Finite Group Databasebeta

← #14670326

Subgroups — #14670326

Order 2816.

420 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#108C211yesmaximal, characteristic
2C2×#10622132C211yesmaximal, characteristic, complemented
3C2×#10622151C211yesmaximal, characteristic, complemented
4#13070226C211yesmaximal, characteristic
5#13068638C211yesmaximal, characteristic
6#13066714C211yesmaximal, characteristic, complemented
7C11×#1383C211yesmaximal, characteristic, complemented
8C2×M16×D11—21no—
9C22×C8×D11C2211yescharacteristic
10C2×C11×M32C2211yescharacteristic
11C2×C11×#108C2211yescharacteristic
12C2×C11×#106C2211yescharacteristic
13C2×#66886—21no—
14C2×#66883C2211yescharacteristic
15C2×#66881C2211yescharacteristic
16C2×#66876C2211yescharacteristic
17#10622600—21no—
18D11×#108—22no—
19D11×#108—22no—
20#10622167—21no—
21#10622151—22no—
22(C2×D11)⋊C16C412yescomplemented
23(C2×D11)⋊C16C412yescomplemented
24#10622132—22no—
25C22×C4×D11D411yescharacteristic
26C2×C11×M16—21no—
27C22×C8×C11C2311yescharacteristic
28C2×C11×C4⋊C4—21no—
29C2×(C2×D11)⋊C4—41no—
30C2×C4⋊Dic11—21no—
31C2×#4318—21no—
32C22×C11⋊C8D411yescharacteristic
33M16×D11—24no—
34M16×D11—42no—
35C2×#4313—41no—
36C2×C8×D11—21no—
37C2×C8×D11—21no—
38C2×C8×D11—21no—
39C2×C8×D11—21no—
40C2×C8×D11—41no—
41C2×C8×D11C2×C411yescharacteristic
42C2×C8×D11C2×C411yescharacteristic
43C2×C8×D11Q811yescharacteristic
44C2×C8×D11Q811yescharacteristic
45C11×M32—21no—
46C11×M32—21no—
47C2×C11×C16C2×C412yes—
48C11×#108—21no—
49C11×#108D412yes—
50C11×#106—21no—
51C11×#106—21no—
52C11⋊#95—41no—
53#66886—24no—
54#66883—21no—
55#66883D412yes—
56#66881—21no—
57#66881—21no—
58#66876—21no—
59#66876—21no—
60C2×C11⋊C16C2×C412yes—
61#12928—111nomaximal, Sylow
62C23×D11SD1611yescharacteristic
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C22×Dic11—41no—
66C22×Dic11SD1611yescharacteristic
67C2×C4×D11—21no—
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11C4⋊C411yescharacteristic
72C2×C4×D11C4⋊C411yescharacteristic
73C2×C4×D11SD1611yescharacteristic
74C2×C4×D11SD1611yescharacteristic
75C11×M16—22no—
76C11×M16—41no—
77C2×C8×C11—41no—
78C2×C8×C11C22×C411yescharacteristic
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×Q811yescharacteristic
82C2×C8×C11#4111yescharacteristic
83C2×C8×C11#4111yescharacteristic
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86(C2×D11)⋊C4—82no—
87C4⋊Dic11—41no—
88C4⋊Dic11—41no—
89#4318—22no—
90#4318—41no—
91C2×C11⋊C8—21no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—41no—
94C2×C11⋊C8C4⋊C411yescharacteristic
95C2×C11⋊C8C4⋊C411yescharacteristic
96#4313—44no—
97C8×D11—21no—
98C8×D11—21no—
99C8×D11—21no—
100C8×D11—21no—
101C8×D11—21no—
102C8×D11—21no—
103C8×D11—21no—
104C8×D11—21no—
105C8×D11—44no—
106C11×C16—22no—
107C11⋊C16—22no—
108C22×#108—111no—
109C2×#365—111no—
110C2×#365—111no—
111#2112—111no—
112#1807—111no—
113#1383—111no—
114#1383D1111yescharacteristic, complemented
115C23×C11C2×SD1611yescharacteristic
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—22no—
119C22×D11—41no—
120C22×D11#10611yescharacteristic
121C22×D11#10611yescharacteristic
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C2×C4⋊C411yescharacteristic
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12311yescharacteristic
128C2×C4×C11C2×SD1611yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C11#13711yescharacteristic
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—81no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11#10611yescharacteristic
137C2×Dic11#10611yescharacteristic
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—21no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—21no—
146C8×C11—42no—
147C8×C11C4×D411yescharacteristic
148C8×C11C4×D411yescharacteristic
149C8×C11C22⋊Q811yescharacteristic
150C8×C11C22⋊Q811yescharacteristic
151C11⋊C8—21no—
152C11⋊C8—21no—
153C11⋊C8—42no—
154C22×M16—221no—
155C23×C8—111no—
156C2×M32—111no—
157C2×M32C2×D1111yescharacteristic
158C2×#108—111no—
159C2×#108—222no—
160C2×#108—221no—
161C2×#108—222no—
162C2×#108C2×D1111yescharacteristic
163C2×#106—111no—
164C2×#106C2×D1111yescharacteristic
165#380—221no—
166#365—222no—
