Subgroups — #15671603

Order 2944.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092247	C₂	1	1	yes	maximal, characteristic
2	#13092245	C₂	1	1	yes	maximal, characteristic
3	C₂₃×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
5	#10625001	—	2	1	no	—
6	#10625000	—	2	1	no	—
7	C₂₃×C₃₂	C₄	1	2	yes	complemented
8	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
9	C₄⋊Dic₂₃	—	4	1	no	—
10	#67267	—	4	1	no	—
11	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
14	C₂×Dic₂₃	—	8	1	no	—
15	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
16	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
17	C₂₃⋊C₈	—	8	1	no	—
18	#1426	—	23	1	no	maximal, Sylow
19	C₂²×C₂₃	SD₃₂	1	1	yes	characteristic
20	C₄×C₂₃	#107	1	1	yes	characteristic
21	C₄×C₂₃	SD₃₂	1	1	yes	characteristic
22	Dic₂₃	—	16	1	no	—
23	M₆₄	D₂₃	1	1	yes	characteristic
24	#368	—	23	1	no	—
25	#367	—	23	1	no	—
26	C₂×C₂₃	—	2	1	no	—
27	C₂×C₂₃	#367	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
29	#108	—	46	1	no	—
30	#107	—	46	1	no	—
31	C₃₂	Dic₂₃	1	2	yes	complemented
32	C₂₃	#1426	1	1	yes	characteristic, complemented, Sylow
33	M₁₆	—	92	1	no	—
34	C₂×C₈	D₉₂	1	1	yes	characteristic
35	C₄⋊C₄	—	92	1	no	—
36	C₁₆	Dic₄₆	1	1	yes	characteristic
37	C₁₆	C₂×Dic₂₃	1	1	yes	characteristic
38	C₂×C₄	—	184	1	no	—
39	C₂×C₄	D₁₈₄	1	1	yes	characteristic
40	C₈	—	184	1	no	—
41	C₈	Dic₉₂	1	1	yes	characteristic
42	C₈	C₄⋊Dic₂₃	1	1	yes	characteristic
43	C₂²	#10624982	1	1	yes	characteristic
44	C₄	—	368	1	no	—
45	C₄	#10624982	1	1	yes	characteristic
46	C₄	#10625000	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	#13092245	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092245
commutator	C₁₆×C₂₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting	C₂₃×M₆₄	C₂
socle	C₂×C₂₃	#367
prime radical	C₂²×C₂₃	SD₃₂
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	M₆₄	D₂₃
hypocenter	C₂₃	#1426
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
7. C₂₃×C₃₂	C₄	semidirect
31. C₃₂	Dic₂₃	semidirect
32. C₂₃	#1426	semidirect

Maximal subgroups

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

subgroup	index
#13092247	2
#13092245	2
C₂₃×M₆₄	2
#1426	23