Finite Group Databasebeta

← #14781773

Subgroups — #14781773

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
1C2×#10622731C211yesmaximal, characteristic, complemented
2C2×#10622845C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4#13071107C211yesmaximal, characteristic, complemented
5C2×#10622834C211yesmaximal, characteristic, complemented
6#13069929C214yesmaximal, complemented
7#13069924C214yesmaximal, complemented
8#13068336C211yesmaximal, characteristic, complemented
9C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C2×C11×AGL(1,ℤ/8)—24no—
13C2×C11×AGL(1,ℤ/8)—24no—
14C2×C11×AGL(1,ℤ/8)—24no—
15C22×C11×SD16C2212yes—
16C22×C11×D8C2212yes—
17C22×C11×M16C2211yescharacteristic
18C22×C22⋊Dic11—22no—
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23#10622845—24no—
24#10622843C2212yescomplemented
25C2×#66899C2212yescomplemented
26#10622834—21no—
27#10622834—21no—
28#10622834C2214yes—
29#10622834C2212yescomplemented
30#10622833—22no—
31#10622828—24no—
32C2×#66896C2214yes—
33C2×#66896C2212yescomplemented
34C4×C22⋊Dic11—21no—
35C4×C22⋊Dic11—21no—
36#10622731—24no—
37C2×Dic11⋊C8C2214yescomplemented
38#10622189C2214yescomplemented
39C25×C11—21no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41D414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11D414yes—
55C22×D4×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—21no—
60C23×Dic11D412yes—
61C11×AGL(1,ℤ/8)—232no—
62C2×C11×SD16—24no—
63C2×C11×SD16—24no—
64C2×C11×SD16—24no—
65C2×C11×D8—24no—
66C2×C11×D8—24no—
67C2×C11×D8—24no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C2×C11×M16D414yes—
71C22×C8×C11C2312yes—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—24no—
76C2×C22⋊Dic11—24no—
77C2×C22⋊Dic11—48no—
78#66979—22no—
79#66979—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2312yes—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11C2312yes—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318—22no—
94C22×C11⋊C8C2312yes—
95#66899—24no—
96#66896—28no—
97#66896—24no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100Dic11⋊C8—28no—
101#23546—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—21no—
104C24×C11—22no—
105C24×C11—44no—
106C24×C11—44no—
107C24×C11—42no—
108C24×C11—42no—
109C24×C11C2×D411yescharacteristic
110C11×#41—28no—
111C11×#41—28no—
112C11×#41—44no—
113C11×#41—44no—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11—21no—
118C2×Q8×C11—21no—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—24no—
121C2×D4×C11—28no—
122C2×D4×C11—24no—
123C2×D4×C11—28no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—22no—
127C2×D4×C11—22no—
128C2×D4×C11—22no—
129C2×D4×C11—22no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11—21no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11C2×D412yes—
141C2×D4×C11C2×D414yes—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11#4112yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—42no—
159C22×Dic11—44no—
160C22×Dic11—42no—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C11×SD16—216no—
164C11×D8—216no—
165C11×M16—28no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11C2×D414yes—
169C22⋊Dic11—44no—
170C22⋊Dic11—48no—
171C22⋊Dic11—44no—
172C22⋊Dic11—48no—
173C22⋊Dic11—42no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—42no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182C4×Dic11—22no—
183C4×Dic11—42no—
184#4318—44no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C22×AGL(1,ℤ/8)D1111yescharacteristic
189C2×#423—111no—
190C2×#417—111no—
191C2×#418—111no—
192#2297—111no—
193C2×#390—111no—
