Finite Group Databasebeta

← #14755183

Subgroups — #14755183

Order 2816.

1766 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623035C211yesmaximal, characteristic
3C2×#10622726C211yesmaximal, characteristic
4#13071202C211yesmaximal, characteristic, complemented
5#13068954C214yesmaximal, complemented
6#13068947C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068312C211yesmaximal, characteristic, complemented
9C22×C11×#103C211yesmaximal, characteristic, complemented
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×#4326C2212yes—
15C2×#66995—24no—
16C2×#66995—24no—
17C2×#66995C418yescomplemented
18C22×#4325C2212yes—
19C2×C4×C22⋊D11—22no—
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10623035—24no—
24#10623035—24no—
25C2×#66946C2212yes—
26C2×#66945—21no—
27C2×C4⋊C4×D11—21no—
28C2×#66940C2212yes—
29C2×C11×#103—24no—
30C2×C11×#103C2214yes—
31#10622843—21no—
32#10622843—21no—
33#10622843C2214yes—
34#10622824—22no—
35#10622726—24no—
36C2×#66885C2212yes—
37C2×#66880C2212yes—
38#10622188C2214yes—
39#10622167C2214yes—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—22no—
43C22×Q8×C11—22no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11C2×C414yescomplemented
47C22×Q8×C11C2312yes—
48C23×C4×C11—21no—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339C2×C414yes—
56C2×#4339D414yes—
57C2×#4339D414yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—22no—
61C22×Dic22C2311yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11—22no—
65C22×C8×C11C2312yes—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4D414yes—
69C2×C11×C4⋊C4C2312yes—
70C2×C22⋊Dic11—21no—
71C2×C22⋊Dic11D412yes—
72C2×#4326—24no—
73C2×#4326—24no—
74C2×#4326C2×C418yescomplemented
75#66995—232no—
76C2×#4325—24no—
77C2×#4325—24no—
78C2×#4325C2×C418yescomplemented
79C4×C22⋊D11—216no—
80C2×(C2×D11)⋊C4—22no—
81#66979—22no—
82#66979—22no—
83#66979—22no—
84#66979—22no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11D411yescharacteristic
87C2×C4⋊Dic11C2312yes—
88C2×Dic11⋊C4—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2312yes—
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318C2×C414yescomplemented
95C22×C11⋊C8C2312yes—
96#66946—24no—
97#66946—24no—
98#66945—28no—
99C4⋊C4×D11—28no—
100#66940—24no—
101#66940—24no—
102C11×#103—28no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105#66885—24no—
106#66880—24no—
107#20931—111nomaximal, Sylow
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—28no—
113C2×Q8×C11—28no—
114C2×Q8×C11—22no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—44no—
121C2×Q8×C11—44no—
122C2×Q8×C11C22×C414yes—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—42no—
128C22×C4×C11—42no—
129C22×C4×C11—82no—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D412yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—24no—
139C2×C22⋊D11—24no—
140C2×C22⋊D11—24no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11C2×D412yes—
144C22×Dic11C2×D412yes—
145#4339—28no—
146#4339—28no—
147#4339—28no—
148#4339C22⋊C4116yes—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C22×C412yes—
153C2×D44C2×D412yes—
154C2×D44C2×D412yes—
155C2×C4×D11—28no—
156C2×C4×D11—24no—
157C2×C4×D11—24no—
158C2×C4×D11—24no—
159C2×C4×D11—84no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22C22×C412yes—
164C2×Dic22C2×D412yes—
165C2×Dic22C2×D412yes—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—44no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D414yes—
173C22⋊Dic11—24no—
174C22⋊Dic11—42no—
175#4326—216no—
176#4325—216no—
177(C2×D11)⋊C4—28no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182Dic11⋊C4—28no—
183C4×Dic11—28no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—42no—
