Subgroups — D₇×Dic₂₇ #13094119

Order 1512.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇×C₂₇	C₂	1	1	yes	maximal, characteristic
2	Dic₁₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×Dic₉	—	3	1	no	maximal
5	C₂×C₇×C₂₇	C₂²	1	1	yes	characteristic
6	D₇×C₂₇	C₄	1	2	yes	complemented
7	C₂×C₉×D₇	D₃	1	1	yes	characteristic
8	Dic₆₃	—	3	1	no	—
9	C₇×Dic₉	—	3	1	no	—
10	C₂×Dic₂₇	—	7	1	no	maximal, Hall
11	C₇×C₂₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	Dic₃×D₇	—	9	1	no	—
13	C₂×C₇×C₉	C₂×D₃	1	1	yes	characteristic
14	C₉×D₇	Dic₃	1	2	yes	—
15	C₂²×C₂₇	—	7	1	no	—
16	Dic₂₇	—	7	1	no	—
17	Dic₂₇	D₇	1	1	yes	characteristic, direct product factor
18	C₂×C₃×D₇	D₉	1	1	yes	characteristic
19	Dic₂₁	—	9	1	no	—
20	C₇×Dic₃	—	9	1	no	—
21	C₂×Dic₉	—	21	1	no	—
22	C₇×C₉	C₂×Dic₃	1	1	yes	characteristic
23	C₄×D₇	—	27	1	no	Hall
24	C₂×C₂₇	—	7	2	no	—
25	C₂×C₂₇	C₂×D₇	1	1	yes	characteristic
26	C₂×C₃×C₇	C₂×D₉	1	1	yes	characteristic
27	C₃×D₇	Dic₉	1	2	yes	—
28	C₂²×C₉	—	7	1	no	—
29	Dic₉	—	3	1	no	—
30	Dic₉	—	21	1	no	—
31	C₂×D₇	D₂₇	1	1	yes	characteristic
32	C₄×C₇	—	27	1	no	—
33	Dic₇	—	27	1	no	—
34	C₂₇	C₄×D₇	1	1	yes	characteristic, complemented, Sylow
35	C₂×Dic₃	—	63	1	no	—
36	C₃×C₇	C₂×Dic₉	1	1	yes	characteristic
37	C₂×C₉	—	7	2	no	—
38	C₂×C₉	D₃×D₇	1	1	yes	characteristic
39	C₂×C₇	C₂×D₂₇	1	1	yes	characteristic
40	D₇	Dic₂₇	1	2	yes	direct product factor
41	C₂²×C₃	—	7	1	no	—
42	Dic₃	—	9	1	no	—
43	Dic₃	—	63	1	no	—
44	C₉	Dic₃×D₇	1	1	yes	characteristic
45	C₂×C₄	—	189	1	no	Sylow
46	C₇	C₂×Dic₂₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	—	7	2	no	—
48	C₂×C₃	D₇×D₉	1	1	yes	characteristic
49	C₂²	—	7	1	no	—
50	C₄	—	27	1	no	—
51	C₄	—	189	1	no	—
52	C₃	D₇×Dic₉	1	1	yes	characteristic
53	C₂	—	7	2	no	—
54	C₂	D₇×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂	D₇×D₂₇
commutator, hypocenter	C₇×C₂₇	C₂×C₄
Frattini	C₂×C₉	D₃×D₇
Fitting, cosocle	C₂×C₇×C₂₇	C₂²
socle	C₂×C₃×C₇	C₂×D₉
prime radical	C₂×C₃×D₇	D₉
LCS	G ▷ C₇×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₈₉	C₂	semidirect
3. C₇×Dic₂₇	C₂	semidirect
6. D₇×C₂₇	C₄	semidirect
11. C₇×C₂₇	C₂×C₄	semidirect
17. Dic₂₇	D₇	direct (N × H)
34. C₂₇	C₄×D₇	semidirect
40. D₇	Dic₂₇	direct (N × H)
46. C₇	C₂×Dic₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₇×C₂₇	2
Dic₁₈₉	2
C₇×Dic₂₇	2
D₇×Dic₉	3
C₂×Dic₂₇	7

Subgroups — D7×Dic27 #13094119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×Dic₂₇ #13094119