Finite Group Databasebeta

← #14664613

Subgroups — #14664613

Order 2816.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079346C211yesmaximal, characteristic
2#13070425C211yesmaximal, characteristic, complemented
3#13068763C211yesmaximal, characteristic, complemented
4#13066610C211yesmaximal, characteristic, complemented
5#13066608C211yesmaximal, characteristic
6#13066600C211yesmaximal, characteristic
7C11×#1340C211yesmaximal, characteristic, complemented
8#10623155—21no—
9C11×#470C2211yescharacteristic
10#10622804C411yescharacteristic, complemented
11#10622797C411yescharacteristic, complemented
12#10622748C2211yescharacteristic
13M16×Dic11C2211yescharacteristic
14#10622662—21no—
15#10622482C411yescharacteristic, complemented
16#10622471C411yescharacteristic, complemented
17#10622430—21no—
18#10622413—21no—
19C11×#349C2211yescharacteristic
20C11×H(3,ℤ/4)C2211yescharacteristic
21C11⋊#338C2211yescharacteristic
22#10622191C2211yescharacteristic
23#10622171—21no—
24#10622170—21no—
25#10622150—21no—
26#10622149—21no—
27C2×C11×Q16C2×C411yescharacteristic
28C2×C11×M16C2311yescharacteristic
29C11×C22⋊Q8—21no—
30C11×#117—21no—
31#67000—21no—
32Q8×Dic11—21no—
33C2×#4325—21no—
34#66983—21no—
35C2×C4×Dic11D411yescharacteristic
36C2×#4318—21no—
37C2×#4318D411yescharacteristic
38C2×D88C2×C411yescharacteristic
39#66951—41no—
40#66946—21no—
41#66945—41no—
42#66943—21no—
43#66939—41no—
44(C22⋊D11)⋊C4—41no—
45C11×M32—21no—
46C11×#106C2×C411yescharacteristic
47C11×#103—21no—
48#66899—21no—
49#66885—21no—
50#66881C2×C411yescharacteristic
51#66879C2×C411yescharacteristic
52#66879D411yescharacteristic
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11D411yescharacteristic
55#66876—21no—
56#66873—21no—
57#66871—21no—
58#11836—111nomaximal, Sylow
59C2×Q8×C11—21no—
60C22×C4×C11C2×D411yescharacteristic
61C2×C22⋊D11—41no—
62C22×Dic11—21no—
63C2×D44—21no—
64C2×C4×D11—41no—
65C11×Q16—41no—
66C11×M16—41no—
67C2×C8×C11C22×C411yescharacteristic
68C2×C8×C11C2×D411yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—41no—
71C11×C4⋊C4—41no—
72C11×C22⋊C4—41no—
73C11×C22⋊C4—41no—
74C42×C11—41no—
75#4325—42no—
76(C2×D11)⋊C4—41no—
77(C2×D11)⋊C4—41no—
78(C2×D11)⋊C4—41no—
79(C2×D11)⋊C4—41no—
80C4⋊Dic11—21no—
81C4⋊Dic11—41no—
82C4⋊Dic11—41no—
83Dic11⋊C4—41no—
84C4×Dic11—21no—
85C4×Dic11—41no—
86C4×Dic11C22⋊C411yescharacteristic
87C4×Dic11C22⋊C411yescharacteristic
88#4318—41no—
89#4318—41no—
90#4318—41no—
91C2×C11⋊C8—41no—
92C2×C11⋊C8C22⋊C411yescharacteristic
93C2×C11⋊C8C22⋊C411yescharacteristic
94D88—41no—
95C11×C16—41no—
96C11⋊C16—41no—
97#3183—111no—
98#2165—111no—
99#1841—111no—
100#1342—111no—
101#1341—111no—
102#1340D1111yescharacteristic, complemented
103#1339—111no—
104C23×C11AGL(1,ℤ/8)11yescharacteristic
105C22×D11—41no—
106Q8×C11—41no—
107Q8×C11—41no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—41no—
111C2×C4×C11—41no—
112C2×C4×C11—81no—
113C2×C4×C11C2×C22⋊C411yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C22⋊D11—82no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—41no—
119C2×Dic11—81no—
120D44—41no—
121D44—41no—
122C4×D11—82no—
123C8×C11—21no—
124C8×C11—21no—
125C11⋊C8—21no—
126C11⋊C8—21no—
127C11⋊C8—81no—
128#529—221no—
129#499—111no—
130#495—111no—
131#488—221no—
132#470C2×D1111yescharacteristic
133#469—111no—
134#468—221no—
135#442—111no—
136#441—111no—
