Finite Group Databasebeta

← #14730485

Subgroups — #14730485

Order 2816.

964 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079843C211yesmaximal, characteristic, complemented
2#13079163C211yesmaximal, characteristic, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13067900C212yesmaximal, complemented
5#13067879C212yesmaximal, complemented
6#13067872C212yesmaximal, complemented
7#13067851C212yesmaximal, complemented
8#13067316C211yesmaximal, characteristic, complemented
9#13067059C211yesmaximal, characteristic, complemented
10#13067029C211yesmaximal, characteristic, complemented
11C11×#3520C211yesmaximal, characteristic
12C11×#556C2211yescharacteristic
13C11×#554—21no—
14C11×#552—21no—
15C11×#551—22no—
16D4×Q8×C11C2211yescharacteristic
17C11×#548—21no—
18C11×#547C2211yescharacteristic
19C11×#547C2211yescharacteristic
20C11×#546—21no—
21C11×#542—21no—
22C11×#539—22no—
23C11×#533C2211yescharacteristic
24C11×#529C2211yescharacteristic
25C11×#525—21no—
26C2×C11×C22⋊Q8—21no—
27C11×#520—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C22×#4324—21no—
30C2×#66922C2211yescharacteristic
31#10622692C2212yescomplemented
32#10622691C2212yescomplemented
33#10622678—21no—
34#10622678—22no—
35#10622668—21no—
36#10622657—21no—
37#10622647—21no—
38#10622633C2212yescomplemented
39#10622632—21no—
40#10622632—21no—
41#10622632C2212yes—
42#10622632C2212yes—
43#10622620C2212yescomplemented
44#10622608—22no—
45C2×#66874—21no—
46#10622539C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C4×#4318C2211yescharacteristic
49#10622185C2212yescomplemented
50#10622185C2212yescomplemented
51Q8⋊(C11⋊C8)C2212yescomplemented
52D4⋊(C11⋊C8)C2212yes—
53D4⋊(C11⋊C8)C2212yes—
54D4⋊(C11⋊C8)C2212yescomplemented
55C2×C11×#41—21no—
56C2×C11×#41—21no—
57C22×Q8×C11—21no—
58C22×D4×C11D411yescharacteristic
59C23×C4×C11—21no—
60C22×Dic22—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8C2311yescharacteristic
63C11×C4⋊Q8C2311yescharacteristic
64C11×#126—22no—
65C11×#126—22no—
66C11×#126—21no—
67C11×#125—22no—
68C11×#125D411yescharacteristic
69C11×#125D412yes—
70C11×#124—22no—
71C11×#124—21no—
72C11×#124D411yescharacteristic
73C11×#123—22no—
74C11×#123—22no—
75C11×#123—21no—
76C11×#123—22no—
77C11×#123—22no—
78C11×C22⋊Q8—22no—
79C11×C22⋊Q8—22no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—21no—
82C11×C22⋊Q8—21no—
83C11×C22⋊Q8—21no—
84C11×C22⋊Q8—21no—
85C11×C22⋊Q8—21no—
86C11×C22⋊Q8—22no—
87C11×C22⋊Q8—21no—
88C11×C22⋊Q8D411yescharacteristic
89C11×#121—22no—
90C11×#121—21no—
91C11×#121—21no—
92C11×#121D411yescharacteristic
93C11×#120—22no—
94C4×Q8×C11—21no—
95C4×Q8×C11—21no—
96C4×Q8×C11—21no—
97C4×Q8×C11C2311yescharacteristic
98C4×D4×C11—22no—
99C4×D4×C11—22no—
100C4×D4×C11—22no—
101C4×D4×C11—21no—
102C4×D4×C11—21no—
103C4×D4×C11—21no—
104C4×D4×C11—21no—
105C4×D4×C11D411yescharacteristic
106C4×D4×C11D411yescharacteristic
107C4×D4×C11C2311yescharacteristic
108C4×D4×C11C2311yescharacteristic
109C4×D4×C11C2311yescharacteristic
110C11×#117—22no—
111C11×#117—21no—
112C11×#117—21no—
113C11×#117D412yes—
114C2×C11×C4⋊C4—22no—
115C2×C11×C4⋊C4—21no—
116C2×C11×C4⋊C4—21no—
117C2×C11×C4⋊C4D411yescharacteristic
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—21no—
120C2×C42×C11C2311yescharacteristic
121C2×#4324—22no—
122C2×#4324—22no—
123C2×#4324—44no—
124C2×C4⋊Dic11—21no—
