Subgroups — #28385397

Order 14368.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813318	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×D₄₄₉	C₂	1	1	yes	maximal, characteristic
3	#16813318	—	2	2	no	—
4	C₂²×D₄₄₉	C₄	1	1	yes	characteristic
5	C₂×Dic₄₄₉	C₂²	1	1	yes	characteristic
6	C₄×D₄₄₉	—	2	2	no	—
7	C₂×C₄×C₄₄₉	C₄	1	1	yes	characteristic
8	C₂²×C₄₄₉	C₂×C₄	1	1	yes	characteristic
9	C₂×D₄₄₉	—	2	1	no	—
10	C₂×D₄₄₉	—	2	1	no	—
11	C₂×D₄₄₉	C₈	1	2	yes	complemented
12	C₄×C₄₄₉	—	2	1	no	—
13	Dic₄₄₉	D₄	1	2	yes	—
14	C₂×C₄₄₉	C₂²⋊C₄	1	1	yes	characteristic
15	C₂×C₄₄₉	C₂×C₈	1	1	yes	characteristic
16	C₂×C₄₄₉	M₁₆	1	1	yes	characteristic
17	D₄₄₉	—	2	2	no	—
18	C₄₄₉	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	449	1	no	maximal, Sylow
20	C₂²×C₄	—	449	1	no	—
21	C₂×C₈	—	449	2	no	—
22	C₂³	—	449	1	no	—
23	C₂×C₄	—	898	2	no	—
24	C₂×C₄	—	449	1	no	—
25	C₂×C₄	#14267798	1	1	yes	characteristic
26	C₈	—	898	2	no	—
27	C₂²	—	898	1	no	—
28	C₂²	—	898	1	no	—
29	C₂²	—	449	2	no	—
30	C₂²	C₂×#14267798	1	1	yes	characteristic
31	C₄	—	2	1	no	—
32	C₄	—	449	2	no	—
33	C₂	—	898	2	no	—
34	C₂	C₂²⋊#14267798	1	1	yes	characteristic
35	C₂	#20297744	1	1	yes	characteristic
36	C₂	#20297746	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.