Subgroups — C₂⁴×C₇×Dic₃ #13062366

Order 1344.

2724 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₃×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₇×Dic₃	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×C₄×C₇	—	3	1	no	maximal, Hall
4	C₂⁴×C₃×C₇	C₄	1	16	yes	complemented
5	C₂⁴×C₃×C₇	C₂²	1	15	yes	—
6	C₂²×C₇×Dic₃	C₂²	1	140	yes	direct product factor
7	C₂⁵×C₇	D₃	1	1	yes	characteristic
8	C₂³×C₄×C₇	—	3	30	no	—
9	C₂⁴×Dic₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₇	C₂×C₄	1	120	yes	complemented
11	C₂³×C₃×C₇	C₂³	1	35	yes	—
12	C₂×C₇×Dic₃	C₂³	1	120	yes	direct product factor
13	C₂⁴×C₇	Dic₃	1	16	yes	direct product factor
14	C₂⁴×C₇	C₂×D₃	1	15	yes	—
15	C₂²×C₄×C₇	—	3	140	no	—
16	C₂⁵×C₃	C₂×C₇	1	1	yes	characteristic
17	C₂³×Dic₃	C₂×C₇	1	30	yes	direct product factor
18	C₂²×C₃×C₇	C₂²×C₄	1	140	yes	complemented
19	C₂²×C₃×C₇	C₂⁴	1	15	yes	—
20	C₇×Dic₃	C₂⁴	1	16	yes	direct product factor
21	C₂⁴×C₄	—	3	1	no	Sylow
22	C₂³×C₇	C₂×Dic₃	1	120	yes	direct product factor
23	C₂³×C₇	C₂²×D₃	1	35	yes	—
24	C₂×C₄×C₇	—	3	120	no	—
25	C₂⁴×C₃	C₄×C₇	1	16	yes	complemented
26	C₂⁴×C₃	C₂²×C₇	1	15	yes	—
27	C₂²×Dic₃	C₂²×C₇	1	140	yes	direct product factor
28	C₂×C₃×C₇	C₂³×C₄	1	30	yes	complemented
29	C₂×C₃×C₇	C₂⁵	1	1	yes	characteristic
30	C₂⁵	D₃×C₇	1	1	yes	characteristic
31	C₂³×C₄	—	3	30	no	—
32	C₂²×C₇	C₂²×Dic₃	1	140	yes	direct product factor
33	C₂²×C₇	C₂³×D₃	1	15	yes	—
34	C₄×C₇	—	3	16	no	—
35	C₂³×C₃	C₂×C₄×C₇	1	120	yes	complemented
36	C₂³×C₃	C₂³×C₇	1	35	yes	—
37	C₂×Dic₃	C₂³×C₇	1	120	yes	direct product factor
38	C₃×C₇	C₂⁴×C₄	1	1	yes	characteristic, complemented, Hall
39	C₂⁴	C₇×Dic₃	1	16	yes	direct product factor
40	C₂⁴	C₂×D₃×C₇	1	15	yes	—
41	C₂²×C₄	—	3	140	no	—
42	C₂×C₇	C₂³×Dic₃	1	30	yes	direct product factor
43	C₂×C₇	C₂⁴×D₃	1	1	yes	characteristic
44	C₂²×C₃	C₂²×C₄×C₇	1	140	yes	complemented
45	C₂²×C₃	C₂⁴×C₇	1	15	yes	—
46	Dic₃	C₂⁴×C₇	1	16	yes	direct product factor
47	C₂³	C₂×C₇×Dic₃	1	120	yes	direct product factor
48	C₂³	C₂²×D₃×C₇	1	35	yes	—
49	C₂×C₄	—	3	120	no	—
50	C₇	C₂⁴×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₂×C₃	C₂³×C₄×C₇	1	30	yes	complemented
52	C₂×C₃	C₂⁵×C₇	1	1	yes	characteristic
53	C₂²	C₂²×C₇×Dic₃	1	140	yes	direct product factor
54	C₂²	C₂³×D₃×C₇	1	15	yes	—
55	C₄	—	3	16	no	—
56	C₃	C₂⁴×C₄×C₇	1	1	yes	characteristic, complemented, Sylow
57	C₂	C₂³×C₇×Dic₃	1	30	yes	direct product factor
58	C₂	C₂⁴×D₃×C₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁵×C₇	D₃
commutator, hypocenter	C₃	C₂⁴×C₄×C₇
Frattini	C₂	C₂⁴×D₃×C₇
Fitting, socle, prime radical	C₂⁵×C₃×C₇	C₂
cosocle	C₂×C₃	C₂⁵×C₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁵×C₇

Complements

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

N	H ≅ G/N	type
2. C₂³×C₇×Dic₃	C₂	direct (N × H)
4. C₂⁴×C₃×C₇	C₄	semidirect
6. C₂²×C₇×Dic₃	C₂²	direct (N × H)
9. C₂⁴×Dic₃	C₇	direct (N × H)
10. C₂³×C₃×C₇	C₂×C₄	semidirect
12. C₂×C₇×Dic₃	C₂³	direct (N × H)
13. C₂⁴×C₇	Dic₃	direct (N × H)
17. C₂³×Dic₃	C₂×C₇	direct (N × H)
18. C₂²×C₃×C₇	C₂²×C₄	semidirect
20. C₇×Dic₃	C₂⁴	direct (N × H)
22. C₂³×C₇	C₂×Dic₃	direct (N × H)
25. C₂⁴×C₃	C₄×C₇	semidirect
27. C₂²×Dic₃	C₂²×C₇	direct (N × H)
28. C₂×C₃×C₇	C₂³×C₄	semidirect
32. C₂²×C₇	C₂²×Dic₃	direct (N × H)
35. C₂³×C₃	C₂×C₄×C₇	semidirect
37. C₂×Dic₃	C₂³×C₇	direct (N × H)
38. C₃×C₇	C₂⁴×C₄	semidirect
39. C₂⁴	C₇×Dic₃	direct (N × H)
42. C₂×C₇	C₂³×Dic₃	direct (N × H)
44. C₂²×C₃	C₂²×C₄×C₇	semidirect
46. Dic₃	C₂⁴×C₇	direct (N × H)
47. C₂³	C₂×C₇×Dic₃	direct (N × H)
50. C₇	C₂⁴×Dic₃	direct (N × H)
51. C₂×C₃	C₂³×C₄×C₇	semidirect
53. C₂²	C₂²×C₇×Dic₃	direct (N × H)
56. C₃	C₂⁴×C₄×C₇	semidirect
57. C₂	C₂³×C₇×Dic₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₃×C₇	2
C₂³×C₇×Dic₃	2
C₂⁴×C₄×C₇	3
C₂⁴×Dic₃	7

Subgroups — C24×C7×Dic3 #13062366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₇×Dic₃ #13062366