Subgroups — C₂³×C₂₃⋊C₈ #13093174

Order 1472.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂₃⋊C₈	C₂	1	14	yes	maximal, direct product factor
3	C₂⁴×C₂₃	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₂₃	C₄	1	7	yes	—
5	C₂²×C₄×C₂₃	C₂²	1	7	yes	—
6	C₂×C₂₃⋊C₈	C₂²	1	28	yes	direct product factor
7	C₂³×C₂₃	C₈	1	8	yes	complemented
8	C₂³×C₂₃	C₂×C₄	1	7	yes	—
9	C₂×C₄×C₂₃	C₂×C₄	1	21	yes	—
10	C₂×C₄×C₂₃	C₂³	1	7	yes	—
11	C₂₃⋊C₈	C₂³	1	8	yes	direct product factor
12	C₂²×C₂₃	C₂×C₈	1	28	yes	complemented
13	C₂²×C₂₃	C₂²×C₄	1	7	yes	—
14	C₄×C₂₃	C₂²×C₄	1	7	yes	—
15	C₄×C₂₃	C₂⁴	1	1	yes	characteristic
16	C₂³×C₈	—	23	1	no	maximal, Sylow
17	C₂×C₂₃	C₂²×C₈	1	14	yes	complemented
18	C₂×C₂₃	C₂³×C₄	1	1	yes	characteristic
19	C₂³×C₄	D₂₃	1	1	yes	characteristic
20	C₂²×C₈	—	23	14	no	—
21	C₂₃	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
22	C₂⁴	Dic₂₃	1	1	yes	characteristic
23	C₂²×C₄	Dic₂₃	1	7	yes	—
24	C₂²×C₄	C₂×D₂₃	1	7	yes	—
25	C₂×C₈	—	23	28	no	—
26	C₂³	C₂₃⋊C₈	1	8	yes	direct product factor
27	C₂³	C₂×Dic₂₃	1	7	yes	—
28	C₂×C₄	C₂×Dic₂₃	1	21	yes	—
29	C₂×C₄	C₂²×D₂₃	1	7	yes	—
30	C₈	—	23	8	no	—
31	C₂²	C₂×C₂₃⋊C₈	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₂₃	1	7	yes	—
33	C₄	C₂²×Dic₂₃	1	7	yes	—
34	C₄	C₂³×D₂₃	1	1	yes	characteristic
35	C₂	C₂²×C₂₃⋊C₈	1	14	yes	direct product factor
36	C₂	C₂³×Dic₂₃	1	1	yes	characteristic

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

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