Finite Group Databasebeta

← #14727704

Subgroups — #14727704

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079369C211yesmaximal, characteristic, complemented
2#13079364C211yesmaximal, characteristic, complemented
3#13074350C211yesmaximal, characteristic, complemented
4#13067630C214yesmaximal, complemented
5#13067562C214yesmaximal, complemented
6#13067188C211yesmaximal, characteristic, complemented
7#13067184C211yesmaximal, characteristic, complemented
8C2×#10622163C211yesmaximal, 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
25#10622840—21no—
26#10622830—21no—
27#10622826—21no—
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622661—22no—
32#10622659C2212yescomplemented
33#10622656C2212yescomplemented
34#10622651—22no—
35#10622649C2212yescomplemented
36#10622646C2212yescomplemented
37#10622581—21no—
38#10622580—21no—
39#10622574—22no—
40#10622573C2212yescomplemented
41#10622566C2212yescomplemented
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—22no—
95C2×C22⋊Dic11—21no—
96C2×#4325—22no—
97C2×#4323—22no—
98#66983—21no—
99#66983—21no—
100#66983—21no—
101#66983—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2311yescharacteristic
106C22×C11⋊C8—21no—
107C22×C11⋊C8—21no—
108#66899—22no—
109#66896—22no—
110C11⋊#95—22no—
111C11⋊#95C2312yes—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)C2312yes—
115C22⋊(C11⋊C8)C2312yes—
116#66873—22no—
117#66873—22no—
118#66872—22no—
119#66871—22no—
120#18296—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—81no—
127C24×C11—81no—
128C24×C11C2×D412yes—
129C24×C11C2×D411yescharacteristic
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—42no—
140C2×D4×C11—42no—
141C2×D4×C11—81no—
142C2×D4×C11—82no—
143C2×D4×C11—82no—
144C2×D4×C11C2×D412yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—24no—
150C22×C4×C11—21no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11—82no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—44no—
162C2×C22⋊D11—41no—
163C2×C22⋊D11—41no—
164C2×C22⋊D11—42no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—82no—
167C2×C22⋊D11—82no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—81no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C2×D412yes—
179C11×C4⋊C4C2×D412yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—24no—
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—
190C11×C22⋊C4—22no—
191C42×C11—24no—
192C22⋊Dic11—44no—
193C22⋊Dic11—42no—
194#4325—82no—
195#4323—82no—
196(C2×D11)⋊C4—41no—
197(C2×D11)⋊C4—41no—
198(C2×D11)⋊C4—82no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—81no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—81no—
205C2×C11⋊C8—81no—
206C2×#538D1111yescharacteristic, complemented
207#3187—111no—
208#3186—111no—
209#2617—111no—
210#1612—114no—
211#1600—114no—
212#1520—111no—
213#1519—111no—
214C2×#323—111no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—42no—
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—81no—
231C23×C11—81no—
232C23×C11—84no—
233C23×C11—84no—
234C23×C11#12011yescharacteristic
235C23×C11#12011yescharacteristic
236C23×C11#13512yes—
237C23×C11AGL(1,ℤ/8)12yes—
238C23×C11C22×D411yescharacteristic
239C22×D11—42no—
240C22×D11—42no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244Q8×C11—42no—
245Q8×C11—81no—
246D4×C11—42no—
247D4×C11—42no—
248D4×C11—42no—
249D4×C11—44no—
250D4×C11—81no—
251D4×C11—84no—
252D4×C11—84no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—81no—
269C2×C4×C11—84no—
270C2×C4×C11#12011yescharacteristic
