Subgroups — C₂×C₇×Dic₂₆ #13089882

Order 1456.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×Dic₁₃	C₂	1	2	yes	maximal
3	C₇×Dic₂₆	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×C₁₃	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₁₃	C₂²	1	2	yes	—
6	C₇×Dic₁₃	C₂²	1	4	yes	—
7	C₂×Dic₂₆	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₇×C₁₃	Q₈	1	2	yes	complemented
9	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
10	C₂×C₇×Q₈	—	13	1	no	maximal, Hall
11	C₂×C₄×C₁₃	C₂×C₇	1	1	yes	characteristic
12	C₂×Dic₁₃	C₂×C₇	1	2	yes	—
13	Dic₂₆	C₂×C₇	1	4	yes	direct product factor
14	C₇×C₁₃	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
15	C₇×Q₈	—	13	4	no	—
16	C₂×C₄×C₇	—	13	2	no	—
17	C₂×C₄×C₇	D₁₃	1	1	yes	characteristic
18	C₂²×C₁₃	C₂²×C₇	1	1	yes	characteristic
19	C₄×C₁₃	C₂²×C₇	1	2	yes	—
20	Dic₁₃	C₂²×C₇	1	4	yes	—
21	C₂²×C₇	C₂×D₁₃	1	1	yes	characteristic
22	C₄×C₇	—	13	4	no	—
23	C₄×C₇	C₂×D₁₃	1	2	yes	—
24	C₂×C₁₃	C₇×Q₈	1	2	yes	complemented
25	C₂×C₁₃	C₂³×C₇	1	1	yes	characteristic
26	C₂×Q₈	—	13	1	no	Sylow
27	C₂×C₇	Dic₂₆	1	2	yes	direct product factor
28	C₂×C₇	C₂²×D₁₃	1	1	yes	characteristic
29	C₁₃	C₂×C₇×Q₈	1	1	yes	characteristic, complemented, Sylow
30	Q₈	—	13	4	no	—
31	C₂×C₄	—	13	2	no	—
32	C₂×C₄	C₇×D₁₃	1	1	yes	characteristic
33	C₇	C₂×Dic₂₆	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	C₂×C₇×D₁₃	1	1	yes	characteristic
35	C₄	—	13	4	no	—
36	C₄	C₂×C₇×D₁₃	1	2	yes	—
37	C₂	C₇×Dic₂₆	1	2	yes	direct product factor
38	C₂	C₂²×C₇×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇	C₂×D₁₃
commutator, cosocle	C₂×C₁₃	C₂³×C₇
Frattini	C₂	C₂²×C₇×D₁₃
Fitting	C₂×C₄×C₇×C₁₃	C₂
socle, prime radical	C₂²×C₇×C₁₃	C₂²
hypercenter	C₂×C₄×C₇	D₁₃
hypocenter	C₁₃	C₂×C₇×Q₈
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₄×C₇

Complements

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

N	H ≅ G/N	type
3. C₇×Dic₂₆	C₂	direct (N × H)
7. C₂×Dic₂₆	C₇	direct (N × H)
8. C₂×C₇×C₁₃	Q₈	semidirect
13. Dic₂₆	C₂×C₇	direct (N × H)
14. C₇×C₁₃	C₂×Q₈	semidirect
24. C₂×C₁₃	C₇×Q₈	semidirect
27. C₂×C₇	Dic₂₆	direct (N × H)
29. C₁₃	C₂×C₇×Q₈	semidirect
33. C₇	C₂×Dic₂₆	direct (N × H)
37. C₂	C₇×Dic₂₆	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×C₄×C₇×C₁₃	2
C₂×C₇×Dic₁₃	2
C₇×Dic₂₆	2
C₂×Dic₂₆	7
C₂×C₇×Q₈	13

Subgroups — C2×C7×Dic26 #13089882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×Dic₂₆ #13089882