Subgroups — #15671599

Order 2944.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092243	C₂	1	2	yes	maximal
2	C₂×C₂₃×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₂₃	C₂²	1	1	yes	characteristic
4	#10625000	—	2	2	no	—
5	C₂₃×C₃₂	C₄	1	2	yes	complemented
6	C₂×C₈×C₂₃	D₄	1	1	yes	characteristic
7	C₄⋊Dic₂₃	—	4	2	no	—
8	C₁₆×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₂₃	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₂₃	D₈	1	1	yes	characteristic
11	C₂×Dic₂₃	—	8	2	no	—
12	C₈×C₂₃	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₂₃	Q₁₆	1	1	yes	characteristic
14	#1424	—	23	1	no	maximal, Sylow
15	C₂²×C₂₃	D₁₆	1	1	yes	characteristic
16	C₄×C₂₃	#107	1	1	yes	characteristic
17	C₄×C₂₃	Q₃₂	1	1	yes	characteristic
18	Dic₂₃	—	16	2	no	—
19	C₂×C₃₂	D₂₃	1	1	yes	characteristic
20	#366	—	23	2	no	—
21	C₂×C₂₃	#366	1	1	yes	characteristic
22	C₂×C₂₃	SD₆₄	1	2	yes	—
23	C₂×C₁₆	C₂×D₂₃	1	1	yes	characteristic
24	#107	—	46	2	no	—
25	C₃₂	Dic₂₃	1	2	yes	complemented
26	C₂₃	#1424	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₈	D₉₂	1	1	yes	characteristic
28	C₄⋊C₄	—	92	2	no	—
29	C₁₆	Dic₄₆	1	1	yes	characteristic
30	C₁₆	C₂×Dic₂₃	1	1	yes	characteristic
31	C₂×C₄	—	184	2	no	—
32	C₂×C₄	D₁₈₄	1	1	yes	characteristic
33	C₈	Dic₉₂	1	1	yes	characteristic
34	C₈	C₄⋊Dic₂₃	1	1	yes	characteristic
35	C₂²	D₃₆₈	1	1	yes	characteristic
36	C₄	—	368	2	no	—
37	C₄	Dic₁₈₄	1	1	yes	characteristic
38	C₄	#10625000	1	1	yes	characteristic
39	C₂	#13092243	1	1	yes	characteristic
40	C₂	#13092256	1	2	yes	—

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

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