Finite Group Databasebeta

← #14781780

Subgroups — #14781780

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×#66961C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13071104C211yesmaximal, characteristic, complemented
6C2×#10622601C211yesmaximal, characteristic, complemented
7#13069935C214yesmaximal, complemented
8#13069928C214yesmaximal, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×D44C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×(C2×D11)⋊C4—22no—
16C22×C4×Dic11C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C2×#66961—24no—
19C2×#66961—24no—
20C2×#66961—24no—
21C22×D88C2212yes—
22C22×#4314C2212yes—
23#10622731—24no—
24C2×Dic11⋊C8C2214yescomplemented
25#10622614—24no—
26#10622601—21no—
27#10622601—21no—
28#10622601C2214yes—
29#10622601C2212yescomplemented
30#10622587C2212yescomplemented
31C2×#66874C2212yescomplemented
32#10622579—24no—
33C2×#66873C2214yes—
34C2×#66873C2212yescomplemented
35#10622571—22no—
36C4×(C2×D11)⋊C4—21no—
37C4×(C2×D11)⋊C4—21no—
38C11×#340C2214yescomplemented
39C24×D11—21no—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C23×Dic11D412yes—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339D414yes—
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2311yescharacteristic
61C2×C11×M16—22no—
62C2×C11×M16—22no—
63C2×C11×M16D414yes—
64C22×C8×C11C2312yes—
65C11×#117—22no—
66C11×#117—22no—
67C2×C11×C4⋊C4—22no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C4⋊C4C2312yes—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—48no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11D411yescharacteristic
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11C2312yes—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C22×C11⋊C8C2312yes—
88#66961—232no—
89C2×D88—24no—
90C2×D88—24no—
91C2×D88—24no—
92C2×#4314—24no—
93C2×#4314—24no—
94C2×#4314—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97Dic11⋊C8—28no—
98#66874—24no—
99#66873—28no—
100#66873—24no—
101#23546—111nomaximal, Sylow
102C24×C11C2×D411yescharacteristic
103C23×D11—24no—
104C23×D11—21no—
105C23×D11—22no—
106C23×D11—44no—
107C23×D11—44no—
108C23×D11—42no—
109C23×D11—42no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—44no—
113C22×C4×C11—42no—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C2×C22⋊D11—24no—
123C2×C22⋊D11—42no—
124C2×C22⋊D11—42no—
125C22×Dic11—24no—
126C22×Dic11—24no—
127C22×Dic11—21no—
128C22×Dic11—42no—
129C22×Dic11C2×D412yes—
130C22×Dic11C2×D412yes—
131#4339—28no—
132#4339—28no—
133#4339—44no—
134#4339—44no—
135C2×D44—28no—
136C2×D44—24no—
137C2×D44—28no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—22no—
143C2×D44—21no—
144C2×D44—22no—
145C2×D44—22no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—42no—
149C2×D44—42no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44C2×D414yes—
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—28no—
164C2×C8×C11—22no—
165C2×C8×C11—22no—
166C2×C8×C11C2×D414yes—
167C11×C4⋊C4—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—42no—
172C11×C22⋊C4—42no—
173C42×C11—42no—
174(C2×D11)⋊C4—44no—
175(C2×D11)⋊C4—48no—
176(C2×D11)⋊C4—44no—
177(C2×D11)⋊C4—48no—
178C4×Dic11—22no—
179C4×Dic11—22no—
180C4×Dic11—22no—
181C4×Dic11—22no—
182#4318—44no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186D88—216no—
187#4314—216no—
188C22×AGL(1,ℤ/8)—111no—
189C2×#423—111no—
190C2×#417—111no—
191C2×#418—111no—
192#2297—111no—
193C2×#390—111no—
194#2055—114no—
195#2054—114no—
196#1736D1111yescharacteristic, complemented
197C23×C11—22no—
