Finite Group Databasebeta

← #14788899

Subgroups — #14788899

Order 2816.

1558 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67000C211yesmaximal, characteristic
2C2×#10622798C212yesmaximal, complemented
3C2×#10622659C211yesmaximal, characteristic
4C22⋊Q8×Dic11C211yesmaximal, characteristic, complemented
5#13069854C212yesmaximal, complemented
6#13069707C212yesmaximal, complemented
7#13069545C212yesmaximal, complemented
8#13068594C211yesmaximal, characteristic, complemented
9#13068551C211yesmaximal, characteristic, complemented
10#13068548C211yesmaximal, characteristic
11C2×C11×#451C211yesmaximal, characteristic, complemented
12C23×Q8×C11C2211yescharacteristic
13C23×D44C2211yescharacteristic
14C22×C11×Q16C2212yescomplemented
15C2×C11×C22⋊Q8C2211yescharacteristic
16C2×#67000—28no—
17C2×#67000—21no—
18C2×#67000—21no—
19C2×#67000C2212yes—
20C2×#67000C2212yes—
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C22×#4325C2212yes—
23C22×(C2×D11)⋊C4—21no—
24C22×(C2×D11)⋊C4—21no—
25C22×C4×Dic11C2211yescharacteristic
26C11×#451—24no—
27C2×C11×#103C2212yescomplemented
28C2×C11×C22⋊C8C2211yescharacteristic
29#10622843C2211yescharacteristic, complemented
30C2×#66899C2212yescomplemented
31C2×#66899C2212yescomplemented
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622798—28no—
35C2×#66885C2212yes—
36C2×#66885C2212yes—
37C2×Dic11⋊C8C2212yescomplemented
38#10622659—24no—
39#10622598C2211yescharacteristic, complemented
40#10622594—21no—
41C4⋊C4×Dic11—21no—
42C4⋊C4×Dic11C2211yescharacteristic, complemented
43C2×#66873C2212yes—
44#10622563—21no—
45C22⋊C4×Dic11—21no—
46#10622188C2212yescomplemented
47C24×D11—21no—
48C22×Q8×C11—24no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11—22no—
52C22×Q8×C11—42no—
53C22×Q8×C11C2311yescharacteristic
54C22×Q8×C11C2312yes—
55C23×C4×C11—21no—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11D411yescharacteristic
58C23×Dic11D411yescharacteristic
59C22×D44—21no—
60C22×D44—24no—
61C22×D44—22no—
62C22×D44—22no—
63C22×D44—42no—
64C22×D44C2312yes—
65C2×C11×Q16—24no—
66C2×C11×Q16—24no—
67C2×C11×Q16—42no—
68C22×C8×C11C2312yes—
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8D414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C22⋊Dic11—21no—
75#67000—28no—
76#67000—28no—
77#67000—24no—
78#67000—24no—
79#67000—24no—
80#67000D418yes—
81Q8×Dic11—24no—
82C2×#4325—24no—
83C2×#4325—24no—
84C2×#4325—42no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—28no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4×Dic11—24no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103C11×#103—24no—
104C11×C22⋊C8—22no—
105#66899—24no—
106#66899—42no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—22no—
113#66885—24no—
114#66885—42no—
115Dic11⋊C8—24no—
116#66873—24no—
117#24217—111nomaximal, Sylow
118C24×C11C2×D411yescharacteristic
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—42no—
122C23×D11—42no—
123C23×D11—42no—
124C23×D11—42no—
125C23×D11—42no—
126C23×D11—42no—
127C2×Q8×C11—24no—
128C2×Q8×C11—22no—
129C2×Q8×C11—21no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—48no—
137C2×Q8×C11—48no—
138C2×Q8×C11—42no—
139C2×Q8×C11—42no—
140C2×Q8×C11C2×D414yes—
141C2×Q8×C11C2×D412yes—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11C2411yescharacteristic
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—41no—
161C22×Dic11—41no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C2×D44—24no—
167C2×D44—22no—
168C2×D44—22no—
169C2×D44—22no—
170C2×D44—22no—
171C2×D44—22no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44—42no—
175C2×D44—42no—
176C2×D44C2×D414yes—
177C11×Q16—48no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D412yes—
184C11×C22⋊C4—24no—
185C22⋊Dic11—42no—
186#4325—48no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—28no—
191C4⋊Dic11—22no—
192C4⋊Dic11—22no—
193C4⋊Dic11—42no—
194C4⋊Dic11—42no—
195C4×Dic11—22no—
196C4×Dic11—22no—
