Subgroups — #19212109

Order 5888.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃⋊C₆₄	C₂	1	1	yes	maximal, characteristic
2	#15671601	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#1425	C₂	1	1	yes	maximal, characteristic
4	#13092247	—	2	1	no	—
5	C₂₃⋊C₆₄	C₄	1	2	yes	—
6	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
7	C₂₃×#368	—	2	1	no	—
8	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
9	C₂₃×#108	—	4	1	no	—
10	#10625001	—	4	1	no	—
11	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₂₃×C₃₂	Q₈	1	1	yes	characteristic
13	M₁₆×C₂₃	—	8	1	no	—
14	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
15	#67267	—	8	1	no	—
16	C₁₆×C₂₃	C₄⋊C₄	1	1	yes	characteristic
17	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
18	#7547	—	23	1	no	maximal, Sylow
19	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
20	C₈×C₂₃	—	16	1	no	—
21	C₈×C₂₃	#107	1	1	yes	characteristic
22	C₈×C₂₃	Q₃₂	1	1	yes	characteristic
23	C₂₃⋊C₈	—	16	1	no	—
24	C₂×C₆₄	—	23	1	no	—
25	#1425	—	23	1	no	—
26	#1425	D₂₃	1	1	yes	characteristic
27	C₂²×C₂₃	Q₆₄	1	1	yes	characteristic
28	C₄×C₂₃	#366	1	1	yes	characteristic
29	C₄×C₂₃	D₃₂	1	1	yes	characteristic
30	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
31	#368	—	2	1	no	—
32	#368	—	46	1	no	—
33	C₆₄	—	23	2	no	—
34	C₂×C₂₃	—	2	1	no	—
35	C₂×C₂₃	#1423	1	1	yes	characteristic
36	C₂×C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
37	#108	—	4	1	no	—
38	#108	—	92	1	no	—
39	C₃₂	Dic₄₆	1	1	yes	characteristic
40	C₃₂	C₄×D₂₃	1	1	yes	characteristic
41	C₂₃	#7547	1	1	yes	characteristic, complemented, Sylow
42	M₁₆	—	8	1	no	—
43	M₁₆	—	184	1	no	—
44	C₂×C₈	#67272	1	1	yes	characteristic
45	C₁₆	Dic₂₃⋊C₄	1	1	yes	characteristic
46	C₁₆	#67275	1	1	yes	characteristic
47	C₂×C₄	#10625008	1	1	yes	characteristic
48	C₈	—	16	1	no	—
49	C₈	—	368	1	no	—
50	C₈	#10624989	1	1	yes	characteristic
51	C₈	#10625011	1	1	yes	characteristic
52	C₂²	#13092257	1	1	yes	characteristic
53	C₄	#13092242	1	1	yes	characteristic
54	C₄	#13092252	1	1	yes	characteristic
55	C₂	—	2	1	no	—
56	C₂	#15671596	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#13092252
commutator	C₂₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₂₃
Fitting	C₂₃×#1425	C₂
socle	C₂×C₂₃	#1423
hypercenter	#1425	D₂₃
hypocenter	C₂₃	#7547
LCS	G ▷ C₂₃×C₃₂ ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1425

Complements

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

N	H ≅ G/N	type
41. C₂₃	#7547	semidirect