198C23×C11—22no—
199C23×C11#12112yes—
200C23×C11#12112yes—
201C23×C11#12112yes—
202C23×C11C22×D411yescharacteristic
203C22×D11—22no—
204C22×D11—24no—
205C22×D11—416no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—42no—
209C22×D11—42no—
210C22×D11—44no—
211C22×D11—42no—
212C22×D11—42no—
213C22×D11—44no—
214C22×D11—48no—
215C22×D11—84no—
216C22×D11—84no—
217C22×D11—88no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—84no—
224C2×C4×C11#12014yes—
225C2×C4×C11#12112yes—
226C2×C4×C11#12112yes—
227C2×C4×C11#12112yes—
228C2×C4×C11#12314yes—
229C2×C4×C11#12314yes—
230C2×C4×C11#12414yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C2×C4×C11C2×#4111yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C22⋊D11—48no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—48no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11AGL(1,ℤ/8)14yescomplemented
248D44—24no—
249D44—22no—
250D44—24no—
251D44—22no—
252D44—42no—
253D44—41no—
254D44—42no—
255D44—41no—
256D44—48no—
257C4×D11—48no—
258Dic22—22no—
259Dic22—22no—
260Dic22—41no—
261Dic22—41no—
262C8×C11—24no—
263C11⋊C8—42no—
264C22×#41—111no—
265C23×D4—111no—
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⋊C4C2×D1111yescharacteristic
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#340C2×D1114yescomplemented
293C22×C11—24no—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—24no—
297C22×C11#39414yes—
298C22×C11C2×#12111yescharacteristic
299C22×C11C2×#12111yescharacteristic
300C22×C11C2×#12111yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)12yes—
302C22×C11#57512yes—
303C2×D11—44no—
304C2×D11—42no—
305C2×D11—48no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—816no—
309C2×D11—82no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—82no—
313C2×D11—84no—
314C4×C11—82no—
315C4×C11—82no—
316C4×C11#39414yes—
317C4×C11C2×#12011yescharacteristic
318C4×C11C2×#12311yescharacteristic
319C4×C11C2×#12311yescharacteristic
320C4×C11C2×#12411yescharacteristic
321Dic11—24no—
322Dic11—42no—
323Dic11—42no—
324C25—221no—
325C2×#41—114no—
326C2×#41—222no—
327C2×#41—222no—
328C2×#41—222no—
329C2×#41—222no—
330C2×#41—222no—
331C22×Q8—111no—
332C22×D4—114no—
333C22×D4—111no—
334C22×D4—112no—
335C22×D4—221no—
336C22×D4—222no—
337C22×D4—222no—
338C22×D4—222no—
339C22×D4—222no—
340C22×D4—221no—
341C22×D4—222no—
342C23×C4—21no—
343C23×C4—112no—
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—222no—
356C2×M16—222no—
357C2×M16—222no—
358C2×M16D4414yes—
359C22×C8—112no—
360C22×C8C22×D1112yes—
361#117—22no—
362#117—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4C22×D1112yes—
367C2×C4⋊C4C22×D1112yes—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—224no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
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—224no—
383#102—228no—
384#95—222no—
385#95—222no—
386C2×C11—24no—
387C2×C11C2×#39411yescharacteristic
388C2×C11#303612yes—
389C2×C11#303811yescharacteristic
390C2×C11#304011yescharacteristic
391C2×C11#305512yes—
392D11—82no—
393D11—84no—
394C24—224no—
395C24—221no—
396C24—222no—
397C24—444no—
398C24—444no—
399C24—442no—
400C24—442no—
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—112no—
413C2×D4—114no—
414C2×D4—224no—
415C2×D4—228no—
416C2×D4—224no—
417C2×D4—228no—
418C2×D4—221no—
419C2×D4—222no—
420C2×D4—222no—
421C2×D4—221no—
422C2×D4—222no—
423C2×D4—221no—
424C2×D4—221no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—221no—
428C2×D4—442no—
429C2×D4—442no—
430C2×D4—444no—
431C2×D4—442no—
