Finite Group Databasebeta

← #14727976

Subgroups — #14727976

Order 2816.

1192 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079418C211yesmaximal, characteristic, complemented
2#13079413C211yesmaximal, characteristic, complemented
3#13073547C211yesmaximal, characteristic, complemented
4#13067664C214yesmaximal, complemented
5#13067562C214yesmaximal, complemented
6#13067136C211yesmaximal, characteristic, complemented
7#13067132C211yesmaximal, characteristic, complemented
8#13066943C211yesmaximal, characteristic, complemented
9C2×C11×#538C211yesmaximal, characteristic, complemented
10C11×#538—22no—
11C11×#538—22no—
12C11×#538—22no—
13C11×#538C2214yes—
14C2×C11×#126—21no—
15C2×C11×#124—21no—
16C2×C11×#123—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121—21no—
19C2×C11×#121C2211yescharacteristic
20C2×C11×#120—21no—
21C2×C4×D4×C11—21no—
22C22×C11×C22⋊C4C2211yescharacteristic
23C2×#67006—21no—
24C2×#66983C2211yescharacteristic
25C2×#66982—21no—
26#10622840—21no—
27#10622830—21no—
28C4×C22⋊Dic11C2211yescharacteristic
29#10622820C2211yescharacteristic
30#10622820C2211yescharacteristic
31#10622662—22no—
32#10622659C2212yescomplemented
33#10622657C2212yescomplemented
34#10622652—22no—
35#10622649C2212yescomplemented
36#10622647C2212yescomplemented
37#10622581—21no—
38#10622580—21no—
39#10622573C2212yescomplemented
40#10622570—22no—
41#10622562C2212yescomplemented
42#10622176C2214yescomplemented
43#10622175C2214yescomplemented
44#10622163C2214yescomplemented
45C25×C11D411yescharacteristic
46C22×Q8×C11D411yescharacteristic, complemented
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11D411yescharacteristic, complemented
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C22×C22⋊D11—22no—
56C22×D44C2311yescharacteristic
57C11×#126—24no—
58C11×#126—24no—
59C11×#124—24no—
60C11×#124—24no—
61C11×#123—24no—
62C11×#123—24no—
63C11×C22⋊Q8—21no—
64C11×C22⋊Q8—21no—
65C11×C22⋊Q8D412yescomplemented
66C11×C22⋊Q8C2312yes—
67C11×#121—24no—
68C11×#121—24no—
69C11×#121—21no—
70C11×#121—21no—
71C11×#121D412yescomplemented
72C11×#121C2312yes—
73C11×#120—24no—
74C11×#120—24no—
75C4×D4×C11—24no—
76C4×D4×C11—24no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic, complemented
80C2×C11×C4⋊C4D411yescharacteristic, complemented
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4—21no—
90C2×C11×C22⋊C4D412yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C42×C11—21no—
93#67006—44no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—22no—
96C2×#4325—22no—
97C2×#4323—22no—
98#66983—21no—
99#66983—21no—
100#66983—21no—
101#66983—21no—
102#66982—44no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—22no—
107C2×C4×Dic11—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110#66899—22no—
111#66896—22no—
112C11⋊#95C2312yes—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115C22⋊(C11⋊C8)C2312yes—
116C22⋊(C11⋊C8)C2312yes—
117#66873—22no—
118#66873—22no—
119#66872—22no—
120#66871—22no—
121#18328—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—42no—
126C24×C11—42no—
127C24×C11—81no—
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D412yes—
130C23×D11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—81no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—44no—
140C2×D4×C11—81no—
141C2×D4×C11—82no—
142C2×D4×C11—82no—
143C2×D4×C11C2×D412yes—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11—82no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—42no—
161C2×C22⋊D11—42no—
162C2×C22⋊D11—44no—
163C2×C22⋊D11—44no—
164C2×C22⋊D11—41no—
165C2×C22⋊D11—41no—
166C2×C22⋊D11—82no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—81no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4C2×D412yes—
178C11×C4⋊C4C2×D412yes—
179C11×C22⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—22no—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—22no—
188C11×C22⋊C4—22no—
189C11×C22⋊C4—22no—
190C42×C11—24no—
191C22⋊Dic11—24no—
192C22⋊Dic11—44no—
193#4325—82no—
