Subgroups — #13066833

Order 1408.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

N	H ≅ G/N	type
27. C₁₁	Q₁₂₈	semidirect

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