187#4318—28no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8C22×C414yes—
191C22×#137—111no—
192C2×#520—111no—
193C2×#416—111no—
194C22×#103D1111yescharacteristic, complemented
195#2310—111no—
196#1878—114no—
197#1877—114no—
198#1736—111no—
199#1729—111no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11C4×D412yes—
203C23×C11#12012yes—
204C23×C11#12112yes—
205C23×C11C22×D411yescharacteristic
206C22×D11—22no—
207C22×D11—22no—
208C22×D11—22no—
209C22×D11—42no—
210C22×D11—42no—
211Q8×C11—24no—
212Q8×C11—24no—
213Q8×C11—42no—
214Q8×C11—42no—
215Q8×C11—48no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—48no—
222C2×C4×C11—84no—
223C2×C4×C11C2×C22⋊C414yes—
224C2×C4×C11C4×D412yes—
225C2×C4×C11C4×D414yes—
226C2×C4×C11#12012yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12114yes—
229C2×C4×C11#12314yes—
230C2×C4×C11C23×C411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C22⋊D11—216no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247D44—22no—
248D44—22no—
249D44—22no—
250D44C2×C22⋊C414yes—
251C4×D11—216no—
252C4×D11—88no—
253Dic22—22no—
254Dic22—22no—
255Dic22—22no—
256Dic22C2×C22⋊C414yes—
257C8×C11—42no—
258C11⋊C8—24no—
259C22×#41—111no—
260C23×Q8C2×D1111yescharacteristic
261C2×#137—118no—
262C2×#137—224no—
263C2×#137—224no—
264C22×Q16—112no—
265C22×SD16—112no—
266C22×M16—111no—
267C23×C8C2×D1111yescharacteristic
268#520—224no—
269#520—224no—
270C2×C4×Q8—112no—
271C2×C4×D4—112no—
272C2×C4×D4—222no—
273C2×#117—111no—
274C2×#117—111no—
275C2×#117—221no—
276C22×C4⋊C4—221no—
277C22×C4⋊C4C2×D1111yescharacteristic
278#416—224no—
279C2×#103—24no—
280C2×#103—112no—
281C2×#103C2×D1114yes—
282C2×#102—112no—
283#391—114no—
284#391—221no—
285#391—221no—
286#381—222no—
287#340—114no—
288#336—114no—
289C22×C11—24no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—24no—
293C22×C11#38614yes—
294C22×C11C2×C4×D411yescharacteristic
295C22×C11C2×#12011yescharacteristic
296C22×C11C2×#12111yescharacteristic
297C22×C11#57712yes—
298C22×C11#57812yes—
299C2×D11—24no—
300C2×D11—44no—
301C2×D11—42no—
302C2×D11—42no—
303C2×D11—44no—
304C4×C11—44no—
305C4×C11—44no—
306C4×C11#38614yes—
307C4×C11C22×C22⋊C411yescharacteristic
308C4×C11C2×C4×D411yescharacteristic
309C4×C11C2×#12111yescharacteristic
310C4×C11C2×#12311yescharacteristic
311Dic11—24no—
312Dic11—42no—
313Dic11—42no—
314Dic11—82no—
315C2×#41—114no—
316C2×#41—114no—
317C2×#41—114no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—222no—
321C22×Q8—21no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8—22no—
327C22×Q8—111no—
328C22×Q8C4×D1114yescomplemented
329C22×Q8C22×D1112yes—
330C22×D4—111no—
331C22×D4—221no—
332C23×C4—21no—
333C23×C4—21no—
334C23×C4—222no—
335C23×C4—221no—
336C23×C4C22×D1111yescharacteristic
337#137—2232no—
338C2×Q16—118no—
339C2×Q16—224no—
340C2×Q16—224no—
341C2×SD16—118no—
342C2×SD16—224no—
343C2×SD16—224no—
344C2×M16—114no—
345C2×M16—222no—
346C2×M16—222no—
347C22×C8—22no—
348C22×C8—22no—
349C22×C8—22no—
350C22×C8—112no—
351C22×C8C22×D1112yes—
352C4×Q8—224no—
353C4×Q8—224no—
354C4×D4—224no—
355C4×D4—2216no—
356C4×D4—224no—
357#117—228no—
358#117—222no—
359#117—222no—
360#117—222no—
361#117—222no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4—228no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4C22⋊D1114yes—
370C2×C4⋊C4C22×D1112yes—
371C2×C22⋊C4—112no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—221no—
374C2×C42—112no—
375C2×C42—222no—
376C2×C42—221no—
377#103—28no—
378#103—224no—
379#102—224no—
380#95—224no—
381#95—224no—
382C2×C11—24no—
383C2×C11C2×#38611yescharacteristic
384C2×C11#294712yes—
385C2×C11#300911yescharacteristic
386C2×C11#301111yescharacteristic
387C2×C11#304612yes—
388D11—44no—
389C24—221no—
390C24D4×D1111yescharacteristic