125C2×C4⋊Dic11—21no—
126C2×#4318—21no—
127C22×C11⋊C8—21no—
128#66922—21no—
129#66922—21no—
130#66922—21no—
131#66922C2312yes—
132#66899—22no—
133#66896—22no—
134C22⋊(C11⋊C8)—21no—
135#66874—22no—
136#66874—22no—
137#66872—24no—
138#66872—22no—
139#66871—24no—
140#66871—22no—
141C4⋊(C11⋊C8)—21no—
142C4⋊(C11⋊C8)C2312yes—
143C4⋊(C11⋊C8)C2312yes—
144#66867—21no—
145#66867—21no—
146C4×C11⋊C8C2312yes—
147#18586—111nomaximal, Sylow
148C24×C11—21no—
149C11×#41—42no—
150C11×#41—42no—
151C11×#41—82no—
152C2×Q8×C11—22no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—82no—
156C2×Q8×C11C2×D411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—22no—
161C2×D4×C11—21no—
162C2×D4×C11—41no—
163C2×D4×C11C2×D411yescharacteristic
164C2×D4×C11C2×D411yescharacteristic
165C2×D4×C11C2×D411yescharacteristic
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—82no—
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×Dic11—41no—
180C2×Dic22—22no—
181C2×Dic22—42no—
182C2×Dic22—42no—
183C2×Dic22—41no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—22no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4C2×D411yescharacteristic
198C11×C4⋊C4C2×D412yes—
199C11×C4⋊C4C2×D411yescharacteristic
200C11×C4⋊C4C2×D412yes—
201C11×C4⋊C4C2×D411yescharacteristic
202C11×C4⋊C4C2×D411yescharacteristic
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—22no—
207C11×C22⋊C4—22no—
208C11×C22⋊C4—21no—
209C11×C22⋊C4—22no—
210C11×C22⋊C4—21no—
211C11×C22⋊C4—21no—
212C11×C22⋊C4—21no—
213C11×C22⋊C4—21no—
214C11×C22⋊C4—21no—
215C11×C22⋊C4—21no—
216C11×C22⋊C4—21no—
217C11×C22⋊C4—21no—
218C42×C11—22no—
219C42×C11—22no—
220C42×C11—21no—
221C42×C11C2×D411yescharacteristic
222C42×C11C2×D411yescharacteristic
223C42×C11C2×D411yescharacteristic
224C42×C11C2411yescharacteristic
225#4324—44no—
226#4324—44no—
227C4⋊Dic11—22no—
228C4⋊Dic11—22no—
229C4⋊Dic11—41no—
230C4⋊Dic11—41no—
231#4318—24no—
232C2×C11⋊C8—22no—
233C2×C11⋊C8—22no—
234C2×C11⋊C8—22no—
235C2×C11⋊C8—42no—
236#3520D1111yescharacteristic
237#3239—111no—
238#3165—111no—
239C2×#461—111no—
240#1654—112no—
241#1651—112no—
242#1650—112no—
243#1647—112no—
244#1552—111no—
245#1490—111no—
246#1483—111no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11—42no—
251C23×C11—42no—
252C23×C11—81no—
253C23×C11#12011yescharacteristic
254Q8×C11—22no—
255Q8×C11—41no—
256Q8×C11—41no—
257Q8×C11—42no—
258Q8×C11—82no—
259D4×C11—21no—
260D4×C11—21no—
261D4×C11—21no—
262D4×C11—22no—
263D4×C11—42no—
264D4×C11—44no—
265D4×C11—42no—
266D4×C11—82no—
267D4×C11AGL(1,ℤ/8)12yes—
268C2×C4×C11—22no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—22no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—44no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—81no—
285C2×C4×C11—81no—
286C2×C4×C11—81no—
287C2×C4×C11—82no—
288C2×C4×C11—82no—
289C2×C4×C11#12011yescharacteristic
290C2×C4×C11#12011yescharacteristic
291C2×C4×C11#12011yescharacteristic
292C2×C4×C11C22×D411yescharacteristic
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×Dic11—42no—
296C2×Dic11—82no—
297Dic22—42no—
298Dic22—42no—
299Dic22—82no—
300C11⋊C8—24no—
301C11⋊C8—42no—
302C11⋊C8—42no—
303C22×SD16—221no—
304#556C2×D1111yescharacteristic
305#554—21no—
306#552—21no—
307#551—22no—
308D4×Q8C2×D1111yescharacteristic
309#548—21no—
310#547C2×D1111yescharacteristic
311#547C2×D1111yescharacteristic
