Finite Group Databasebeta

← #14755015

Subgroups — #14755015

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C2×#10622617C212yesmaximal, complemented
3C2×#10622820C211yesmaximal, characteristic
4#13068928C214yesmaximal, complemented
5#13068923C214yesmaximal, complemented
6#13068337C212yesmaximal, complemented
7C22×C11×#117C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C2×C11×#117—21no—
11C2×C11×#117—21no—
12C2×C11×#117—28no—
13C2×C11×#117C2212yes—
14C2×C11×#117C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4—21no—
17C22×C42×C11—21no—
18C22×C22⋊Dic11—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66977—24no—
21C2×#66977—21no—
22C2×#66977—21no—
23C2×#66977C418yescomplemented
24C2×#66977C2212yes—
25C2×#66977C2212yes—
26C22×Dic11⋊C4—21no—
27C22×#4318C2212yes—
28#10622820—24no—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yes—
31#10622617—28no—
32C2×#66874C2218yescomplemented
33#10622167C2218yescomplemented
34C25×C11D411yescharacteristic
35C23×C4×C11—24no—
36C23×C4×C11—24no—
37C23×C4×C11—22no—
38C23×C4×C11C2×C414yes—
39C23×C4×C11D414yes—
40C23×C4×C11D411yescharacteristic
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11—21no—
47C23×Dic11—21no—
48C22×Dic22—24no—
49C22×Dic22—24no—
50C22×Dic22—22no—
51C22×Dic22—21no—
52C22×Dic22C2×C414yescomplemented
53C22×Dic22C2312yes—
54C11×#117—28no—
55C11×#117—28no—
56C11×#117—24no—
57C11×#117—28no—
58C11×#117D418yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—28no—
61C2×C11×C4⋊C4C2314yes—
62C2×C11×C22⋊C4—28no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—22no—
65C2×C42×C11—28no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C22⋊Dic11—28no—
69C2×C22⋊Dic11—22no—
70C2×C22⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2×C414yescomplemented
74C2×C4⋊Dic11C2312yes—
75#66977—28no—
76#66977—28no—
77#66977—24no—
78#66977—24no—
79#66977C2×C418yes—
80#66977C2×C418yescomplemented
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×#4318—24no—
85C2×#4318—24no—
86C2×#4318—24no—
87C22×C11⋊C8C2314yes—
88C22⋊(C11⋊C8)—24no—
89C22⋊(C11⋊C8)—24no—
90#66874—216no—
91#20911—111nomaximal, Sylow
92C24×C11—22no—
93C24×C11—22no—
94C24×C11—24no—
95C24×C11—42no—
96C24×C11C22⋊C414yes—
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D411yescharacteristic
99C24×C11C2×D411yescharacteristic
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—216no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—216no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—28no—
113C22×C4×C11—24no—
114C22×C4×C11—44no—
115C22×C4×C11—44no—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22⋊C414yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D414yes—
129C22×C4×C11#4114yes—
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—44no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C2×Dic22—24no—
139C2×Dic22—216no—
140C2×Dic22—24no—
141C2×Dic22—22no—
142C2×Dic22—24no—
143C2×Dic22—42no—
144C2×Dic22—48no—
145C2×Dic22—42no—
146C2×Dic22C22×C414yes—
147C11×C4⋊C4—28no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4C2×D418yes—
150C11×C22⋊C4—28no—
151C11×C22⋊C4—28no—
152C42×C11—28no—
153C42×C11—28no—
154C22⋊Dic11—28no—
155C22⋊Dic11—28no—
156C4⋊Dic11—24no—
157C4⋊Dic11—22no—
158C4⋊Dic11C22×C414yes—
159Dic11⋊C4—28no—
160Dic11⋊C4—28no—
161#4318—48no—
162C2×C11⋊C8—24no—
163C2×C11⋊C8—24no—
164C2×C11⋊C8—24no—
165C22×C22⋊Q8—111no—
166C22×#117D1111yescharacteristic
167C2×#419—112no—
168C2×#407—111no—
169#1873—114no—
170#1872—114no—
171#1736—112no—
172C23×C11—21no—
173C23×C11—21no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—21no—
178C23×C11—21no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—28no—