391#41—1116no—
392#41—228no—
393#41—228no—
394#41—228no—
395C2×Q8—24no—
396C2×Q8—22no—
397C2×Q8—28no—
398C2×Q8—28no—
399C2×Q8—22no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—44no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8—44no—
407C2×Q8—112no—
408C2×Q8—112no—
409C2×Q8—112no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×Q8—221no—
413C2×Q8C2×C4×D1114yes—
414C2×D4—112no—
415C2×D4—112no—
416C2×D4—112no—
417C2×D4—224no—
418C2×D4—224no—
419C2×D4—224no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—24no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—82no—
430C22×C4—112no—
431C22×C4—112no—
432C22×C4—228no—
433C22×C4—221no—
434C22×C4—224no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—884no—
439C22×C4C2×C4×D1112yes—
440C22×C4#433912yes—
441C22×C4D4×D1112yes—
442C22×C4D4×D1112yes—
443C22×C4D4×D1111yescharacteristic
444C22×C4#434112yes—
445C22×C4C2×C22⋊D1112yes—
446C22×C4C23×D1111yescharacteristic
447Q16—2216no—
448SD16—2216no—
449M16—228no—
450C2×C8—22no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—44no—
454C2×C8—114no—
455C2×C8—222no—
456C2×C8—222no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—228no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4C2×C22⋊D1114yes—
465C22⋊C4—228no—
466C22⋊C4—224no—
467C22⋊C4—442no—
468C42—228no—
469C42—222no—
470C42—222no—
471C42—442no—
472C11#2093111yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—442no—
479C23—442no—
480C23(C22⋊D11)⋊C412yes—
481C23#6693712yes—
482C23#6699012yes—
483C23C2×D4×D1111yescharacteristic
484Q8—24no—
485Q8—24no—
486Q8—42no—
487Q8—42no—
488Q8—48no—
489Q8—114no—
490Q8—222no—
491Q8—222no—
492Q8—222no—
493D4—114no—
494D4—2216no—
495D4—222no—
496D4—222no—
497D4—222no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—48no—
504C2×C4—84no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—222no—
508C2×C4—2216no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—888no—
517C2×C4C22⋊C4×D1114yes—
518C2×C4(C22⋊D11)⋊C412yes—
519C2×C4#6693614yes—
520C2×C4#6693712yes—
521C2×C4C4×C22⋊D1114yes—
522C2×C4#6699012yes—
523C2×C4#6699114yes—
524C2×C4C22×C4×D1111yescharacteristic
525C2×C4C2×#433911yescharacteristic
526C2×C4C2×D4×D1111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434111yescharacteristic
529C2×C4C22×C22⋊D1111yescharacteristic
530C8—42no—
531C8—224no—
532C22—22no—
533C22—22no—
534C22—24no—
535C22—24no—
536C22—224no—
537C22—442no—
538C22—442no—
539C22—444no—
540C22—444no—
541C22#1062256914yes—
542C22C2×(C22⋊D11)⋊C411yescharacteristic
543C22C2×#6693711yescharacteristic
544C22#1062329312yes—
545C22#1062329712yes—
546C22C2×#6699011yescharacteristic
547C4—44no—
548C4—44no—
549C4—224no—
550C4—442no—
551C4—442no—
552C4—882no—
553C4#1062256914yes—
554C4C2×C22⋊C4×D1111yescharacteristic
555C4C2×#6693611yescharacteristic
556C4C2×C4×C22⋊D1111yescharacteristic
557C4C2×#6699111yescharacteristic
558C2—24no—
559C2—444no—
560C2C2×#1062256911yescharacteristic
561C2#1307745312yes—
562C2#1307788911yescharacteristic
563C2#1307790711yescharacteristic
564C2#1307817112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenterC22×#103D11
hypocenterC11#20931
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
4. #13071202C2semidirect
5. #13068954C2semidirect
6. #13068947C2semidirect
7. #13068335C2semidirect
8. #13068312C2semidirect
9. C22×C11×#103C2semidirect
17. C2×#66995C4semidirect
46. C22×Q8×C11C2×C4semidirect
74. C2×#4326C2×C4semidirect
78. C2×#4325C2×C4semidirect
94. C2×#4318C2×C4semidirect
194. C22×#103D11semidirect
328. C22×Q8C4×D11semidirect
472. C11#20931semidirect

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106230352
C2×#106227262
#130712022
#130689542
#130689472
#130683352
#130683122
C22×C11×#1032
#2093111