Subgroups — C₄²×C₇×Dic₃ #13055963

Order 1344.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₇×Dic₃	C₂	1	6	yes	maximal
3	C₄³×C₇	—	3	1	no	maximal, Hall
4	C₂²×C₃×C₄×C₇	C₂²	1	3	yes	—
5	C₂²×C₇×Dic₃	C₂²	1	4	yes	—
6	C₃×C₄²×C₇	C₄	1	4	yes	complemented
7	C₄×C₇×Dic₃	C₄	1	24	yes	direct product factor
8	C₂×C₄²×C₇	—	3	6	no	—
9	C₂×C₄²×C₇	D₃	1	1	yes	characteristic
10	C₄²×Dic₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×C₇	C₂³	1	1	yes	characteristic
12	C₂×C₃×C₄×C₇	C₂×C₄	1	12	yes	—
13	C₂×C₃×C₄×C₇	C₂×C₄	1	6	yes	—
14	C₂×C₇×Dic₃	C₂×C₄	1	24	yes	—
15	C₂²×C₄×C₇	—	3	4	no	—
16	C₂²×C₄×C₇	C₂×D₃	1	3	yes	—
17	C₄²×C₇	—	3	24	no	—
18	C₄²×C₇	Dic₃	1	4	yes	direct product factor
19	C₂×C₃×C₄²	C₂×C₇	1	1	yes	characteristic
20	C₂×C₄×Dic₃	C₂×C₇	1	6	yes	—
21	C₂²×C₃×C₇	C₂²×C₄	1	6	yes	—
22	C₂²×C₃×C₇	C₂²×C₄	1	1	yes	characteristic
23	C₃×C₄×C₇	C₄²	1	12	yes	complemented
24	C₇×Dic₃	C₄²	1	16	yes	direct product factor
25	C₄³	—	3	1	no	Sylow
26	C₂³×C₇	C₂²×D₃	1	1	yes	characteristic
27	C₂×C₄×C₇	—	3	24	no	—
28	C₂×C₄×C₇	C₄×D₃	1	12	yes	—
29	C₂×C₄×C₇	C₂×Dic₃	1	6	yes	—
30	C₂²×C₃×C₄	C₂²×C₇	1	3	yes	—
31	C₂²×Dic₃	C₂²×C₇	1	4	yes	—
32	C₃×C₄²	C₄×C₇	1	4	yes	complemented
33	C₄×Dic₃	C₄×C₇	1	24	yes	direct product factor
34	C₂×C₃×C₇	C₂×C₄²	1	4	yes	—
35	C₂×C₃×C₇	C₂×C₄²	1	3	yes	—
36	C₂×C₄²	—	3	6	no	—
37	C₂×C₄²	D₃×C₇	1	1	yes	characteristic
38	C₂²×C₇	C₂×C₄×D₃	1	6	yes	—
39	C₂²×C₇	C₂²×Dic₃	1	1	yes	characteristic
40	C₄×C₇	—	3	16	no	—
41	C₄×C₇	C₄×Dic₃	1	12	yes	direct product factor
42	C₂³×C₃	C₂³×C₇	1	1	yes	characteristic
43	C₂×C₃×C₄	C₂×C₄×C₇	1	12	yes	—
44	C₂×C₃×C₄	C₂×C₄×C₇	1	6	yes	—
45	C₂×Dic₃	C₂×C₄×C₇	1	24	yes	—
46	C₃×C₇	C₄³	1	1	yes	characteristic, complemented, Hall
47	C₂²×C₄	—	3	4	no	—
48	C₂²×C₄	C₂×D₃×C₇	1	3	yes	—
49	C₄²	—	3	24	no	—
50	C₄²	C₇×Dic₃	1	4	yes	direct product factor
51	C₂×C₇	C₄²×D₃	1	4	yes	—
52	C₂×C₇	C₂×C₄×Dic₃	1	3	yes	—
53	C₂²×C₃	C₂²×C₄×C₇	1	6	yes	—
54	C₂²×C₃	C₂²×C₄×C₇	1	1	yes	characteristic
55	C₃×C₄	C₄²×C₇	1	12	yes	complemented
56	Dic₃	C₄²×C₇	1	16	yes	direct product factor
57	C₂³	C₂²×D₃×C₇	1	1	yes	characteristic
58	C₂×C₄	—	3	24	no	—
59	C₂×C₄	C₄×D₃×C₇	1	12	yes	—
60	C₂×C₄	C₂×C₇×Dic₃	1	6	yes	—
61	C₇	C₄²×Dic₃	1	1	yes	characteristic, direct product factor, Sylow
62	C₂×C₃	C₂×C₄²×C₇	1	4	yes	—
63	C₂×C₃	C₂×C₄²×C₇	1	3	yes	—
64	C₂²	C₂×C₄×D₃×C₇	1	6	yes	—
65	C₂²	C₂²×C₇×Dic₃	1	1	yes	characteristic
66	C₄	—	3	16	no	—
67	C₄	C₄×C₇×Dic₃	1	12	yes	direct product factor
68	C₃	C₄³×C₇	1	1	yes	characteristic, complemented, Sylow
69	C₂	C₄²×D₃×C₇	1	4	yes	—
70	C₂	C₂×C₄×C₇×Dic₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²×C₇	D₃
commutator, hypocenter	C₃	C₄³×C₇
Frattini	C₂³	C₂²×D₃×C₇
Fitting	C₂×C₃×C₄²×C₇	C₂
socle, prime radical	C₂³×C₃×C₇	C₂³
cosocle	C₂³×C₃	C₂³×C₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₄²×C₇

Complements

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

N	H ≅ G/N	type
6. C₃×C₄²×C₇	C₄	semidirect
7. C₄×C₇×Dic₃	C₄	direct (N × H)
10. C₄²×Dic₃	C₇	direct (N × H)
18. C₄²×C₇	Dic₃	direct (N × H)
23. C₃×C₄×C₇	C₄²	semidirect
24. C₇×Dic₃	C₄²	direct (N × H)
32. C₃×C₄²	C₄×C₇	semidirect
33. C₄×Dic₃	C₄×C₇	direct (N × H)
41. C₄×C₇	C₄×Dic₃	direct (N × H)
46. C₃×C₇	C₄³	semidirect
50. C₄²	C₇×Dic₃	direct (N × H)
55. C₃×C₄	C₄²×C₇	semidirect
56. Dic₃	C₄²×C₇	direct (N × H)
61. C₇	C₄²×Dic₃	direct (N × H)
67. C₄	C₄×C₇×Dic₃	direct (N × H)
68. C₃	C₄³×C₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄²×C₇	2
C₂×C₄×C₇×Dic₃	2
C₄³×C₇	3
C₄²×Dic₃	7

Subgroups — C42×C7×Dic3 #13055963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₇×Dic₃ #13055963