Finite Group Databasebeta

← #14759432

Subgroups — #14759432

Order 2816.

1868 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622659C211yesmaximal, characteristic
3C2×#10622430C212yesmaximal, complemented
4C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
5#13068947C212yesmaximal, complemented
6#13068864C212yesmaximal, complemented
7#13068804C211yesmaximal, characteristic, complemented
8#13068548C211yesmaximal, characteristic
9#13068440C212yesmaximal, complemented
10#13068380C211yesmaximal, characteristic, complemented
11C11×#1872C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11—21no—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×Q8×Dic11C2211yescharacteristic, complemented
17C22×#4325C2212yes—
18C22×(C2×D11)⋊C4—21no—
19C22×C4×Dic11C2211yescharacteristic
20C2×#66946—21no—
21C2×#66946—21no—
22C2×#66946—28no—
23C2×#66946C2212yes—
24C2×#66946C2212yes—
25C2×C11×#103C2212yescomplemented
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622843C2211yescharacteristic, complemented
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×#66885C2212yes—
31C2×#66885C2212yes—
32C2×#66879C2212yescomplemented
33#10622659C418yescomplemented
34#10622598C2211yescharacteristic, complemented
35#10622594—21no—
36C4⋊C4×Dic11—21no—
37C4⋊C4×Dic11C2211yescharacteristic, complemented
38C2×#66873C2212yes—
39C2×#66871C2212yescomplemented
40#10622563—21no—
41C22⋊C4×Dic11—21no—
42#10622430—28no—
43C11×#340C2212yescomplemented
44#10622188C2212yescomplemented
45#10622167C2212yescomplemented
46C24×D11—21no—
47C22×Q8×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11D411yescharacteristic
51C23×Dic11D411yescharacteristic
52C22×D44—21no—
53C22×D44—22no—
54C22×D44—24no—
55C22×D44—24no—
56C22×D44C2×C414yes—
57C22×D44C2312yes—
58C22×C4×D11—28no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—44no—
62C22×C4×D11—44no—
63C22×C8×C11C2312yes—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8C2×C414yescomplemented
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2312yes—
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73Q8×Dic11—24no—
74C2×#4325—24no—
75C2×#4325—24no—
76C2×#4325C2×C418yescomplemented
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4×Dic11—24no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2312yes—
92#66946—28no—
93#66946—28no—
94#66946—24no—
95#66946—24no—
96#66946—24no—
97#66946D418yes—
98C11×#103—24no—
99C11×C22⋊C8—22no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C22⋊(C11⋊C8)C2×C414yescomplemented
106#66885—24no—
107#66885—24no—
108#66879—24no—
109#66873C2×C418yescomplemented
110#66871—24no—
111#21453—111nomaximal, Sylow
112C24×C11C2×D411yescharacteristic
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—22no—
117C23×D11—42no—
118C23×D11—42no—
119C23×D11—42no—
120C23×D11—42no—
121C2×Q8×C11—21no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11C22×C412yescomplemented
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11#4112yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—41no—
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C2×D44—24no—
150C2×D44—24no—
151C2×D44—216no—
152C2×D44—216no—
153C2×D44—24no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44C22×C414yes—
158C2×D44C2×D414yes—
159C2×D44#4114yes—
160C2×C4×D11—28no—
161C2×C4×D11—28no—
162C2×C4×D11—432no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11—44no—
166C2×C4×D11—44no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4C22×C412yescomplemented
175C11×C4⋊C4C2×D414yes—
176C11×C22⋊C4—24no—
177C22⋊Dic11—42no—
178#4325—216no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181C4⋊Dic11—22no—
182C4⋊Dic11—22no—
183C4⋊Dic11—42no—
184C4⋊Dic11—42no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C4×Dic11—42no—
189C4×Dic11—42no—
190C4×Dic11C2×D414yes—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C22×C414yescomplemented
194C22×C4×D4—111no—
195C2×#450—111no—
