Subgroups — #15671533

Order 2944.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092251	C₂	1	2	yes	maximal
2	C₂₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃⋊C₃₂	C₄	1	4	yes	complemented
7	C₂×C₈×C₂₃	C₈	1	1	yes	characteristic
8	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₄²×C₂₃	C₈	1	1	yes	characteristic
10	C₁₆×C₂₃	C₈	1	2	yes	—
11	C₁₆×C₂₃	C₂×C₄	1	2	yes	—
12	C₂×C₄×C₂₃	—	2	1	no	—
13	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
14	C₈×C₂₃	—	2	1	no	—
15	C₈×C₂₃	C₄²	1	1	yes	characteristic
16	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
17	#1398	—	23	1	no	maximal, Sylow
18	C₂²×C₂₃	M₃₂	1	1	yes	characteristic
19	C₄×C₂₃	—	4	1	no	—
20	C₄×C₂₃	C₄×C₈	1	1	yes	characteristic
21	C₄×C₂₃	M₃₂	1	1	yes	characteristic
22	M₆₄	—	23	2	no	—
23	#346	D₂₃	1	1	yes	characteristic
24	C₂×C₂₃	—	2	1	no	—
25	C₂×C₂₃	#346	1	1	yes	characteristic
26	C₂×C₁₆	Dic₂₃	1	1	yes	characteristic
27	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
28	C₄×C₈	Dic₂₃	1	1	yes	characteristic
29	C₃₂	—	23	4	no	—
30	C₂₃	#1398	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₈	C₂₃⋊C₈	1	1	yes	characteristic
32	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
33	C₄²	C₂₃⋊C₈	1	1	yes	characteristic
34	C₁₆	C₂₃⋊C₈	1	2	yes	—
35	C₁₆	C₄×D₂₃	1	2	yes	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
38	C₈	—	2	1	no	—
39	C₈	C₂×C₂₃⋊C₈	1	1	yes	characteristic
40	C₈	C₄×Dic₂₃	1	1	yes	characteristic
41	C₂²	#10624994	1	1	yes	characteristic
42	C₄	—	4	1	no	—
43	C₄	C₄×C₂₃⋊C₈	1	1	yes	characteristic
44	C₄	#10624994	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#13092193	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₄×Dic₂₃
commutator	C₄×C₂₃	C₄×C₈
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting	C₂₃×#346	C₂
socle	C₂×C₂₃	#346
prime radical	C₂²×C₂₃	M₃₂
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	#346	D₂₃
hypocenter	C₂₃	#1398
LCS	G ▷ C₄×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
6. C₂₃⋊C₃₂	C₄	semidirect
30. C₂₃	#1398	semidirect

Maximal subgroups

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

subgroup	index
#13092251	2
C₂₃×#346	2
#1398	23