Subgroups — D₄×D₂₇ #88400

Order 432.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₂₇	C₂	1	2	yes	maximal, complemented
2	D₄×C₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#6171	C₂	1	2	yes	maximal, complemented
4	D₁₀₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₂₇	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₉	—	3	1	no	maximal
7	C₂²×C₂₇	C₂²	1	2	yes	complemented
8	C₂×D₂₇	—	2	4	no	—
9	C₂×D₂₇	C₂²	1	1	yes	characteristic
10	C₂×D₂₇	C₂²	1	2	yes	complemented
11	C₄×C₂₇	C₂²	1	1	yes	characteristic, complemented
12	Dic₂₇	C₂²	1	1	yes	characteristic, complemented
13	C₂²×D₉	—	3	2	no	—
14	D₄×C₉	D₃	1	1	yes	characteristic
15	#611	—	3	2	no	—
16	D₃₆	—	3	1	no	—
17	C₄×D₉	—	3	1	no	—
18	C₂×C₂₇	—	2	2	no	—
19	C₂×C₂₇	C₂³	1	1	yes	characteristic
20	D₂₇	—	2	2	no	—
21	D₂₇	D₄	1	2	yes	direct product factor
22	D₃×D₄	—	9	1	no	—
23	C₂²×C₉	C₂×D₃	1	2	yes	—
24	C₂×D₉	—	3	1	no	—
25	C₂×D₉	—	3	2	no	—
26	C₂×D₉	—	6	4	no	—
27	C₄×C₉	C₂×D₃	1	1	yes	characteristic
28	Dic₉	—	3	1	no	—
29	C₂₇	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
30	C₂²×D₃	—	9	2	no	—
31	C₃×D₄	D₉	1	1	yes	characteristic
32	#67	—	9	2	no	—
33	D₁₂	—	9	1	no	—
34	C₄×D₃	—	9	1	no	—
35	C₂×C₉	—	2	2	no	—
36	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
37	D₉	—	3	2	no	—
38	D₉	—	6	2	no	—
39	C₂×D₄	—	27	1	no	Sylow
40	C₂²×C₃	C₂×D₉	1	2	yes	—
41	C₂×D₃	—	9	1	no	—
42	C₂×D₃	—	9	2	no	—
43	C₂×D₃	—	18	4	no	—
44	C₃×C₄	C₂×D₉	1	1	yes	characteristic
45	Dic₃	—	9	1	no	—
46	C₉	D₃×D₄	1	1	yes	characteristic
47	C₂³	—	27	2	no	—
48	D₄	—	27	2	no	—
49	D₄	—	27	1	no	—
50	D₄	D₂₇	1	1	yes	characteristic, direct product factor
51	C₂×C₄	—	27	1	no	—
52	C₂×C₃	—	2	2	no	—
53	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
54	D₃	—	9	2	no	—
55	D₃	—	18	2	no	—
56	C₂²	—	27	1	no	—
57	C₂²	—	27	2	no	—
58	C₂²	—	54	4	no	—
59	C₂²	C₂×D₂₇	1	2	yes	complemented
60	C₄	—	27	1	no	—
61	C₄	C₂×D₂₇	1	1	yes	characteristic, complemented
62	C₃	D₄×D₉	1	1	yes	characteristic
63	C₂	—	2	2	no	—
64	C₂	—	27	2	no	—
65	C₂	—	54	2	no	—
66	C₂	C₂²×D₂₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₂₇
commutator, cosocle	C₂×C₂₇	C₂³
Frattini	C₂×C₉	C₂²×D₃
Fitting	D₄×C₂₇	C₂
socle	C₂×C₃	C₂²×D₉
hypercenter	D₄	D₂₇
hypocenter	C₂₇	C₂×D₄
LCS	G ▷ C₂×C₂₇ ▷ C₂₇
UCS	C₁ ◁ C₂ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×D₂₇	C₂	semidirect
2. D₄×C₂₇	C₂	semidirect
3. #6171	C₂	semidirect
4. D₁₀₈	C₂	semidirect
5. C₄×D₂₇	C₂	semidirect
7. C₂²×C₂₇	C₂²	semidirect
10. C₂×D₂₇	C₂²	semidirect
11. C₄×C₂₇	C₂²	semidirect
12. Dic₂₇	C₂²	semidirect
21. D₂₇	D₄	direct (N × H)
29. C₂₇	C₂×D₄	semidirect
50. D₄	D₂₇	direct (N × H)
59. C₂²	C₂×D₂₇	semidirect
61. C₄	C₂×D₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₂₇	2
D₄×C₂₇	2
#6171	2
D₁₀₈	2
C₄×D₂₇	2
D₄×D₉	3

Subgroups — D4×D27 #88400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×D₂₇ #88400