Subgroups — M₁₆×Dic₂₃ #13092368

Order 1472.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#67267	C₂	1	1	yes	maximal, characteristic
4	#10624997	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₂₃	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₃	C₄	1	2	yes	—
8	M₁₆×C₂₃	C₄	1	4	yes	complemented
9	C₂×C₈×C₂₃	C₂²	1	2	yes	—
10	C₄×Dic₂₃	C₄	1	2	yes	—
11	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
12	C₄×Dic₂₃	C₂²	1	1	yes	characteristic
13	#67267	C₄	1	4	yes	complemented
14	C₂×C₂₃⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₂₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₂₃	—	2	4	no	—
21	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
22	C₂×Dic₂₃	C₂×C₄	1	2	yes	—
23	C₈×C₂₃	C₂×C₄	1	4	yes	complemented
24	C₂₃⋊C₈	C₂×C₄	1	4	yes	complemented
25	C₂²×C₂₃	—	2	2	no	—
26	C₂²×C₂₃	C₄²	1	2	yes	—
27	C₂²×C₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₄×C₂₃	C₄²	1	2	yes	—
29	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
31	Dic₂₃	—	2	2	no	—
32	Dic₂₃	M₁₆	1	4	yes	direct product factor
33	C₄×M₁₆	—	23	1	no	maximal, Sylow
34	C₂×C₂₃	—	2	2	no	—
35	C₂×C₂₃	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₂₃	C₂×M₁₆	1	2	yes	—
37	C₂×M₁₆	—	23	1	no	—
38	C₂×M₁₆	D₂₃	1	1	yes	characteristic
39	C₂×C₄²	—	23	1	no	—
40	#97	—	23	2	no	—
41	C₄×C₈	—	23	2	no	—
42	C₂₃	C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	—	23	2	no	—
44	C₂²×C₄	C₂×D₂₃	1	1	yes	characteristic
45	M₁₆	—	23	4	no	—
46	M₁₆	Dic₂₃	1	4	yes	direct product factor
47	C₂×C₈	—	23	2	no	—
48	C₂×C₈	C₂×D₂₃	1	2	yes	—
49	C₄²	—	23	2	no	—
50	C₄²	—	23	1	no	—
51	C₄²	—	23	1	no	—
52	C₂³	C₄×D₂₃	1	1	yes	characteristic
53	C₂×C₄	—	23	2	no	—
54	C₂×C₄	—	23	2	no	—
55	C₂×C₄	—	46	4	no	—
56	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
57	C₂×C₄	C₄×D₂₃	1	2	yes	—
58	C₂×C₄	C₂×Dic₂₃	1	2	yes	—
59	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
60	C₈	—	23	4	no	—
61	C₈	C₂×Dic₂₃	1	4	yes	complemented
62	C₂²	—	2	2	no	—
63	C₂²	C₄×Dic₂₃	1	2	yes	—
64	C₂²	C₂×C₄×D₂₃	1	1	yes	characteristic
65	C₄	—	23	4	no	—
66	C₄	—	46	2	no	—
67	C₄	C₄×Dic₂₃	1	2	yes	—
68	C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
69	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	M₁₆×D₂₃	1	2	yes	—
72	C₂	C₂×C₄×Dic₂₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂×C₄²
Fitting	C₂×M₁₆×C₂₃	C₂
socle	C₂²×C₂₃	C₂²×C₄
prime radical	C₂³×C₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂³
hypercenter	C₂×M₁₆	D₂₃
hypocenter	C₂₃	C₄×M₁₆
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #10624997	C₂	semidirect
5. C₈×Dic₂₃	C₂	semidirect
8. M₁₆×C₂₃	C₄	semidirect
13. #67267	C₄	semidirect
23. C₈×C₂₃	C₂×C₄	semidirect
24. C₂₃⋊C₈	C₂×C₄	semidirect
32. Dic₂₃	M₁₆	direct (N × H)
42. C₂₃	C₄×M₁₆	semidirect
46. M₁₆	Dic₂₃	direct (N × H)
61. C₈	C₂×Dic₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×C₂₃	2
C₂×C₄×Dic₂₃	2
C₂×#67267	2
#10624997	2
C₈×Dic₂₃	2
C₄×M₁₆	23

Subgroups — M16×Dic23 #13092368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×Dic₂₃ #13092368