271C2×C4×C11#12011yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C22⋊D11—88no—
275C22⋊D11—82no—
276C22⋊D11—82no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—42no—
282C2×Dic11—41no—
283D44—42no—
284D44—42no—
285C11⋊C8—42no—
286C11⋊C8—42no—
287#538—22no—
288#538—22no—
289#538—22no—
290#538C2×D1114yes—
291C2×#126—21no—
292C2×#124—21no—
293C2×#123—21no—
294C2×C22⋊Q8C2×D1111yescharacteristic
295C2×#121—21no—
296C2×#121—111no—
297C2×#121C2×D1111yescharacteristic
298C2×#120—21no—
299C2×#120—221no—
300C2×C4×D4—21no—
301C22×C22⋊C4C2×D1111yescharacteristic
302#483—112no—
303#481—221no—
304#480—112no—
305#480—221no—
306#466—222no—
307#465—222no—
308#450—112no—
309#448—221no—
310#447—112no—
311#447—221no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314#397—112no—
315#394—222no—
316#392—112no—
317#386—221no—
318#380—111no—
319#328—114no—
320#327—114no—
321#323—114no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—21no—
325C22×C11—21no—
326C22×C11—21no—
327C22×C11—21no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—44no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—42no—
336C22×C11—42no—
337C22×C11—82no—
338C22×C11—84no—
339C22×C11—84no—
340C22×C11—84no—
341C22×C11#44912yes—
342C22×C11#44912yes—
343C22×C11C2×#12011yescharacteristic
344C22×C11C2×#13511yescharacteristic
345C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
346C2×D11—82no—
347C2×D11—82no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—42no—
356C4×C11—42no—
357C4×C11—42no—
358C4×C11—42no—
359Dic11—82no—
360Dic11—81no—
361C25C22⋊D1111yescharacteristic
362C22×Q8C22⋊D1111yescharacteristic, complemented
363C22×D4—21no—
364C22×D4—21no—
365C22×D4—21no—
366C22×D4—111no—
367C22×D4—221no—
368C22×D4—222no—
369C22×D4C22⋊D1111yescharacteristic, complemented
370C23×C4—21no—
371C23×C4C22⋊D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C2×SD16—222no—
374C2×D8—222no—
375C22×C8—221no—
376C22×C8—221no—
377#126—24no—
378#126—24no—
379#124—24no—
380#124—24no—
381#123—24no—
382#123—24no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8C22⋊D1112yescomplemented
386C22⋊Q8C22×D1112yes—
387#121—24no—
388#121—24no—
389#121—21no—
390#121—21no—
391#121—221no—
392#121—221no—
393#121—221no—
394#121—221no—
395#121C22⋊D1112yescomplemented
396#121C22×D1112yes—
397#120—24no—
398#120—24no—
399#120—444no—
400C4×D4—24no—
401C4×D4—24no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
407C2×C4⋊C4C22⋊D1111yescharacteristic, complemented
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—221no—
418C2×C22⋊C4—222no—
419C2×C22⋊C4—221no—
420C2×C22⋊C4—222no—
421C2×C22⋊C4C22⋊D1112yes—
422C2×C22⋊C4C22×D1112yes—
423C2×C42—21no—
424#107—222no—
425#106—222no—
426#103—222no—
427#102—222no—
428#102—222no—
429#102—222no—
430C22⋊C8—112no—
431C22⋊C8—112no—
432C22⋊C8—221no—
433C22⋊C8—221no—
434#95—112no—
435#95—222no—
436C2×C11—21no—
437C2×C11—21no—
438C2×C11—22no—
439C2×C11—22no—
440C2×C11—82no—
441C2×C11—82no—
442C2×C11C2×#44911yescharacteristic
443C2×C11#301911yescharacteristic
444C2×C11#302611yescharacteristic
445D11—161no—
446C24—21no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—21no—
451C24—81no—
452C24—81no—
453C24—221no—
454C24C2×C22⋊D1112yes—
455C24C2×C22⋊D1111yescharacteristic
456C2×Q8—21no—
457C2×Q8—81no—
458C2×Q8C2×C22⋊D1112yes—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—24no—
462C2×D4—24no—
463C2×D4—21no—
464C2×D4—42no—
465C2×D4—42no—
466C2×D4—81no—
467C2×D4—82no—
468C2×D4—82no—
469C2×D4—221no—
470C2×D4—221no—
471C2×D4—444no—
