Subgroups — C₂×C₇×C₂²⋊C₂₇ #13094194

Order 1512.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂²⋊C₂₇	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₇×C₉	C₃	1	1	yes	maximal, characteristic
3	C₂×C₇×C₂₇	—	4	1	no	maximal
4	C₂²×C₇×C₉	—	3	1	no	—
5	C₂²×C₇×C₉	—	3	1	no	—
6	C₂²×C₇×C₉	C₂×C₃	1	1	yes	characteristic
7	C₂×C₂²⋊C₂₇	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₇×C₂₇	—	4	1	no	Hall
9	C₂³×C₃×C₇	C₉	1	1	yes	characteristic
10	C₂×C₇×C₉	—	3	1	no	—
11	C₂×C₇×C₉	—	3	1	no	—
12	C₂×C₇×C₉	A₄	1	1	yes	characteristic
13	C₂²⋊C₂₇	C₂×C₇	1	1	yes	characteristic, direct product factor
14	C₂²×C₃×C₇	—	3	1	no	—
15	C₂²×C₃×C₇	—	3	1	no	—
16	C₂²×C₃×C₇	C₂×C₉	1	1	yes	characteristic
17	C₂³×C₉	C₃×C₇	1	1	yes	characteristic
18	C₇×C₉	C₂×A₄	1	1	yes	characteristic
19	C₂³×C₇	C₂₇	1	1	yes	characteristic, complemented, Hall
20	C₂×C₂₇	—	4	1	no	—
21	C₂×C₃×C₇	—	3	1	no	—
22	C₂×C₃×C₇	—	3	1	no	—
23	C₂×C₃×C₇	C₂²⋊C₉	1	1	yes	characteristic
24	C₂²×C₉	—	3	1	no	—
25	C₂²×C₉	—	3	1	no	—
26	C₂²×C₉	C₂×C₃×C₇	1	1	yes	characteristic
27	C₂²×C₇	—	3	1	no	—
28	C₂²×C₇	—	3	1	no	—
29	C₂²×C₇	C₂×C₂₇	1	1	yes	characteristic, complemented
30	C₂₇	—	4	1	no	Sylow
31	C₂³×C₃	C₇×C₉	1	1	yes	characteristic
32	C₃×C₇	C₂×C₂²⋊C₉	1	1	yes	characteristic
33	C₂×C₉	—	3	1	no	—
34	C₂×C₉	—	3	1	no	—
35	C₂×C₉	C₇×A₄	1	1	yes	characteristic
36	C₂×C₇	—	3	1	no	—
37	C₂×C₇	—	3	1	no	—
38	C₂×C₇	C₂²⋊C₂₇	1	1	yes	characteristic, direct product factor
39	C₂²×C₃	—	3	1	no	—
40	C₂²×C₃	—	3	1	no	—
41	C₂²×C₃	C₂×C₇×C₉	1	1	yes	characteristic
42	C₉	C₂×C₇×A₄	1	1	yes	characteristic
43	C₂³	C₇×C₂₇	1	1	yes	characteristic, complemented, Sylow
44	C₇	C₂×C₂²⋊C₂₇	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₃	—	3	1	no	—
46	C₂×C₃	—	3	1	no	—
47	C₂×C₃	C₇×C₂²⋊C₉	1	1	yes	characteristic
48	C₂²	—	3	1	no	—
49	C₂²	—	3	1	no	—
50	C₂²	C₂×C₇×C₂₇	1	1	yes	characteristic, complemented
51	C₃	C₂×C₇×C₂²⋊C₉	1	1	yes	characteristic
52	C₂	—	3	1	no	—
53	C₂	—	3	1	no	—
54	C₂	C₇×C₂²⋊C₂₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇×C₉	A₄
commutator, hypocenter	C₂²	C₂×C₇×C₂₇
Frattini	C₉	C₂×C₇×A₄
Fitting	C₂³×C₇×C₉	C₃
socle, prime radical	C₂³×C₃×C₇	C₉
cosocle	C₂²×C₉	C₂×C₃×C₇
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂×C₇×C₉

Complements

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

N	H ≅ G/N	type
1. C₇×C₂²⋊C₂₇	C₂	direct (N × H)
7. C₂×C₂²⋊C₂₇	C₇	direct (N × H)
13. C₂²⋊C₂₇	C₂×C₇	direct (N × H)
19. C₂³×C₇	C₂₇	semidirect
29. C₂²×C₇	C₂×C₂₇	semidirect
38. C₂×C₇	C₂²⋊C₂₇	direct (N × H)
43. C₂³	C₇×C₂₇	semidirect
44. C₇	C₂×C₂²⋊C₂₇	direct (N × H)
50. C₂²	C₂×C₇×C₂₇	semidirect
54. C₂	C₇×C₂²⋊C₂₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×C₂²⋊C₂₇	2
C₂³×C₇×C₉	3
C₂×C₇×C₂₇	4
C₂×C₂²⋊C₂₇	7

Subgroups — C2×C7×C22⋊C27 #13094194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₂²⋊C₂₇ #13094194