Subgroups — D₂₃×Q₆₄ #15675700

Order 2944.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₃₂×D₂₃	C₂	1	2	yes	maximal
2	Dic₃₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13092257	C₂	1	2	yes	maximal, complemented
4	C₃₂×D₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂₃×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₁₆×D₂₃	—	2	2	no	—
7	C₂₃×Q₃₂	C₂²	1	2	yes	—
8	#10625011	—	2	2	no	—
9	Dic₁₈₄	C₂²	1	2	yes	—
10	C₁₆×D₂₃	C₂²	1	1	yes	characteristic
11	C₂₃×C₃₂	C₂²	1	1	yes	characteristic
12	C₂₃⋊C₃₂	C₂²	1	1	yes	characteristic
13	Q₈×D₂₃	—	4	2	no	—
14	Q₁₆×C₂₃	—	2	2	no	—
15	#67275	—	4	2	no	—
16	Dic₉₂	—	2	2	no	—
17	C₈×D₂₃	D₄	1	1	yes	characteristic
18	C₁₆×C₂₃	C₂³	1	1	yes	characteristic
19	C₂₃⋊C₁₆	D₄	1	1	yes	characteristic
20	Q₈×C₂₃	—	4	2	no	—
21	C₄×D₂₃	—	8	2	no	—
22	C₄×D₂₃	D₈	1	1	yes	characteristic
23	Dic₄₆	—	4	2	no	—
24	Dic₄₆	—	8	2	no	—
25	C₈×C₂₃	C₂×D₄	1	1	yes	characteristic
26	C₂₃⋊C₈	D₈	1	1	yes	characteristic
27	C₂×Q₆₄	—	23	1	no	maximal, Sylow
28	C₂×D₂₃	D₁₆	1	1	yes	characteristic
29	C₄×C₂₃	—	8	2	no	—
30	C₄×C₂₃	C₂×D₈	1	1	yes	characteristic
31	Dic₂₃	—	8	2	no	—
32	Dic₂₃	D₁₆	1	1	yes	characteristic
33	C₂×Q₃₂	—	23	2	no	—
34	Q₆₄	—	23	2	no	—
35	Q₆₄	—	23	1	no	—
36	Q₆₄	D₂₃	1	1	yes	characteristic, direct product factor
37	C₂×C₃₂	—	23	1	no	—
38	C₂×C₂₃	C₂×D₁₆	1	1	yes	characteristic
39	D₂₃	Q₆₄	1	2	yes	direct product factor
40	C₂×Q₁₆	—	46	2	no	—
41	Q₃₂	—	23	2	no	—
42	Q₃₂	—	46	2	no	—
43	Q₃₂	C₂×D₂₃	1	2	yes	—
44	C₂×C₁₆	—	23	1	no	—
45	C₃₂	—	23	1	no	—
46	C₃₂	C₂×D₂₃	1	1	yes	characteristic
47	C₂₃	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
48	C₂×Q₈	—	92	2	no	—
49	Q₁₆	—	2	2	no	—
50	Q₁₆	—	46	2	no	—
51	Q₁₆	—	92	2	no	—
52	C₂×C₈	—	23	1	no	—
53	C₁₆	—	23	1	no	—
54	C₁₆	C₂²×D₂₃	1	1	yes	characteristic
55	Q₈	—	4	2	no	—
56	Q₈	—	92	2	no	—
57	Q₈	—	184	2	no	—
58	C₂×C₄	—	23	1	no	—
59	C₂×C₄	—	184	2	no	—
60	C₈	—	23	1	no	—
61	C₈	D₄×D₂₃	1	1	yes	characteristic
62	C₂²	—	23	1	no	—
63	C₄	—	8	2	no	—
64	C₄	—	23	1	no	—
65	C₄	—	184	2	no	—
66	C₄	D₈×D₂₃	1	1	yes	characteristic
67	C₂	—	23	2	no	—
68	C₂	D₁₆×D₂₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₆×D₂₃
commutator, cosocle	C₁₆×C₂₃	C₂³
Frattini	C₁₆	C₂²×D₂₃
Fitting	C₂₃×Q₆₄	C₂
socle	C₂×C₂₃	C₂×D₁₆
prime radical	C₂×D₂₃	D₁₆
hypercenter	Q₆₄	D₂₃
hypocenter	C₂₃	C₂×Q₆₄
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ Q₆₄

Complements

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

N	H ≅ G/N	type
2. Dic₃₆₈	C₂	semidirect
3. #13092257	C₂	semidirect
5. C₂₃×Q₆₄	C₂	semidirect
36. Q₆₄	D₂₃	direct (N × H)
39. D₂₃	Q₆₄	direct (N × H)
47. C₂₃	C₂×Q₆₄	semidirect

Maximal subgroups

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

subgroup	index
Q₃₂×D₂₃	2
Dic₃₆₈	2
#13092257	2
C₃₂×D₂₃	2
C₂₃×Q₆₄	2
C₂×Q₆₄	23

Subgroups — D23×Q64 #15675700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₃×Q₆₄ #15675700