312#546—21no—
313#542—21no—
314#539—22no—
315#533C2×D1111yescharacteristic
316C2×C4⋊Q8—111no—
317#529C2×D1111yescharacteristic
318#525—21no—
319C2×C22⋊Q8—21no—
320#520—21no—
321C2×C4×D4C2×D1111yescharacteristic
322#501—222no—
323#501—221no—
324#500—112no—
325#498—112no—
326#489—221no—
327#484—221no—
328#481—221no—
329#475—112no—
330#474—112no—
331#461—112no—
332#461—112no—
333#461—221no—
334#461—221no—
335#432—111no—
336#428—222no—
337C2×C4⋊C8—111no—
338C2×#103—221no—
339C4×M16—111no—
340#332—112no—
341#332—112no—
342Q8⋊C8—112no—
343D4⋊C8—112no—
344D4⋊C8—112no—
345D4⋊C8—112no—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—84no—
358C22×C11#45612yes—
359C22×C11C2×#12011yescharacteristic
360C4×C11—21no—
361C4×C11—21no—
362C4×C11—21no—
363C4×C11—21no—
364C4×C11—41no—
365C4×C11—42no—
366C4×C11—41no—
367C4×C11—41no—
368C4×C11—42no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
372C4×C11#57511yescharacteristic
373C4×C11#57712yes—
374Dic11—82no—
375C2×#41—21no—
376C2×#41—21no—
377C22×Q8—21no—
378C22×Q8—221no—
379C22×D4C22⋊D1111yescharacteristic
380C23×C4—21no—
381C2×SD16—222no—
382C2×SD16—222no—
383C2×SD16—444no—
384C2×M16—221no—
385C22×C8—221no—
386C4⋊Q8—21no—
387C4⋊Q8—112no—
388C4⋊Q8—221no—
389C4⋊Q8—221no—
390C4⋊Q8—221no—
391C4⋊Q8C22×D1111yescharacteristic
392C4⋊Q8C22×D1111yescharacteristic
393#126—22no—
394#126—22no—
395#126—21no—
396#125—22no—
397#125C22⋊D1111yescharacteristic
398#125C22⋊D1112yes—
399#124—22no—
400#124—21no—
401#124C22⋊D1111yescharacteristic
402#123—22no—
403#123—22no—
404#123—21no—
405#123—22no—
406#123—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—22no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—21no—
414C22⋊Q8—21no—
415C22⋊Q8—22no—
416C22⋊Q8—21no—
417C22⋊Q8C22⋊D1111yescharacteristic
418#121—22no—
419#121—21no—
420#121—21no—
421#121C22⋊D1111yescharacteristic
422#120—22no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8C22×D1111yescharacteristic
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4—21no—
434C4×D4C22⋊D1111yescharacteristic
435C4×D4C22⋊D1111yescharacteristic
436C4×D4C22×D1111yescharacteristic
437C4×D4C22×D1111yescharacteristic
438C4×D4C22×D1111yescharacteristic
439#117—22no—
440#117—21no—
441#117—21no—
442#117C22⋊D1112yes—
443C2×C4⋊C4—22no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—221no—
447C2×C4⋊C4—221no—
448C2×C4⋊C4C22⋊D1111yescharacteristic
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C42C22×D1111yescharacteristic
452#107—224no—
453#107—222no—
454#106—224no—
455#106—222no—
456C4⋊C8—112no—
457C4⋊C8—112no—
458C4⋊C8—221no—
459#103—222no—
460#103—222no—
461#103—222no—
462#102—222no—
463C22⋊C8—221no—
464#97—221no—
465#97—221no—
466C4×C8—112no—
467C2×C11—22no—
468C2×C11—42no—
469C2×C11—81no—
470C2×C11—81no—
471C2×C11#300611yescharacteristic
472C2×C11#300911yescharacteristic
473C2×C11C2×#45611yescharacteristic
474C24—21no—
475#41—42no—
476#41—42no—
477#41—82no—
478C2×Q8—22no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—82no—
482C2×Q8—222no—
483C2×Q8—442no—
484C2×Q8—442no—
485C2×Q8—441no—
486C2×Q8C2×C22⋊D1111yescharacteristic
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—41no—
493C2×D4C2×C22⋊D1111yescharacteristic
494C2×D4C2×C22⋊D1111yescharacteristic
495C2×D4C2×C22⋊D1111yescharacteristic
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—82no—
506C22×C4—441no—
