Finite Group Databasebeta

← #14781776

Subgroups — #14781776

Order 2816.

1674 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4#13071104C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic, complemented
6#13069932C214yesmaximal, complemented
7#13069925C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×C11×#418C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C22⋊Dic11—22no—
15C22×#4324C2212yes—
16C2×#66985—24no—
17C2×#66985—24no—
18C2×#66985—24no—
19C22×#4323C2212yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#418—24no—
24C2×C11×#102C2214yes—
25#10622834—21no—
26#10622834—21no—
27#10622834C2214yes—
28#10622746—24no—
29#10622731—24no—
30C2×#66885C2212yescomplemented
31C2×#66880C2212yescomplemented
32C2×Dic11⋊C8C2214yescomplemented
33#10622601C2212yescomplemented
34#10622587C2212yescomplemented
35#10622571—22no—
36C4×(C2×D11)⋊C4—21no—
37C4×(C2×D11)⋊C4—21no—
38#10622167C2214yescomplemented
39C25×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11D414yes—
47C22×D4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—21no—
50C23×Dic11—21no—
51C23×Dic11D412yes—
52C2×#4339—22no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339D414yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16—22no—
64C22×C8×C11C2312yes—
65C11×#117—22no—
66C11×#117—22no—
67C2×C11×C4⋊C4C2312yes—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—21no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—48no—
73C2×#4324—24no—
74C2×#4324—24no—
75C2×#4324—24no—
76#66985—232no—
77C2×#4323—24no—
78C2×#4323—24no—
79C2×#4323—24no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2312yes—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2312yes—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318D414yes—
94C22×C11⋊C8C2312yes—
95C11×#102—28no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98#66885—24no—
99#66880—24no—
100Dic11⋊C8—28no—
101#23546—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—44no—
105C24×C11—44no—
106C24×C11—42no—
107C24×C11—42no—
108C24×C11C2×D411yescharacteristic
109C23×D11—21no—
110C2×D4×C11—28no—
111C2×D4×C11—24no—
112C2×D4×C11—28no—
113C2×D4×C11—22no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—42no—
119C2×D4×C11—42no—
120C2×D4×C11—44no—
121C2×D4×C11—44no—
122C2×D4×C11C2×D414yes—
123C22×C4×C11—22no—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11C2411yescharacteristic
132C2×C22⋊D11—24no—
133C2×C22⋊D11—42no—
134C2×C22⋊D11—42no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—21no—
138C22×Dic11—22no—
139C22×Dic11—42no—
140C22×Dic11—44no—
141C22×Dic11—42no—
142C22×Dic11C2×D412yes—
143C22×Dic11C2×D412yes—
144#4339—28no—
145#4339—28no—
146#4339—44no—
147#4339—44no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44C2×D412yes—
154C2×C4×D11—24no—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22C2×D412yes—
163C11×M16—44no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11—22no—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C22⋊C4—42no—
170C42×C11—42no—
171C22⋊Dic11—48no—
172C22⋊Dic11—48no—
173#4324—216no—
174#4323—216no—
175(C2×D11)⋊C4—44no—
176(C2×D11)⋊C4—44no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11—42no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184#4318—28no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2×D414yes—
188C22×AGL(1,ℤ/8)—111no—
189C2×#423—111no—
190C2×#417—111no—
191C2×#418D1111yescharacteristic, complemented
192#2297—111no—
193C2×#390—111no—
194#2055—114no—
195#2054—114no—
196#1736—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—24no—
200C23×C11—416no—
201C23×C11—42no—
202C23×C11—42no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11—84no—
207C23×C11—84no—
