Subgroups — Q₃₂×D₂₃ #13092843

Order 1472.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂	D₈×D₂₃
commutator, cosocle	C₈×C₂₃	C₂³
Frattini	C₈	C₂²×D₂₃
Fitting	C₂₃×Q₃₂	C₂
socle	C₂×C₂₃	C₂×D₈
prime radical	C₂×D₂₃	D₈
hypercenter	Q₃₂	D₂₃
hypocenter	C₂₃	C₂×Q₃₂
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
2. C₂₃×Q₃₂	C₂	semidirect
3. #10625011	C₂	semidirect
4. Dic₁₈₄	C₂	semidirect
27. D₂₃	Q₃₂	direct (N × H)
31. Q₃₂	D₂₃	direct (N × H)
33. C₂₃	C₂×Q₃₂	semidirect

Maximal subgroups

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

subgroup	index
Q₁₆×D₂₃	2
C₂₃×Q₃₂	2
#10625011	2
Dic₁₈₄	2
C₁₆×D₂₃	2
C₂×Q₃₂	23

Subgroups — Q32×D23 #13092843

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₃₂×D₂₃ #13092843