Subgroups — #14641678

Order 2816.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066827	C₂	1	1	yes	maximal, characteristic
2	#13066820	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1424	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
5	C₁₁×#366	—	2	1	no	—
6	#10622144	—	2	1	no	—
7	C₁₁⋊C₆₄	C₄	1	2	yes	complemented
8	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
9	C₁₁×#107	—	4	1	no	—
10	#66883	—	4	1	no	—
11	C₁₁×C₃₂	C₂×C₄	1	1	yes	characteristic
12	C₁₁×C₃₂	Q₈	1	1	yes	characteristic
13	#7548	—	11	1	no	maximal, Sylow
14	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
15	C₁₁×C₄⋊C₄	—	8	1	no	—
16	#4318	—	8	1	no	—
17	C₁₁×C₁₆	C₄⋊C₄	1	1	yes	characteristic
18	C₁₁×C₁₆	Q₁₆	1	1	yes	characteristic
19	M₁₂₈	—	11	1	no	—
20	#1425	—	11	1	no	—
21	#1424	D₁₁	1	1	yes	characteristic
22	C₂×C₄×C₁₁	—	16	1	no	—
23	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
24	C₈×C₁₁	#107	1	1	yes	characteristic
25	C₈×C₁₁	Q₃₂	1	1	yes	characteristic
26	C₁₁⋊C₈	—	16	1	no	—
27	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
28	#368	—	22	1	no	—
29	#366	—	2	1	no	—
30	C₆₄	—	11	2	no	—
31	C₂²×C₁₁	SD₆₄	1	1	yes	characteristic
32	C₄×C₁₁	—	32	1	no	—
33	C₄×C₁₁	#366	1	1	yes	characteristic
34	C₄×C₁₁	SD₆₄	1	1	yes	characteristic
35	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
36	#108	—	44	1	no	—
37	#107	—	4	1	no	—
38	C₃₂	Dic₂₂	1	1	yes	characteristic
39	C₃₂	C₄×D₁₁	1	1	yes	characteristic
40	C₂×C₁₁	—	2	1	no	—
41	C₂×C₁₁	#1424	1	1	yes	characteristic
42	M₁₆	—	88	1	no	—
43	C₂×C₈	#4323	1	1	yes	characteristic
44	C₄⋊C₄	—	8	1	no	—
45	C₁₆	Dic₁₁⋊C₄	1	1	yes	characteristic
46	C₁₆	#4326	1	1	yes	characteristic
47	C₁₁	#7548	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	—	16	1	no	—
49	C₂×C₄	#66890	1	1	yes	characteristic
50	C₈	—	176	1	no	—
51	C₈	#66871	1	1	yes	characteristic
52	C₈	#66893	1	1	yes	characteristic
53	C₂²	#10622158	1	1	yes	characteristic
54	C₄	—	32	1	no	—
55	C₄	#10622127	1	1	yes	characteristic
56	C₄	#10622159	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#13066817	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13066817
commutator	C₁₁×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×#1424	C₂
socle	C₂×C₁₁	#1424
prime radical	C₂²×C₁₁	SD₆₄
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	#1424	D₁₁
hypocenter	C₁₁	#7548
LCS	G ▷ C₁₁×C₃₂ ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ #1424

Complements

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

N	H ≅ G/N	type
7. C₁₁⋊C₆₄	C₄	semidirect
47. C₁₁	#7548	semidirect

Maximal subgroups

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

subgroup	index
#13066827	2
#13066820	2
C₁₁×#1424	2
#7548	11