194#2055—114no—
195#2054—114no—
196#1736—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—24no—
201C23×C11—416no—
202C23×C11—41no—
203C23×C11—41no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—44no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11—84no—
212C23×C11—84no—
213C23×C11—88no—
214C23×C11#12112yes—
215C23×C11#12112yes—
216C23×C11#12112yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—41no—
221Q8×C11—41no—
222D4×C11—22no—
223D4×C11—24no—
224D4×C11—24no—
225D4×C11—22no—
226D4×C11—48no—
227D4×C11—42no—
228D4×C11—41no—
229D4×C11—42no—
230D4×C11—41no—
231D4×C11—48no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—48no—
236C2×C4×C11#12014yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12314yes—
241C2×C4×C11#12314yes—
242C2×C4×C11#12414yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—84no—
261C2×Dic11AGL(1,ℤ/8)14yescomplemented
262C8×C11—24no—
263C11⋊C8—42no—
264C22×#41C2×D1111yescharacteristic
265C23×D4C2×D1111yescharacteristic
266C2×AGL(1,ℤ/8)—24no—
267C2×AGL(1,ℤ/8)—24no—
268C2×AGL(1,ℤ/8)—24no—
269C22×SD16C2×D1112yes—
270C22×D8C2×D1112yes—
271C22×M16—111no—
272C22×M16C2×D1111yescharacteristic
273C2×#117—111no—
274C22×C4⋊C4—111no—
275C22×C22⋊C4—222no—
276C22×C42—111no—
277#423—224no—
278C2×C4⋊C8—114no—
279#418—224no—
280#417—224no—
281C2×#103—112no—
282C2×#102—112no—
283C2×#102—114no—
284#391—112no—
285#390—112no—
286#390—114no—
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—42no—
298C22×C11—44no—
299C22×C11—48no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—816no—
303C22×C11—82no—
304C22×C11—82no—
305C22×C11—82no—
306C22×C11—82no—
307C22×C11—84no—
308C22×C11#39414yes—
309C22×C11C2×#12111yescharacteristic
310C22×C11C2×#12111yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C2×AGL(1,ℤ/8)12yes—
313C22×C11#57512yes—
314C4×C11—42no—
315C4×C11#39414yes—
316C4×C11C2×#12011yescharacteristic
317C4×C11C2×#12311yescharacteristic
318C4×C11C2×#12311yescharacteristic
319C4×C11C2×#12411yescharacteristic
320Dic11—24no—
321Dic11—42no—
322Dic11—82no—
323Dic11—82no—
324C25—21no—
325C2×#41—22no—
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—22no—
329C2×#41—22no—
330C2×#41C22⋊D1114yes—
331C22×Q8C22×D1111yescharacteristic
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4C22⋊D1114yes—
340C22×D4C22×D1111yescharacteristic
341C22×D4C22×D1112yes—
342C23×C4—21no—
343C23×C4—112no—
344C23×C4—221no—
345C23×C4C22×D1111yescharacteristic
346AGL(1,ℤ/8)—232no—
347C2×SD16—24no—
348C2×SD16—24no—
349C2×SD16—24no—
350C2×D8—24no—
351C2×D8—24no—
352C2×D8—24no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—222no—
356C2×M16—222no—
357C2×M16—222no—
358C2×M16C22⋊D1114yes—
359C22×C8—112no—
360C22×C8C22×D1112yes—
361#117—222no—
362#117—222no—
363C2×C4⋊C4—112no—
364C2×C4⋊C4—112no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—221no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—448no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—112no—
377C2×C42—222no—
378C2×C42—222no—
379C2×C42—221no—
380C4⋊C8—228no—
381#103—224no—
382#102—224no—
383#102—228no—
384#95—222no—
385#95—222no—
386C2×C11—24no—
387C2×C11—82no—
388C2×C11—84no—
389C2×C11C2×#39411yescharacteristic
390C2×C11#303612yes—
391C2×C11#303811yescharacteristic
392C2×C11#304011yescharacteristic
393C2×C11#305512yes—
394C24—24no—
395C24—21no—
396C24—22no—
397C24—44no—
398C24—44no—
399C24—42no—
400C24—42no—
401C24D4×D1111yescharacteristic
402#41—28no—
403#41—28no—
404#41—44no—
405#41—44no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8C2×C22⋊D1112yes—
