Finite Group Databasebeta

← #14755008

Subgroups — #14755008

Order 2816.

1954 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic
2C2×#10622579C212yesmaximal, complemented
3C2×#10622820C211yesmaximal, characteristic, complemented
4#13068938C214yesmaximal, complemented
5#13068928C214yesmaximal, complemented
6#13068335C212yesmaximal, complemented
7C22×C11×#117C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C22×#4339C2211yescharacteristic
10C2×C11×#117—22no—
11C2×C11×#117—28no—
12C2×C11×#117C2214yes—
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C22⋊C4—21no—
15C22×C42×C11—21no—
16C2×#67006—21no—
17#10623322—24no—
18#10623322C418yescomplemented
19C2×#66983C2212yes—
20C2×#66982—21no—
21C2×C4×C22⋊D11—22no—
22C2×#66979C2211yescharacteristic
23C2×#66977C2212yes—
24C22×#4318C2212yes—
25#10622820—24no—
26C2×C22⋊(C11⋊C8)C2214yes—
27C2×#66874C2214yescomplemented
28#10622579—28no—
29C2×#66873C2214yescomplemented
30#10622167C2218yescomplemented
31C25×C11D411yescharacteristic
32C23×C4×C11—24no—
33C23×C4×C11—24no—
34C23×C4×C11—22no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D414yes—
37C23×C4×C11D412yes—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—22no—
42C22×C22⋊D11—21no—
43C2×#4339—22no—
44C2×#4339—24no—
45C2×#4339—24no—
46C2×#4339C2×C414yes—
47C22×D44C2311yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22C2311yescharacteristic
50C11×#117—216no—
51C11×#117—216no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—24no—
54C2×C11×C4⋊C4D418yescomplemented
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C22⋊C4—28no—
57C2×C11×C22⋊C4—24no—
58C2×C42×C11—28no—
59C2×C42×C11—24no—
60#67006—28no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—21no—
63#66983—24no—
64#66983C2×C418yescomplemented
65#66982—28no—
66C4×C22⋊D11—216no—
67C2×(C2×D11)⋊C4—22no—
68#66979—22no—
69#66979C2×C414yes—
70C2×C4⋊Dic11C2312yes—
71#66977—24no—
72#66977C2×C418yescomplemented
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11—21no—
75C2×#4318—24no—
76C2×#4318—24no—
77C2×#4318—24no—
78C22×C11⋊C8C2314yes—
79C22⋊(C11⋊C8)—28no—
80#66874—28no—
81#66873—28no—
82#20910—111nomaximal, Sylow
83C24×C11—22no—
84C24×C11—22no—
85C24×C11—44no—
86C24×C11C22⋊C414yes—
87C24×C11C2×D412yes—
88C24×C11C2×D411yescharacteristic
89C23×D11—21no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—216no—
93C22×C4×C11—24no—
94C22×C4×C11—216no—
95C22×C4×C11—24no—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—28no—
99C22×C4×C11—24no—
100C22×C4×C11—48no—
101C22×C4×C11C22⋊C418yes—
102C22×C4×C11C22⋊C414yes—
103C22×C4×C11C22×C414yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2×D414yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D414yes—
110C22×C4×C11#4114yes—
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—28no—
113C2×C22⋊D11—24no—
114C2×C22⋊D11—48no—
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C22×Dic11—22no—
118C22×Dic11—21no—
119#4339—216no—
120#4339—48no—
121C2×D44—21no—
122C2×D44—22no—
123C2×D44—22no—
124C2×D44C22×C412yes—
125C2×C4×D11—24no—
126C2×C4×D11—42no—
127C2×C4×D11—42no—
128C2×Dic22—22no—
129C2×Dic22—21no—
130C2×Dic22—22no—
131C2×Dic22C22×C412yes—
132C11×C4⋊C4—28no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4C2×D418yes—
135C11×C22⋊C4—216no—
136C42×C11—216no—
137C22⋊Dic11—28no—
138C22⋊Dic11—24no—
139(C2×D11)⋊C4—28no—
140C4⋊Dic11—22no—
141C4⋊Dic11C22×C414yes—
142Dic11⋊C4—28no—
143C4×Dic11—24no—
