Subgroups — #15671581

Order 2944.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃⋊C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#13092247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#508	C₂	1	1	yes	maximal, characteristic
4	C₂₃×#135	—	2	1	no	—
5	C₂₃×Q₃₂	C₄	1	1	yes	characteristic
6	C₂₃×SD₃₂	—	2	1	no	—
7	C₂₃×D₁₆	C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
9	#10625001	—	2	1	no	—
10	C₂₃⋊C₃₂	—	2	1	no	—
11	#41×C₂₃	—	4	1	no	—
12	Q₁₆×C₂₃	—	2	1	no	—
13	SD₁₆×C₂₃	—	4	1	no	—
14	D₈×C₂₃	—	2	1	no	—
15	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
16	#67267	—	4	1	no	—
17	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
18	C₁₆×C₂₃	D₄	1	1	yes	characteristic
19	Q₈×C₂₃	—	4	1	no	—
20	D₄×C₂₃	—	4	1	no	—
21	D₄×C₂₃	—	8	1	no	—
22	C₂×C₄×C₂₃	—	8	1	no	—
23	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
24	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
26	C₂₃⋊C₈	—	8	1	no	—
27	#1417	—	23	1	no	maximal, Sylow
28	C₂²×C₂₃	—	8	1	no	—
29	C₂²×C₂₃	SD₃₂	1	1	yes	characteristic
30	C₄×C₂₃	—	8	1	no	—
31	C₄×C₂₃	#102	1	1	yes	characteristic
32	C₄×C₂₃	D₁₆	1	1	yes	characteristic
33	#508	D₂₃	1	1	yes	characteristic
34	C₂×C₃₂	—	23	1	no	—
35	#368	—	23	1	no	—
36	C₂×C₂₃	—	2	1	no	—
37	C₂×C₂₃	—	16	1	no	—
38	C₂×C₂₃	#357	1	1	yes	characteristic
39	#135	—	2	1	no	—
40	Q₃₂	Dic₂₃	1	1	yes	characteristic
41	SD₃₂	—	2	1	no	—
42	D₁₆	Dic₂₃	1	1	yes	characteristic
43	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
44	#108	—	46	1	no	—
45	C₃₂	—	46	1	no	—
46	C₂₃	#1417	1	1	yes	characteristic, complemented, Sylow
47	#41	—	4	1	no	—
48	Q₁₆	—	2	1	no	—
49	SD₁₆	—	4	1	no	—
50	D₈	—	2	1	no	—
51	M₁₆	—	92	1	no	—
52	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
53	C₁₆	C₂×Dic₂₃	1	1	yes	characteristic
54	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
55	Q₈	—	4	1	no	—
56	D₄	—	4	1	no	—
57	D₄	—	8	1	no	—
58	C₂×C₄	—	8	1	no	—
59	C₂×C₄	#67272	1	1	yes	characteristic
60	C₈	—	184	1	no	—
61	C₈	#67273	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
63	C₂²	—	8	1	no	—
64	C₂²	#10625009	1	1	yes	characteristic
65	C₄	—	8	1	no	—
66	C₄	#10625008	1	1	yes	characteristic
67	C₄	#10625014	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	16	1	no	—
70	C₂	#13092218	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#10625008
commutator	C₁₆×C₂₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting, prime radical	C₂₃×#508	C₂
socle	C₂×C₂₃	#357
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	#508	D₂₃
hypocenter	C₂₃	#1417
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #508

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃⋊C₃₂	C₂	semidirect
2. #13092247	C₂	semidirect
46. C₂₃	#1417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃⋊C₃₂	2
#13092247	2
C₂₃×#508	2
#1417	23