Subgroups — Q₁₆×D₄₄₉ #28385356

Order 14368.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₄₄₉	C₂	1	2	yes	maximal
2	Dic₁₇₉₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#20297726	C₂	1	2	yes	maximal, complemented
4	C₈×D₄₄₉	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×C₄₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₈₉₈	—	2	2	no	—
7	Dic₈₉₈	C₂²	1	2	yes	—
8	C₄×D₄₄₉	—	2	2	no	—
9	C₄×D₄₄₉	C₂²	1	1	yes	characteristic
10	#16813311	C₂²	1	1	yes	characteristic
11	Q₈×C₄₄₉	C₂²	1	2	yes	—
12	C₈×C₄₄₉	C₂²	1	1	yes	characteristic
13	C₂×D₄₄₉	D₄	1	1	yes	characteristic
14	C₄×C₄₄₉	—	2	2	no	—
15	C₄×C₄₄₉	C₂³	1	1	yes	characteristic
16	Dic₄₄₉	—	2	2	no	—
17	Dic₄₄₉	D₄	1	1	yes	characteristic
18	C₂×C₄₄₉	C₂×D₄	1	1	yes	characteristic
19	D₄₄₉	Q₁₆	1	2	yes	direct product factor
20	C₄₄₉	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	449	1	no	maximal, Sylow
22	C₂×Q₈	—	449	2	no	—
23	Q₁₆	—	449	2	no	—
24	Q₁₆	—	449	1	no	—
25	Q₁₆	D₄₄₉	1	1	yes	characteristic, direct product factor
26	C₂×C₈	—	449	1	no	—
27	Q₈	—	898	2	no	—
28	Q₈	—	449	2	no	—
29	Q₈	C₂×D₄₄₉	1	2	yes	—
30	C₂×C₄	—	898	2	no	—
31	C₂×C₄	—	449	1	no	—
32	C₈	—	449	1	no	—
33	C₈	C₂×D₄₄₉	1	1	yes	characteristic
34	C₂²	—	449	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	898	2	no	—
37	C₄	—	449	1	no	—
38	C₄	C₂²×D₄₄₉	1	1	yes	characteristic
39	C₂	—	449	2	no	—
40	C₂	D₄×D₄₄₉	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.