Subgroups — #14641476

Order 2816.

166 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622144	C₂	1	2	yes	maximal
2	C₂²×C₁₁×C₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
4	C₂×#66883	—	2	2	no	—
5	C₂×C₁₁×C₃₂	—	2	2	no	—
6	C₂×C₁₁×C₃₂	C₄	1	2	yes	—
7	#10622144	—	2	2	no	—
8	#10622144	C₄	1	4	yes	—
9	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
10	C₂×#4318	—	4	2	no	—
11	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
12	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
14	C₂×C₁₁×C₁₆	Q₈	1	1	yes	characteristic
15	#66883	—	2	4	no	—
16	#66883	—	4	2	no	—
17	C₁₁×C₃₂	—	2	2	no	—
18	#7472	—	11	1	no	maximal, Sylow
19	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
20	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
21	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
23	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
24	#4318	—	4	4	no	—
25	#4318	—	8	2	no	—
26	C₂×C₁₁⋊C₈	—	8	2	no	—
27	C₁₁×C₁₆	C₄²	1	1	yes	characteristic
28	C₁₁×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
29	C₁₁×C₁₆	C₄⋊C₄	1	2	yes	—
30	C₂²×C₃₂	D₁₁	1	1	yes	characteristic
31	C₂×#368	—	11	2	no	—
32	C₂³×C₁₁	Q₃₂	1	1	yes	characteristic
33	C₂×C₄×C₁₁	#102	1	2	yes	—
34	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
35	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
36	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
37	C₈×C₁₁	#95	1	1	yes	characteristic
38	C₈×C₁₁	#103	1	2	yes	—
39	C₈×C₁₁	#106	1	1	yes	characteristic
40	C₁₁⋊C₈	—	8	4	no	—
41	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
42	C₂×#108	—	22	2	no	—
43	C₂×C₃₂	—	2	2	no	—
44	C₂×C₃₂	Dic₁₁	1	2	yes	—
45	#368	—	11	4	no	—
46	#368	—	22	2	no	—
47	C₂²×C₁₁	—	2	2	no	—
48	C₂²×C₁₁	#358	1	2	yes	—
49	C₂²×C₁₁	#366	1	1	yes	characteristic
50	C₄×C₁₁	#340	1	1	yes	characteristic
51	C₄×C₁₁	#357	1	2	yes	—
52	C₄×C₁₁	#367	1	1	yes	characteristic
53	C₂×M₁₆	—	44	2	no	—
54	C₂²×C₈	D₄₄	1	1	yes	characteristic
55	C₂×C₁₆	Dic₂₂	1	1	yes	characteristic
56	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
57	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
58	C₂×C₁₆	C₂²⋊D₁₁	1	2	yes	—
59	#108	—	22	4	no	—
60	#108	—	44	2	no	—
61	C₃₂	—	2	2	no	—
62	C₂×C₁₁	—	2	2	no	—
63	C₂×C₁₁	#1380	1	1	yes	characteristic
64	C₂×C₁₁	#1425	1	2	yes	—
65	C₂²×C₄	D₈₈	1	1	yes	characteristic
66	M₁₆	—	44	4	no	—
67	M₁₆	—	88	2	no	—
68	C₂×C₈	—	88	2	no	—
69	C₂×C₈	#4314	1	2	yes	—
70	C₂×C₈	Dic₄₄	1	1	yes	characteristic
71	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
72	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
73	C₁₆	C₄×Dic₁₁	1	1	yes	characteristic
74	C₁₆	Dic₁₁⋊C₄	1	2	yes	—
75	C₁₆	C₂²⋊Dic₁₁	1	1	yes	characteristic
76	C₁₁	#7472	1	1	yes	characteristic, complemented, Sylow
77	C₂³	Dic₈₈	1	1	yes	characteristic
78	C₂×C₄	D₁₇₆	1	1	yes	characteristic
79	C₂×C₄	#66864	1	2	yes	—
80	C₂×C₄	#66882	1	1	yes	characteristic
81	C₂×C₄	#66885	1	2	yes	—
82	C₈	—	88	4	no	—
83	C₈	#66880	1	2	yes	—
84	C₈	#66881	1	1	yes	characteristic
85	C₈	C₁₁⋊#95	1	1	yes	characteristic
86	C₂²	—	2	2	no	—
87	C₂²	#10622141	1	2	yes	—
88	C₂²	#10622142	1	1	yes	characteristic
89	C₄	#10622143	1	1	yes	characteristic
90	C₄	#10622147	1	2	yes	—
91	C₄	#10622189	1	1	yes	characteristic
92	C₂	—	2	2	no	—
93	C₂	#13066708	1	1	yes	characteristic
94	C₂	#13066820	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₇₆
commutator	C₁₁×C₁₆	C₄²
Frattini	C₂²×C₁₆	C₂×D₁₁
Fitting	C₂²×C₁₁×C₃₂	C₂
socle	C₂²×C₁₁	#366
prime radical	C₂³×C₁₁	Q₃₂
cosocle	C₂²×C₁₁×C₁₆	C₂²
hypercenter	C₂²×C₃₂	D₁₁
hypocenter	C₁₁	#7472
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

Complements

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

N	H ≅ G/N	type
76. C₁₁	#7472	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622144	2
C₂²×C₁₁×C₃₂	2
#7472	11