Subgroups — C₄⋊#20264378 #38787216

Order 25664.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20264378	C₂	1	2	yes	maximal
2	C₄×#15692006	C₂	1	1	yes	maximal, characteristic
3	#20264378	—	2	2	no	—
4	C₂×#15692006	C₄	1	1	yes	characteristic
5	C₂×#15692006	C₂²	1	1	yes	characteristic
6	C₄×Dic₄₀₁	C₄	1	1	yes	characteristic
7	#15692006	—	2	1	no	—
8	#15692006	D₄	1	1	yes	characteristic
9	#15692006	Q₈	1	1	yes	characteristic
10	C₂×Dic₄₀₁	C₈	1	1	yes	characteristic
11	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₀₁	C₈	1	1	yes	characteristic
13	C₂²×C₄₀₁	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₀₁	C₁₆	1	2	yes	complemented
15	Dic₄₀₁	—	2	1	no	—
16	Dic₄₀₁	C₄⋊C₄	1	1	yes	characteristic
17	Dic₄₀₁	M₁₆	1	1	yes	characteristic
18	C₂×C₄₀₁	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₄₀₁	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₄₀₁	M₃₂	1	1	yes	characteristic
21	C₄₀₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	401	1	no	maximal, Sylow
23	C₂×C₁₆	—	401	2	no	—
24	C₄×C₈	—	401	1	no	—
25	C₂×C₈	—	401	1	no	—
26	C₂×C₈	—	401	1	no	—
27	C₄²	—	401	1	no	—
28	C₁₆	—	802	2	no	—
29	C₂×C₄	—	401	1	no	—
30	C₂×C₄	—	401	1	no	—
31	C₂×C₄	#15692008	1	1	yes	characteristic
32	C₈	—	802	1	no	—
33	C₈	—	401	1	no	—
34	C₈	—	401	1	no	—
35	C₂²	C₂×#15692008	1	1	yes	characteristic
36	C₄	—	802	1	no	—
37	C₄	—	401	1	no	—
38	C₄	—	401	1	no	—
39	C₄	#20264378	1	2	yes	complemented
40	C₂	C₄⋊#15692008	1	1	yes	characteristic
41	C₂	C₂×#20264378	1	1	yes	characteristic
42	C₂	#27165834	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.