Subgroups — #15671595

Order 2944.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092251	C₂	1	2	yes	maximal
2	C₄×C₁₆×C₂₃	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	—	2	2	no	—
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	—	2	1	no	—
11	C₁₆×C₂₃	D₄	1	1	yes	characteristic
12	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₂₃	—	2	1	no	—
14	C₂×C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
15	C₈×C₂₃	C₁₆	1	2	yes	—
16	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₃	M₁₆	1	1	yes	characteristic
18	#1422	—	23	1	no	maximal, Sylow
19	C₂²×C₂₃	M₃₂	1	1	yes	characteristic
20	C₄×C₂₃	—	2	2	no	—
21	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
22	C₄×C₂₃	C₂×C₁₆	1	1	yes	characteristic
23	M₆₄	—	23	2	no	—
24	C₄×C₁₆	D₂₃	1	1	yes	characteristic
25	C₂×C₂₃	—	2	1	no	—
26	C₂×C₂₃	C₄⋊C₁₆	1	1	yes	characteristic
27	C₂×C₁₆	Dic₂₃	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
29	C₄×C₈	Dic₂₃	1	1	yes	characteristic
30	C₃₂	—	46	2	no	—
31	C₂₃	#1422	1	1	yes	characteristic, complemented, Sylow
32	C₂×C₈	C₂₃⋊C₈	1	1	yes	characteristic
33	C₂×C₈	C₂×Dic₂₃	1	1	yes	characteristic
34	C₄²	C₂₃⋊C₈	1	1	yes	characteristic
35	C₁₆	—	2	1	no	—
36	C₁₆	Dic₄₆	1	1	yes	characteristic
37	C₁₆	D₉₂	1	1	yes	characteristic
38	C₂×C₄	—	2	1	no	—
39	C₂×C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
40	C₈	C₂₃⋊C₁₆	1	2	yes	—
41	C₈	#67267	1	1	yes	characteristic
42	C₈	C₄⋊Dic₂₃	1	1	yes	characteristic
43	C₂²	#10624994	1	1	yes	characteristic
44	C₄	—	2	2	no	—
45	C₄	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic
46	C₄	C₂×C₂₃⋊C₁₆	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	C₄⋊(C₂₃⋊C₁₆)	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₉₂
commutator	C₄×C₂₃	C₂×C₁₆
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting	C₄×C₁₆×C₂₃	C₂
socle	C₂×C₂₃	C₄⋊C₁₆
prime radical	C₂²×C₂₃	M₃₂
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	C₄×C₁₆	D₂₃
hypocenter	C₂₃	#1422
LCS	G ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₂₃	#1422	semidirect

Maximal subgroups

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

subgroup	index
#13092251	2
C₄×C₁₆×C₂₃	2
#1422	23