Subgroups — #14641580

Order 2816.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13066827	C₂	1	2	yes	maximal
2	C₁₁×#1397	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₃₂	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₃₂	C₂²	1	1	yes	characteristic
5	C₄×C₁₁×C₁₆	C₄	1	1	yes	characteristic
6	C₁₁⋊C₆₄	C₄	1	4	yes	complemented
7	C₂×C₁₁×C₁₆	C₈	1	1	yes	characteristic
8	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₁	C₈	1	1	yes	characteristic
10	C₁₁×C₃₂	C₈	1	2	yes	—
11	C₁₁×C₃₂	C₂×C₄	1	2	yes	—
12	#7511	—	11	1	no	maximal, Sylow
13	C₂×C₈×C₁₁	C₁₆	1	1	yes	characteristic
14	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
15	C₄²×C₁₁	C₁₆	1	1	yes	characteristic
16	C₁₁×C₁₆	C₁₆	1	2	yes	—
17	C₁₁×C₁₆	C₄²	1	1	yes	characteristic
18	C₁₁×C₁₆	C₂×C₈	1	1	yes	characteristic
19	M₁₂₈	—	11	2	no	—
20	#1397	D₁₁	1	1	yes	characteristic
21	C₂×C₄×C₁₁	—	2	1	no	—
22	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
23	C₈×C₁₁	—	2	1	no	—
24	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
25	C₈×C₁₁	C₂×C₁₆	1	1	yes	characteristic
26	C₂×C₃₂	Dic₁₁	1	1	yes	characteristic
27	C₂×C₃₂	C₂×D₁₁	1	1	yes	characteristic
28	C₄×C₁₆	Dic₁₁	1	1	yes	characteristic
29	C₆₄	—	11	4	no	—
30	C₂²×C₁₁	M₆₄	1	1	yes	characteristic
31	C₄×C₁₁	—	4	1	no	—
32	C₄×C₁₁	C₄×C₁₆	1	1	yes	characteristic
33	C₄×C₁₁	M₆₄	1	1	yes	characteristic
34	C₂×C₁₆	C₁₁⋊C₈	1	1	yes	characteristic
35	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
36	C₄×C₈	C₁₁⋊C₈	1	1	yes	characteristic
37	C₃₂	C₁₁⋊C₈	1	2	yes	—
38	C₃₂	C₄×D₁₁	1	2	yes	—
39	C₂×C₁₁	—	2	1	no	—
40	C₂×C₁₁	#1397	1	1	yes	characteristic
41	C₂×C₈	C₁₁⋊C₁₆	1	1	yes	characteristic
42	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
43	C₄²	C₁₁⋊C₁₆	1	1	yes	characteristic
44	C₁₆	C₁₁⋊C₁₆	1	2	yes	—
45	C₁₆	C₂×C₁₁⋊C₈	1	1	yes	characteristic
46	C₁₆	C₄×Dic₁₁	1	1	yes	characteristic
47	C₁₁	#7511	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₄	—	2	1	no	—
49	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
50	C₈	—	2	1	no	—
51	C₈	C₄×C₁₁⋊C₈	1	1	yes	characteristic
52	C₈	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
53	C₂²	#10622137	1	1	yes	characteristic
54	C₄	—	4	1	no	—
55	C₄	C₄×C₁₁⋊C₁₆	1	1	yes	characteristic
56	C₄	#10622137	1	1	yes	characteristic
57	C₂	—	2	1	no	—
58	C₂	#13066750	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₄×Dic₁₁
commutator	C₄×C₁₁	C₄×C₁₆
Frattini	C₂×C₃₂	C₂×D₁₁
Fitting	C₁₁×#1397	C₂
socle	C₂×C₁₁	#1397
prime radical	C₂²×C₁₁	M₆₄
cosocle	C₂×C₁₁×C₃₂	C₂²
hypercenter	#1397	D₁₁
hypocenter	C₁₁	#7511
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₁₆ ◁ #1397

Complements

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

N	H ≅ G/N	type
6. C₁₁⋊C₆₄	C₄	semidirect
47. C₁₁	#7511	semidirect

Maximal subgroups

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

subgroup	index
#13066827	2
C₁₁×#1397	2
#7511	11