Subgroups — #43273100

Order 28736.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385435	C₂	1	2	yes	maximal
2	C₈×#14267798	C₂	1	1	yes	maximal, characteristic
3	#20297748	C₄	1	4	yes	complemented
4	#20297744	C₂²	1	1	yes	characteristic
5	C₄×#14267798	C₄	1	1	yes	characteristic
6	C₈×D₄₄₉	C₄	1	1	yes	characteristic
7	C₂×#14267798	C₈	1	2	yes	—
8	#16813318	C₂×C₄	1	2	yes	—
9	C₄×D₄₄₉	C₂×C₄	1	1	yes	characteristic
10	#16813311	C₈	1	1	yes	characteristic
11	C₈×C₄₄₉	C₈	1	1	yes	characteristic
12	C₂×D₄₄₉	C₂×C₈	1	1	yes	characteristic
13	#14267798	C₁₆	1	4	yes	complemented
14	C₄×C₄₄₉	C₂×C₈	1	1	yes	characteristic
15	Dic₄₄₉	C₄²	1	1	yes	characteristic
16	C₂×C₄₄₉	C₄×C₈	1	1	yes	characteristic
17	D₄₄₉	C₂×C₁₆	1	2	yes	—
18	C₄₄₉	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₄×C₁₆	—	449	1	no	maximal, Sylow
20	C₂×C₁₆	—	449	2	no	—
21	C₄×C₈	—	449	1	no	—
22	C₂×C₈	—	449	1	no	—
23	C₂×C₈	—	449	1	no	—
24	C₄²	—	449	1	no	—
25	C₁₆	—	449	4	no	—
26	C₂×C₄	—	449	2	no	—
27	C₂×C₄	—	449	1	no	—
28	C₈	—	449	2	no	—
29	C₈	—	449	1	no	—
30	C₈	#16813320	1	1	yes	characteristic
31	C₂²	—	449	1	no	—
32	C₄	—	449	4	no	—
33	C₄	—	449	1	no	—
34	C₄	C₂×#16813320	1	1	yes	characteristic
35	C₂	—	449	2	no	—
36	C₂	C₄×#16813320	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.