182C23×C11—28no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11C2×C22⋊C412yes—
187C23×C11C2×C22⋊C412yes—
188C23×C11C2×C22⋊C412yes—
189C23×C11#12012yes—
190C23×C11#12312yes—
191C23×C11#13714yes—
192C23×C11C22×D411yescharacteristic
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—28no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—24no—
202C2×C4×C11—28no—
203C2×C4×C11—28no—
204C2×C4×C11—28no—
205C2×C4×C11—416no—
206C2×C4×C11—44no—
207C2×C4×C11—44no—
208C2×C4×C11C2×C22⋊C412yes—
209C2×C4×C11C2×C22⋊C412yes—
210C2×C4×C11C2×C22⋊C412yes—
211C2×C4×C11C4×D418yes—
212C2×C4×C11#12012yes—
213C2×C4×C11#12118yes—
214C2×C4×C11#12312yes—
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D412yes—
218C2×C4×C11C2×#4112yes—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—48no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—44no—
225C2×Dic11—48no—
226Dic22—28no—
227Dic22—44no—
228Dic22—48no—
229C11⋊C8—44no—
230C23×Q8—111no—
231C24×C4C2×D1111yescharacteristic
232C22×M16—112no—
233C2×C22⋊Q8—112no—
234C2×C22⋊Q8—112no—
235C2×C22⋊Q8—118no—
236C2×C22⋊Q8—224no—
237C2×C22⋊Q8—221no—
238C2×C22⋊Q8—221no—
239C2×#117—21no—
240C2×#117—21no—
241C2×#117—28no—
242C2×#117C2×D1112yes—
243C2×#117C2×D1112yes—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—221no—
246C22×C4⋊C4C2×D1112yes—
247C22×C22⋊C4—21no—
248C22×C22⋊C4—221no—
249C22×C42—21no—
250#419—228no—
251C2×#103—118no—
252#407—224no—
253C2×C22⋊C8—112no—
254C2×C22⋊C8—112no—
255#340—118no—
256C22×C11—24no—
257C22×C11—24no—
258C22×C11—22no—
259C22×C11—22no—
260C22×C11—22no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—22no—
264C22×C11—22no—
265C22×C11—22no—
266C22×C11—22no—
267C22×C11—416no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11#38614yes—
271C22×C11#41914yescomplemented
272C22×C11C22×C22⋊C411yescharacteristic
273C22×C11C2×#12011yescharacteristic
274C22×C11C2×#12311yescharacteristic
275C22×C11C2×#13712yes—
276C22×C11#57512yes—
277C4×C11—22no—
278C4×C11—22no—
279C4×C11—48no—
280C4×C11#38614yes—
281C4×C11C2×C4×D412yes—
282C4×C11C2×#12112yes—
283Dic11—44no—
284Dic11—44no—
285C25C22⋊D1111yescharacteristic
286C22×Q8—114no—
287C22×Q8—112no—
288C22×Q8—222no—
289C22×Q8—221no—
290C22×Q8—224no—
291C22×Q8—224no—
292C23×C4—24no—
293C23×C4—24no—
294C23×C4—22no—
295C23×C4—221no—
296C23×C4—221no—
297C23×C4C4×D1114yes—
298C23×C4D4414yes—
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22⋊D1111yescharacteristic
301C23×C4C22⋊D1111yescharacteristic
302C23×C4C22×D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C2×M16—224no—
306C2×M16—224no—
307C2×M16—224no—
308C22×C8—114no—
309C22⋊Q8—118no—
310C22⋊Q8—118no—
311C22⋊Q8—228no—
312C22⋊Q8—228no—
313C22⋊Q8—224no—
314C22⋊Q8—224no—
315#117—28no—
316#117—28no—
317#117—24no—
318#117—28no—
319#117C22⋊D1118yes—
320C2×C4⋊C4—22no—
321C2×C4⋊C4—28no—
322C2×C4⋊C4—114no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—228no—
325C2×C4⋊C4—222no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—222no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4C22×D1114yes—
330C2×C22⋊C4—28no—
331C2×C22⋊C4—22no—
332C2×C22⋊C4—22no—
333C2×C22⋊C4—228no—
334C2×C22⋊C4—222no—
335C2×C22⋊C4—222no—
336C2×C42—28no—
337C2×C42—22no—
338C2×C42—22no—
339#103—2216no—
340C22⋊C8—224no—
341C22⋊C8—224no—
342C2×C11—24no—
343C2×C11—24no—
344C2×C11—42no—
345C2×C11C2×#38611yescharacteristic
346C2×C11C2×#41911yescharacteristic
347C2×C11#289611yescharacteristic
348C2×C11#300712yes—
349C2×C11#309512yes—
350C24—22no—
351C24—24no—
352C24—22no—
353C24—42no—
354C24(C2×D11)⋊C414yes—
355C24C2×C22⋊D1111yescharacteristic
356C24C2×C22⋊D1111yescharacteristic