144#4318—48no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—24no—
147C2×C11⋊C8—24no—
148C2×#525—111no—
149C22×#117D1111yescharacteristic, complemented
150C2×#417—112no—
151C2×#407—111no—
152#1875—114no—
153#1873—114no—
154#1736—112no—
155C23×C11—24no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—24no—
160C23×C11—28no—
161C23×C11—48no—
162C23×C11—48no—
163C23×C11—48no—
164C23×C11C2×C22⋊C414yes—
165C23×C11C2×C22⋊C412yes—
166C23×C11#12012yes—
167C23×C11#12312yes—
168C23×C11C22×D411yescharacteristic
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—44no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—28no—
176C2×C4×C11—28no—
177C2×C4×C11—28no—
178C2×C4×C11—216no—
179C2×C4×C11—28no—
180C2×C4×C11—416no—
181C2×C4×C11—48no—
182C2×C4×C11C2×C22⋊C414yes—
183C2×C4×C11C2×C22⋊C412yes—
184C2×C4×C11C4×D418yes—
185C2×C4×C11#12012yes—
186C2×C4×C11#12118yes—
187C2×C4×C11#12312yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×D412yes—
191C2×C4×C11C2×#4112yes—
192C22⋊D11—416no—
193C22⋊D11—48no—
194C2×Dic11—24no—
195C2×Dic11—22no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—44no—
199D44—24no—
200D44—42no—
201C4×D11—48no—
202Dic22—24no—
203Dic22—42no—
204C11⋊C8—44no—
205C22×#41—111no—
206C24×C4C2×D1111yescharacteristic
207C22×M16—112no—
208#525—118no—
209#525—224no—
210C2×#123—221no—
211C2×C22⋊Q8—112no—
212C2×#121—112no—
213C2×#120—221no—
214C2×C4×D4—222no—
215C2×#117—22no—
216C2×#117—28no—
217C2×#117—111no—
218C2×#117C2×D1114yes—
219C22×C4⋊C4C2×D1112yes—
220C22×C22⋊C4—21no—
221C22×C42—21no—
222#417—228no—
223C2×#103—114no—
224C2×#102—114no—
225#407—224no—
226C2×C22⋊C8—114no—
227#340—118no—
228C22×C11—24no—
229C22×C11—24no—
230C22×C11—24no—
231C22×C11—24no—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—416no—
235C22×C11—44no—
236C22×C11—44no—
237C22×C11#38614yes—
238C22×C11C22×C22⋊C411yescharacteristic
239C22×C11C2×#12011yescharacteristic
240C22×C11C2×#12311yescharacteristic
241C22×C11#57514yes—
242C2×D11—44no—
243C2×D11—42no—
244C2×D11—82no—
245C2×D11—82no—
246C4×C11—24no—
247C4×C11—48no—
248C4×C11#38614yes—
249C4×C11C2×C4×D412yes—
250C4×C11C2×#12112yes—
251Dic11—44no—
252Dic11—42no—
253C25C22⋊D1111yescharacteristic
254C2×#41—114no—
255C2×#41—222no—
256C2×#41—224no—
257C2×#41—224no—
258C22×Q8—111no—
259C22×D4—111no—
260C22×D4—222no—
261C22×D4—221no—
262C23×C4—24no—
263C23×C4—24no—
264C23×C4—22no—
265C23×C4—221no—
266C23×C4C4×D1114yes—
267C23×C4D4414yes—
268C23×C4C22⋊D1112yes—
269C23×C4C22⋊D1111yescharacteristic
270C23×C4C22×D1112yes—
271C23×C4C22×D1111yescharacteristic
272C2×M16—224no—
273C2×M16—224no—
274C2×M16—224no—
275C22×C8—114no—
276#123—228no—
277C22⋊Q8—118no—
278C22⋊Q8—224no—
279#121—118no—
280#121—224no—
281#120—228no—
282C4×D4—2216no—
283#117—216no—
284#117—216no—
285#117—114no—
286#117—222no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—24no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4C22⋊D1118yescomplemented
292C2×C4⋊C4C22×D1114yes—
293C2×C22⋊C4—28no—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—221no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C42—28no—
299C2×C42—24no—
300C2×C42—221no—
301#103—228no—
302#102—228no—
303C22⋊C8—228no—
304C2×C11—24no—
305C2×C11—44no—
306C2×C11C2×#38611yescharacteristic
307C2×C11#289612yes—
308C2×C11#300512yes—
309C2×C11#309312yes—
310D11—82no—
311C24—22no—
312C24—22no—
313C24—44no—
314C24—221no—
315C24(C2×D11)⋊C414yes—
316C24C2×C22⋊D1112yes—