194#4323—82no—
195(C2×D11)⋊C4—44no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—41no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200Dic11⋊C4—44no—
201C4×Dic11—81no—
202#4318—81no—
203#4318—81no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×#538D1111yescharacteristic, complemented
207#3193—111no—
208#3192—111no—
209#2539—111no—
210#1618—114no—
211#1600—114no—
212#1508—111no—
213#1507—111no—
214#1462—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11—42no—
230C23×C11—42no—
231C23×C11—81no—
232C23×C11—81no—
233C23×C11—88no—
234C23×C11#12011yescharacteristic
235C23×C11#12011yescharacteristic
236C23×C11C22×D411yescharacteristic
237C22×D11—41no—
238C22×D11—42no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—42no—
242Q8×C11—42no—
243Q8×C11—81no—
244D4×C11—42no—
245D4×C11—44no—
246D4×C11—44no—
247D4×C11—81no—
248D4×C11—84no—
249D4×C11—84no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—81no—
266C2×C4×C11—84no—
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C22⋊D11—88no—
272C22⋊D11—82no—
273C22⋊D11—82no—
274C2×Dic11—24no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280D44—42no—
281D44—42no—
282C11⋊C8—42no—
283C11⋊C8—42no—
284#538—22no—
285#538—22no—
286#538—22no—
287#538C2×D1114yes—
288C2×#126—21no—
289C2×#124—21no—
290C2×#123—21no—
291C2×#123—221no—
292C2×C22⋊Q8C2×D1111yescharacteristic
293C2×#121—21no—
294C2×#121—111no—
295C2×#121C2×D1111yescharacteristic
296C2×#120—21no—
297C2×#120—221no—
298C2×C4×D4—21no—
299C22×C22⋊C4C2×D1111yescharacteristic
300#484—112no—
301#481—112no—
302#481—221no—
303#480—221no—
304#469—222no—
305#468—222no—
306#450—112no—
307#448—221no—
308#447—112no—
309#447—221no—
310#407—111no—
311#407—111no—
312#399—112no—
313#392—112no—
314#390—222no—
315C4×C22⋊C4—111no—
316#328—114no—
317#327—114no—
318#323—114no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—82no—
335C22×C11—84no—
336C22×C11—84no—
337C22×C11—84no—
338C22×C11#45312yes—
339C22×C11C2×#12011yescharacteristic
340C22×C11#57512yes—
341C2×D11—82no—
342C2×D11—82no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C4×C11—21no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—21no—
350C4×C11—42no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—42no—
354Dic11—44no—
355Dic11—81no—
356C25C22⋊D1111yescharacteristic
357C22×Q8C22⋊D1111yescharacteristic, complemented
358C22×D4—21no—
359C22×D4—21no—
360C22×D4—21no—
361C22×D4—111no—
362C22×D4—221no—
363C22×D4—222no—
364C22×D4C22⋊D1111yescharacteristic, complemented
365C23×C4—21no—
366C23×C4C22⋊D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C2×SD16—222no—
369C2×D8—222no—
370C2×M16—221no—
371C2×M16—221no—
372#126—24no—
373#126—24no—
374#124—24no—
375#124—24no—
376#123—24no—
377#123—24no—
378#123—444no—
379C22⋊Q8—21no—
380C22⋊Q8—21no—
381C22⋊Q8C22⋊D1112yescomplemented
382C22⋊Q8C22×D1112yes—
383#121—24no—
384#121—24no—
385#121—21no—
386#121—21no—
387#121—221no—
388#121—221no—
389#121—221no—
390#121—221no—
391#121C22⋊D1112yescomplemented
392#121C22×D1112yes—
393#120—24no—
394#120—24no—
395#120—444no—
396C4×D4—24no—
397C4×D4—24no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
403C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—222no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—222no—
417C2×C22⋊C4C22⋊D1112yes—
418C2×C22⋊C4C22×D1112yes—
419C2×C42—21no—
420C2×C42—221no—
421#107—222no—
422#106—222no—
423#103—222no—
424#102—222no—
425#102—222no—
426#102—222no—
427C22⋊C8—112no—
428C22⋊C8—112no—
429C22⋊C8—221no—
430C22⋊C8—221no—
431#95—112no—
432C2×C11—22no—
433C2×C11—22no—
434C2×C11—41no—
435C2×C11—82no—
436C2×C11—82no—
437C2×C11#300511yescharacteristic
438C2×C11C2×#45311yescharacteristic
439C2×C11#302611yescharacteristic
440D11—161no—
441C24—21no—
442C24—21no—
443C24—21no—
444C24—42no—
445C24—42no—
446C24—81no—
447C24—221no—
448C24C2×C22⋊D1111yescharacteristic
449C24C2×C22⋊D1112yes—
450C2×Q8—21no—
451C2×Q8—81no—
452C2×Q8C2×C22⋊D1112yes—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—21no—
