Subgroups — D₁₈₉⋊C₄ #13094117

Order 1512.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂₇×Dic₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×Dic₂₇	C₂	1	1	yes	maximal, characteristic, complemented
4	D₆₃⋊C₄	—	3	1	no	maximal
5	C₂×C₇×C₂₇	C₂²	1	1	yes	characteristic
6	D₁₈₉	C₄	1	2	yes	complemented
7	C₂×D₆₃	—	3	1	no	—
8	C₉×Dic₇	D₃	1	1	yes	characteristic
9	C₇×Dic₉	—	3	1	no	—
10	C₄×D₂₇	—	7	1	no	maximal, Hall
11	C₇×C₂₇	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	D₂₁⋊C₄	—	9	1	no	—
13	C₂×C₇×C₉	C₂×D₃	1	1	yes	characteristic
14	D₆₃	—	3	2	no	—
15	C₂×D₂₇	—	7	1	no	—
16	C₄×C₂₇	—	7	1	no	—
17	Dic₂₇	D₇	1	1	yes	characteristic, complemented
18	C₂×D₂₁	—	9	1	no	—
19	C₃×Dic₇	D₉	1	1	yes	characteristic
20	C₇×Dic₃	—	9	1	no	—
21	C₄×D₉	—	21	1	no	—
22	C₇×C₉	C₄×D₃	1	1	yes	characteristic
23	C₄×D₇	—	27	1	no	Hall
24	C₂×C₂₇	C₂×D₇	1	1	yes	characteristic
25	D₂₇	—	7	2	no	—
26	C₂×C₃×C₇	C₂×D₉	1	1	yes	characteristic
27	D₂₁	—	9	2	no	—
28	C₂×D₉	—	21	1	no	—
29	C₄×C₉	—	7	1	no	—
30	Dic₉	—	3	1	no	—
31	C₂×D₇	—	27	1	no	—
32	C₄×C₇	—	27	1	no	—
33	Dic₇	D₂₇	1	1	yes	characteristic, complemented
34	C₂₇	C₄×D₇	1	1	yes	characteristic, complemented, Sylow
35	C₄×D₃	—	63	1	no	—
36	C₃×C₇	C₄×D₉	1	1	yes	characteristic
37	C₂×C₉	D₃×D₇	1	1	yes	characteristic
38	D₉	—	21	2	no	—
39	C₂×C₇	C₂×D₂₇	1	1	yes	characteristic
40	D₇	—	27	2	no	—
41	C₂×D₃	—	63	1	no	—
42	C₃×C₄	—	7	1	no	—
43	Dic₃	—	9	1	no	—
44	C₉	D₂₁⋊C₄	1	1	yes	characteristic
45	C₂×C₄	—	189	1	no	Sylow
46	C₇	C₄×D₂₇	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₃	D₇×D₉	1	1	yes	characteristic
48	D₃	—	63	2	no	—
49	C₂²	—	189	1	no	—
50	C₄	—	7	1	no	—
51	C₄	—	27	1	no	—
52	C₃	D₆₃⋊C₄	1	1	yes	characteristic
53	C₂	—	189	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×D₁₈₉	C₂
LCS	G ▷ C₇×C₂₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
2. C₂₇×Dic₇	C₂	semidirect
3. C₇×Dic₂₇	C₂	semidirect
6. D₁₈₉	C₄	semidirect
11. C₇×C₂₇	C₂×C₄	semidirect
17. Dic₂₇	D₇	semidirect
33. Dic₇	D₂₇	semidirect
34. C₂₇	C₄×D₇	semidirect
46. C₇	C₄×D₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₈₉	2
C₂₇×Dic₇	2
C₇×Dic₂₇	2
D₆₃⋊C₄	3
C₄×D₂₇	7

Subgroups — D189⋊C4 #13094117

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₈₉⋊C₄ #13094117