Finite Group Databasebeta

← #14781778

Subgroups — #14781778

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×#10622537C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×#10622828C211yesmaximal, characteristic, complemented
5#13071106C211yesmaximal, characteristic, complemented
6#13069933C214yesmaximal, complemented
7#13069926C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic, complemented
10C23×D4×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4—22no—
14C22×C42×C11C2211yescharacteristic
15C22×#4324C2212yes—
16C2×#66985—24no—
17C2×#66985—24no—
18C2×#66985—24no—
19C22×#4323C2212yes—
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C11×#390—21no—
24C11×#390—21no—
25C11×#390C2214yes—
26#10622828—24no—
27C2×#66896C2214yes—
28#10622826—22no—
29C2×#66874C2212yescomplemented
30#10622579—24no—
31C2×#66873C2212yescomplemented
32#10622552C2212yescomplemented
33C4×(C2×D11)⋊C4—21no—
34C4×(C2×D11)⋊C4—21no—
35#10622542C2212yescomplemented
36#10622537—24no—
37C2×C4⋊(C11⋊C8)C2214yescomplemented
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×C11—21no—
49C23×C4×C11D412yes—
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
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×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—24no—
66C2×C11×C22⋊C4—24no—
67C2×C11×C22⋊C4—48no—
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11D411yescharacteristic
71C2×C42×C11D411yescharacteristic
72C2×C42×C11C2312yes—
73C2×C22⋊Dic11—21no—
74C2×#4324—24no—
75C2×#4324—24no—
76C2×#4324—24no—
77#66985—232no—
78C2×#4323—24no—
79C2×#4323—24no—
80C2×#4323—24no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83#66979—22no—
84#66979—22no—
85C2×C4⋊Dic11C2312yes—
86C2×C4×Dic11—21no—
87C2×#4318—22no—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318—22no—
92C2×#4318D414yes—
93C22×C11⋊C8C2312yes—
94C22×C11⋊C8C2312yes—
95#66896—28no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98#66874—24no—
99#66873—24no—
100C4⋊(C11⋊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—24no—
124C22×C4×C11—24no—
125C22×C4×C11—22no—
126C22×C4×C11—42no—
127C22×C4×C11—44no—
128C22×C4×C11—42no—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—42no—
142C22×Dic11—21no—
143C22×Dic11—22no—
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×C4⋊C4—22no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—42no—
166C11×C22⋊C4—48no—
167C11×C22⋊C4—48no—
168C42×C11—22no—
169C42×C11—22no—
170C42×C11—22no—
171C42×C11—22no—
172C22⋊Dic11—42no—
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—
180#4318—28no—
181#4318—44no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
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×#418—111no—
192#2297—111no—
193C2×#390D1111yescharacteristic, complemented
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—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—48no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—84no—
232C2×C4×C11#12014yes—
233C2×C4×C11#12112yes—
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#12314yes—
237C2×C4×C11#12314yes—
238C2×C4×C11#12414yes—
239C2×C4×C11AGL(1,ℤ/8)14yescomplemented
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—48no—
247C2×Dic11—22no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253D44—22no—
254D44—22no—
255D44—41no—
256D44—41no—
257C4×D11—48no—
258Dic22—22no—
259Dic22—22no—
260Dic22—41no—
261Dic22—41no—
262C11⋊C8—24no—
263C11⋊C8—42no—
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×M16—111no—
273C2×#117—111no—
274C22×C4⋊C4C2×D1111yescharacteristic
275C22×C22⋊C4—22no—
276C22×C42C2×D1111yescharacteristic
277#423—224no—
278C2×C4⋊C8—114no—
279#418—224no—
280#417—224no—
281C2×#103—112no—
282C2×#102—114no—
283C2×#102—112no—
284#391—112no—
285#390—21no—
286#390—21no—
287#390—112no—
288#390C2×D1114yes—
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—24no—
315C4×C11—42no—
316C4×C11—82no—
317C4×C11#39414yes—
318C4×C11C2×#12011yescharacteristic
319C4×C11C2×#12311yescharacteristic
320C4×C11C2×#12311yescharacteristic
321C4×C11C2×#12411yescharacteristic
