Subgroups — C₄⋊#20297748 #43273109

Order 28736.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20297748	C₂	1	2	yes	maximal
2	C₄×#16813318	C₂	1	1	yes	maximal, characteristic
3	#20297748	—	2	2	no	—
4	C₂×#16813318	C₄	1	1	yes	characteristic
5	C₂×#16813318	C₂²	1	1	yes	characteristic
6	C₄×Dic₄₄₉	C₄	1	1	yes	characteristic
7	#16813318	—	2	1	no	—
8	#16813318	D₄	1	1	yes	characteristic
9	#16813318	Q₈	1	1	yes	characteristic
10	C₂×Dic₄₄₉	C₈	1	1	yes	characteristic
11	C₂×Dic₄₄₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₄₉	C₈	1	1	yes	characteristic
13	C₂²×C₄₄₉	C₂×C₈	1	1	yes	characteristic
14	C₄×C₄₄₉	C₁₆	1	2	yes	complemented
15	Dic₄₄₉	—	2	1	no	—
16	Dic₄₄₉	C₄⋊C₄	1	1	yes	characteristic
17	Dic₄₄₉	M₁₆	1	1	yes	characteristic
18	C₂×C₄₄₉	C₄⋊C₈	1	1	yes	characteristic
19	C₂×C₄₄₉	C₂×C₁₆	1	1	yes	characteristic
20	C₂×C₄₄₉	M₃₂	1	1	yes	characteristic
21	C₄₄₉	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄⋊C₁₆	—	449	1	no	maximal, Sylow
23	C₂×C₁₆	—	449	2	no	—
24	C₄×C₈	—	449	1	no	—
25	C₂×C₈	—	449	1	no	—
26	C₂×C₈	—	449	1	no	—
27	C₄²	—	449	1	no	—
28	C₁₆	—	898	2	no	—
29	C₂×C₄	—	449	1	no	—
30	C₂×C₄	—	449	1	no	—
31	C₂×C₄	#16813320	1	1	yes	characteristic
32	C₈	—	898	1	no	—
33	C₈	—	449	1	no	—
34	C₈	—	449	1	no	—
35	C₂²	C₂×#16813320	1	1	yes	characteristic
36	C₄	—	898	1	no	—
37	C₄	—	449	1	no	—
38	C₄	—	449	1	no	—
39	C₄	#20297748	1	2	yes	complemented
40	C₂	C₄⋊#16813320	1	1	yes	characteristic
41	C₂	C₂×#20297748	1	1	yes	characteristic
42	C₂	#28385437	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.