Subgroups — C₂×C₄×C₇⋊Dic₇ #13096562

Order 1568.

540 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇²	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₇⋊Dic₇	C₂	1	2	yes	maximal
3	C₄×C₇⋊Dic₇	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₇²	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₇²	C₄	1	4	yes	complemented
6	C₂×C₄×C₇²	C₂²	1	2	yes	—
7	C₂×C₇⋊Dic₇	C₄	1	8	yes	direct product factor
8	C₂×C₇⋊Dic₇	C₂²	1	4	yes	—
9	C₂×C₄×Dic₇	—	7	8	no	maximal
10	C₂²×C₇²	C₂×C₄	1	4	yes	—
11	C₂²×C₇²	C₂×C₄	1	2	yes	—
12	C₂²×C₇²	C₂³	1	1	yes	characteristic
13	C₄×C₇²	C₂×C₄	1	4	yes	complemented
14	C₇⋊Dic₇	C₂×C₄	1	8	yes	direct product factor
15	C₂²×C₄×C₇	D₇	1	8	yes	—
16	C₂²×Dic₇	—	7	16	no	—
17	C₄×Dic₇	—	7	32	no	—
18	C₂×C₇²	C₄²	1	4	yes	complemented
19	C₂×C₇²	C₂²×C₄	1	2	yes	—
20	C₂×C₇²	C₂²×C₄	1	1	yes	characteristic
21	C₂³×C₇	C₂×D₇	1	8	yes	—
22	C₂×C₄×C₇	Dic₇	1	32	yes	complemented
23	C₂×C₄×C₇	C₂×D₇	1	16	yes	—
24	C₂×Dic₇	—	7	64	no	—
25	C₂×Dic₇	—	7	32	no	—
26	C₇²	C₂×C₄²	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄²	—	49	1	no	Sylow
28	C₂²×C₇	C₄×D₇	1	32	yes	—
29	C₂²×C₇	C₂×Dic₇	1	16	yes	—
30	C₂²×C₇	C₂²×D₇	1	8	yes	—
31	C₄×C₇	C₂×Dic₇	1	32	yes	complemented
32	Dic₇	—	7	64	no	—
33	C₂²×C₄	—	49	2	no	—
34	C₂²×C₄	C₇⋊D₇	1	1	yes	characteristic
35	C₄²	—	49	4	no	—
36	C₂×C₇	C₄×Dic₇	1	32	yes	complemented
37	C₂×C₇	C₂×C₄×D₇	1	16	yes	—
38	C₂×C₇	C₂²×Dic₇	1	8	yes	—
39	C₂³	C₂×C₇⋊D₇	1	1	yes	characteristic
40	C₂×C₄	—	49	8	no	—
41	C₂×C₄	—	49	4	no	—
42	C₂×C₄	C₇⋊Dic₇	1	4	yes	direct product factor
43	C₂×C₄	C₂×C₇⋊D₇	1	2	yes	—
44	C₇	C₂×C₄×Dic₇	1	8	yes	complemented
45	C₂²	C₄×C₇⋊D₇	1	4	yes	—
46	C₂²	C₂×C₇⋊Dic₇	1	2	yes	—
47	C₂²	C₂²×C₇⋊D₇	1	1	yes	characteristic
48	C₄	—	49	8	no	—
49	C₄	C₂×C₇⋊Dic₇	1	4	yes	direct product factor
50	C₂	C₄×C₇⋊Dic₇	1	4	yes	direct product factor
51	C₂	C₂×C₄×C₇⋊D₇	1	2	yes	—
52	C₂	C₂²×C₇⋊Dic₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄	C₇⋊D₇
commutator, hypocenter	C₇²	C₂×C₄²
Frattini	C₂²	C₂²×C₇⋊D₇
Fitting	C₂²×C₄×C₇²	C₂
socle, prime radical	C₂³×C₇²	C₂²
cosocle	C₂²×C₇²	C₂³
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₇⋊Dic₇	C₂	direct (N × H)
5. C₂×C₄×C₇²	C₄	semidirect
7. C₂×C₇⋊Dic₇	C₄	direct (N × H)
13. C₄×C₇²	C₂×C₄	semidirect
14. C₇⋊Dic₇	C₂×C₄	direct (N × H)
18. C₂×C₇²	C₄²	semidirect
22. C₂×C₄×C₇	Dic₇	semidirect
26. C₇²	C₂×C₄²	semidirect
31. C₄×C₇	C₂×Dic₇	semidirect
36. C₂×C₇	C₄×Dic₇	semidirect
42. C₂×C₄	C₇⋊Dic₇	direct (N × H)
44. C₇	C₂×C₄×Dic₇	semidirect
49. C₄	C₂×C₇⋊Dic₇	direct (N × H)
50. C₂	C₄×C₇⋊Dic₇	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×C₄×C₇²	2
C₂²×C₇⋊Dic₇	2
C₄×C₇⋊Dic₇	2
C₂×C₄×Dic₇	7

Subgroups — C2×C4×C7⋊Dic7 #13096562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₇⋊Dic₇ #13096562