Subgroups — #19212099

Order 5888.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15671608	C₂	1	1	yes	maximal, characteristic
2	#15671601	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
4	#13092247	—	2	1	no	—
5	C₂₃⋊C₆₄	—	2	1	no	—
6	C₂×C₂₃×Q₃₂	—	2	1	no	—
7	C₂₃×Q₆₄	—	2	1	no	—
8	C₂₃×Q₆₄	C₄	1	2	yes	—
9	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
10	C₂×Q₁₆×C₂₃	—	4	1	no	—
11	C₂₃×Q₃₂	—	2	2	no	—
12	C₂₃×Q₃₂	—	4	1	no	—
13	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
14	#10625001	—	4	1	no	—
15	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₂₃×C₃₂	D₄	1	1	yes	characteristic
17	C₂×Q₈×C₂₃	—	8	1	no	—
18	Q₁₆×C₂₃	—	4	2	no	—
19	Q₁₆×C₂₃	—	8	1	no	—
20	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
21	#67267	—	8	1	no	—
22	C₁₆×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₂₃	SD₁₆	1	1	yes	characteristic
24	#7542	—	23	1	no	maximal, Sylow
25	Q₈×C₂₃	—	8	2	no	—
26	Q₈×C₂₃	—	16	1	no	—
27	C₂×C₄×C₂₃	—	16	1	no	—
28	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
29	C₈×C₂₃	#102	1	1	yes	characteristic
30	C₈×C₂₃	SD₃₂	1	1	yes	characteristic
31	C₂₃⋊C₈	—	16	1	no	—
32	C₂×Q₆₄	D₂₃	1	1	yes	characteristic
33	M₁₂₈	—	23	1	no	—
34	#1425	—	23	1	no	—
35	C₂²×C₂₃	SD₆₄	1	1	yes	characteristic
36	C₄×C₂₃	—	16	2	no	—
37	C₄×C₂₃	#357	1	1	yes	characteristic
38	C₄×C₂₃	D₃₂	1	1	yes	characteristic
39	C₂×Q₃₂	—	2	1	no	—
40	Q₆₄	—	2	1	no	—
41	Q₆₄	Dic₂₃	1	2	yes	—
42	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
43	#368	—	46	1	no	—
44	C₆₄	—	46	1	no	—
45	C₂×C₂₃	—	2	1	no	—
46	C₂×C₂₃	#1415	1	1	yes	characteristic
47	C₂×Q₁₆	—	4	1	no	—
48	Q₃₂	—	2	2	no	—
49	Q₃₂	—	4	1	no	—
50	C₂×C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
51	#108	—	92	1	no	—
52	C₃₂	C₂×Dic₂₃	1	1	yes	characteristic
53	C₃₂	C₂²⋊D₂₃	1	1	yes	characteristic
54	C₂₃	#7542	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₈	—	8	1	no	—
56	Q₁₆	—	4	2	no	—
57	Q₁₆	—	8	1	no	—
58	M₁₆	—	184	1	no	—
59	C₂×C₈	#67272	1	1	yes	characteristic
60	C₁₆	#67273	1	1	yes	characteristic
61	C₁₆	C₂²⋊Dic₂₃	1	1	yes	characteristic
62	Q₈	—	8	2	no	—
63	Q₈	—	16	1	no	—
64	C₂×C₄	—	16	1	no	—
65	C₂×C₄	#10625008	1	1	yes	characteristic
66	C₈	—	368	1	no	—
67	C₈	#10625009	1	1	yes	characteristic
68	C₈	#10625014	1	1	yes	characteristic
69	C₂²	#13092255	1	1	yes	characteristic
70	C₄	—	16	2	no	—
71	C₄	#13092218	1	1	yes	characteristic
72	C₄	#13092252	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#15671575	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15671575
commutator	C₂₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₂₃
Fitting	C₂×C₂₃×Q₆₄	C₂
socle	C₂×C₂₃	#1415
hypercenter	C₂×Q₆₄	D₂₃
hypocenter	C₂₃	#7542
LCS	G ▷ C₂₃×C₃₂ ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
54. C₂₃	#7542	semidirect