Subgroups — #14641690

Order 2816.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₅₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁⋊C₁₂₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×Q₁₂₈	C₂	1	1	yes	maximal, characteristic
4	C₁₁×Q₆₄	—	2	1	no	—
5	Dic₁₇₆	—	2	1	no	—
6	C₁₁×C₆₄	C₂²	1	1	yes	characteristic
7	C₁₁×Q₃₂	—	4	1	no	—
8	Dic₈₈	—	4	1	no	—
9	C₁₁×C₃₂	D₄	1	1	yes	characteristic
10	Q₂₅₆	—	11	1	no	maximal, Sylow
11	C₁₁×Q₁₆	—	8	1	no	—
12	Dic₄₄	—	8	1	no	—
13	C₁₁×C₁₆	D₈	1	1	yes	characteristic
14	Q₁₂₈	—	11	1	no	—
15	Q₁₂₈	D₁₁	1	1	yes	characteristic
16	C₁₂₈	—	11	1	no	—
17	Q₈×C₁₁	—	16	1	no	—
18	Dic₂₂	—	16	1	no	—
19	C₈×C₁₁	D₁₆	1	1	yes	characteristic
20	Q₆₄	—	2	1	no	—
21	Q₆₄	—	22	1	no	—
22	C₆₄	C₂×D₁₁	1	1	yes	characteristic
23	C₄×C₁₁	—	32	1	no	—
24	C₄×C₁₁	D₃₂	1	1	yes	characteristic
25	Dic₁₁	—	32	1	no	—
26	Q₃₂	—	4	1	no	—
27	Q₃₂	—	44	1	no	—
28	C₃₂	C₂²⋊D₁₁	1	1	yes	characteristic
29	C₂×C₁₁	D₆₄	1	1	yes	characteristic
30	Q₁₆	—	8	1	no	—
31	Q₁₆	—	88	1	no	—
32	C₁₆	#4323	1	1	yes	characteristic
33	C₁₁	Q₂₅₆	1	1	yes	characteristic, complemented, Sylow
34	Q₈	—	16	1	no	—
35	Q₈	—	176	1	no	—
36	C₈	#66890	1	1	yes	characteristic
37	C₄	—	32	1	no	—
38	C₄	—	352	1	no	—
39	C₄	#10622157	1	1	yes	characteristic
40	C₂	#13066828	1	1	yes	characteristic

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

N	H ≅ G/N	type
33. C₁₁	Q₂₅₆	semidirect

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