Subgroups — #15671590

Order 2944.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092251	C₂	1	1	yes	maximal, characteristic
2	#13092247	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃×Q₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₁₆×C₂₃	—	2	1	no	—
5	C₂₃×Q₃₂	—	2	1	no	—
6	C₂₃×Q₃₂	C₄	1	2	yes	—
7	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
8	#10625001	—	2	1	no	—
9	C₂₃⋊C₃₂	—	2	1	no	—
10	C₂×Q₈×C₂₃	—	4	1	no	—
11	Q₁₆×C₂₃	—	2	2	no	—
12	Q₁₆×C₂₃	—	4	1	no	—
13	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
14	#67267	—	4	1	no	—
15	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
16	C₁₆×C₂₃	D₄	1	1	yes	characteristic
17	Q₈×C₂₃	—	4	2	no	—
18	Q₈×C₂₃	—	8	1	no	—
19	C₂×C₄×C₂₃	—	8	1	no	—
20	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
21	C₈×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₈×C₂₃	SD₁₆	1	1	yes	characteristic
23	C₂₃⋊C₈	—	8	1	no	—
24	#1420	—	23	1	no	maximal, Sylow
25	C₂²×C₂₃	SD₃₂	1	1	yes	characteristic
26	C₄×C₂₃	—	8	2	no	—
27	C₄×C₂₃	#102	1	1	yes	characteristic
28	C₄×C₂₃	D₁₆	1	1	yes	characteristic
29	C₂×Q₃₂	D₂₃	1	1	yes	characteristic
30	M₆₄	—	23	1	no	—
31	#368	—	23	1	no	—
32	C₂×C₂₃	—	2	1	no	—
33	C₂×C₂₃	#357	1	1	yes	characteristic
34	C₂×Q₁₆	—	2	1	no	—
35	Q₃₂	—	2	1	no	—
36	Q₃₂	Dic₂₃	1	2	yes	—
37	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
38	#108	—	46	1	no	—
39	C₃₂	—	46	1	no	—
40	C₂₃	#1420	1	1	yes	characteristic, complemented, Sylow
41	C₂×Q₈	—	4	1	no	—
42	Q₁₆	—	2	2	no	—
43	Q₁₆	—	4	1	no	—
44	M₁₆	—	92	1	no	—
45	C₂×C₈	C₂²⋊D₂₃	1	1	yes	characteristic
46	C₁₆	C₂×Dic₂₃	1	1	yes	characteristic
47	C₁₆	C₂²⋊D₂₃	1	1	yes	characteristic
48	Q₈	—	4	2	no	—
49	Q₈	—	8	1	no	—
50	C₂×C₄	—	8	1	no	—
51	C₂×C₄	#67272	1	1	yes	characteristic
52	C₈	—	184	1	no	—
53	C₈	#67273	1	1	yes	characteristic
54	C₈	C₂²⋊Dic₂₃	1	1	yes	characteristic
55	C₂²	#10625009	1	1	yes	characteristic
56	C₄	—	8	2	no	—
57	C₄	#10625008	1	1	yes	characteristic
58	C₄	#10625014	1	1	yes	characteristic
59	C₂	—	2	1	no	—
60	C₂	#13092218	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13092218
commutator	C₁₆×C₂₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₃
Fitting	C₂×C₂₃×Q₃₂	C₂
socle	C₂×C₂₃	#357
prime radical	C₂²×C₂₃	SD₃₂
cosocle	C₂×C₁₆×C₂₃	C₂²
hypercenter	C₂×Q₃₂	D₂₃
hypocenter	C₂₃	#1420
LCS	G ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×Q₃₂

Complements

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

N	H ≅ G/N	type
40. C₂₃	#1420	semidirect

Maximal subgroups

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

subgroup	index
#13092251	2
#13092247	2
C₂×C₂₃×Q₃₂	2
#1420	23