Subgroups — C₂³×#66491 #14581093

Order 2624.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66491	C₂	1	14	yes	maximal, direct product factor
2	C₂³×C₄×C₄₁	C₂	1	1	yes	maximal, characteristic
3	C₂⁴×C₄₁	C₄	1	1	yes	characteristic
4	C₂²×C₄×C₄₁	C₄	1	7	yes	—
5	C₂²×C₄×C₄₁	C₂²	1	7	yes	—
6	C₂×#66491	C₂²	1	28	yes	direct product factor
7	C₂³×C₄₁	C₈	1	8	yes	complemented
8	C₂³×C₄₁	C₂×C₄	1	7	yes	—
9	C₂×C₄×C₄₁	C₂×C₄	1	21	yes	—
10	C₂×C₄×C₄₁	C₂³	1	7	yes	—
11	#66491	C₂³	1	8	yes	direct product factor
12	C₂²×C₄₁	C₂×C₈	1	28	yes	complemented
13	C₂²×C₄₁	C₂²×C₄	1	7	yes	—
14	C₄×C₄₁	C₂²×C₄	1	7	yes	—
15	C₄×C₄₁	C₂⁴	1	1	yes	characteristic
16	C₂×C₄₁	C₂²×C₈	1	14	yes	complemented
17	C₂×C₄₁	C₂³×C₄	1	1	yes	characteristic
18	C₂³×C₈	—	41	1	no	maximal, Sylow
19	C₄₁	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
20	C₂³×C₄	D₄₁	1	1	yes	characteristic
21	C₂²×C₈	—	41	14	no	—
22	C₂⁴	Dic₄₁	1	1	yes	characteristic
23	C₂²×C₄	Dic₄₁	1	7	yes	—
24	C₂²×C₄	C₂×D₄₁	1	7	yes	—
25	C₂×C₈	—	41	28	no	—
26	C₂³	#66491	1	8	yes	direct product factor
27	C₂³	C₂×Dic₄₁	1	7	yes	—
28	C₂×C₄	C₂×Dic₄₁	1	21	yes	—
29	C₂×C₄	C₂²×D₄₁	1	7	yes	—
30	C₈	—	41	8	no	—
31	C₂²	C₂×#66491	1	28	yes	direct product factor
32	C₂²	C₂²×Dic₄₁	1	7	yes	—
33	C₄	C₂²×Dic₄₁	1	7	yes	—
34	C₄	C₂³×D₄₁	1	1	yes	characteristic
35	C₂	C₂²×#66491	1	14	yes	direct product factor
36	C₂	C₂³×Dic₄₁	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.