Subgroups — #13066831

Order 1408.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×D₃₂	C₂	1	1	yes	maximal, characteristic
2	Dic₁₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁⋊C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×D₁₆	—	2	1	no	—
5	Dic₈₈	—	2	1	no	—
6	C₁₁×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₁×D₈	—	4	1	no	—
8	Dic₄₄	—	4	1	no	—
9	C₁₁×C₁₆	D₄	1	1	yes	characteristic
10	SD₁₂₈	—	11	1	no	maximal, Sylow
11	D₄×C₁₁	—	8	1	no	—
12	Dic₂₂	—	8	1	no	—
13	C₈×C₁₁	D₈	1	1	yes	characteristic
14	Q₆₄	—	11	1	no	—
15	D₃₂	D₁₁	1	1	yes	characteristic
16	C₆₄	—	11	1	no	—
17	C₂²×C₁₁	—	16	1	no	—
18	C₄×C₁₁	D₁₆	1	1	yes	characteristic
19	Dic₁₁	—	16	1	no	—
20	Q₃₂	—	22	1	no	—
21	D₁₆	—	2	1	no	—
22	C₃₂	C₂×D₁₁	1	1	yes	characteristic
23	C₂×C₁₁	—	32	1	no	—
24	C₂×C₁₁	D₃₂	1	1	yes	characteristic
25	Q₁₆	—	44	1	no	—
26	D₈	—	4	1	no	—
27	C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
28	C₁₁	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
29	Q₈	—	88	1	no	—
30	D₄	—	8	1	no	—
31	C₈	#4323	1	1	yes	characteristic
32	C₂²	—	16	1	no	—
33	C₄	—	176	1	no	—
34	C₄	#66890	1	1	yes	characteristic
35	C₂	—	32	1	no	—
36	C₂	#10622157	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.