458C2×D4—44no—
459C2×D4—81no—
460C2×D4—82no—
461C2×D4—82no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—444no—
465C2×D4—442no—
466C2×D4—442no—
467C2×D4—444no—
468C2×D4—441no—
469C2×D4—441no—
470C2×D4—881no—
471C2×D4—882no—
472C2×D4C2×C22⋊D1112yes—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—24no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—82no—
482C22×C4—222no—
483C22×C4—221no—
484C22×C4C2×C22⋊D1112yes—
485C22×C4C2×C22⋊D1111yescharacteristic
486C22×C4C2×C22⋊D1111yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C22×C4C2×C22⋊D1111yescharacteristic
489C22×C4C2×C22⋊D1111yescharacteristic
490C22×C4C23×D1111yescharacteristic
491SD16—882no—
492D8—882no—
493M16—881no—
494M16—881no—
495C2×C8—222no—
496C2×C8—222no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—22no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—444no—
505C4⋊C4C2×C22⋊D1112yes—
506C4⋊C4C2×C22⋊D1112yes—
507C22⋊C4—24no—
508C22⋊C4—24no—
509C22⋊C4—24no—
510C22⋊C4—22no—
511C22⋊C4—22no—
512C22⋊C4—22no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—22no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—224no—
519C22⋊C4—444no—
520C22⋊C4—444no—
521C22⋊C4—441no—
522C22⋊C4—441no—
523C42—24no—
524C42—881no—
525C11#1832811yescharacteristic, complemented, Sylow
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—22no—
532C23—41no—
533C23—42no—
534C23—42no—
535C23—42no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—81no—
543C23—81no—
544C23—88no—
545C23—441no—
546C23—441no—
547C23—442no—
548C23—442no—
549C23—441no—
550C23#6700611yescharacteristic
551C23#6700611yescharacteristic
552C23C22×C22⋊D1111yescharacteristic
553Q8—42no—
554Q8—81no—
555D4—42no—
556D4—44no—
557D4—44no—
558D4—81no—
559D4—84no—
560D4—84no—
561D4—442no—
562D4—442no—
563D4—888no—
564D4—882no—
565D4—882no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—81no—
582C2×C4—84no—
583C2×C4—224no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4#6700611yescharacteristic
590C2×C4#6700611yescharacteristic
591C2×C4C22×C22⋊D1111yescharacteristic
592C2×C4C22×C22⋊D1111yescharacteristic
593C8—442no—
594C8—442no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—44no—
603C22—44no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—82no—
611C22—84no—
612C22—84no—
613C22—84no—
614C22—882no—
615C22—882no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22#1062285412yes—
620C22#1062335312yes—
621C22C2×#6700611yescharacteristic
622C4—21no—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—444no—
631C4—881no—
632C2—22no—
633C2—22no—
634C2—41no—
635C2—82no—
636C2—82no—
637C2—1761no—
638C2#1307785811yescharacteristic
639C2C2×#1062285411yescharacteristic
640C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#538C2
socleC22×C11C2×#120
hypercenterC2×#538D11
hypocenterC11#18328
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. #13079418C2semidirect
2. #13079413C2semidirect
3. #13073547C2semidirect
4. #13067664C2semidirect
5. #13067562C2semidirect
6. #13067136C2semidirect
7. #13067132C2semidirect
8. #13066943C2semidirect
9. C2×C11×#538C2semidirect
32. #10622659C22semidirect
33. #10622657C22semidirect
35. #10622649C22semidirect
36. #10622647C22semidirect
39. #10622573C22semidirect
41. #10622562C22semidirect
42. #10622176C22semidirect
43. #10622175C22semidirect
44. #10622163C22semidirect
46. C22×Q8×C11D4semidirect
50. C22×D4×C11D4semidirect
65. C11×C22⋊Q8D4semidirect
71. C11×#121D4semidirect
79. C2×C11×C4⋊C4D4semidirect
80. C2×C11×C4⋊C4D4semidirect
206. C2×#538D11semidirect
357. C22×Q8C22⋊D11semidirect
364. C22×D4C22⋊D11semidirect
381. C22⋊Q8C22⋊D11semidirect
391. #121C22⋊D11semidirect
402. C2×C4⋊C4C22⋊D11semidirect
403. C2×C4⋊C4C22⋊D11semidirect
525. C11#18328semidirect

Maximal subgroups

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

subgroupindex
#130794182
#130794132
#130735472
#130676642
#130675622
#130671362
#130671322
#130669432
C2×C11×#5382
#1832811