Subgroups — #10622293

Order 704.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#66922	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	#66881	C₂	1	4	yes	maximal
4	C₂×Dic₂₂	—	2	2	no	—
5	C₂×C₈×C₁₁	C₂²	1	2	yes	—
6	C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₄⋊Dic₁₁	—	2	2	no	—
8	C₄⋊Dic₁₁	C₂²	1	4	yes	—
9	C₂×C₄×C₁₁	D₄	1	2	yes	—
10	C₂×C₄×C₁₁	C₂³	1	1	yes	characteristic
11	C₂×Dic₁₁	—	2	4	no	—
12	Dic₂₂	—	4	4	no	—
13	C₈×C₁₁	Q₈	1	4	yes	complemented
14	#498	—	11	1	no	maximal, Sylow
15	C₂²×C₁₁	C₂×D₄	1	1	yes	characteristic
16	C₄×C₁₁	SD₁₆	1	4	yes	—
17	C₄×C₁₁	C₂×Q₈	1	2	yes	—
18	Dic₁₁	—	4	4	no	—
19	C₄⋊Q₈	—	11	2	no	—
20	#106	—	11	4	no	—
21	C₄×C₈	D₁₁	1	1	yes	characteristic
22	C₂×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
23	C₂×C₁₁	C₂×SD₁₆	1	2	yes	—
24	C₂×Q₈	—	22	2	no	—
25	C₂×C₈	C₂×D₁₁	1	2	yes	—
26	C₄⋊C₄	—	11	4	no	—
27	C₄⋊C₄	—	22	2	no	—
28	C₄²	C₂×D₁₁	1	1	yes	characteristic
29	C₁₁	#498	1	1	yes	characteristic, complemented, Sylow
30	Q₈	—	44	4	no	—
31	C₂×C₄	—	22	4	no	—
32	C₂×C₄	D₄₄	1	2	yes	—
33	C₂×C₄	C₂²×D₁₁	1	1	yes	characteristic
34	C₈	Dic₂₂	1	4	yes	complemented
35	C₂²	C₂×D₄₄	1	1	yes	characteristic
36	C₄	—	44	4	no	—
37	C₄	#4314	1	4	yes	—
38	C₄	C₂×Dic₂₂	1	2	yes	—
39	C₂	#66922	1	1	yes	characteristic
40	C₂	C₂×#4314	1	2	yes	—

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.