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—22no—
337C22×D4—21no—
338C22×D4—111no—
339C22×D4—221no—
340C22×D4D4414yes—
341C22×D4C22×D1112yes—
342C23×C4—21no—
343C23×C4—221no—
344C23×C4C22⋊D1112yes—
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—114no—
354C2×M16—222no—
355C2×M16—222no—
356C2×M16—222no—
357C2×M16—222no—
358C2×M16—222no—
359C22×C8—112no—
360C22×C8—112no—
361#117—222no—
362#117—222no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—112no—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—24no—
369C2×C22⋊C4—24no—
370C2×C22⋊C4—48no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C42—22no—
375C2×C42—22no—
376C2×C42—221no—
377C2×C42C22⋊D1111yescharacteristic
378C2×C42C22⋊D1111yescharacteristic
379C2×C42C22×D1112yes—
380C4⋊C8—228no—
381#103—224no—
382#102—224no—
383#102—228no—
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—
401C24C2×C22⋊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—44no—
422C2×D4—42no—
423C2×D4—42no—
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×D4414yes—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—42no—
440C22×C4—221no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4C2×D4412yes—
446C22×C4#433912yes—
447C22×C4D4×D1112yes—
448C22×C4D4×D1112yes—
449C22×C4#434112yes—
450C22×C4#434112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455SD16—2216no—
456D8—2216no—
457M16—228no—
458M16—444no—
459C2×C8—114no—
460C2×C8—222no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—42no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C22⋊C4—48no—
471C22⋊C4—48no—
472C22⋊C4—444no—
473C22⋊C4—442no—
474C22⋊C4—444no—
475C42—22no—
476C42—22no—
477C42—22no—
478C42—22no—
479C42—442no—
480C11#2354611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—416no—
485C23—44no—
486C23—42no—
487C23—42no—
488C23—48no—
489C23—44no—
490C23—84no—
491C23—84no—
492C23—88no—
493C23—222no—
494C23—441no—
495C23—442no—
496C23—441no—
497C23—442no—
498C23#6698312yes—
499C23#6699112yes—
500C23#6699212yes—
501C23C22×C22⋊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—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—48no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—84no—
525C2×C4—222no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—448no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4#6693514yes—
533C2×C4#6693614yes—
534C2×C4#6693814yes—
535C2×C4#6693914yes—
536C2×C4#6698312yes—
537C2×C4#6698514yescomplemented
538C2×C4#6699112yes—
539C2×C4#6699212yes—
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×#434111yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C8—224no—
547C8—442no—
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#1062257414yes—
564C22C2×#6698311yescharacteristic
565C22C2×#6698512yes—
566C22C2×#6699111yescharacteristic
567C22C2×#6699211yescharacteristic
568C22#1062335312yes—
569C4—24no—
570C4—42no—
571C4—82no—
572C4—442no—
573C4—882no—
574C4#1062257414yes—
575C4C2×#6693511yescharacteristic
576C4C2×#6693611yescharacteristic
577C4C2×#6693811yescharacteristic
578C4C2×#6693911yescharacteristic
579C2—24no—
580C2—84no—
581C2—882no—
582C2C2×#1062257411yescharacteristic
583C2#1307808012yes—
584C2#1307809211yescharacteristic
585C2#1307810611yescharacteristic
586C2#1307823112yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#390C2
socleC23×C11C22×D4
prime radicalC22×#66985C2
hypercenterC2×#390D11
hypocenterC11#23546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C2×#10622537C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622828C2semidirect
5. #13071106C2semidirect
6. #13069933C2semidirect
7. #13069926C2semidirect
8. #13068335C2semidirect
9. C2×C11×#390C2semidirect
29. C2×#66874C22semidirect
31. C2×#66873C22semidirect
32. #10622552C22semidirect
35. #10622542C22semidirect
37. C2×C4⋊(C11⋊C8)C22semidirect
38. #10622167C22semidirect
193. C2×#390D11semidirect
239. C2×C4×C11AGL(1,ℤ/8)semidirect
480. C11#23546semidirect
537. C2×C4#66985semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106225372
C2×#106225792
C2×#106228282
#130711062
#130699332
#130699262
#130683352
C2×C11×#3902
#2354611