Finite Group Databasebeta

← #14788858

Subgroups — #14788858

Order 2816.

1566 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
1C2×#10622670C212yesmaximal, complemented
2C2×#10622851C212yesmaximal, complemented
3C4×#66983C211yesmaximal, characteristic, complemented
4#13069859C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic, complemented
6#13069699C211yesmaximal, characteristic, complemented
7#13069687C211yesmaximal, characteristic, complemented
8#13069549C212yesmaximal, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068556C212yesmaximal, complemented
11C2×C11×#532C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C11×#532—28no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124C2212yes—
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C22×C42×C11C2211yescharacteristic
22C22×#4325C2212yes—
23C22×#4323C2212yes—
24C2×#66983C2211yescharacteristic
25C2×C4×C22⋊D11—21no—
26C2×C4×D44C2211yescharacteristic
27#10622851—28no—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33C2×#66896C2212yes—
34#10622826—21no—
35#10622825C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622670—28no—
38#10622553—21no—
39#10622552C2211yescharacteristic
40C4×(C2×D11)⋊C4—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2212yes—
44#10622162C2211yescharacteristic
45#10622162C2211yescharacteristic
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11C2312yes—
57C23×C4×C11—22no—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C11×C4⋊Q8—24no—
65C11×#127—24no—
66C11×#124—24no—
67C11×#124D418yescomplemented
68C11×#121—28no—
69C11×#121—28no—
70C4×D4×C11—28no—
71C4×D4×C11—28no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C11×C22⋊C4—22no—
76C2×C42×C11—24no—
77C2×C42×C11D411yescharacteristic
78C2×C42×C11D411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82C2×#4325—24no—
83C2×#4325—24no—
84C2×#4325—42no—
85C2×#4323—24no—
86C2×#4323—24no—
87C2×#4323—42no—
88#66983—22no—
89#66983D414yescomplemented
90C4×C22⋊D11—44no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102C4×D44—24no—
103#66899—24no—
104#66899—24no—
105#66899—42no—
106#66896—24no—
107#66896—24no—
108#66896—42no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C22⋊(C11⋊C8)—24no—
113C4⋊(C11⋊C8)—24no—
114#24214—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11C2×D411yescharacteristic
117C23×D11—21no—
118C11×#41—48no—
119C11×#41—48no—
120C11×#41—48no—
121C11×#41—48no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11—22no—
126C2×Q8×C11—22no—
127C2×Q8×C11C2×D414yes—
128C2×D4×C11—24no—
129C2×D4×C11—24no—
130C2×D4×C11—28no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11C2×D414yes—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—28no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11—44no—
154C22×C4×C11—44no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11#4112yes—
162C22×C4×C11C2411yescharacteristic
163C2×C22⋊D11—24no—
164C2×C22⋊D11—42no—
165C2×C22⋊D11—42no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C2×D44—22no—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44C2×D412yes—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—28no—
180C42×C11—22no—
181C42×C11—22no—
182C42×C11—22no—
183C42×C11C2×D414yes—
184C22⋊Dic11—42no—
185#4325—48no—
186#4323—48no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191C4⋊Dic11—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11—22no—
194C4⋊Dic11C2×D412yes—
195Dic11⋊C4—42no—
196C4×Dic11—42no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8—22no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×#532D1111yescharacteristic, complemented
204C2×#463—112no—
205C2×#449—112no—
206C4×#121—111no—
207#2043—111no—
208#2041—111no—
209#2013—111no—
210#2011—111no—
211#1983—112no—
212#1797—111no—
213#1788—112no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—24no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11#12112yes—
228C23×C11C22×D411yescharacteristic
229C22×D11—22no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236Q8×C11—24no—
237Q8×C11—24no—
238Q8×C11—42no—
239Q8×C11—42no—
240D4×C11—24no—
241D4×C11—24no—
242D4×C11—48no—
243D4×C11—48no—
244D4×C11—416no—
245D4×C11—42no—
246D4×C11—42no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—44no—
261C2×C4×C11—44no—
262C2×C4×C11—416no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11#12012yes—
266C2×C4×C11#12012yes—
267C2×C4×C11#12112yes—
268C2×C4×C11#13512yes—
269C2×C4×C11AGL(1,ℤ/8)12yes—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D412yes—
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)12yes—
274C22⋊D11—48no—
275C2×Dic11—22no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284D44—24no—
285D44—42no—
286C4×D11—84no—
287C11⋊C8—42no—
288C11⋊C8—42no—
289C22×#41C2×D1112yes—
290C22×SD16—112no—