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—24no—
415C2×D4—28no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—22no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—42no—
431C2×D4—42no—
432C2×D4C2×C22⋊D1112yes—
433C2×D4C2×C22⋊D1114yes—
434C22×C4—21no—
435C22×C4—24no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—442no—
445C22×C4—444no—
446C22×C4—442no—
447C22×C4D4×D1111yescharacteristic
448C22×C4#434112yes—
449C22×C4#434112yes—
450C22×C4#434112yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C23×D1111yescharacteristic
455SD16—216no—
456D8—216no—
457M16—28no—
458M16—444no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8C2×C22⋊D1114yes—
465C4⋊C4—222no—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—442no—
470C22⋊C4—448no—
471C22⋊C4—444no—
472C22⋊C4—448no—
473C22⋊C4—444no—
474C22⋊C4—442no—
475C42—222no—
476C42—222no—
477C42—222no—
478C42—222no—
479C42—442no—
480C11#2354611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—22no—
484C23—24no—
485C23—416no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—44no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—42no—
494C23—48no—
495C23—84no—
496C23—84no—
497C23—88no—
498C23#6699112yes—
499C23#6699212yes—
500C23#6699212yes—
501C23C2×D4×D1111yescharacteristic
502Q8—22no—
503Q8—22no—
504Q8—41no—
505Q8—41no—
506D4—24no—
507D4—22no—
508D4—22no—
509D4—24no—
510D4—48no—
511D4—42no—
512D4—41no—
513D4—42no—
514D4—41no—
515D4—48no—
516C2×C4—22no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—48no—
520C2×C4—114no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—448no—
527C2×C4—444no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—884no—
533C2×C4#6698814yes—
534C2×C4#6698814yes—
535C2×C4#6698914yes—
536C2×C4#6699112yes—
537C2×C4#6699212yes—
538C2×C4#6699212yes—
539C2×C4#6700614yes—
540C2×C4C2×#434111yescharacteristic
541C2×C4C2×#434111yescharacteristic
542C2×C4C2×#434111yescharacteristic
543C2×C4C22×C22⋊D1111yescharacteristic
544C2×C4C22×C22⋊D1111yescharacteristic
545C2×C4C22×C22⋊D1111yescharacteristic
546C8—24no—
547C8—442no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—48no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—44no—
557C22—816no—
558C22—82no—
559C22—82no—
560C22—82no—
561C22—84no—
562C22—82no—
563C22#1062283514yes—
564C22D11×AGL(1,ℤ/8)12yes—
565C22#1062330412yes—
566C22C2×#6699111yescharacteristic
567C22C2×#6699211yescharacteristic
568C22C2×#6699211yescharacteristic
569C4—42no—
570C4—224no—
571C4—442no—
572C4—882no—
573C4—882no—
574C4#1062283514yes—
575C4C2×#6698811yescharacteristic
576C4C2×#6698811yescharacteristic
577C4C2×#6698911yescharacteristic
578C4C2×#6700611yescharacteristic
579C2—24no—
580C2—84no—
581C2—82no—
582C2C2×#1062283511yescharacteristic
583C2#1307807712yes—
584C2#1307809411yescharacteristic
585C2#1307810811yescharacteristic
586C2#1307822912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC23×C11C22×D4
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11#23546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10622731C2semidirect
2. C2×#10622845C2semidirect
3. C2×#10622828C2semidirect
4. #13071107C2semidirect
5. C2×#10622834C2semidirect
6. #13069929C2semidirect
7. #13069924C2semidirect
8. #13068336C2semidirect
24. #10622843C22semidirect
25. C2×#66899C22semidirect
29. #10622834C22semidirect
33. C2×#66896C22semidirect
37. C2×Dic11⋊C8C22semidirect
38. #10622189C22semidirect
261. 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
C2×#106227312
C2×#106228452
C2×#106228282
#130711072
C2×#106228342
#130699292
#130699242
#130683362
C22×C11×AGL(1,ℤ/8)2
#2354611