Subgroups — #66873

Order 352.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄₄	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₁	—	2	1	no	—
5	C₂×C₄×C₁₁	—	2	1	no	—
6	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
7	D₄₄	—	2	1	no	—
8	D₄₄	C₄	1	2	yes	complemented
9	C₁₁⋊C₈	—	2	1	no	—
10	C₂²×C₁₁	D₄	1	1	yes	characteristic
11	C₂×D₁₁	—	2	2	no	—
12	C₂×D₁₁	—	4	1	no	—
13	C₂×D₁₁	—	4	1	no	—
14	C₄×C₁₁	—	4	1	no	—
15	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₁	D₄	1	1	yes	characteristic
17	#102	—	11	1	no	maximal, Sylow
18	C₂×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₁₁	D₈	1	1	yes	characteristic
20	C₂×C₁₁	SD₁₆	1	1	yes	characteristic
21	D₁₁	—	4	2	no	—
22	C₂×D₄	—	11	1	no	—
23	C₂×C₈	—	11	1	no	—
24	C₄⋊C₄	D₁₁	1	1	yes	characteristic, complemented
25	C₁₁	#102	1	1	yes	characteristic, complemented, Sylow
26	C₂³	—	22	1	no	—
27	D₄	—	11	2	no	—
28	D₄	—	22	1	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
31	C₈	—	22	1	no	—
32	C₂²	—	22	2	no	—
33	C₂²	—	44	1	no	—
34	C₂²	—	44	1	no	—
35	C₂²	C₂²⋊D₁₁	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₁₁	1	1	yes	characteristic
38	C₄	D₄₄	1	1	yes	characteristic
39	C₂	—	44	2	no	—
40	C₂	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
41	C₂	#4323	1	1	yes	characteristic
42	C₂	#4325	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.