196C2×#440—112no—
197C4×C22⋊Q8—111no—
198#1877—112no—
199#1872D1111yescharacteristic, complemented
200#1862—112no—
201#1852—111no—
202#1786—111no—
203#1762—112no—
204#1749—111no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11C4×D412yes—
210C23×C11AGL(1,ℤ/8)12yes—
211C23×C11#13712yes—
212C23×C11C22×D411yescharacteristic
213C22×D11—216no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—48no—
218C22×D11—48no—
219C22×D11—48no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—48no—
227Q8×C11—24no—
228Q8×C11—42no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—48no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11C4×D412yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4112yes—
248C2×Dic11—28no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—44no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11#12012yes—
266C2×Dic11#12012yes—
267C2×Dic11AGL(1,ℤ/8)12yes—
268D44—216no—
269D44—24no—
270D44—24no—
271D44—24no—
272D44C4×D418yes—
273C4×D11—416no—
274C4×D11—416no—
275C8×C11—42no—
276C11⋊C8—24no—
277C23×D4—111no—
278C24×C4—221no—
279C22×SD16—112no—
280C2×C22⋊Q8C2×D1111yescharacteristic
281C2×C4×Q8—111no—
282C2×C4×D4—112no—
283C2×C4×D4—112no—
284C2×C4×D4—221no—
285C2×C4×D4—221no—
286C2×C4×D4—228no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C22⋊C4—221no—
289C22×C42—111no—
290#450—118no—
291#440—228no—
292C2×#107—112no—
293C2×#103C2×D1112yescomplemented
294C2×#102—112no—
295C2×#102—112no—
296C2×#102—112no—
297C2×C22⋊C8—111no—
298C2×C22⋊C8C2×D1111yescharacteristic
299C2×#97—112no—
300#391—111no—
301#389—111no—
302#387—221no—
303#385—221no—
304#380—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—221no—
307C4×C22⋊C4—221no—
308#340—112no—
309#340C2×D1112yescomplemented
310#336—112no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11#44014yescomplemented
318C22×C11C2×C4×D411yescharacteristic
319C22×C11C2×#12011yescharacteristic
320C22×C11#52511yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11#57511yescharacteristic
325C2×D11—28no—
326C2×D11—432no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11C2×C4×D412yes—
338C4×C11#52512yes—
339Dic11—22no—
340Dic11—22no—
341Dic11—22no—
342Dic11—41no—
343Dic11—81no—
344Dic11—81no—
345C25—221no—
346C22×Q8C22×D1111yescharacteristic
347C22×D4—114no—
348C22×D4—112no—
349C22×D4—224no—
350C22×D4—224no—
351C22×D4—221no—
352C22×D4—222no—
353C23×C4—21no—
354C23×C4—111no—
355C23×C4—111no—
356C23×C4—222no—
357C23×C4—222no—
358C23×C4—228no—
359C23×C4—444no—
360C23×C4—444no—
361C23×C4C22×D1111yescharacteristic
362C2×SD16—118no—
363C2×SD16—224no—
364C2×SD16—224no—
365C22×C8—112no—
366C22×C8C22×D1112yes—
367C22⋊Q8—22no—
368C22⋊Q8C4×D1114yescomplemented
369C4×Q8—224no—
370C4×D4—118no—
371C4×D4—224no—
372C4×D4—224no—
373C4×D4—228no—
374C4×D4—228no—
375C4×D4—224no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—24no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1112yes—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C22⋊C4—228no—
389C2×C22⋊C4—221no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—224no—
395C2×C42—221no—
396C2×C42—221no—
397#107—224no—
398#103—24no—
399#102—118no—
400#102—224no—
401#102—224no—
402C22⋊C8—22no—
403C22⋊C8—114no—
404#97—224no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410C2×C11—24no—
411C2×C11C4×#12011yescharacteristic
412C2×C11C2×#44011yescharacteristic
413C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
414C2×C11#300311yescharacteristic
415C2×C11#300711yescharacteristic
416C2×C11#311011yescharacteristic
417C2×C11#311411yescharacteristic
418D11—48no—
419C24—224no—
420C24—224no—
421C24—224no—
422C24—222no—
423C24—442no—
424C24—442no—
425C24—442no—
426C24—442no—
427C24D4×D1111yescharacteristic
428C2×Q8—21no—
429C2×Q8—22no—
430C2×Q8—22no—
431C2×Q8C2×C4×D1112yescomplemented
432C2×D4—114no—
433C2×D4—114no—
434C2×D4—114no—
435C2×D4—2216no—
436C2×D4—224no—
437C2×D4—224no—
438C2×D4—2216no—
