Subgroups — #13092237

Order 1472.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic
3	#10624994	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₄×Dic₂₃	C₄	1	1	yes	characteristic
6	C₂×C₂₃⋊C₈	C₄	1	1	yes	characteristic
7	C₁₆×C₂₃	—	2	1	no	—
8	C₂₃⋊C₁₆	—	2	1	no	—
9	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂×Dic₂₃	—	2	1	no	—
11	C₈×C₂₃	D₄	1	1	yes	characteristic
12	C₈×C₂₃	Q₈	1	1	yes	characteristic
13	C₂₃⋊C₈	C₈	1	2	yes	—
14	C₂²×C₂₃	M₁₆	1	1	yes	characteristic
15	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
17	Dic₂₃	—	2	2	no	—
18	#364	—	23	1	no	maximal, Sylow
19	C₂×C₂₃	—	2	1	no	—
20	C₂×C₂₃	C₄⋊C₈	1	1	yes	characteristic
21	M₃₂	—	23	1	no	—
22	M₃₂	D₂₃	1	1	yes	characteristic
23	C₄×C₈	—	23	1	no	—
24	C₂₃	#364	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₈	—	23	1	no	—
26	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
27	C₄²	—	23	1	no	—
28	C₁₆	—	2	1	no	—
29	C₁₆	—	46	1	no	—
30	C₂×C₄	—	46	1	no	—
31	C₂×C₄	C₄×D₂₃	1	1	yes	characteristic
32	C₈	—	23	2	no	—
33	C₈	Dic₄₆	1	1	yes	characteristic
34	C₈	C₂²⋊D₂₃	1	1	yes	characteristic
35	C₂²	#67262	1	1	yes	characteristic
36	C₄	—	46	2	no	—
37	C₄	C₈×D₂₃	1	1	yes	characteristic
38	C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
39	C₂	—	2	1	no	—
40	C₂	Dic₂₃⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
24. C₂₃	#364	semidirect

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