Subgroups — #13066826

Order 1408.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₁	C₄	1	1	yes	characteristic
5	C₁₁×C₃₂	C₂²	1	1	yes	characteristic
6	C₁₁⋊C₃₂	C₄	1	1	yes	characteristic
7	C₈×D₁₁	C₈	1	1	yes	characteristic
8	C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₁₁⋊C₁₆	C₈	1	1	yes	characteristic
10	M₁₂₈	—	11	1	no	maximal, Sylow
11	C₄×D₁₁	C₁₆	1	1	yes	characteristic
12	C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
13	C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
14	C₂×C₃₂	—	11	1	no	—
15	C₆₄	—	11	1	no	—
16	C₆₄	D₁₁	1	1	yes	characteristic, complemented
17	C₂×D₁₁	C₃₂	1	1	yes	characteristic
18	C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
19	Dic₁₁	C₃₂	1	1	yes	characteristic
20	C₂×C₁₆	—	11	1	no	—
21	C₃₂	—	11	1	no	—
22	C₃₂	C₂×D₁₁	1	1	yes	characteristic
23	C₂×C₁₁	C₂×C₃₂	1	1	yes	characteristic
24	D₁₁	—	2	1	no	—
25	C₂×C₈	—	11	1	no	—
26	C₁₆	—	11	1	no	—
27	C₁₆	C₄×D₁₁	1	1	yes	characteristic
28	C₁₁	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₄	—	11	1	no	—
30	C₈	—	11	1	no	—
31	C₈	C₈×D₁₁	1	1	yes	characteristic
32	C₂²	—	11	1	no	—
33	C₄	—	11	1	no	—
34	C₄	C₁₆×D₁₁	1	1	yes	characteristic
35	C₂	—	22	1	no	—
36	C₂	D₁₁×C₃₂	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.