197C4×Dic11—22no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11C2×D414yes—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C22×#124—111no—
205C2×#464—112no—
206C2×#451D1111yescharacteristic, complemented
207C2×#450—111no—
208C4×C22⋊Q8—111no—
209#2042—112no—
210#2015—112no—
211#1983—112no—
212#1797—111no—
213#1787—111no—
214#1786—111no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11#12112yes—
220C23×C11#13512yes—
221C23×C11#13712yes—
222C23×C11C22×D411yescharacteristic
223C22×D11—24no—
224C22×D11—48no—
225C22×D11—48no—
226C22×D11—48no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11—42no—
233C22×D11—84no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—84no—
237Q8×C11—24no—
238Q8×C11—24no—
239Q8×C11—24no—
240Q8×C11—48no—
241Q8×C11—42no—
242Q8×C11—42no—
243Q8×C11—42no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—48no—
252C2×C4×C11—41no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11#12112yes—
259C2×C4×C11C22×D412yes—
260C2×C4×C11C22×D411yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)12yes—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11#12012yes—
282C2×Dic11#12012yes—
283D44—24no—
284D44—24no—
285D44—48no—
286D44—42no—
287D44—42no—
288C8×C11—42no—
289C11⋊C8—42no—
290C23×Q8C2×D1111yescharacteristic
291C23×D4—111no—
292C22×Q16C2×D1112yescomplemented
293C22×SD16—112no—
294C2×#124—112no—
295C2×#124—112no—
296C2×#124—221no—
297C2×#124—221no—
298C2×#124—228no—
299C2×C22⋊Q8C2×D1111yescharacteristic
300C2×C4×Q8—111no—
301C22×C22⋊C4—221no—
302C22×C22⋊C4—221no—
303C22×C42—111no—
304#464—228no—
305#451—24no—
306#450—224no—
307C2×C4⋊C8—112no—
308C2×#103—112no—
309C2×#103—112no—
310C2×#103C2×D1112yescomplemented
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×C22⋊C8—111no—
315C2×C22⋊C8C2×D1111yescharacteristic
316#391—111no—
317#389—111no—
318#387—221no—
319#385—221no—
320#380—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—221no—
323C4×C22⋊C4—221no—
324#336—112no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—22no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11#46414yescomplemented
332C22×C11C2×#12011yescharacteristic
333C22×C11C2×#12111yescharacteristic
334C22×C11#53511yescharacteristic
335C22×C11C2×#13511yescharacteristic
336C22×C11C2×#13711yescharacteristic
337C22×C11#57511yescharacteristic
338C22×C11#57511yescharacteristic
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—816no—
343C2×D11—82no—
344C2×D11—82no—
345C2×D11—82no—
346C2×D11—82no—
347C4×C11—22no—
348C4×C11—44no—
349C4×C11—42no—
350C4×C11—42no—
351C4×C11D4212yes—
352C4×C11#54612yes—
353Dic11—22no—
354Dic11—22no—
355Dic11—41no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359C25—221no—
360C22×Q8—24no—
361C22×Q8—21no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—42no—
365C22×Q8C22×D1112yes—
366C22×Q8C22×D1111yescharacteristic
367C22×D4—112no—
368C22×D4—224no—
369C22×D4—221no—
370C22×D4—222no—
371C22×D4—222no—
372C22×D4—442no—
373C23×C4—21no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4C22×D1111yescharacteristic
377C2×Q16—24no—
378C2×Q16—24no—
379C2×Q16—42no—
380C2×SD16—224no—
381C2×SD16—224no—
382C2×SD16—442no—
383C22×C8—112no—
384C22×C8C22×D1112yes—
385#124—118no—
386#124—224no—
387#124—224no—
388#124—228no—
389#124—228no—
390#124—224no—
391C22⋊Q8—22no—
392C22⋊Q8C22⋊D1114yes—
393C4×Q8—224no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—222no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—228no—
406C2×C22⋊C4—228no—
407C2×C22⋊C4—221no—
408C2×C42—111no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—224no—
413C2×C42—221no—
414C2×C42—221no—
415C4⋊C8—224no—
416#103—24no—
417#103—224no—
418#103—442no—
419#102—224no—
420#102—224no—
421#102—442no—
422C22⋊C8—22no—
423C22⋊C8—222no—
424#95—221no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429C2×C11—24no—
430C2×C11#240811yescharacteristic
431C2×C11#300211yescharacteristic
432C2×C11#300711yescharacteristic
433C2×C11C2×#46411yescharacteristic
434C2×C11#304011yescharacteristic
435C2×C11#321111yescharacteristic
