Subgroups — D₁₀₄₉⋊M₁₆ #46777036

Order 33568.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30680926	C₂	1	2	yes	maximal, complemented
2	#30680925	C₂	1	2	yes	maximal, complemented
3	#30680924	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₁₀₄₉	C₂	1	1	yes	maximal, characteristic
5	#22554216	C₂²	1	4	yes	complemented
6	C₂²×D₁₀₄₉	C₄	1	1	yes	characteristic
7	C₂×Dic₁₀₄₉	C₂²	1	1	yes	characteristic
8	C₄×D₁₀₄₉	C₄	1	1	yes	characteristic
9	C₄×D₁₀₄₉	C₄	1	1	yes	characteristic
10	C₄×D₁₀₄₉	C₂²	1	1	yes	characteristic
11	C₄×D₁₀₄₉	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₁₀₄₉	C₄	1	1	yes	characteristic
13	C₂²×C₁₀₄₉	C₂×C₄	1	1	yes	characteristic
14	C₂×D₁₀₄₉	—	2	2	no	—
15	C₂×D₁₀₄₉	C₂×C₄	1	1	yes	characteristic
16	C₂×D₁₀₄₉	C₂×C₄	1	1	yes	characteristic
17	C₄×C₁₀₄₉	C₂×C₄	1	1	yes	characteristic
18	C₄×C₁₀₄₉	C₂×C₄	1	1	yes	characteristic
19	Dic₁₀₄₉	C₂×C₄	1	1	yes	characteristic
20	Dic₁₀₄₉	C₂³	1	1	yes	characteristic
21	C₂×C₁₀₄₉	—	2	1	no	—
22	C₂×C₁₀₄₉	C₂²×C₄	1	1	yes	characteristic
23	D₁₀₄₉	—	2	1	no	—
24	D₁₀₄₉	M₁₆	1	2	yes	complemented
25	C₁₀₄₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	1049	1	no	maximal, Sylow
27	C₂²×C₄	—	1049	1	no	—
28	M₁₆	—	1049	2	no	—
29	M₁₆	—	1049	2	no	—
30	C₂×C₈	—	1049	2	no	—
31	C₂³	—	1049	1	no	—
32	C₂×C₄	—	1049	1	no	—
33	C₂×C₄	—	1049	1	no	—
34	C₂×C₄	—	1049	1	no	—
35	C₂×C₄	—	1049	1	no	—
36	C₂×C₄	—	1049	1	no	—
37	C₂×C₄	#16862310	1	1	yes	characteristic
38	C₈	—	1049	4	no	—
39	C₂²	—	1049	1	no	—
40	C₂²	—	1049	1	no	—
41	C₂²	—	2098	2	no	—
42	C₂²	C₂×#16862310	1	1	yes	characteristic
43	C₄	—	1049	1	no	—
44	C₄	—	1049	1	no	—
45	C₄	C₂×#16862310	1	1	yes	characteristic
46	C₄	C₂×#16862310	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	1049	2	no	—
49	C₂	—	2098	1	no	—
50	C₂	C₂²×#16862310	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#16862310
commutator, socle	C₂×C₁₀₄₉	C₂²×C₄
Frattini	C₂	C₂²×#16862310
Fitting	C₂×C₄×C₁₀₄₉	C₄
prime radical	C₂²×D₁₀₄₉	C₄
cosocle	Dic₁₀₄₉	C₂³
hypercenter	C₂×C₄	#16862310
hypocenter	C₁₀₄₉	C₂×M₁₆
LCS	G ▷ C₂×C₁₀₄₉ ▷ C₁₀₄₉
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #30680926	C₂	semidirect
2. #30680925	C₂	semidirect
3. #30680924	C₂	semidirect
5. #22554216	C₂²	semidirect
24. D₁₀₄₉	M₁₆	semidirect
25. C₁₀₄₉	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#30680926	2
#30680925	2
#30680924	2
C₂×C₄×D₁₀₄₉	2
C₂×M₁₆	1049

Subgroups — D1049⋊M16 #46777036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₀₄₉⋊M₁₆ #46777036