208C23×C11—88no—
209C23×C11#12112yes—
210C23×C11#12112yes—
211C23×C11#12112yes—
212C23×C11C22×D411yescharacteristic
213C22×D11—22no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—42no—
217C22×D11—42no—
218D4×C11—24no—
219D4×C11—24no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—48no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11#12014yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12112yes—
229C2×C4×C11#12112yes—
230C2×C4×C11#12314yes—
231C2×C4×C11#12314yes—
232C2×C4×C11#12414yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C22⋊D11—48no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—48no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—42no—
250C2×Dic11—44no—
251C2×Dic11—84no—
252C2×Dic11AGL(1,ℤ/8)14yescomplemented
253D44—22no—
254D44—22no—
255D44—41no—
256D44—41no—
257C4×D11—48no—
258Dic22—22no—
259Dic22—22no—
260Dic22—41no—
261Dic22—41no—
262C8×C11—42no—
263C11⋊C8—24no—
264C22×#41—111no—
265C23×D4C2×D1111yescharacteristic
266C2×AGL(1,ℤ/8)—224no—
267C2×AGL(1,ℤ/8)—224no—
268C2×AGL(1,ℤ/8)—224no—
269C22×SD16—112no—
270C22×D8—112no—
271C22×M16—111no—
272C22×M16C2×D1111yescharacteristic
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C22⋊C4—222no—
276C22×C42—111no—
277#423—224no—
278C2×C4⋊C8—114no—
279#418—24no—
280#417—224no—
281C2×#103—112no—
282C2×#102—112no—
283C2×#102C2×D1114yes—
284#391—112no—
285#390—114no—
286#390—112no—
287#390—221no—
288#390—221no—
289#386—222no—
290C4×C22⋊C4—221no—
291C4×C22⋊C4—221no—
292#340—114no—
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11—44no—
298C22×C11—48no—
299C22×C11—816no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11—84no—
303C22×C11#39414yes—
304C22×C11C2×#12111yescharacteristic
305C22×C11C2×#12111yescharacteristic
306C22×C11C2×#12111yescharacteristic
307C22×C11C2×AGL(1,ℤ/8)12yes—
308C22×C11#57512yes—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—82no—
313C2×D11—82no—
314C4×C11—82no—
315C4×C11#39414yes—
316C4×C11C2×#12011yescharacteristic
317C4×C11C2×#12311yescharacteristic
318C4×C11C2×#12311yescharacteristic
319C4×C11C2×#12411yescharacteristic
320Dic11—24no—
321Dic11—42no—
322Dic11—42no—
323Dic11—82no—
324C25—21no—
325C2×#41—114no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C22×Q8—111no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—21no—
337C22×D4—22no—
338C22×D4—111no—
339C22×D4—221no—
340C22×D4C22⋊D1114yes—
341C22×D4C22×D1112yes—
342C23×C4—112no—
343C23×C4—221no—
344C23×C4—221no—
345C23×C4C22×D1111yescharacteristic
346AGL(1,ℤ/8)—2232no—
347C2×SD16—224no—
348C2×SD16—224no—
349C2×SD16—224no—
350C2×D8—224no—
351C2×D8—224no—
352C2×D8—224no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—22no—
356C2×M16—114no—
357C2×M16—222no—
358C2×M16—222no—
359C22×C8—112no—
360C22×C8C22×D1112yes—
361#117—22no—
362#117—22no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—224no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—448no—
374C2×C42—21no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42—222no—
379C2×C42—222no—
380C4⋊C8—228no—
381#103—224no—
382#102—28no—
383#102—224no—
384#95—222no—
385#95—222no—
386C2×C11—24no—
387C2×C11—84no—
388C2×C11C2×#39411yescharacteristic
389C2×C11#303612yes—
390C2×C11#303811yescharacteristic
391C2×C11#304011yescharacteristic
392C2×C11#305512yes—
393D11—82no—
394C24—24no—
395C24—22no—
396C24—44no—
397C24—44no—
398C24—42no—
399C24—42no—
400C24—221no—
401C24D4×D1111yescharacteristic
402#41—228no—
403#41—228no—
404#41—444no—
405#41—444no—
406C2×Q8—112no—
407C2×Q8—221no—
408C2×Q8—221no—
409C2×Q8—221no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×D4—28no—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—22no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—44no—
