C₃²	direct (N × H)
13. C₂²×C₃³	C₂×C₇	semidirect
14. C₃³×C₄	C₂×C₇	semidirect
15. C₂²×C₃×C₇	C₂×C₃²	semidirect
16. C₃×C₄×C₇	C₂×C₃²	semidirect
17. C₃²×D₄	C₃×C₇	direct (N × H)
18. C₃²×C₇	C₃×D₄	direct (N × H)
19. C₇×D₄	C₃³	direct (N × H)
24. C₂²×C₃²	C₂×C₃×C₇	semidirect
25. C₃²×C₄	C₂×C₃×C₇	semidirect
26. C₂²×C₇	C₂×C₃³	semidirect
27. C₄×C₇	C₂×C₃³	semidirect
28. C₃³	C₇×D₄	direct (N × H)
29. C₃×D₄	C₃²×C₇	direct (N × H)
30. C₃×C₇	C₃²×D₄	direct (N × H)
35. C₂²×C₃	C₂×C₃²×C₇	semidirect
36. C₃×C₄	C₂×C₃²×C₇	semidirect
37. C₃²	C₃×C₇×D₄	direct (N × H)
38. D₄	C₃³×C₇	direct (N × H)
39. C₇	C₃³×D₄	direct (N × H)
42. C₂²	C₂×C₃³×C₇	semidirect
43. C₄	C₂×C₃³×C₇	semidirect
44. C₃	C₃²×C₇×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃³×C₇	2
C₃³×C₄×C₇	2
C₃²×C₇×D₄	3
C₃³×D₄	7

Subgroups — C33×C7×D4 #13094880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃³×C₇×D₄ #13094880