Subgroups — #66879

Order 352.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₁	C₄	1	2	yes	—
6	C₈×C₁₁	C₄	1	2	yes	complemented
7	C₁₁⋊C₈	C₄	1	2	yes	complemented
8	C₂²×C₁₁	C₂×C₄	1	1	yes	characteristic
9	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
10	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
11	Dic₁₁	—	2	2	no	—
12	#97	—	11	1	no	maximal, Sylow
13	C₂×C₁₁	C₄²	1	1	yes	characteristic
14	C₂×C₁₁	M₁₆	1	2	yes	—
15	C₂×C₈	—	11	1	no	—
16	C₂×C₈	D₁₁	1	1	yes	characteristic
17	C₄²	—	11	1	no	—
18	C₁₁	#97	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₄	—	11	2	no	—
20	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
21	C₈	—	11	2	no	—
22	C₈	Dic₁₁	1	2	yes	complemented
23	C₂²	C₄×D₁₁	1	1	yes	characteristic
24	C₄	—	22	2	no	—
25	C₄	C₄×D₁₁	1	1	yes	characteristic
26	C₄	C₂×Dic₁₁	1	1	yes	characteristic
27	C₂	#4313	1	2	yes	—
28	C₂	C₄×Dic₁₁	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.