Subgroups — C₂³×#11717581 #20266247

Order 6464.

338 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11717581	C₂	1	14	yes	maximal, direct product factor
2	C₂³×Dic₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#11717581	C₂²	1	28	yes	direct product factor
4	C₂²×Dic₁₀₁	C₄	1	7	yes	—
5	C₂²×Dic₁₀₁	C₂²	1	7	yes	—
6	C₂⁴×C₁₀₁	C₄	1	1	yes	characteristic
7	C₂³×C₁₀₁	C₈	1	8	yes	complemented
8	C₂³×C₁₀₁	C₂×C₄	1	7	yes	—
9	C₂×Dic₁₀₁	C₂×C₄	1	21	yes	—
10	C₂×Dic₁₀₁	C₂³	1	7	yes	—
11	#11717581	C₂³	1	8	yes	direct product factor
12	C₂²×C₁₀₁	C₂×C₈	1	28	yes	complemented
13	C₂²×C₁₀₁	C₂²×C₄	1	7	yes	—
14	Dic₁₀₁	C₂²×C₄	1	7	yes	—
15	Dic₁₀₁	C₂⁴	1	1	yes	characteristic
16	C₂×C₁₀₁	C₂²×C₈	1	14	yes	complemented
17	C₂×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
18	C₁₀₁	C₂³×C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂³×C₈	—	101	1	no	maximal, Sylow
20	C₂³×C₄	—	101	1	no	—
21	C₂²×C₈	—	101	14	no	—
22	C₂⁴	#87938	1	1	yes	characteristic
23	C₂²×C₄	—	101	7	no	—
24	C₂²×C₄	—	101	7	no	—
25	C₂×C₈	—	101	28	no	—
26	C₂³	#11717581	1	8	yes	direct product factor
27	C₂³	C₂×#87938	1	7	yes	—
28	C₂×C₄	—	101	7	no	—
29	C₂×C₄	—	101	21	no	—
30	C₈	—	101	8	no	—
31	C₂²	C₂×#11717581	1	28	yes	direct product factor
32	C₂²	C₂²×#87938	1	7	yes	—
33	C₄	—	101	1	no	—
34	C₄	—	101	7	no	—
35	C₂	C₂²×#11717581	1	14	yes	direct product factor
36	C₂	C₂³×#87938	1	1	yes	characteristic

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