Subgroups — D₄₀₉⋊M₁₆ #27189802

Order 13088.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20266998	C₂	1	2	yes	maximal, complemented
2	#20266997	C₂	1	2	yes	maximal, complemented
3	#20266996	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₄₀₉	C₂	1	1	yes	maximal, characteristic
5	#15692550	C₂²	1	4	yes	complemented
6	C₂²×D₄₀₉	C₄	1	1	yes	characteristic
7	C₂×Dic₄₀₉	C₂²	1	1	yes	characteristic
8	C₄×D₄₀₉	C₄	1	1	yes	characteristic
9	C₄×D₄₀₉	C₄	1	1	yes	characteristic
10	C₄×D₄₀₉	C₂²	1	1	yes	characteristic
11	C₄×D₄₀₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₄₀₉	C₄	1	1	yes	characteristic
13	C₂²×C₄₀₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₄₀₉	—	2	2	no	—
15	C₂×D₄₀₉	C₂×C₄	1	1	yes	characteristic
16	C₂×D₄₀₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₄₀₉	C₂×C₄	1	1	yes	characteristic
19	Dic₄₀₉	C₂×C₄	1	1	yes	characteristic
20	Dic₄₀₉	C₂³	1	1	yes	characteristic
21	C₂×C₄₀₉	—	2	1	no	—
22	C₂×C₄₀₉	C₂²×C₄	1	1	yes	characteristic
23	D₄₀₉	—	2	1	no	—
24	D₄₀₉	M₁₆	1	2	yes	complemented
25	C₄₀₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	409	1	no	maximal, Sylow
27	C₂²×C₄	—	409	1	no	—
28	M₁₆	—	409	2	no	—
29	M₁₆	—	409	2	no	—
30	C₂×C₈	—	409	2	no	—
31	C₂³	—	409	1	no	—
32	C₂×C₄	—	409	1	no	—
33	C₂×C₄	—	409	1	no	—
34	C₂×C₄	—	409	1	no	—
35	C₂×C₄	—	409	1	no	—
36	C₂×C₄	—	409	1	no	—
37	C₂×C₄	#13109888	1	1	yes	characteristic
38	C₈	—	409	4	no	—
39	C₂²	—	818	2	no	—
40	C₂²	—	409	1	no	—
41	C₂²	—	409	1	no	—
42	C₂²	C₂×#13109888	1	1	yes	characteristic
43	C₄	—	409	1	no	—
44	C₄	—	409	1	no	—
45	C₄	C₂×#13109888	1	1	yes	characteristic
46	C₄	C₂×#13109888	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	818	1	no	—
49	C₂	—	409	2	no	—
50	C₂	C₂²×#13109888	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13109888
commutator, socle	C₂×C₄₀₉	C₂²×C₄
Frattini	C₂	C₂²×#13109888
Fitting	C₂×C₄×C₄₀₉	C₄
prime radical	C₂²×D₄₀₉	C₄
cosocle	Dic₄₀₉	C₂³
hypercenter	C₂×C₄	#13109888
hypocenter	C₄₀₉	C₂×M₁₆
LCS	G ▷ C₂×C₄₀₉ ▷ C₄₀₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20266998	C₂	semidirect
2. #20266997	C₂	semidirect
3. #20266996	C₂	semidirect
5. #15692550	C₂²	semidirect
24. D₄₀₉	M₁₆	semidirect
25. C₄₀₉	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#20266998	2
#20266997	2
#20266996	2
C₂×C₄×D₄₀₉	2
C₂×M₁₆	409

Subgroups — D409⋊M16 #27189802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₀₉⋊M₁₆ #27189802