Subgroups — Dic₁₄⋊C₂₇ #13094110

Order 1512.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇⋊C₂₇	C₂	1	1	yes	maximal, characteristic
2	Dic₇⋊C₂₇	C₂	1	2	yes	maximal
3	C₉×Dic₁₄	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇⋊C₂₇	C₂²	1	1	yes	characteristic
5	C₄×C₇×C₉	C₂×C₃	1	1	yes	characteristic
6	C₉×Dic₇	C₂×C₃	1	2	yes	—
7	Q₈×C₂₇	—	7	1	no	maximal, Hall
8	C₇⋊C₂₇	Q₈	1	1	yes	characteristic, complemented, Hall
9	C₃×Dic₁₄	C₉	1	1	yes	characteristic
10	C₂×C₇×C₉	C₂²×C₃	1	1	yes	characteristic
11	C₄×C₂₇	—	7	2	no	—
12	C₄×C₂₇	—	7	1	no	—
13	C₃×C₄×C₇	C₂×C₉	1	1	yes	characteristic
14	C₃×Dic₇	C₂×C₉	1	2	yes	—
15	Q₈×C₉	—	7	1	no	—
16	C₇×C₉	C₃×Q₈	1	1	yes	characteristic
17	Dic₁₄	C₂₇	1	1	yes	characteristic, complemented, Hall
18	C₂×C₂₇	—	7	1	no	—
19	C₂×C₃×C₇	C₂²×C₉	1	1	yes	characteristic
20	C₄×C₉	—	7	2	no	—
21	C₄×C₉	AGL(1,𝔽₇)	1	1	yes	characteristic
22	C₄×C₇	C₂×C₂₇	1	1	yes	characteristic
23	Dic₇	C₂×C₂₇	1	2	yes	—
24	C₂₇	—	7	1	no	Sylow
25	C₃×Q₈	—	7	1	no	—
26	C₃×C₇	Q₈×C₉	1	1	yes	characteristic
27	C₂×C₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
28	C₂×C₇	C₂²×C₂₇	1	1	yes	characteristic
29	C₃×C₄	—	7	2	no	—
30	C₃×C₄	D₇⋊C₉	1	1	yes	characteristic
31	C₉	ΓL(1,𝔽₈)⋊Q₈	1	1	yes	characteristic
32	Q₈	—	7	1	no	Sylow
33	C₇	Q₈×C₂₇	1	1	yes	characteristic, complemented, Sylow
34	C₂×C₃	C₂×D₇⋊C₉	1	1	yes	characteristic
35	C₄	—	7	2	no	—
36	C₄	D₇⋊C₂₇	1	1	yes	characteristic
37	C₃	Dic₁₄⋊C₉	1	1	yes	characteristic
38	C₂	C₂×D₇⋊C₂₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₉	C₂×AGL(1,𝔽₇)
commutator	C₂×C₇	C₂²×C₂₇
Fitting	C₄×C₇×C₉	C₂×C₃
socle, prime radical	C₂×C₃×C₇	C₂²×C₉
cosocle	C₂×C₇×C₉	C₂²×C₃
hypercenter	C₄×C₉	AGL(1,𝔽₇)
hypocenter	C₇	Q₈×C₂₇
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₉ ◁ C₄×C₉

Complements

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

N	H ≅ G/N	type
8. C₇⋊C₂₇	Q₈	semidirect
17. Dic₁₄	C₂₇	semidirect
33. C₇	Q₈×C₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₇⋊C₂₇	2
Dic₇⋊C₂₇	2
C₉×Dic₁₄	3
Q₈×C₂₇	7

Subgroups — Dic14⋊C27 #13094110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₄⋊C₂₇ #13094110