Subgroups — #13092166

Order 1472.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₂₃⋊C₈)	C₂	1	2	yes	maximal
3	C₂×Q₈×C₂₃	C₄	1	2	yes	—
4	C₄⋊C₄×C₂₃	—	2	2	no	—
5	C₄²×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃⋊C₈	—	2	2	no	—
7	Q₈×C₂₃	—	4	2	no	—
8	C₂×C₄×C₂₃	—	2	2	no	—
9	C₂×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
10	C₂×C₄×C₂₃	D₄	1	2	yes	—
11	C₂₃⋊C₈	—	4	2	no	—
12	C₂²×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₂₃	—	2	1	no	—
14	C₄×C₂₃	—	4	2	no	—
15	C₄×C₂₃	SD₁₆	1	2	yes	—
16	C₄×C₂₃	Q₁₆	1	2	yes	—
17	#333	—	23	1	no	maximal, Sylow
18	C₂×C₂₃	#100	1	1	yes	characteristic
19	C₂×C₂₃	#103	1	2	yes	—
20	C₄⋊Q₈	D₂₃	1	1	yes	characteristic
21	C₄⋊C₈	—	23	2	no	—
22	C₂₃	#333	1	1	yes	characteristic, complemented, Sylow
23	C₂×Q₈	Dic₂₃	1	2	yes	—
24	C₂×C₈	—	46	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₂₃	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₂₃	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₂₃	1	2	yes	—
31	C₈	—	92	2	no	—
32	C₂²	C₂²⋊Dic₂₃	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#67274	1	2	yes	—
36	C₄	#67275	1	2	yes	—
37	C₂	#10625015	1	1	yes	characteristic
38	C₂	#10625017	1	2	yes	—

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

N	H ≅ G/N	type
22. C₂₃	#333	semidirect

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