Subgroups — #14641438

Order 2816.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₁₁⋊C₃₂)	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₃₂	—	2	1	no	—
5	C₄×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₁₁⋊C₃₂	—	2	1	no	—
7	C₄×C₁₁⋊C₁₆	C₄	1	1	yes	characteristic
8	C₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
9	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
10	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₁₁⋊C₁₆	—	2	1	no	—
13	C₄×C₁₁⋊C₈	C₈	1	1	yes	characteristic
14	C₄×C₁₁⋊C₈	C₈	1	1	yes	characteristic
15	C₁₁×C₃₂	—	4	1	no	—
16	C₁₁⋊C₃₂	—	4	1	no	—
17	#7455	—	11	1	no	maximal, Sylow
18	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₁	M₁₆	1	1	yes	characteristic
20	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
21	C₂×C₁₁⋊C₈	—	2	1	no	—
22	C₂×C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
23	C₂×C₁₁⋊C₈	C₁₆	1	1	yes	characteristic
24	C₁₁×C₁₆	—	2	1	no	—
25	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
26	C₁₁×C₁₆	SD₁₆	1	1	yes	characteristic
27	C₁₁⋊C₁₆	—	2	2	no	—
28	C₄⋊C₃₂	—	11	1	no	—
29	C₄⋊C₃₂	D₁₁	1	1	yes	characteristic
30	C₈×C₁₆	—	11	1	no	—
31	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₁	M₃₂	1	1	yes	characteristic
34	C₈×C₁₁	—	2	1	no	—
35	C₈×C₁₁	#106	1	1	yes	characteristic
36	C₈×C₁₁	#108	1	1	yes	characteristic
37	C₁₁⋊C₈	—	2	2	no	—
38	C₁₁⋊C₈	—	2	1	no	—
39	C₁₁⋊C₈	C₃₂	1	2	yes	complemented
40	C₂×C₃₂	—	2	1	no	—
41	C₂×C₃₂	—	22	1	no	—
42	C₄×C₁₆	—	11	1	no	—
43	C₄×C₁₆	C₂×D₁₁	1	1	yes	characteristic
44	C₈²	—	11	1	no	—
45	C₂²×C₁₁	C₄⋊C₁₆	1	1	yes	characteristic
46	C₄×C₁₁	—	2	1	no	—
47	C₄×C₁₁	#334	1	1	yes	characteristic
48	C₄×C₁₁	#364	1	1	yes	characteristic
49	C₄×C₁₁	C₂×C₃₂	1	1	yes	characteristic
50	C₄×C₁₁	M₆₄	1	1	yes	characteristic
51	C₂×C₁₆	—	22	1	no	—
52	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
53	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
54	C₄×C₈	—	11	1	no	—
55	C₄×C₈	—	11	1	no	—
56	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
57	C₃₂	—	4	1	no	—
58	C₃₂	—	44	1	no	—
59	C₂×C₁₁	#1367	1	1	yes	characteristic
60	C₂×C₁₁	C₄⋊C₃₂	1	1	yes	characteristic
61	C₂×C₁₁	#1422	1	1	yes	characteristic
62	C₂×C₈	—	11	1	no	—
63	C₂×C₈	—	11	1	no	—
64	C₂×C₈	—	22	1	no	—
65	C₂×C₈	#4313	1	1	yes	characteristic
66	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
67	C₄²	C₈×D₁₁	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	22	2	no	—
70	C₁₆	#4324	1	1	yes	characteristic
71	C₁₆	#4325	1	1	yes	characteristic
72	C₁₁	#7455	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₄	C₁₆×D₁₁	1	1	yes	characteristic
74	C₂×C₄	#66862	1	1	yes	characteristic
75	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	11	2	no	—
78	C₈	—	22	2	no	—
79	C₈	—	22	1	no	—
80	C₈	#66872	1	1	yes	characteristic
81	C₈	#66886	1	1	yes	characteristic
82	C₂²	Dic₁₁⋊C₁₆	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	D₁₁×C₃₂	1	1	yes	characteristic
85	C₄	#10622085	1	1	yes	characteristic
86	C₄	#10622118	1	1	yes	characteristic
87	C₄	#10622149	1	1	yes	characteristic
88	C₂	#13066679	1	1	yes	characteristic
89	C₂	Dic₁₁⋊C₃₂	1	1	yes	characteristic
90	C₂	#13066813	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₃₂
Frattini	C₄×C₁₆	C₂×D₁₁
Fitting	C₁₁×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₁₁	C₄⋊C₁₆
cosocle	C₄×C₁₁×C₁₆	C₂²
hypercenter	C₄⋊C₃₂	D₁₁
hypocenter	C₁₁	#7455
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
39. C₁₁⋊C₈	C₃₂	semidirect
72. C₁₁	#7455	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊(C₁₁⋊C₃₂)	2
C₁₆×C₁₁⋊C₈	2
C₁₁×C₄⋊C₃₂	2
#7455	11