Subgroups — #28385271

Order 14368.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16813311	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₄₄₉	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₄₄₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₄₉	—	2	1	no	—
5	#16813311	C₄	1	2	yes	complemented
6	C₂×C₄×C₄₄₉	—	2	1	no	—
7	C₂×C₄×C₄₄₉	C₂²	1	1	yes	characteristic
8	C₂²×C₄₄₉	D₄	1	1	yes	characteristic
9	C₄×C₄₄₉	—	4	1	no	—
10	C₄×C₄₄₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₄₄₉	Q₈	1	1	yes	characteristic
12	Dic₄₄₉	—	4	1	no	—
13	C₂×C₄₄₉	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₄₄₉	SD₁₆	1	1	yes	characteristic
15	C₂×C₄₄₉	SD₁₆	1	1	yes	characteristic
16	C₄₄₉	#106	1	1	yes	characteristic, complemented, Sylow
17	#106	—	449	1	no	maximal, Sylow
18	C₂×C₈	—	449	1	no	—
19	C₄⋊C₄	—	449	1	no	—
20	C₄⋊C₄	D₄₄₉	1	1	yes	characteristic
21	C₂×C₄	—	2	1	no	—
22	C₂×C₄	—	898	1	no	—
23	C₂×C₄	C₂×D₄₄₉	1	1	yes	characteristic
24	C₈	—	449	2	no	—
25	C₂²	C₂²⋊D₄₄₉	1	1	yes	characteristic
26	C₄	—	4	1	no	—
27	C₄	—	1796	1	no	—
28	C₄	C₄×D₄₄₉	1	1	yes	characteristic
29	C₄	Dic₈₉₈	1	1	yes	characteristic
30	C₂	#20297715	1	1	yes	characteristic
31	C₂	#20297723	1	1	yes	characteristic
32	C₂	#20297724	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #16813311	C₄	semidirect
16. C₄₄₉	#106	semidirect

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