472C2×D4—442no—
473C2×D4—442no—
474C2×D4—441no—
475C2×D4—441no—
476C2×D4—881no—
477C2×D4—882no—
478C2×D4—882no—
479C2×D4C2×C22⋊D1112yes—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—81no—
487C22×C4—81no—
488C22×C4—82no—
489C22×C4—222no—
490C22×C4—221no—
491C22×C4C2×C22⋊D1112yes—
492C22×C4C2×C22⋊D1111yescharacteristic
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C2×C22⋊D1111yescharacteristic
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498SD16—882no—
499D8—882no—
500C2×C8—222no—
501C2×C8—222no—
502C2×C8—881no—
503C2×C8—881no—
504C4⋊C4—24no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—22no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—881no—
512C4⋊C4C2×C22⋊D1112yes—
513C4⋊C4C2×C22⋊D1112yes—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—24no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—444no—
526C22⋊C4—442no—
527C22⋊C4—441no—
528C22⋊C4—441no—
529C22⋊C4—882no—
530C42—24no—
531C11#1829611yescharacteristic, complemented, Sylow
532C23—22no—
533C23—22no—
534C23—22no—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—81no—
548C23—81no—
549C23—84no—
550C23—84no—
551C23—442no—
552C23—442no—
553C23—441no—
554C23—441no—
555C23—441no—
556C23#6700212yes—
557C23#6700312yes—
558C23#6700611yescharacteristic
559C23#6700611yescharacteristic
560C23C22×C22⋊D1111yescharacteristic
561Q8—42no—
562Q8—81no—
563D4—42no—
564D4—42no—
565D4—42no—
566D4—44no—
567D4—81no—
568D4—84no—
569D4—84no—
570D4—442no—
571D4—442no—
572D4—888no—
573D4—882no—
574D4—882no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—81no—
591C2×C4—84no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4#6700611yescharacteristic
599C2×C4#6700611yescharacteristic
600C2×C4C22×C22⋊D1111yescharacteristic
601C2×C4C22×C22⋊D1111yescharacteristic
602C8—442no—
603C8—442no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—42no—
611C22—42no—
612C22—44no—
613C22—42no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—82no—
620C22—84no—
621C22—84no—
622C22—84no—
623C22—882no—
624C22—882no—
625C22—881no—
626C22—881no—
627C22—881no—
628C22#1062285112yes—
629C22#1062285112yes—
630C22C2×#6700211yescharacteristic
631C22C2×#6700311yescharacteristic
632C22C2×#6700611yescharacteristic
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—882no—
642C4—881no—
643C2—21no—
644C2—22no—
645C2—21no—
646C2—22no—
647C2—82no—
648C2—82no—
649C2—1761no—
650C2C2×#1062285111yescharacteristic
651C2#1307797311yescharacteristic
652C2#1307801311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#538C2
socleC22×C11C2×#120
hypercenterC2×#538D11
hypocenterC11#18296
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. #13079369C2semidirect
2. #13079364C2semidirect
3. #13074350C2semidirect
4. #13067630C2semidirect
5. #13067562C2semidirect
6. #13067188C2semidirect
7. #13067184C2semidirect
8. C2×#10622163C2semidirect
9. C2×C11×#538C2semidirect
32. #10622659C22semidirect
33. #10622656C22semidirect
35. #10622649C22semidirect
36. #10622646C22semidirect
40. #10622573C22semidirect
41. #10622566C22semidirect
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
362. C22×Q8C22⋊D11semidirect
369. C22×D4C22⋊D11semidirect
385. C22⋊Q8C22⋊D11semidirect
395. #121C22⋊D11semidirect
406. C2×C4⋊C4C22⋊D11semidirect
407. C2×C4⋊C4C22⋊D11semidirect
531. C11#18296semidirect

Maximal subgroups

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

subgroupindex
#130793692
#130793642
#130743502
#130676302
#130675622
#130671882
#130671842
C2×#106221632
C2×C11×#5382
#1829611