Subgroups — #66880

Order 352.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₁	—	2	1	no	—
6	C₂×Dic₁₁	—	2	1	no	—
7	Dic₂₂	—	2	1	no	—
8	Dic₂₂	C₄	1	2	yes	complemented
9	C₈×C₁₁	—	2	1	no	—
10	C₂²×C₁₁	D₄	1	1	yes	characteristic
11	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₄×C₁₁	D₄	1	1	yes	characteristic
13	Dic₁₁	—	2	2	no	—
14	Dic₁₁	—	4	1	no	—
15	#103	—	11	1	no	maximal, Sylow
16	C₂×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
17	C₂×C₁₁	SD₁₆	1	1	yes	characteristic
18	C₂×C₁₁	Q₁₆	1	1	yes	characteristic
19	C₂×Q₈	—	11	1	no	—
20	C₂×C₈	D₁₁	1	1	yes	characteristic
21	C₄⋊C₄	—	11	1	no	—
22	C₁₁	#103	1	1	yes	characteristic, complemented, Sylow
23	Q₈	—	11	2	no	—
24	Q₈	—	22	1	no	—
25	C₂×C₄	—	22	1	no	—
26	C₂×C₄	—	22	1	no	—
27	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
28	C₈	—	2	1	no	—
29	C₂²	D₄₄	1	1	yes	characteristic
30	C₄	—	22	2	no	—
31	C₄	—	44	1	no	—
32	C₄	C₄×D₁₁	1	1	yes	characteristic
33	C₄	C₂²⋊D₁₁	1	1	yes	characteristic
34	C₂	#4314	1	1	yes	characteristic
35	C₂	Dic₄₄	1	1	yes	characteristic
36	C₂	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. Dic₂₂	C₄	semidirect
22. C₁₁	#103	semidirect

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