167#365—222no—
168C22⋊C16—112no—
169C22⋊C16—112no—
170#340—221no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11C2×#10611yescharacteristic
174C22×C11#44811yescharacteristic
175C22×C11#48111yescharacteristic
176C2×D11—21no—
177C2×D11—21no—
178C2×D11—21no—
179C2×D11—21no—
180C2×D11—21no—
181C2×D11—42no—
182C2×D11—42no—
183C2×D11#36512yescomplemented
184C4×C11—161no—
185C4×C11#38511yescharacteristic
186C4×C11#42811yescharacteristic
187C4×C11#45011yescharacteristic
188C4×C11#48311yescharacteristic
189Dic11—21no—
190Dic11—21no—
191Dic11—161no—
192C23×C4—111no—
193C2×M16—21no—
194C2×M16—224no—
195C2×M16—221no—
196C2×M16—441no—
197C2×M16—442no—
198C22×C8—111no—
199C22×C8—111no—
200C22×C8—111no—
201C22×C8—111no—
202C22×C8—111no—
203C22×C8—221no—
204C22×C8—221no—
205C22×C8—221no—
206C22×C8—221no—
207C22×C8—441no—
208C22×C8C22×D1111yescharacteristic
209C2×C4⋊C4—21no—
210C2×C4⋊C4—221no—
211C2×C22⋊C4—441no—
212M32—21no—
213M32—21no—
214M32—221no—
215M32—221no—
216C2×C16—112no—
217C2×C16C4×D1112yes—
218#108—21no—
219#108—112no—
220#108—224no—
221#108—221no—
222#108D4412yes—
223#106—21no—
224#106—21no—
225#106—221no—
226#106—221no—
227#95—441no—
228C2×C11—21no—
229C2×C11—21no—
230C2×C11#185311yescharacteristic
231C2×C11C2×#36511yescharacteristic
232C2×C11#215511yescharacteristic
233D11—22no—
234D11—41no—
235C24—111no—
236C22×C4—41no—
237C22×C4—111no—
238C22×C4—111no—
239C22×C4—111no—
240C22×C4—111no—
241C22×C4—111no—
242C22×C4—221no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—441no—
247C22×C4D4×D1111yescharacteristic
248M16—22no—
249M16—41no—
250M16—222no—
251M16—444no—
252M16—441no—
253C2×C8—41no—
254C2×C8—111no—
255C2×C8—111no—
256C2×C8—221no—
257C2×C8—221no—
258C2×C8—221no—
259C2×C8—221no—
260C2×C8—221no—
261C2×C8—221no—
262C2×C8—221no—
263C2×C8—221no—
264C2×C8—221no—
265C2×C8—221no—
266C2×C8—444no—
267C2×C8—441no—
268C2×C8C2×C4×D1111yescharacteristic
269C2×C8C2×D4411yescharacteristic
270C2×C8#433911yescharacteristic
271C2×C8D4×D1111yescharacteristic
272C2×C8#434111yescharacteristic
273C2×C8Q8×D1111yescharacteristic
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—441no—
277C4⋊C4—441no—
278C22⋊C4—882no—
279C16—22no—
280C16—222no—
281C11#1292811yescharacteristic, complemented, Sylow
282C23—111no—
283C23—111no—
284C23—222no—
285C23—221no—
286C23—221no—
287C23—441no—
288C23SD16×D1111yescharacteristic
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—881no—
305C2×C4—881no—
306C2×C4—881no—
307C2×C4#6693511yescharacteristic
308C2×C4#6693611yescharacteristic
309C2×C4C4⋊C4×D1111yescharacteristic
310C2×C4#6696411yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C2×C4#6697111yescharacteristic
313C8—42no—
314C8—221no—
315C8—221no—
316C8—442no—
317C8C4×D4411yescharacteristic
318C8(C22⋊D11)⋊C411yescharacteristic
319C8#6694911yescharacteristic
320C8#6695011yescharacteristic
321C22—21no—
322C22—21no—
323C22—112no—
324C22—221no—
325C22—221no—
326C22—221no—
327C22—221no—
328C22—221no—
329C22—442no—
330C22—442no—
331C22#1062239011yescharacteristic
332C22#1062241911yescharacteristic
333C22D11×#10611yescharacteristic
334C4—161no—
335C4—221no—
336C4—221no—
337C4—1761no—
338C4#1062228111yescharacteristic
339C4#1062238911yescharacteristic
340C4#1062241811yescharacteristic
341C4#1062249411yescharacteristic
342C2—21no—
343C2—21no—
344C2—222no—
345C2—441no—
346C2#1306881011yescharacteristic
347C2D11×#36511yescharacteristic
348C2#1307038711yescharacteristic
subgroupG/H
centerC22D11×#106
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1383C2
socleC22×C11C2×#106
prime radicalC23×D11SD16
cosocleC22×C8×C11C23
hypercenter#1383D11
hypocenterC11#12928
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1383

Complements

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

NH ≅ G/Ntype
2. C2×#10622132C2semidirect
3. C2×#10622151C2semidirect
6. #13066714C2semidirect
7. C11×#1383C2semidirect
22. (C2×D11)⋊C16C4semidirect
23. (C2×D11)⋊C16C4semidirect
114. #1383D11semidirect
183. C2×D11#365semidirect
281. C11#12928semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1082
C2×#106221322
C2×#106221512
#130702262
#130686382
#130667142
C11×#13832
#1292811