Subgroups — D₂₃₃⋊M₁₆ #21418620

Order 7456.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16836604	C₂	1	2	yes	maximal, complemented
2	#16836603	C₂	1	2	yes	maximal, complemented
3	#16836602	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×D₂₃₃	C₂	1	1	yes	maximal, characteristic
5	#14272345	C₂²	1	4	yes	complemented
6	C₂²×D₂₃₃	C₄	1	1	yes	characteristic
7	C₂×Dic₂₃₃	C₂²	1	1	yes	characteristic
8	C₄×D₂₃₃	C₄	1	1	yes	characteristic
9	C₄×D₂₃₃	C₄	1	1	yes	characteristic
10	C₄×D₂₃₃	C₂²	1	1	yes	characteristic
11	C₄×D₂₃₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₂₃₃	C₄	1	1	yes	characteristic
13	C₂²×C₂₃₃	C₂×C₄	1	1	yes	characteristic
14	C₂×D₂₃₃	—	2	2	no	—
15	C₂×D₂₃₃	C₂×C₄	1	1	yes	characteristic
16	C₂×D₂₃₃	C₂×C₄	1	1	yes	characteristic
17	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
19	Dic₂₃₃	C₂×C₄	1	1	yes	characteristic
20	Dic₂₃₃	C₂³	1	1	yes	characteristic
21	C₂×C₂₃₃	—	2	1	no	—
22	C₂×C₂₃₃	C₂²×C₄	1	1	yes	characteristic
23	D₂₃₃	—	2	1	no	—
24	D₂₃₃	M₁₆	1	2	yes	complemented
25	C₂₃₃	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
26	C₂×M₁₆	—	233	1	no	maximal, Sylow
27	C₂²×C₄	—	233	1	no	—
28	M₁₆	—	233	2	no	—
29	M₁₆	—	233	2	no	—
30	C₂×C₈	—	233	2	no	—
31	C₂³	—	233	1	no	—
32	C₂×C₄	—	233	1	no	—
33	C₂×C₄	—	233	1	no	—
34	C₂×C₄	—	233	1	no	—
35	C₂×C₄	—	233	1	no	—
36	C₂×C₄	—	233	1	no	—
37	C₂×C₄	#11745400	1	1	yes	characteristic
38	C₈	—	233	4	no	—
39	C₂²	—	466	2	no	—
40	C₂²	—	233	1	no	—
41	C₂²	—	233	1	no	—
42	C₂²	C₂×#11745400	1	1	yes	characteristic
43	C₄	—	233	1	no	—
44	C₄	—	233	1	no	—
45	C₄	C₂×#11745400	1	1	yes	characteristic
46	C₄	C₂×#11745400	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	466	1	no	—
49	C₂	—	233	2	no	—
50	C₂	C₂²×#11745400	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#11745400
commutator, socle	C₂×C₂₃₃	C₂²×C₄
Frattini	C₂	C₂²×#11745400
Fitting	C₂×C₄×C₂₃₃	C₄
hypercenter	C₂×C₄	#11745400
hypocenter	C₂₃₃	C₂×M₁₆
LCS	G ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #16836604	C₂	semidirect
2. #16836603	C₂	semidirect
3. #16836602	C₂	semidirect
5. #14272345	C₂²	semidirect
24. D₂₃₃	M₁₆	semidirect
25. C₂₃₃	C₂×M₁₆	semidirect

Subgroups — D233⋊M16 #21418620

Conjugacy classes of subgroups

Complements

Subgroups — D₂₃₃⋊M₁₆ #21418620