Subgroups — C₄²×#13109888 #39910181

Order 26176.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#13109888	C₂	1	6	yes	maximal
2	C₄²×D₄₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13109888	C₂²	1	4	yes	—
4	C₄×#13109888	C₄	1	24	yes	direct product factor
5	C₂×C₄×D₄₀₉	C₂²	1	3	yes	—
6	C₄×Dic₄₀₉	C₄	1	3	yes	complemented
7	C₄²×C₄₀₉	C₄	1	1	yes	characteristic, complemented
8	C₂×#13109888	C₂×C₄	1	24	yes	—
9	C₂²×D₄₀₉	C₂³	1	1	yes	characteristic
10	C₂×Dic₄₀₉	C₂×C₄	1	3	yes	—
11	C₄×D₄₀₉	C₂×C₄	1	12	yes	—
12	C₂×C₄×C₄₀₉	C₂×C₄	1	3	yes	—
13	C₂²×C₄₀₉	C₂²×C₄	1	1	yes	characteristic
14	C₂×D₄₀₉	C₂²×C₄	1	6	yes	—
15	#13109888	C₄²	1	16	yes	direct product factor
16	C₄×C₄₀₉	C₄²	1	6	yes	complemented
17	Dic₄₀₉	C₄²	1	6	yes	complemented
18	C₂×C₄₀₉	C₂×C₄²	1	3	yes	—
19	D₄₀₉	C₂×C₄²	1	4	yes	—
20	C₄₀₉	C₄³	1	1	yes	characteristic, complemented, Sylow
21	C₄³	—	409	1	no	maximal, Sylow
22	C₂×C₄²	—	409	6	no	—
23	C₂×C₄²	—	409	1	no	—
24	C₂²×C₄	—	409	4	no	—
25	C₂²×C₄	—	409	3	no	—
26	C₄²	—	409	24	no	—
27	C₄²	—	409	3	no	—
28	C₄²	#13109888	1	1	yes	characteristic, direct product factor
29	C₂³	—	409	1	no	—
30	C₂×C₄	—	409	24	no	—
31	C₂×C₄	—	409	3	no	—
32	C₂×C₄	—	409	12	no	—
33	C₂×C₄	C₂×#13109888	1	3	yes	—
34	C₂²	—	409	6	no	—
35	C₂²	C₂²×#13109888	1	1	yes	characteristic
36	C₄	—	409	16	no	—
37	C₄	—	409	6	no	—
38	C₄	C₄×#13109888	1	6	yes	direct product factor
39	C₂	—	409	4	no	—
40	C₂	C₂×C₄×#13109888	1	3	yes	—

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.