Subgroups — D₃₅₃⋊M₁₆ #26015077

Order 11296.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19150747	C₂	1	2	yes	maximal, complemented
2	#19150746	C₂	1	2	yes	maximal, complemented
3	#19150745	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₃₅₃	C₂	1	1	yes	maximal, characteristic
5	#15667732	C₂²	1	4	yes	complemented
6	C₂²×D₃₅₃	C₄	1	1	yes	characteristic
7	C₂×Dic₃₅₃	C₂²	1	1	yes	characteristic
8	C₄×D₃₅₃	C₄	1	1	yes	characteristic
9	C₄×D₃₅₃	C₄	1	1	yes	characteristic
10	C₄×D₃₅₃	C₂²	1	1	yes	characteristic
11	C₄×D₃₅₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₃₅₃	C₄	1	1	yes	characteristic
13	C₂²×C₃₅₃	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₅₃	—	2	2	no	—
15	C₂×D₃₅₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₃₅₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₃₅₃	C₂×C₄	1	1	yes	characteristic
19	Dic₃₅₃	C₂×C₄	1	1	yes	characteristic
20	Dic₃₅₃	C₂³	1	1	yes	characteristic
21	C₂×C₃₅₃	—	2	1	no	—
22	C₂×C₃₅₃	C₂²×C₄	1	1	yes	characteristic
23	D₃₅₃	—	2	1	no	—
24	D₃₅₃	M₁₆	1	2	yes	complemented
25	C₃₅₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	353	1	no	maximal, Sylow
27	C₂²×C₄	—	353	1	no	—
28	M₁₆	—	353	2	no	—
29	M₁₆	—	353	2	no	—
30	C₂×C₈	—	353	2	no	—
31	C₂³	—	353	1	no	—
32	C₂×C₄	—	353	1	no	—
33	C₂×C₄	—	353	1	no	—
34	C₂×C₄	—	353	1	no	—
35	C₂×C₄	—	353	1	no	—
36	C₂×C₄	—	353	1	no	—
37	C₂×C₄	#13083443	1	1	yes	characteristic
38	C₈	—	353	4	no	—
39	C₂²	—	353	1	no	—
40	C₂²	—	353	1	no	—
41	C₂²	—	706	2	no	—
42	C₂²	C₂×#13083443	1	1	yes	characteristic
43	C₄	—	353	1	no	—
44	C₄	—	353	1	no	—
45	C₄	C₂×#13083443	1	1	yes	characteristic
46	C₄	C₂×#13083443	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	353	2	no	—
49	C₂	—	706	1	no	—
50	C₂	C₂²×#13083443	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13083443
commutator, socle	C₂×C₃₅₃	C₂²×C₄
Frattini	C₂	C₂²×#13083443
Fitting	C₂×C₄×C₃₅₃	C₄
prime radical	C₂²×D₃₅₃	C₄
cosocle	Dic₃₅₃	C₂³
hypercenter	C₂×C₄	#13083443
hypocenter	C₃₅₃	C₂×M₁₆
LCS	G ▷ C₂×C₃₅₃ ▷ C₃₅₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #19150747	C₂	semidirect
2. #19150746	C₂	semidirect
3. #19150745	C₂	semidirect
5. #15667732	C₂²	semidirect
24. D₃₅₃	M₁₆	semidirect
25. C₃₅₃	C₂×M₁₆	semidirect

Maximal subgroups

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

subgroup	index
#19150747	2
#19150746	2
#19150745	2
C₂×C₄×D₃₅₃	2
C₂×M₁₆	353

Subgroups — D353⋊M16 #26015077

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₅₃⋊M₁₆ #26015077