Subgroups — #13092241

Order 1472.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#108	C₂	1	1	yes	maximal, characteristic
2	#10624999	C₂	1	1	yes	maximal, characteristic
3	#10624994	C₂	1	1	yes	maximal, characteristic
4	M₁₆×C₂₃	—	2	1	no	—
5	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
6	C₄⋊Dic₂₃	—	2	1	no	—
7	C₂₃⋊C₁₆	C₄	1	2	yes	complemented
8	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
9	C₂×Dic₂₃	—	4	1	no	—
10	C₈×C₂₃	—	4	1	no	—
11	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₃	Q₈	1	1	yes	characteristic
13	C₂²×C₂₃	SD₁₆	1	1	yes	characteristic
14	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₃	SD₁₆	1	1	yes	characteristic
16	Dic₂₃	—	8	1	no	—
17	#365	—	23	1	no	maximal, Sylow
18	C₂×C₂₃	—	2	1	no	—
19	C₂×C₂₃	#106	1	1	yes	characteristic
20	M₃₂	—	23	1	no	—
21	#108	D₂₃	1	1	yes	characteristic
22	#106	—	23	1	no	—
23	C₂₃	#365	1	1	yes	characteristic, complemented, Sylow
24	M₁₆	—	2	1	no	—
25	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
26	C₄⋊C₄	—	46	1	no	—
27	C₁₆	—	23	2	no	—
28	C₂×C₄	—	92	1	no	—
29	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
30	C₈	—	4	1	no	—
31	C₈	Dic₄₆	1	1	yes	characteristic
32	C₈	C₄×D₂₃	1	1	yes	characteristic
33	C₂²	#67274	1	1	yes	characteristic
34	C₄	—	184	1	no	—
35	C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
36	C₄	#67273	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#10624990	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₂₃⋊C₁₆	C₄	semidirect
23. C₂₃	#365	semidirect

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