Subgroups — C₂⁶×Dic₇ #14267671

Order 1792.

111198 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁷×C₇	C₂	1	1	yes	maximal, characteristic
2	C₂⁵×Dic₇	C₂	1	126	yes	maximal, direct product factor
3	C₂⁶×C₇	C₄	1	64	yes	complemented
4	C₂⁶×C₇	C₂²	1	63	yes	—
5	C₂⁴×Dic₇	C₂²	1	2604	yes	direct product factor
6	C₂⁶×C₄	—	7	1	no	maximal, Sylow
7	C₂⁵×C₇	C₂×C₄	1	2016	yes	complemented
8	C₂⁵×C₇	C₂³	1	651	yes	—
9	C₂³×Dic₇	C₂³	1	11160	yes	direct product factor
10	C₂⁷	D₇	1	1	yes	characteristic
11	C₂⁵×C₄	—	7	126	no	—
12	C₂⁴×C₇	C₂²×C₄	1	10416	yes	complemented
13	C₂⁴×C₇	C₂⁴	1	1395	yes	—
14	C₂²×Dic₇	C₂⁴	1	10416	yes	direct product factor
15	C₂⁶	Dic₇	1	64	yes	direct product factor
16	C₂⁶	C₂×D₇	1	63	yes	—
17	C₂⁴×C₄	—	7	2604	no	—
18	C₂³×C₇	C₂³×C₄	1	11160	yes	complemented
19	C₂³×C₇	C₂⁵	1	651	yes	—
20	C₂×Dic₇	C₂⁵	1	2016	yes	direct product factor
21	C₂⁵	C₂×Dic₇	1	2016	yes	direct product factor
22	C₂⁵	C₂²×D₇	1	651	yes	—
23	C₂³×C₄	—	7	11160	no	—
24	C₂²×C₇	C₂⁴×C₄	1	2604	yes	complemented
25	C₂²×C₇	C₂⁶	1	63	yes	—
26	Dic₇	C₂⁶	1	64	yes	direct product factor
27	C₂⁴	C₂²×Dic₇	1	10416	yes	direct product factor
28	C₂⁴	C₂³×D₇	1	1395	yes	—
29	C₂²×C₄	—	7	10416	no	—
30	C₂×C₇	C₂⁵×C₄	1	126	yes	complemented
31	C₂×C₇	C₂⁷	1	1	yes	characteristic
32	C₂³	C₂³×Dic₇	1	11160	yes	direct product factor
33	C₂³	C₂⁴×D₇	1	651	yes	—
34	C₂×C₄	—	7	2016	no	—
35	C₇	C₂⁶×C₄	1	1	yes	characteristic, complemented, Sylow
36	C₂²	C₂⁴×Dic₇	1	2604	yes	direct product factor
37	C₂²	C₂⁵×D₇	1	63	yes	—
38	C₄	—	7	64	no	—
39	C₂	C₂⁵×Dic₇	1	126	yes	direct product factor
40	C₂	C₂⁶×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁷	D₇
commutator, hypocenter	C₇	C₂⁶×C₄
Frattini	C₂	C₂⁶×D₇
Fitting, socle, prime radical	C₂⁷×C₇	C₂
cosocle	C₂×C₇	C₂⁷
LCS	G ▷ C₇
UCS	C₁ ◁ C₂⁷

Complements

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

N	H ≅ G/N	type
2. C₂⁵×Dic₇	C₂	direct (N × H)
3. C₂⁶×C₇	C₄	semidirect
5. C₂⁴×Dic₇	C₂²	direct (N × H)
7. C₂⁵×C₇	C₂×C₄	semidirect
9. C₂³×Dic₇	C₂³	direct (N × H)
12. C₂⁴×C₇	C₂²×C₄	semidirect
14. C₂²×Dic₇	C₂⁴	direct (N × H)
15. C₂⁶	Dic₇	direct (N × H)
18. C₂³×C₇	C₂³×C₄	semidirect
20. C₂×Dic₇	C₂⁵	direct (N × H)
21. C₂⁵	C₂×Dic₇	direct (N × H)
24. C₂²×C₇	C₂⁴×C₄	semidirect
26. Dic₇	C₂⁶	direct (N × H)
27. C₂⁴	C₂²×Dic₇	direct (N × H)
30. C₂×C₇	C₂⁵×C₄	semidirect
32. C₂³	C₂³×Dic₇	direct (N × H)
35. C₇	C₂⁶×C₄	semidirect
36. C₂²	C₂⁴×Dic₇	direct (N × H)
39. C₂	C₂⁵×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
C₂⁷×C₇	2
C₂⁵×Dic₇	2
C₂⁶×C₄	7

Subgroups — C26×Dic7 #14267671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁶×Dic₇ #14267671