421C2×D4—42no—
422C2×D4—42no—
423C2×D4—44no—
424C2×D4—112no—
425C2×D4—224no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4C2×C22⋊D1114yes—
434C22×C4—22no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—221no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—442no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—444no—
446C22×C4—442no—
447C22×C4#433912yes—
448C22×C4#433912yes—
449C22×C4D4×D1112yes—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1112yes—
452C22×C4#434112yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C23×D1111yescharacteristic
455SD16—2216no—
456D8—2216no—
457M16—44no—
458M16—228no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—22no—
462C2×C8—114no—
463C2×C8—222no—
464C2×C8—222no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—442no—
470C22⋊C4—42no—
471C22⋊C4—444no—
472C22⋊C4—444no—
473C22⋊C4—448no—
474C22⋊C4—448no—
475C42—42no—
476C42—222no—
477C42—222no—
478C42—222no—
479C42—222no—
480C11#2354611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—416no—
485C23—42no—
486C23—42no—
487C23—44no—
488C23—44no—
489C23—48no—
490C23—84no—
491C23—84no—
492C23—88no—
493C23—222no—
494C23—441no—
495C23—442no—
496C23—442no—
497C23—441no—
498C23#6693712yes—
499C23#6693712yes—
500C23#6699212yes—
501C23C2×D4×D1111yescharacteristic
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506D4—24no—
507D4—24no—
508D4—42no—
509D4—42no—
510D4—48no—
511D4—222no—
512D4—222no—
513D4—448no—
514D4—441no—
515D4—441no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—114no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—448no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—448no—
530C2×C4—442no—
531C2×C4—444no—
532C2×C4—884no—
533C2×C4#6693614yes—
534C2×C4#6693712yes—
535C2×C4#6693712yes—
536C2×C4#6693814yes—
537C2×C4#6698214yes—
538C2×C4#6699014yes—
539C2×C4#6699212yes—
540C2×C4C2×#433911yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×#434111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—42no—
547C8—224no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—48no—
553C22—44no—
554C22—816no—
555C22—82no—
556C22—82no—
557C22—84no—
558C22—442no—
559C22—442no—
560C22—442no—
561C22—882no—
562C22—882no—
563C22#1062257214yes—
564C22C2×#6693711yescharacteristic
565C22C2×#6693711yescharacteristic
566C22D11×AGL(1,ℤ/8)12yes—
567C22#1062330412yes—
568C22C2×#6699211yescharacteristic
569C4—82no—
570C4—224no—
571C4—442no—
572C4—442no—
573C4—882no—
574C4#1062257214yes—
575C4C2×#6693611yescharacteristic
576C4C2×#6693811yescharacteristic
577C4C2×#6698211yescharacteristic
578C4C2×#6699011yescharacteristic
579C2—24no—
580C2—84no—
581C2—882no—
582C2C2×#1062257211yescharacteristic
583C2#1307807712yes—
584C2#1307809511yescharacteristic
585C2#1307810911yescharacteristic
586C2#1307823312yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#418C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
hypercenterC2×#418D11
hypocenterC11#23546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
2. C2×#10622731C2semidirect
3. C2×#10622746C2semidirect
4. #13071104C2semidirect
5. C2×#10622834C2semidirect
6. #13069932C2semidirect
7. #13069925C2semidirect
8. #13068337C2semidirect
9. C2×C11×#418C2semidirect
30. C2×#66885C22semidirect
31. C2×#66880C22semidirect
32. C2×Dic11⋊C8C22semidirect
33. #10622601C22semidirect
34. #10622587C22semidirect
38. #10622167C22semidirect
191. C2×#418D11semidirect
252. C2×Dic11AGL(1,ℤ/8)semidirect
480. C11#23546semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106227312
C2×#106227462
#130711042
C2×#106228342
#130699322
#130699252
#130683372
C2×C11×#4182
#2354611