Subgroups — C₂×C₄×D₂₇ #88397

Order 432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₂₇	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄×D₉	—	3	1	no	maximal
6	C₂²×C₂₇	C₂²	1	1	yes	characteristic
7	C₂×D₂₇	C₄	1	4	yes	direct product factor
8	C₂×D₂₇	C₂²	1	2	yes	—
9	C₄×C₂₇	C₂²	1	2	yes	complemented
10	Dic₂₇	C₂²	1	2	yes	complemented
11	C₂²×D₉	—	3	1	no	—
12	C₂×C₄×C₉	D₃	1	1	yes	characteristic
13	C₂×Dic₉	—	3	1	no	—
14	C₄×D₉	—	3	4	no	—
15	C₂×C₂₇	C₂×C₄	1	2	yes	complemented
16	C₂×C₂₇	C₂³	1	1	yes	characteristic
17	D₂₇	C₂×C₄	1	4	yes	direct product factor
18	C₂×C₄×D₃	—	9	1	no	—
19	C₂²×C₉	C₂×D₃	1	1	yes	characteristic
20	C₂×D₉	—	3	4	no	—
21	C₂×D₉	—	3	2	no	—
22	C₄×C₉	C₂×D₃	1	2	yes	—
23	Dic₉	—	3	2	no	—
24	C₂₇	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
25	C₂²×D₃	—	9	1	no	—
26	C₂×C₃×C₄	D₉	1	1	yes	characteristic
27	C₂×Dic₃	—	9	1	no	—
28	C₄×D₃	—	9	4	no	—
29	C₂×C₉	C₄×D₃	1	2	yes	—
30	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
31	D₉	—	3	4	no	—
32	C₂²×C₄	—	27	1	no	Sylow
33	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
34	C₂×D₃	—	9	4	no	—
35	C₂×D₃	—	9	2	no	—
36	C₃×C₄	C₂×D₉	1	2	yes	—
37	Dic₃	—	9	2	no	—
38	C₉	C₂×C₄×D₃	1	1	yes	characteristic
39	C₂³	—	27	1	no	—
40	C₂×C₄	—	27	1	no	—
41	C₂×C₄	—	27	4	no	—
42	C₂×C₄	D₂₇	1	1	yes	characteristic, direct product factor
43	C₂×C₃	C₄×D₉	1	2	yes	—
44	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
45	D₃	—	9	4	no	—
46	C₂²	—	27	4	no	—
47	C₂²	—	27	2	no	—
48	C₂²	C₂×D₂₇	1	1	yes	characteristic
49	C₄	—	27	2	no	—
50	C₄	C₂×D₂₇	1	2	yes	direct product factor
51	C₃	C₂×C₄×D₉	1	1	yes	characteristic
52	C₂	—	27	4	no	—
53	C₂	C₄×D₂₇	1	2	yes	direct product factor
54	C₂	C₂²×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₂₇
commutator, hypocenter	C₂₇	C₂²×C₄
Frattini	C₂×C₉	C₂²×D₃
Fitting	C₂×C₄×C₂₇	C₂
socle	C₂²×C₃	C₂×D₉
prime radical	C₂²×D₂₇	C₂
cosocle	C₂×C₂₇	C₂³
LCS	G ▷ C₂₇
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₂₇	C₂	semidirect
3. C₂×Dic₂₇	C₂	semidirect
4. C₄×D₂₇	C₂	direct (N × H)
7. C₂×D₂₇	C₄	direct (N × H)
9. C₄×C₂₇	C₂²	semidirect
10. Dic₂₇	C₂²	semidirect
15. C₂×C₂₇	C₂×C₄	semidirect
17. D₂₇	C₂×C₄	direct (N × H)
24. C₂₇	C₂²×C₄	semidirect
42. C₂×C₄	D₂₇	direct (N × H)
50. C₄	C₂×D₂₇	direct (N × H)
53. C₂	C₄×D₂₇	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×D₂₇	2
C₂×C₄×C₂₇	2
C₂×Dic₂₇	2
C₄×D₂₇	2
C₂×C₄×D₉	3

Subgroups — C2×C4×D27 #88397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₂₇ #88397