317C24C2×C22⋊D1111yescharacteristic
318#41—2216no—
319#41—448no—
320C2×Q8—112no—
321C2×Q8—221no—
322C2×Q8—222no—
323C2×Q8—222no—
324C2×D4—112no—
325C2×D4—228no—
326C2×D4—224no—
327C2×D4—221no—
328C2×D4—222no—
329C2×D4—222no—
330C2×D4—448no—
331C2×D4—442no—
332C2×D4—442no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—216no—
336C22×C4—24no—
337C22×C4—216no—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—28no—
342C22×C4—24no—
343C22×C4—48no—
344C22×C4—222no—
345C22×C4—221no—
346C22×C4—224no—
347C22×C4—442no—
348C22×C4—442no—
349C22×C4(C2×D11)⋊C418yes—
350C22×C4(C2×D11)⋊C414yes—
351C22×C4C2×C4×D1114yes—
352C22×C4C2×C4×D1112yes—
353C22×C4C2×D4414yes—
354C22×C4C2×D4412yes—
355C22×C4#433914yes—
356C22×C4C2×C22⋊D1112yes—
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1114yes—
359C22×C4C23×D1111yescharacteristic
360M16—448no—
361C2×C8—224no—
362C2×C8—224no—
363C2×C8—224no—
364C4⋊C4—28no—
365C4⋊C4—24no—
366C4⋊C4—114no—
367C4⋊C4—228no—
368C4⋊C4—222no—
369C4⋊C4C2×C22⋊D1118yes—
370C22⋊C4—216no—
371C22⋊C4—224no—
372C22⋊C4—228no—
373C22⋊C4—228no—
374C42—216no—
375C42—224no—
376C11#2091011yescharacteristic, complemented, Sylow
377C23—24no—
378C23—22no—
379C23—28no—
380C23—24no—
381C23—24no—
382C23—22no—
383C23—48no—
384C23—48no—
385C23—48no—
386C23—222no—
387C23—441no—
388C23—444no—
389C23—441no—
390C23C2×(C2×D11)⋊C414yes—
391C23C2×(C2×D11)⋊C412yes—
392C23#6698212yes—
393C23#6700612yes—
394C23C22×C22⋊D1111yescharacteristic
395Q8—224no—
396Q8—442no—
397D4—224no—
398D4—4416no—
399D4—448no—
400D4—442no—
401C2×C4—22no—
402C2×C4—28no—
403C2×C4—22no—
404C2×C4—28no—
405C2×C4—28no—
406C2×C4—216no—
407C2×C4—28no—
408C2×C4—416no—
409C2×C4—48no—
410C2×C4—224no—
411C2×C4—222no—
412C2×C4—441no—
413C2×C4—444no—
414C2×C4—441no—
415C2×C4—448no—
416C2×C4C2×(C2×D11)⋊C414yes—
417C2×C4C2×(C2×D11)⋊C412yes—
418C2×C4C4×C22⋊D1118yes—
419C2×C4#6698212yes—
420C2×C4#6698318yes—
421C2×C4#6700612yes—
422C2×C4C22×C4×D1111yescharacteristic
423C2×C4C22×D4411yescharacteristic
424C2×C4C2×#433912yes—
425C2×C4C22×C22⋊D1112yes—
426C8—444no—
427C22—24no—
428C22—24no—
429C22—24no—
430C22—24no—
431C22—24no—
432C22—24no—
433C22—416no—
434C22—44no—
435C22—44no—
436C22—444no—
437C22—442no—
438C22—882no—
439C22—882no—
440C22#1062282614yes—
441C22C22×(C2×D11)⋊C411yescharacteristic
442C22C2×#6698211yescharacteristic
443C22#1062335314yes—
444C22C2×#6700611yescharacteristic
445C4—24no—
446C4—48no—
447C4—444no—
448C4—442no—
449C4#1062282614yes—
450C4C2×C4×C22⋊D1112yes—
451C4C2×#6698312yes—
452C2—24no—
453C2—44no—
454C2—882no—
455C2C2×#1062282611yescharacteristic
456C2#1307713312yes—
457C2#1307785812yes—
458C2#1307854712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#117C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
cosocleC22×C4×C11C24
hypercenterC22×#117D11
hypocenterC11#20910
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
2. C2×#10622579C2semidirect
3. C2×#10622820C2semidirect
4. #13068938C2semidirect
5. #13068928C2semidirect
6. #13068335C2semidirect
7. C22×C11×#117C2semidirect
18. #10623322C4semidirect
27. C2×#66874C22semidirect
29. C2×#66873C22semidirect
30. #10622167C22semidirect
54. C2×C11×C4⋊C4D4semidirect
64. #66983C2×C4semidirect
72. #66977C2×C4semidirect
149. C22×#117D11semidirect
291. C2×C4⋊C4C22⋊D11semidirect
376. C11#20910semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
C2×#106225792
C2×#106228202
#130689382
#130689282
#130683352
C22×C11×#1172
#2091011