Subgroups — #15671464

Order 2944.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092238	C₂	1	1	yes	maximal, characteristic
2	#13092193	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#364	C₂	1	1	yes	maximal, characteristic
4	C₂₃×M₃₂	—	2	1	no	—
5	C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	#10624994	—	2	1	no	—
7	C₂×C₂₃⋊C₁₆	C₄	1	1	yes	characteristic
8	C₂×C₂₃⋊C₁₆	C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
11	C₄²×C₂₃	Q₈	1	1	yes	characteristic
12	C₁₆×C₂₃	—	4	1	no	—
13	C₂₃⋊C₁₆	—	2	1	no	—
14	C₂₃⋊C₁₆	—	4	1	no	—
15	C₂₃⋊C₁₆	C₈	1	2	yes	—
16	C₂×C₄×C₂₃	—	2	1	no	—
17	C₂×C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
18	C₈×C₂₃	C₂×C₈	1	1	yes	characteristic
19	C₈×C₂₃	M₁₆	1	1	yes	characteristic
20	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
21	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
22	#1369	—	23	1	no	maximal, Sylow
23	C₂²×C₂₃	#108	1	1	yes	characteristic
24	C₄×C₂₃	—	4	1	no	—
25	C₄×C₂₃	C₄⋊C₈	1	1	yes	characteristic
26	C₄×C₂₃	#106	1	1	yes	characteristic
27	#364	—	23	1	no	—
28	#364	D₂₃	1	1	yes	characteristic
29	#346	—	23	1	no	—
30	C₂×C₂₃	—	2	1	no	—
31	C₂×C₂₃	#334	1	1	yes	characteristic
32	M₃₂	—	2	1	no	—
33	M₃₂	—	46	1	no	—
34	C₂×C₁₆	—	23	1	no	—
35	C₂×C₁₆	—	23	1	no	—
36	C₄×C₈	C₂×D₂₃	1	1	yes	characteristic
37	C₂₃	#1369	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₈	C₄×D₂₃	1	1	yes	characteristic
39	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
40	C₄²	Dic₄₆	1	1	yes	characteristic
41	C₁₆	—	4	1	no	—
42	C₁₆	—	23	2	no	—
43	C₁₆	—	46	1	no	—
44	C₁₆	—	92	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
47	C₈	C₈×D₂₃	1	1	yes	characteristic
48	C₈	#67262	1	1	yes	characteristic
49	C₈	#67273	1	1	yes	characteristic
50	C₈	#67274	1	1	yes	characteristic
51	C₂²	#10625004	1	1	yes	characteristic
52	C₄	—	4	1	no	—
53	C₄	#10624990	1	1	yes	characteristic
54	C₄	Dic₂₃⋊C₈	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#13092167	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10624990
commutator	C₈×C₂₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₂₃
Fitting	C₂₃×#364	C₂
socle	C₂×C₂₃	#334
prime radical	C₂²×C₂₃	#108
cosocle	C₄×C₈×C₂₃	C₂²
hypercenter	#364	D₂₃
hypocenter	C₂₃	#1369
LCS	G ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
37. C₂₃	#1369	semidirect

Maximal subgroups

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

subgroup	index
#13092238	2
#13092193	2
C₂₃×#364	2
#1369	23