Subgroups — C₄⋊#20264380 #38787241

Order 25664.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20264380	C₂	1	2	yes	maximal
2	C₄×#15692008	C₂	1	1	yes	maximal, characteristic
3	#20264380	—	2	2	no	—
4	C₂×#15692008	C₄	1	1	yes	characteristic
5	C₂×#15692008	C₂²	1	1	yes	characteristic
6	C₄×#13107944	C₄	1	1	yes	characteristic
7	#15692008	—	2	1	no	—
8	#15692008	D₄	1	1	yes	characteristic
9	#15692008	Q₈	1	1	yes	characteristic
10	C₂×#13107944	C₈	1	1	yes	characteristic
11	C₂×#13107944	C₂×C₄	1	1	yes	characteristic
12	C₄×D₄₀₁	C₈	1	1	yes	characteristic
13	C₂×D₄₀₁	C₂×C₈	1	1	yes	characteristic
14	#13107944	—	2	1	no	—
15	#13107944	C₄⋊C₄	1	1	yes	characteristic
16	#13107944	M₁₆	1	1	yes	characteristic
17	C₄×C₄₀₁	C₁₆	1	1	yes	characteristic, complemented
18	Dic₄₀₁	C₁₆	1	1	yes	characteristic, complemented
19	C₂×C₄₀₁	C₂×C₁₆	1	1	yes	characteristic
20	D₄₀₁	C₄⋊C₈	1	1	yes	characteristic
21	D₄₀₁	M₃₂	1	1	yes	characteristic
22	C₄₀₁	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
23	C₄⋊C₁₆	—	401	1	no	maximal, Sylow
24	C₂×C₁₆	—	401	2	no	—
25	C₄×C₈	—	401	1	no	—
26	C₂×C₈	—	401	1	no	—
27	C₂×C₈	—	401	1	no	—
28	C₄²	—	401	1	no	—
29	C₁₆	—	802	2	no	—
30	C₂×C₄	—	401	1	no	—
31	C₂×C₄	—	401	1	no	—
32	C₂×C₄	—	401	1	no	—
33	C₈	—	802	1	no	—
34	C₈	—	401	1	no	—
35	C₈	—	401	1	no	—
36	C₂²	—	401	1	no	—
37	C₄	—	802	1	no	—
38	C₄	—	401	1	no	—
39	C₄	—	401	1	no	—
40	C₄	—	401	1	no	—
41	C₄	#20264380	1	1	yes	characteristic, complemented
42	C₂	—	401	1	no	—
43	C₂	—	401	1	no	—
44	C₂	C₂×#20264380	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.