Subgroups — C₁₁×#498 #10622985

Order 704.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₄²×C₁₁ ◁ G

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.