Subgroups — C₂×C₂₇×Dic₇ #13094130

Order 1512.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂₇×Dic₇	C₂	direct (N × H)
4. C₂×C₇×C₂₇	C₄	semidirect
9. C₇×C₂₇	C₂×C₄	semidirect
19. C₂×Dic₇	C₂₇	direct (N × H)
20. C₂×C₂₇	Dic₇	direct (N × H)
27. Dic₇	C₂×C₂₇	direct (N × H)
28. C₂₇	C₂×Dic₇	direct (N × H)
33. C₂×C₇	C₄×C₂₇	semidirect
39. C₇	C₂×C₄×C₂₇	semidirect
45. C₂	C₂₇×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×C₇×C₂₇	2
C₂₇×Dic₇	2
C₂×C₉×Dic₇	3
C₂×C₄×C₂₇	7

Subgroups — C2×C27×Dic7 #13094130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₇×Dic₇ #13094130