Subgroups — #43273116

Order 28736.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28385430	C₂	1	2	yes	maximal, complemented
2	#28385413	C₂	1	1	yes	maximal, characteristic
3	#20297739	C₄	1	1	yes	characteristic
4	#20297739	C₂²	1	1	yes	characteristic
5	C₈×D₄₄₉	C₄	1	1	yes	characteristic
6	C₄×D₄₄₉	C₈	1	1	yes	characteristic
7	#16813311	C₂×C₄	1	1	yes	characteristic
8	C₈×C₄₄₉	C₈	1	1	yes	characteristic
9	C₂×D₄₄₉	C₁₆	1	1	yes	characteristic
10	C₄×C₄₄₉	C₂×C₈	1	1	yes	characteristic
11	Dic₄₄₉	C₁₆	1	1	yes	characteristic
12	C₂×C₄₄₉	C₂×C₁₆	1	1	yes	characteristic
13	D₄₄₉	—	2	1	no	—
14	C₄₄₉	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	449	1	no	maximal, Sylow
16	C₂×C₁₆	—	449	1	no	—
17	C₃₂	—	449	2	no	—
18	C₂×C₈	—	449	1	no	—
19	C₁₆	—	449	1	no	—
20	C₁₆	—	449	1	no	—
21	C₂×C₄	—	449	1	no	—
22	C₈	—	449	1	no	—
23	C₈	#16813320	1	1	yes	characteristic
24	C₂²	—	449	1	no	—
25	C₄	—	449	1	no	—
26	C₄	C₂×#16813320	1	1	yes	characteristic
27	C₂	—	898	1	no	—
28	C₂	#28385435	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #28385430	C₂	semidirect
14. C₄₄₉	M₆₄	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.