439C2×D4—224no—
440C2×D4—222no—
441C2×D4—222no—
442C2×D4—222no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—24no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—228no—
456C22×C4—228no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—444no—
465C22×C4—4432no—
466C22×C4—444no—
467C22×C4—444no—
468C22×C4—444no—
469C22×C4—441no—
470C22×C4C2×C4×D1112yes—
471C22×C4D4×D1111yescharacteristic
472C22×C4#434112yes—
473C22×C4C23×D1111yescharacteristic
474SD16—2216no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—114no—
479C2×C8—222no—
480C2×C8—222no—
481C4⋊C4—24no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—222no—
486C4⋊C4—222no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4C2×C4×D1112yescomplemented
490C4⋊C4D4×D1114yes—
491C22⋊C4—24no—
492C22⋊C4—228no—
493C22⋊C4—228no—
494C22⋊C4—442no—
495C42—114no—
496C42—222no—
497C42—222no—
498C42—222no—
499C42—442no—
500C42—442no—
501C11#2145311yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—2216no—
507C23—224no—
508C23—224no—
509C23—224no—
510C23—448no—
511C23—448no—
512C23—448no—
513C23—448no—
514C23—448no—
515C23—442no—
516C23—442no—
517C23—442no—
518C23—442no—
519C23—448no—
520C23(C22⋊D11)⋊C412yes—
521C23#6696712yes—
522C23#6697112yes—
523C23C2×D4×D1111yescharacteristic
524Q8—24no—
525Q8—42no—
526D4—118no—
527D4—2216no—
528D4—224no—
529D4—224no—
530D4—224no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—228no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—4416no—
559C2×C4—4416no—
560C2×C4—444no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4(C22⋊D11)⋊C412yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×D4×D1112yes—
570C2×C4C2×#434111yescharacteristic
571C2×C4#41×D1112yes—
572C8—42no—
573C8—224no—
574C22—22no—
575C22—22no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—22no—
580C22—228no—
581C22—4432no—
582C22—444no—
583C22—444no—
584C22—444no—
585C22—444no—
586C22—444no—
587C22—444no—
588C22#1062243014yescomplemented
589C22C2×(C22⋊D11)⋊C411yescharacteristic
590C22D11×#12011yescharacteristic
591C22#1062318711yescharacteristic
592C22C2×#6696711yescharacteristic
593C22C2×#6697111yescharacteristic
594C22D11×AGL(1,ℤ/8)11yescharacteristic
595C22#1062330811yescharacteristic
596C4—22no—
597C4—42no—
598C4—44no—
599C4—42no—
600C4—222no—
601C4—222no—
602C4—222no—
603C4—441no—
604C4—881no—
605C4—881no—
606C4C4×D4×D1112yes—
607C4#1062313712yes—
608C2—24no—
609C2—448no—
610C2#1307112111yescharacteristic
611C2C2×#1062243011yescharacteristic
612C2#1307742911yescharacteristic
613C2#1307784411yescharacteristic
614C2#1307787511yescharacteristic
615C2#1307871211yescharacteristic
616C2#1307875711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#21453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
3. C2×#10622430C2semidirect
4. C22⋊Q8×Dic11C2semidirect
5. #13068947C2semidirect
6. #13068864C2semidirect
7. #13068804C2semidirect
9. #13068440C2semidirect
10. #13068380C2semidirect
11. C11×#1872C2semidirect
16. C2×Q8×Dic11C22semidirect
25. C2×C11×#103C22semidirect
27. #10622843C22semidirect
32. C2×#66879C22semidirect
33. #10622659C4semidirect
34. #10622598C22semidirect
37. C4⋊C4×Dic11C22semidirect
39. C2×#66871C22semidirect
43. C11×#340C22semidirect
44. #10622188C22semidirect
45. #10622167C22semidirect
65. C11×C22⋊Q8C2×C4semidirect
76. C2×#4325C2×C4semidirect
105. C22⋊(C11⋊C8)C2×C4semidirect
109. #66873C2×C4semidirect
124. C2×Q8×C11C22×C4semidirect
174. C11×C4⋊C4C22×C4semidirect
193. C2×C11⋊C8C22×C4semidirect
199. #1872D11semidirect
293. C2×#103C2×D11semidirect
309. #340C2×D11semidirect
317. C22×C11#440semidirect
368. C22⋊Q8C4×D11semidirect
431. C2×Q8C2×C4×D11semidirect
489. C4⋊C4C2×C4×D11semidirect
501. C11#21453semidirect
588. C22#10622430semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106226592
C2×#106224302
C22⋊Q8×Dic112
#130689472
#130688642
#130688042
#130685482
#130684402
#130683802
C11×#18722
#2145311