Subgroups — C₃²×C₄×C₇⋊D₇ #72277862

Order 3528.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₄×C₇²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₇⋊Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×C₇⋊D₇	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃²×C₇²	C₂²	1	1	yes	characteristic
6	C₃²×C₇⋊D₇	C₄	1	2	yes	direct product factor
7	C₂×C₃×C₇⋊D₇	C₂×C₃	1	4	yes	—
8	C₃×C₄×C₇²	C₂×C₃	1	4	yes	complemented
9	C₃×C₇⋊Dic₇	C₂×C₃	1	4	yes	complemented
10	C₃²×C₄×D₇	—	7	8	no	maximal
11	C₃²×C₇²	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₄×C₇⋊D₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃×C₇²	C₂²×C₃	1	4	yes	—
14	C₃×C₇⋊D₇	C₃×C₄	1	8	yes	direct product factor
15	C₂×C₃²×D₇	—	7	8	no	—
16	C₃²×C₄×C₇	D₇	1	8	yes	complemented
17	C₃²×Dic₇	—	7	8	no	—
18	C₂×C₇⋊D₇	C₂×C₃²	1	1	yes	characteristic
19	C₄×C₇²	C₂×C₃²	1	1	yes	characteristic, complemented
20	C₇⋊Dic₇	C₂×C₃²	1	1	yes	characteristic, complemented
21	C₃×C₄×D₇	—	7	32	no	—
22	C₃×C₇²	C₂×C₃×C₄	1	4	yes	complemented
23	C₂×C₃²×C₇	C₂×D₇	1	8	yes	—
24	C₃²×D₇	—	7	16	no	—
25	C₂×C₇²	C₂²×C₃²	1	1	yes	characteristic
26	C₇⋊D₇	C₃²×C₄	1	2	yes	direct product factor
27	C₂×C₃×D₇	—	7	32	no	—
28	C₃×C₄×C₇	C₃×D₇	1	32	yes	complemented
29	C₃×Dic₇	—	7	32	no	—
30	C₂×C₃²×C₄	—	49	1	no	Hall
31	C₃²×C₇	C₄×D₇	1	8	yes	complemented
32	C₄×D₇	—	7	8	no	—
33	C₇²	C₂×C₃²×C₄	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃×C₇	C₂×C₃×D₇	1	32	yes	—
35	C₃×D₇	—	7	64	no	—
36	C₂²×C₃²	—	49	1	no	—
37	C₃²×C₄	—	49	1	no	—
38	C₃²×C₄	C₇⋊D₇	1	1	yes	characteristic, direct product factor
39	C₂×D₇	—	7	8	no	—
40	C₄×C₇	C₃²×D₇	1	8	yes	complemented
41	Dic₇	—	7	8	no	—
42	C₂×C₃×C₄	—	49	4	no	—
43	C₃×C₇	C₃×C₄×D₇	1	32	yes	complemented
44	C₂×C₃²	—	49	2	no	—
45	C₂×C₃²	C₂×C₇⋊D₇	1	1	yes	characteristic
46	C₂×C₇	C₂×C₃²×D₇	1	8	yes	—
47	D₇	—	7	16	no	—
48	C₂²×C₃	—	49	4	no	—
49	C₃×C₄	—	49	4	no	—
50	C₃×C₄	C₃×C₇⋊D₇	1	4	yes	direct product factor
51	C₃²	C₄×C₇⋊D₇	1	1	yes	characteristic, direct product factor, Sylow
52	C₂×C₄	—	49	1	no	Sylow
53	C₇	C₃²×C₄×D₇	1	8	yes	complemented
54	C₂×C₃	—	49	8	no	—
55	C₂×C₃	C₂×C₃×C₇⋊D₇	1	4	yes	—
56	C₂²	—	49	1	no	—
57	C₄	—	49	1	no	—
58	C₄	C₃²×C₇⋊D₇	1	1	yes	characteristic, direct product factor
59	C₃	C₃×C₄×C₇⋊D₇	1	4	yes	direct product factor
60	C₂	—	49	2	no	—
61	C₂	C₂×C₃²×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃²×C₄	C₇⋊D₇
commutator, hypocenter	C₇²	C₂×C₃²×C₄
Frattini	C₂	C₂×C₃²×C₇⋊D₇
Fitting	C₃²×C₄×C₇²	C₂
socle	C₂×C₃²×C₇²	C₂²
prime radical	C₂×C₃²×C₇⋊D₇	C₂
cosocle	C₂×C₇²	C₂²×C₃²
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃²×C₄

Complements

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

N	H ≅ G/N	type
2. C₃²×C₄×C₇²	C₂	semidirect
3. C₃²×C₇⋊Dic₇	C₂	semidirect
4. C₃×C₄×C₇⋊D₇	C₃	direct (N × H)
6. C₃²×C₇⋊D₇	C₄	direct (N × H)
8. C₃×C₄×C₇²	C₂×C₃	semidirect
9. C₃×C₇⋊Dic₇	C₂×C₃	semidirect
11. C₃²×C₇²	C₂×C₄	semidirect
12. C₄×C₇⋊D₇	C₃²	direct (N × H)
14. C₃×C₇⋊D₇	C₃×C₄	direct (N × H)
16. C₃²×C₄×C₇	D₇	semidirect
19. C₄×C₇²	C₂×C₃²	semidirect
20. C₇⋊Dic₇	C₂×C₃²	semidirect
22. C₃×C₇²	C₂×C₃×C₄	semidirect
26. C₇⋊D₇	C₃²×C₄	direct (N × H)
28. C₃×C₄×C₇	C₃×D₇	semidirect
31. C₃²×C₇	C₄×D₇	semidirect
33. C₇²	C₂×C₃²×C₄	semidirect
38. C₃²×C₄	C₇⋊D₇	direct (N × H)
40. C₄×C₇	C₃²×D₇	semidirect
43. C₃×C₇	C₃×C₄×D₇	semidirect
50. C₃×C₄	C₃×C₇⋊D₇	direct (N × H)
51. C₃²	C₄×C₇⋊D₇	direct (N × H)
53. C₇	C₃²×C₄×D₇	semidirect
58. C₄	C₃²×C₇⋊D₇	direct (N × H)
59. C₃	C₃×C₄×C₇⋊D₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₇⋊D₇	2
C₃²×C₄×C₇²	2
C₃²×C₇⋊Dic₇	2
C₃×C₄×C₇⋊D₇	3
C₃²×C₄×D₇	7

Subgroups — C32×C4×C7⋊D7 #72277862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₄×C₇⋊D₇ #72277862