Subgroups — C₂₃⋊#564 #13093172

Order 1472.

172 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#125	C₂	1	1	yes	maximal, characteristic
2	#10625061	C₂	1	4	yes	maximal
3	#10625060	C₂	1	4	yes	maximal
4	#10625060	C₂	1	4	yes	maximal
5	#10625041	C₂	1	2	yes	maximal
6	C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₃	C₂²	1	4	yes	—
8	C₄²×C₂₃	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₃	C₂²	1	2	yes	—
10	C₄⋊Dic₂₃	C₂²	1	2	yes	—
11	C₄⋊Dic₂₃	C₂²	1	4	yes	—
12	Dic₂₃⋊C₄	C₂²	1	4	yes	—
13	Dic₂₃⋊C₄	C₂²	1	4	yes	—
14	Dic₂₃⋊C₄	C₂²	1	4	yes	—
15	Dic₂₃⋊C₄	C₂²	1	4	yes	—
16	C₄×Dic₂₃	C₂²	1	4	yes	—
17	C₂×C₄×C₂₃	C₂³	1	4	yes	—
18	C₂×C₄×C₂₃	C₂³	1	1	yes	characteristic
19	C₂×C₄×C₂₃	C₂³	1	2	yes	—
20	C₂×Dic₂₃	C₂³	1	4	yes	—
21	C₂×Dic₂₃	C₂³	1	4	yes	—
22	C₂²×C₂₃	C₂⁴	1	1	yes	characteristic
23	C₄×C₂₃	—	2	1	no	—
24	C₄×C₂₃	—	2	4	no	—
25	C₄×C₂₃	—	2	2	no	—
26	Dic₂₃	—	2	4	no	—
27	Dic₂₃	—	2	4	no	—
28	#564	—	23	1	no	maximal, Sylow
29	C₂×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
30	C₂×C₂₃	2₋¹⁺⁴	1	2	yes	—
31	#125	—	23	4	no	—
32	#125	—	23	4	no	—
33	#125	—	23	4	no	—
34	#125	—	23	2	no	—
35	#125	D₂₃	1	1	yes	characteristic
36	C₂₃	#564	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊C₄	—	23	4	no	—
38	C₄⋊C₄	—	23	4	no	—
39	C₄⋊C₄	—	23	4	no	—
40	C₄⋊C₄	—	23	4	no	—
41	C₄⋊C₄	—	23	4	no	—
42	C₄⋊C₄	—	23	2	no	—
43	C₄⋊C₄	—	23	2	no	—
44	C₄⋊C₄	C₂×D₂₃	1	2	yes	—
45	C₄⋊C₄	C₂×D₂₃	1	4	yes	—
46	C₄²	—	23	4	no	—
47	C₄²	C₂×D₂₃	1	1	yes	characteristic
48	C₂×C₄	—	23	4	no	—
49	C₂×C₄	—	23	4	no	—
50	C₂×C₄	C₂²×D₂₃	1	4	yes	—
51	C₂×C₄	C₂²×D₂₃	1	1	yes	characteristic
52	C₂×C₄	C₂²×D₂₃	1	2	yes	—
53	C₂²	C₂³×D₂₃	1	1	yes	characteristic
54	C₄	—	2	1	no	—
55	C₄	—	2	4	no	—
56	C₄	—	2	2	no	—
57	C₄	—	46	4	no	—
58	C₄	—	46	4	no	—
59	C₂	#10625158	1	1	yes	characteristic
60	C₂	#10625161	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₃
commutator, socle, prime radical, cosocle	C₂²×C₂₃	C₂⁴
Fitting	C₂₃×#125	C₂
hypercenter	#125	D₂₃
hypocenter	C₂₃	#564
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
36. C₂₃	#564	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#125	2
#10625061	2
#10625060	2
#10625041	2
#564	23

Subgroups — C23⋊#564 #13093172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃⋊#564 #13093172