Subgroups — #28385394

Order 14368.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20297744	C₂	1	1	yes	maximal, characteristic
2	C₄×#14267798	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#14267798	C₄	1	2	yes	—
5	#16813318	C₄	1	2	yes	complemented
6	C₄×D₄₄₉	C₂²	1	1	yes	characteristic
7	#16813311	C₄	1	1	yes	characteristic, complemented
8	C₈×C₄₄₉	C₄	1	1	yes	characteristic, complemented
9	C₂×D₄₄₉	C₂×C₄	1	1	yes	characteristic
10	#14267798	—	2	2	no	—
11	C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
12	Dic₄₄₉	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄₄₉	C₄²	1	1	yes	characteristic
14	D₄₄₉	M₁₆	1	2	yes	—
15	C₄₄₉	#97	1	1	yes	characteristic, complemented, Sylow
16	#97	—	449	1	no	maximal, Sylow
17	C₂×C₈	—	449	1	no	—
18	C₂×C₈	—	449	1	no	—
19	C₄²	—	449	1	no	—
20	C₂×C₄	—	449	2	no	—
21	C₂×C₄	—	449	1	no	—
22	C₈	—	449	2	no	—
23	C₈	—	449	1	no	—
24	C₈	#14267798	1	1	yes	characteristic, complemented
25	C₂²	—	449	1	no	—
26	C₄	—	898	2	no	—
27	C₄	—	449	1	no	—
28	C₄	C₂×#14267798	1	1	yes	characteristic
29	C₂	—	449	2	no	—
30	C₂	C₄×#14267798	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.