Subgroups — #19212110

Order 5888.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15671601	C₂	1	2	yes	maximal
2	C₂×C₂₃×C₆₄	C₂	1	1	yes	maximal, characteristic
3	#13092247	—	2	2	no	—
4	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
5	C₂₃×C₆₄	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
7	#10625001	—	4	2	no	—
8	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
9	C₂₃×C₃₂	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
11	#67267	—	8	2	no	—
12	C₁₆×C₂₃	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₂₃	Q₁₆	1	1	yes	characteristic
14	#7547	—	23	1	no	maximal, Sylow
15	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
16	C₈×C₂₃	#107	1	1	yes	characteristic
17	C₈×C₂₃	Q₃₂	1	1	yes	characteristic
18	C₂₃⋊C₈	—	16	2	no	—
19	C₂×C₆₄	D₂₃	1	1	yes	characteristic
20	#1425	—	23	2	no	—
21	C₂²×C₂₃	Q₆₄	1	1	yes	characteristic
22	C₄×C₂₃	#366	1	1	yes	characteristic
23	C₄×C₂₃	D₃₂	1	1	yes	characteristic
24	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
25	#368	—	46	2	no	—
26	C₆₄	Dic₂₃	1	2	yes	—
27	C₂×C₂₃	—	2	1	no	—
28	C₂×C₂₃	#1423	1	1	yes	characteristic
29	C₂×C₁₆	D₉₂	1	1	yes	characteristic
30	#108	—	92	2	no	—
31	C₃₂	Dic₄₆	1	1	yes	characteristic
32	C₃₂	C₂×Dic₂₃	1	1	yes	characteristic
33	C₂₃	#7547	1	1	yes	characteristic, complemented, Sylow
34	M₁₆	—	184	2	no	—
35	C₂×C₈	D₁₈₄	1	1	yes	characteristic
36	C₁₆	Dic₉₂	1	1	yes	characteristic
37	C₁₆	C₄⋊Dic₂₃	1	1	yes	characteristic
38	C₂×C₄	D₃₆₈	1	1	yes	characteristic
39	C₈	—	368	2	no	—
40	C₈	Dic₁₈₄	1	1	yes	characteristic
41	C₈	#10625000	1	1	yes	characteristic
42	C₂²	Dic₃₆₈	1	1	yes	characteristic
43	C₄	#13092243	1	1	yes	characteristic
44	C₄	D₇₃₆	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#15671597	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₇₃₆
commutator	C₂₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₂₃
Fitting	C₂×C₂₃×C₆₄	C₂
socle	C₂×C₂₃	#1423
hypercenter	C₂×C₆₄	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 ◁ C₂×C₆₄

Complements

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

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