436C2×C11#321511yescharacteristic
437D11—84no—
438C24—224no—
439C24—222no—
440C24—442no—
441C24—442no—
442C24—442no—
443C24—442no—
444C24—442no—
445C24—442no—
446C24D4×D1111yescharacteristic
447C2×Q8—24no—
448C2×Q8—22no—
449C2×Q8—21no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—22no—
455C2×Q8—22no—
456C2×Q8—48no—
457C2×Q8—48no—
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8D4×D1114yes—
461C2×Q8C2×C22⋊D1112yes—
462C2×D4—114no—
463C2×D4—224no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—222no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—448no—
470C2×D4—448no—
471C2×D4—442no—
472C2×D4—442no—
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—441no—
492C22×C4—441no—
493C22×C4D4×D1111yescharacteristic
494C22×C4#434112yes—
495C22×C4C2×C22⋊D1112yes—
496C22×C4C23×D1111yescharacteristic
497Q16—48no—
498SD16—448no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—222no—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4C2×C22⋊D1112yes—
512C22⋊C4—24no—
513C22⋊C4—228no—
514C22⋊C4—228no—
515C22⋊C4—228no—
516C22⋊C4—228no—
517C22⋊C4—442no—
518C42—114no—
519C42—222no—
520C42—222no—
521C42—222no—
522C42—442no—
523C42—442no—
524C11#2421711yescharacteristic, complemented, Sylow
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—224no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—884no—
540C23—884no—
541C23—884no—
542C23—884no—
543C23#6697112yes—
544C23#6697212yes—
545C23#6699212yes—
546C23C2×D4×D1111yescharacteristic
547Q8—24no—
548Q8—24no—
549Q8—24no—
550Q8—48no—
551Q8—42no—
552Q8—42no—
553Q8—42no—
554D4—224no—
555D4—224no—
556D4—448no—
557D4—442no—
558D4—442no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—48no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—112no—
574C2×C4—112no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—444no—
586C2×C4—444no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4#6699212yes—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×#434111yescharacteristic
596C2×C4#6703712yes—
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—42no—
599C8—442no—
600C22—22no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—444no—
607C22—444no—
608C22—444no—
609C22—8816no—
610C22—882no—
611C22—882no—
612C22—882no—
613C22—882no—
614C22#1062279814yescomplemented
615C22D11×#12011yescharacteristic
616C22#1062312311yescharacteristic
617C22C2×#6697111yescharacteristic
618C22C2×#6697211yescharacteristic
619C22#1062330811yescharacteristic
620C22#1062330811yescharacteristic
621C22C2×#6699211yescharacteristic
622C4—22no—
623C4—42no—
624C4—44no—
625C4—42no—
626C4—222no—
627C4—222no—
628C4—441no—
629C4—441no—
630C4—881no—
631C4—881no—
632C4#1062312212yes—
633C4D4×C22⋊D1112yes—
634C2—24no—
635C2—884no—
636C2#1307196911yescharacteristic
637C2#1307783911yescharacteristic
638C2#1307787511yescharacteristic
639C2C2×#1062279811yescharacteristic
640C2#1307811211yescharacteristic
641C2#1307958611yescharacteristic
642C2#1307961811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenterC2×#451D11
hypocenterC11#24217
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#10622798C2semidirect
4. C22⋊Q8×Dic11C2semidirect
5. #13069854C2semidirect
6. #13069707C2semidirect
7. #13069545C2semidirect
8. #13068594C2semidirect
9. #13068551C2semidirect
11. C2×C11×#451C2semidirect
14. C22×C11×Q16C22semidirect
21. C2×Q8×Dic11C22semidirect
27. C2×C11×#103C22semidirect
29. #10622843C22semidirect
30. C2×#66899C22semidirect
31. C2×#66899C22semidirect
37. C2×Dic11⋊C8C22semidirect
39. #10622598C22semidirect
42. C4⋊C4×Dic11C22semidirect
46. #10622188C22semidirect
206. C2×#451D11semidirect
292. C22×Q16C2×D11semidirect
310. C2×#103C2×D11semidirect
331. C22×C11#464semidirect
524. C11#24217semidirect
614. C22#10622798semidirect

Maximal subgroups

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

subgroupindex
C22×#670002
C2×#106227982
C2×#106226592
C22⋊Q8×Dic112
#130698542
#130697072
#130695452
#130685942
#130685512
#130685482
C2×C11×#4512
#2421711