357C24C2×C22⋊D1111yescharacteristic
358C2×Q8—114no—
359C2×Q8—224no—
360C2×Q8—222no—
361C2×Q8—2216no—
362C2×Q8—224no—
363C2×Q8—224no—
364C2×Q8—442no—
365C2×Q8—448no—
366C2×Q8—442no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—216no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—216no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—28no—
380C22×C4—24no—
381C22×C4—44no—
382C22×C4—44no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—444no—
388C22×C4—442no—
389C22×C4—442no—
390C22×C4(C2×D11)⋊C414yes—
391C22×C4(C2×D11)⋊C414yes—
392C22×C4(C2×D11)⋊C414yes—
393C22×C4C2×C4×D1112yes—
394C22×C4C2×C4×D1112yes—
395C22×C4C2×C4×D1112yes—
396C22×C4C2×D4412yes—
397C22×C4C2×D4412yes—
398C22×C4C2×D4412yes—
399C22×C4#433914yes—
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C22×C4C2×C22⋊D1111yescharacteristic
403C22×C4C2×C22⋊D1114yes—
404C22×C4C23×D1111yescharacteristic
405M16—448no—
406C2×C8—224no—
407C2×C8—224no—
408C2×C8—224no—
409C4⋊C4—28no—
410C4⋊C4—24no—
411C4⋊C4—114no—
412C4⋊C4—224no—
413C4⋊C4—228no—
414C4⋊C4—228no—
415C4⋊C4—222no—
416C4⋊C4C2×C22⋊D1118yes—
417C22⋊C4—28no—
418C22⋊C4—28no—
419C22⋊C4—228no—
420C22⋊C4—228no—
421C42—28no—
422C42—28no—
423C11#2091111yescharacteristic, complemented, Sylow
424C23—21no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—21no—
429C23—21no—
430C23—28no—
431C23—22no—
432C23—22no—
433C23—21no—
434C23—28no—
435C23—44no—
436C23—48no—
437C23—48no—
438C23C2×(C2×D11)⋊C412yes—
439C23C2×(C2×D11)⋊C412yes—
440C23C2×(C2×D11)⋊C412yes—
441C23#6698212yes—
442C23#6700414yes—
443C23#6700612yes—
444C23C22×C22⋊D1111yescharacteristic
445Q8—228no—
446Q8—444no—
447Q8—448no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—28no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—28no—
458C2×C4—28no—
459C2×C4—28no—
460C2×C4—416no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—224no—
464C2×C4—224no—
465C2×C4—448no—
466C2×C4—442no—
467C2×C4—448no—
468C2×C4—444no—
469C2×C4—442no—
470C2×C4C2×(C2×D11)⋊C412yes—
471C2×C4C2×(C2×D11)⋊C412yes—
472C2×C4C2×(C2×D11)⋊C412yes—
473C2×C4C4×C22⋊D1118yes—
474C2×C4#6698212yes—
475C2×C4#6698318yes—
476C2×C4#6700612yes—
477C2×C4C22×C4×D1111yescharacteristic
478C2×C4C22×D4411yescharacteristic
479C2×C4C2×#433912yes—
480C2×C4C22×C22⋊D1112yes—
481C8—444no—
482C22—24no—
483C22—24no—
484C22—24no—
485C22—24no—
486C22—22no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—416no—
494C22—42no—
495C22—42no—
496C22#1062261714yescomplemented
497C22#1062282614yes—
498C22C22×(C2×D11)⋊C411yescharacteristic
499C22C2×#6698211yescharacteristic
500C22#1062335312yes—
501C22C2×#6700412yes—
502C22C2×#6700611yescharacteristic
503C4—22no—
504C4—22no—
505C4—48no—
506C4—444no—
507C4—444no—
508C4#1062282614yes—
509C4C2×C4×C22⋊D1112yes—
510C4C2×#6698312yes—
511C2—24no—
512C2—24no—
513C2—42no—
514C2C2×#1062282611yescharacteristic
515C2C2×#1062261711yescharacteristic
516C2#1307713311yescharacteristic
517C2#1307787612yes—
518C2#1307856412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#117C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC22×#117D11
hypocenterC11#20911
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×#10622617C2semidirect
4. #13068928C2semidirect
5. #13068923C2semidirect
6. #13068337C2semidirect
23. C2×#66977C4semidirect
32. C2×#66874C22semidirect
33. #10622167C22semidirect
52. C22×Dic22C2×C4semidirect
73. C2×C4⋊Dic11C2×C4semidirect
80. #66977C2×C4semidirect
271. C22×C11#419semidirect
423. C11#20911semidirect
496. C22#10622617semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106226172
C2×#106228202
#130689282
#130689232
#130683372
C22×C11×#1172
#2091111