Subgroups — #13092834

Order 1472.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#131	C₂	1	1	yes	maximal, characteristic
2	#10624994	C₂	1	3	yes	maximal, complemented
3	C₂×C₂₃⋊C₁₆	C₂	1	3	yes	maximal, complemented
4	#41×C₂₃	C₄	1	1	yes	characteristic
5	M₁₆×C₂₃	C₄	1	3	yes	—
6	C₂×C₈×C₂₃	C₂²	1	3	yes	—
7	C₂₃⋊C₁₆	C₂²	1	1	yes	characteristic
8	C₂₃⋊C₁₆	C₂²	1	3	yes	—
9	Q₈×C₂₃	C₈	1	1	yes	characteristic
10	D₄×C₂₃	C₈	1	3	yes	—
11	C₂×C₄×C₂₃	C₂×C₄	1	3	yes	—
12	C₈×C₂₃	C₂×C₄	1	3	yes	—
13	C₈×C₂₃	C₂³	1	1	yes	characteristic
14	C₂²×C₂₃	C₂×C₈	1	3	yes	—
15	C₄×C₂₃	C₂×C₈	1	3	yes	—
16	C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
17	#504	—	23	1	no	maximal, Sylow
18	C₂×C₂₃	—	2	3	no	—
19	C₂×C₂₃	C₂²×C₈	1	1	yes	characteristic
20	#131	D₂₃	1	1	yes	characteristic
21	M₃₂	—	23	3	no	—
22	C₂×C₁₆	—	23	3	no	—
23	C₂₃	#504	1	1	yes	characteristic, complemented, Sylow
24	#41	Dic₂₃	1	1	yes	characteristic
25	M₁₆	Dic₂₃	1	3	yes	—
26	C₂×C₈	C₂×D₂₃	1	3	yes	—
27	C₁₆	—	23	1	no	—
28	C₁₆	—	23	3	no	—
29	Q₈	C₂₃⋊C₈	1	1	yes	characteristic
30	D₄	C₂₃⋊C₈	1	3	yes	—
31	C₂×C₄	C₂×Dic₂₃	1	3	yes	—
32	C₈	C₂×Dic₂₃	1	3	yes	—
33	C₈	C₂²×D₂₃	1	1	yes	characteristic
34	C₂²	C₂×C₂₃⋊C₈	1	3	yes	—
35	C₄	C₂×C₂₃⋊C₈	1	3	yes	—
36	C₄	C₂²×Dic₂₃	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	C₂	C₂²×C₂₃⋊C₈	1	1	yes	characteristic

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.