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C2×C22⋊D1111yescharacteristic
510SD16—444no—
511SD16—444no—
512M16—224no—
513C2×C8—222no—
514C2×C8—222no—
515C2×C8—222no—
516C2×C8—442no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—22no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—22no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—22no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—222no—
531C4⋊C4—222no—
532C4⋊C4—441no—
533C4⋊C4—441no—
534C4⋊C4C2×C22⋊D1111yescharacteristic
535C4⋊C4C2×C22⋊D1111yescharacteristic
536C4⋊C4C2×C22⋊D1111yescharacteristic
537C4⋊C4C2×C22⋊D1112yes—
538C4⋊C4C2×C22⋊D1111yescharacteristic
539C4⋊C4C2×C22⋊D1112yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—22no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—21no—
550C22⋊C4—21no—
551C22⋊C4—21no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—21no—
555C42—22no—
556C42—22no—
557C42—21no—
558C42C2×C22⋊D1111yescharacteristic
559C42C2×C22⋊D1111yescharacteristic
560C42C2×C22⋊D1111yescharacteristic
561C42C23×D1111yescharacteristic
562C11#1858611yescharacteristic, complemented, Sylow
563C23—21no—
564C23—21no—
565C23—21no—
566C23—42no—
567C23—42no—
568C23—81no—
569C23#6700611yescharacteristic
570Q8—22no—
571Q8—41no—
572Q8—41no—
573Q8—42no—
574Q8—82no—
575Q8—442no—
576Q8—442no—
577Q8—882no—
578D4—21no—
579D4—21no—
580D4—21no—
581D4—22no—
582D4—42no—
583D4—44no—
584D4—42no—
585D4—82no—
586D4#6700212yes—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—44no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—81no—
604C2×C4—81no—
605C2×C4—81no—
606C2×C4—82no—
607C2×C4—82no—
608C2×C4—442no—
609C2×C4—882no—
610C2×C4#6700611yescharacteristic
611C2×C4#6700611yescharacteristic
612C2×C4#6700611yescharacteristic
613C2×C4C22×C22⋊D1111yescharacteristic
614C2×C4C22×C22⋊D1111yescharacteristic
615C2×C4C22×C22⋊D1111yescharacteristic
616C8—224no—
617C8—442no—
618C8—442no—
619C22—21no—
620C22—21no—
621C22—22no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—84no—
631C22#1062285912yes—
632C22C2×#6700611yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—882no—
645C4C2×#6700211yescharacteristic
646C4#1062335311yescharacteristic
647C4#1062336712yes—
648C2—22no—
649C2—42no—
650C2—81no—
651C2—81no—
652C2#1307786811yescharacteristic
653C2#1307789311yescharacteristic
654C2C2×#1062285911yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC11×#3520C2
socleC22×C11C2×#120
hypercenter#3520D11
hypocenterC11#18586
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3520

Complements

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

NH ≅ G/Ntype
1. #13079843C2semidirect
2. #13079163C2semidirect
3. C2×#10622632C2semidirect
4. #13067900C2semidirect
5. #13067879C2semidirect
6. #13067872C2semidirect
7. #13067851C2semidirect
8. #13067316C2semidirect
9. #13067059C2semidirect
10. #13067029C2semidirect
31. #10622692C22semidirect
32. #10622691C22semidirect
38. #10622633C22semidirect
43. #10622620C22semidirect
49. #10622185C22semidirect
50. #10622185C22semidirect
51. Q8⋊(C11⋊C8)C22semidirect
54. D4⋊(C11⋊C8)C22semidirect
562. C11#18586semidirect

Maximal subgroups

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

subgroupindex
#130798432
#130791632
C2×#106226322
#130679002
#130678792
#130678722
#130678512
#130673162
#130670592
#130670292
C11×#35202
#1858611