Subgroups — #13092238

Order 1472.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₈×C₂₃	C₂	1	1	yes	maximal, characteristic
2	#10624994	C₂	1	2	yes	maximal
3	C₂×C₈×C₂₃	C₄	1	1	yes	characteristic
4	C₂×C₈×C₂₃	C₂²	1	1	yes	characteristic
5	C₄²×C₂₃	C₄	1	1	yes	characteristic
6	C₂₃⋊C₁₆	—	2	2	no	—
7	C₂×C₄×C₂₃	—	2	1	no	—
8	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₂₃	C₈	1	2	yes	—
10	C₈×C₂₃	D₄	1	1	yes	characteristic
11	C₈×C₂₃	Q₈	1	1	yes	characteristic
12	C₂²×C₂₃	M₁₆	1	1	yes	characteristic
13	C₄×C₂₃	—	2	2	no	—
14	C₄×C₂₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₂₃	C₂×C₈	1	1	yes	characteristic
16	#364	—	23	1	no	maximal, Sylow
17	C₂×C₂₃	—	2	1	no	—
18	C₂×C₂₃	C₄⋊C₈	1	1	yes	characteristic
19	M₃₂	—	23	2	no	—
20	C₄×C₈	D₂₃	1	1	yes	characteristic
21	C₂₃	#364	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₈	Dic₂₃	1	1	yes	characteristic
23	C₂×C₈	C₂×D₂₃	1	1	yes	characteristic
24	C₄²	Dic₂₃	1	1	yes	characteristic
25	C₁₆	—	46	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
28	C₈	C₂₃⋊C₈	1	2	yes	—
29	C₈	Dic₄₆	1	1	yes	characteristic
30	C₈	D₉₂	1	1	yes	characteristic
31	C₂²	#67267	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₂×C₂₃⋊C₈	1	1	yes	characteristic
34	C₄	C₄⋊Dic₂₃	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	C₄⋊(C₂₃⋊C₈)	1	1	yes	characteristic

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

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

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