137#440—221no—
138C4×M16—111no—
139#364—221no—
140#349—111no—
141#349C2×D1111yescharacteristic
142#347—221no—
143#344—221no—
144#339—221no—
145#338—111no—
146H(3,ℤ/4)C2×D1111yescharacteristic
147C22×C11—21no—
148C22×C11—41no—
149C22×C11#41811yescharacteristic
150C2×D11—81no—
151C2×D11—81no—
152C2×D11—81no—
153C4×C11—21no—
154C4×C11—81no—
155C4×C11—81no—
156C4×C11—161no—
157C4×C11#41011yescharacteristic
158C4×C11#42111yescharacteristic
159Dic11—41no—
160Dic11—41no—
161Dic11—81no—
162C2×Q16C4×D1111yescharacteristic
163C2×SD16—221no—
164C2×D8—111no—
165C2×M16—111no—
166C2×M16—221no—
167C2×M16C22×D1111yescharacteristic
168#126—441no—
169#125—221no—
170#124—221no—
171#123—441no—
172C22⋊Q8—21no—
173#121—221no—
174C4×Q8—221no—
175C4×D4—221no—
176C4×D4—441no—
177#117—21no—
178#117—441no—
179C2×C42—111no—
180M32—21no—
181M32—221no—
182#107—221no—
183#106—111no—
184#106C4×D1111yescharacteristic
185#103—21no—
186#103—221no—
187#102—221no—
188#102—221no—
189#97—111no—
190#97—111no—
191C4×C8—111no—
192C4×C8—111no—
193C2×C11—21no—
194C2×C11—41no—
195C2×C11#151411yescharacteristic
196D11—161no—
197C2×Q8—21no—
198C2×D4—221no—
199C2×D4—441no—
200C22×C4—221no—
201C22×C4—441no—
202C22×C4D4×D1111yescharacteristic
203Q16—41no—
204SD16—442no—
205D8—441no—
206M16—41no—
207M16—441no—
208M16—441no—
209M16—441no—
210C2×C8—111no—
211C2×C8—111no—
212C2×C8—441no—
213C2×C8C2×C4×D1111yescharacteristic
214C2×C8D4×D1111yescharacteristic
215C4⋊C4—21no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—221no—
219C4⋊C4—441no—
220C4⋊C4—441no—
221C4⋊C4—441no—
222C22⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—441no—
225C22⋊C4—441no—
226C22⋊C4—441no—
227C22⋊C4—441no—
228C42—41no—
229C42—111no—
230C42—111no—
231C42—221no—
232C42—441no—
233C16—41no—
234C16—441no—
235C11#1183611yescharacteristic, complemented, Sylow
236C23—441no—
237C23#6696411yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—441no—
241D4—441no—
242D4—882no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—81no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—441no—
251C2×C4—882no—
252C2×C4—881no—
253C2×C4C22⋊C4×D1111yescharacteristic
254C2×C4#6696711yescharacteristic
255C8—21no—
256C8—21no—
257C8—221no—
258C8—221no—
259C8—881no—
260C22—21no—
261C22—41no—
262C22—881no—
263C22—881no—
264C22—881no—
265C22#1062238311yescharacteristic
266C4—21no—
267C4—81no—
268C4—81no—
269C4—161no—
270C4—441no—
271C4—441no—
272C4—881no—
273C4#1062235311yescharacteristic
274C4#1062243411yescharacteristic
275C2—21no—
276C2—41no—
277C2—1761no—
278C2#1306716111yescharacteristic
subgroupG/H
centerC2#13067161
commutatorC2×C8×C11C22×C4
FrattiniC2×M16C22×D11
FittingC11×#1340C2
socleC2×C11#1514
prime radical#10622748C22
cosocleC2×C11×M16C23
hypercenter#1340D11
hypocenterC11#11836
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1340

Complements

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

NH ≅ G/Ntype
2. #13070425C2semidirect
3. #13068763C2semidirect
4. #13066610C2semidirect
7. C11×#1340C2semidirect
10. #10622804C4semidirect
11. #10622797C4semidirect
15. #10622482C4semidirect
16. #10622471C4semidirect
102. #1340D11semidirect
235. C11#11836semidirect

Maximal subgroups

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

subgroupindex
#130793462
#130704252
#130687632
#130666102
#130666082
#130666002
C11×#13402
#1183611