Subgroups — #13092244

Order 1472.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#107	C₂	1	1	yes	maximal, characteristic
2	#10625000	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₂₃	—	2	1	no	—
6	C₄⋊Dic₂₃	—	2	1	no	—
7	C₂₃⋊C₁₆	C₄	1	2	yes	complemented
8	C₂×C₄×C₂₃	—	4	1	no	—
9	C₂×C₄×C₂₃	D₄	1	1	yes	characteristic
10	C₂×Dic₂₃	—	4	1	no	—
11	C₈×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₂₃	Q₈	1	1	yes	characteristic
13	C₂²×C₂₃	D₈	1	1	yes	characteristic
14	C₄×C₂₃	—	8	1	no	—
15	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₂₃	Q₁₆	1	1	yes	characteristic
17	Dic₂₃	—	8	1	no	—
18	#367	—	23	1	no	maximal, Sylow
19	C₂×C₂₃	#107	1	1	yes	characteristic
20	C₂×C₂₃	SD₃₂	1	1	yes	characteristic
21	C₂×C₂₃	SD₃₂	1	1	yes	characteristic
22	C₂×C₁₆	—	23	1	no	—
23	#107	—	23	1	no	—
24	#107	D₂₃	1	1	yes	characteristic
25	C₂₃	#367	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
27	C₄⋊C₄	—	2	1	no	—
28	C₄⋊C₄	—	46	1	no	—
29	C₁₆	—	23	2	no	—
30	C₂×C₄	—	4	1	no	—
31	C₂×C₄	—	92	1	no	—
32	C₂×C₄	C₂²⋊D₂₃	1	1	yes	characteristic
33	C₈	Dic₄₆	1	1	yes	characteristic
34	C₈	C₄×D₂₃	1	1	yes	characteristic
35	C₂²	#67272	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	184	1	no	—
38	C₄	Dic₂₃⋊C₄	1	1	yes	characteristic
39	C₄	#67275	1	1	yes	characteristic
40	C₂	#10624989	1	1	yes	characteristic
41	C₂	#10625009	1	1	yes	characteristic
42	C₂	#10625010	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₂₃⋊C₁₆	C₄	semidirect
25. C₂₃	#367	semidirect

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