Subgroups — C₄²×#14267798 #43272941

Order 28736.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#14267798	C₂	1	6	yes	maximal
2	C₄²×D₄₄₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#14267798	C₂²	1	4	yes	—
4	C₄×#14267798	C₄	1	24	yes	direct product factor
5	C₂×C₄×D₄₄₉	C₂²	1	3	yes	—
6	C₄×Dic₄₄₉	C₄	1	3	yes	complemented
7	C₄²×C₄₄₉	C₄	1	1	yes	characteristic, complemented
8	C₂×#14267798	C₂×C₄	1	24	yes	—
9	C₂²×D₄₄₉	C₂³	1	1	yes	characteristic
10	C₂×Dic₄₄₉	C₂×C₄	1	3	yes	—
11	C₄×D₄₄₉	C₂×C₄	1	12	yes	—
12	C₂×C₄×C₄₄₉	C₂×C₄	1	3	yes	—
13	C₂²×C₄₄₉	C₂²×C₄	1	1	yes	characteristic
14	C₂×D₄₄₉	C₂²×C₄	1	6	yes	—
15	#14267798	C₄²	1	16	yes	direct product factor
16	C₄×C₄₄₉	C₄²	1	6	yes	complemented
17	Dic₄₄₉	C₄²	1	6	yes	complemented
18	C₂×C₄₄₉	C₂×C₄²	1	3	yes	—
19	D₄₄₉	C₂×C₄²	1	4	yes	—
20	C₄₄₉	C₄³	1	1	yes	characteristic, complemented, Sylow
21	C₄³	—	449	1	no	maximal, Sylow
22	C₂×C₄²	—	449	6	no	—
23	C₂×C₄²	—	449	1	no	—
24	C₂²×C₄	—	449	4	no	—
25	C₂²×C₄	—	449	3	no	—
26	C₄²	—	449	24	no	—
27	C₄²	—	449	3	no	—
28	C₄²	#14267798	1	1	yes	characteristic, direct product factor
29	C₂³	—	449	1	no	—
30	C₂×C₄	—	449	24	no	—
31	C₂×C₄	—	449	3	no	—
32	C₂×C₄	—	449	12	no	—
33	C₂×C₄	C₂×#14267798	1	3	yes	—
34	C₂²	—	449	6	no	—
35	C₂²	C₂²×#14267798	1	1	yes	characteristic
36	C₄	—	449	16	no	—
37	C₄	—	449	6	no	—
38	C₄	C₄×#14267798	1	6	yes	direct product factor
39	C₂	—	449	4	no	—
40	C₂	C₂×C₄×#14267798	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.