432C2×D4—444no—
433C2×D4—442no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—42no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—221no—
443C22×C4—224no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4C2×D4412yes—
448C22×C4#433912yes—
449C22×C4#433912yes—
450C22×C4D4×D1112yes—
451C22×C4D4×D1112yes—
452C22×C4D4×D1111yescharacteristic
453C22×C4#434312yes—
454C22×C4C23×D1111yescharacteristic
455SD16—2216no—
456D8—2216no—
457M16—28no—
458M16—444no—
459C2×C8—22no—
460C2×C8—22no—
461C2×C8—222no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8C2×D4414yes—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—42no—
470C22⋊C4—42no—
471C22⋊C4—448no—
472C22⋊C4—444no—
473C22⋊C4—448no—
474C22⋊C4—444no—
475C42—42no—
476C42—222no—
477C42—222no—
478C42—222no—
479C42—222no—
480C11#2354611yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—222no—
484C23—224no—
485C23—4416no—
486C23—441no—
487C23—442no—
488C23—441no—
489C23—442no—
490C23—444no—
491C23—442no—
492C23—442no—
493C23—444no—
494C23—448no—
495C23—884no—
496C23—884no—
497C23—888no—
498C23#6693712yes—
499C23#6693712yes—
500C23#6694812yes—
501C23C2×D4×D1111yescharacteristic
502Q8—222no—
503Q8—222no—
504Q8—441no—
505Q8—441no—
506D4—222no—
507D4—224no—
508D4—224no—
509D4—222no—
510D4—448no—
511D4—442no—
512D4—441no—
513D4—442no—
514D4—441no—
515D4—448no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—84no—
522C2×C4—114no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—448no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—448no—
533C2×C4#6692814yes—
534C2×C4#6693514yes—
535C2×C4#6693712yes—
536C2×C4#6693712yes—
537C2×C4#6694714yes—
538C2×C4#6694714yes—
539C2×C4#6694812yes—
540C2×C4C22×D4411yescharacteristic
541C2×C4C2×#433911yescharacteristic
542C2×C4C2×#433911yescharacteristic
543C2×C4C2×D4×D1111yescharacteristic
544C2×C4C2×D4×D1111yescharacteristic
545C2×C4C2×#434311yescharacteristic
546C8—24no—
547C8—442no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—448no—
553C22—442no—
554C22—442no—
555C22—442no—
556C22—444no—
557C22—8816no—
558C22—882no—
559C22—882no—
560C22—882no—
561C22—884no—
562C22—882no—
563C22#1062228514yes—
564C22C2×#6693711yescharacteristic
565C22C2×#6693711yescharacteristic
566C22C2×#6694811yescharacteristic
567C22D11×AGL(1,ℤ/8)12yes—
568C22#1062330812yes—
569C4—82no—
570C4—82no—
571C4—224no—
572C4—442no—
573C4—442no—
574C4#1062228514yes—
575C4C2×#6692811yescharacteristic
576C4C2×#6693511yescharacteristic
577C4C2×#6694711yescharacteristic
578C4C2×#6694711yescharacteristic
579C2—24no—
580C2—884no—
581C2—882no—
582C2C2×#1062228511yescharacteristic
583C2#1307807912yes—
584C2#1307809511yescharacteristic
585C2#1307811311yescharacteristic
586C2#1307823612yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
hypercenter#1736D11
hypocenterC11#23546
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10622731C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622614C2semidirect
5. #13071104C2semidirect
6. C2×#10622601C2semidirect
7. #13069935C2semidirect
8. #13069928C2semidirect
9. C11×#1736C2semidirect
24. C2×Dic11⋊C8C22semidirect
29. #10622601C22semidirect
30. #10622587C22semidirect
31. C2×#66874C22semidirect
34. C2×#66873C22semidirect
38. C11×#340C22semidirect
196. #1736D11semidirect
247. C2×Dic11AGL(1,ℤ/8)semidirect
292. #340C2×D11semidirect
480. C11#23546semidirect

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106227312
C2×#106225792
C2×#106226142
#130711042
C2×#106226012
#130699352
#130699282
C11×#17362
#2354611