291C22×D8—112no—
292#532—28no—
293C2×C4⋊Q8C2×D1111yescharacteristic
294C2×#127C2×D1111yescharacteristic
295C2×#124C2×D1112yes—
296C2×#121—21no—
297C2×#121—21no—
298C2×#121—111no—
299C2×C4×D4—21no—
300C2×C4×D4—21no—
301C2×C4×D4—111no—
302C2×C4×D4—221no—
303C22×C42C2×D1111yescharacteristic
304#463—228no—
305#449—228no—
306C2×C4⋊C8—112no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#103—112no—
310C2×#102—112no—
311C2×#102—112no—
312C2×#102—112no—
313C2×C22⋊C8—112no—
314#390—111no—
315#389—111no—
316#388—221no—
317#386—221no—
318#380—111no—
319C4×C4⋊C4—111no—
320C4×C22⋊C4—221no—
321#336—111no—
322#336—111no—
323C22×C11—22no—
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—44no—
333C22×C11—82no—
334C22×C11—82no—
335C22×C11—82no—
336C22×C11—82no—
337C22×C11C2×#12011yescharacteristic
338C22×C11C2×#12111yescharacteristic
339C22×C11#53511yescharacteristic
340C22×C11C2×#13511yescharacteristic
341C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57511yescharacteristic
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—81no—
350C2×D11—81no—
351C4×C11—22no—
352C4×C11—22no—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—44no—
357C4×C11D4212yes—
358C4×C11#54612yes—
359Dic11—42no—
360Dic11—81no—
361Dic11—81no—
362C2×#41—24no—
363C2×#41—24no—
364C2×#41—24no—
365C2×#41—24no—
366C2×#41—42no—
367C2×#41—42no—
368C22×Q8C22×D1112yes—
369C22×D4—22no—
370C22×D4—21no—
371C22×D4—21no—
372C22×D4—111no—
373C22×D4—221no—
374C22×D4C22×D1112yes—
375C23×C4—22no—
376C23×C4—221no—
377C23×C4C22⋊D1111yescharacteristic
378C23×C4C22⋊D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C2×SD16—224no—
381C2×SD16—224no—
382C2×SD16—442no—
383C2×D8—224no—
384C2×D8—224no—
385C2×D8—442no—
386C22×C8—112no—
387C22×C8—112no—
388C4⋊Q8—24no—
389#127—24no—
390#124—24no—
391#124C22⋊D1118yescomplemented
392#121—28no—
393#121—28no—
394#121—114no—
395#121—222no—
396C4×D4—28no—
397C4×D4—28no—
398C4×D4—224no—
399C4×D4—444no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—221no—
406C2×C22⋊C4—22no—
407C2×C22⋊C4—22no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C42—24no—
414C2×C42—221no—
415C2×C42C22⋊D1111yescharacteristic
416C2×C42C22⋊D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C2×C42C22×D1111yescharacteristic
419C4⋊C8—224no—
420#103—224no—
421#103—224no—
422#103—442no—
423#102—224no—
424#102—224no—
425#102—442no—
426C22⋊C8—224no—
427#95—221no—
428#95—221no—
429#95—221no—
430C2×C11—42no—
431C2×C11—84no—
432C2×C11#240811yescharacteristic
433C2×C11#300211yescharacteristic
434C2×C11#300611yescharacteristic
435C2×C11#303511yescharacteristic
436C2×C11#303611yescharacteristic
437C2×C11#320711yescharacteristic
438C2×C11#321911yescharacteristic
439D11—82no—
440C24—22no—
441C24—221no—
442C24C2×C22⋊D1111yescharacteristic
443#41—48no—
444#41—48no—
445#41—48no—
446#41—48no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8C2×C22⋊D1114yes—
453C2×D4—24no—
454C2×D4—24no—
455C2×D4—28no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—44no—
465C2×D4—42no—
466C2×D4—42no—
467C2×D4—112no—
468C2×D4—224no—
469C2×D4—221no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—442no—
473C2×D4—442no—
474C2×D4C2×C22⋊D1114yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—28no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—44no—
486C22×C4—44no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—442no—
491C22×C4—442no—
492C22×C4—442no—
493C22×C4D4×D1112yes—
494C22×C4#434112yes—
495C22×C4C2×C22⋊D1111yescharacteristic
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1111yescharacteristic
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C23×D1111yescharacteristic
501SD16—448no—
502D8—448no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C2×C8—222no—
507C2×C8—222no—
508C2×C8—222no—
509C4⋊C4—24no—
510C4⋊C4—24no—
511C4⋊C4—112no—
512C4⋊C4—221no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—442no—
516C22⋊C4—28no—
517C22⋊C4—28no—
518C22⋊C4—224no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C42—22no—
524C42—22no—
525C42—22no—
526C42—442no—
527C42C2×C22⋊D1114yes—
528C11#2421411yescharacteristic, complemented, Sylow
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—24no—
536C23—42no—
537C23—42no—
538C23—42no—
539C23—42no—
540C23—42no—
541C23—42no—
542C23—222no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23#6699112yes—
550C23C22×C22⋊D1111yescharacteristic
551Q8—24no—
552Q8—24no—
553Q8—42no—
554Q8—42no—
555D4—24no—
556D4—24no—
557D4—48no—
558D4—48no—
559D4—416no—
560D4—42no—
561D4—42no—
562D4—224no—
563D4—448no—
564D4—442no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—44no—
579C2×C4—44no—
580C2×C4—416no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—222no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—884no—
593C2×C4#6699112yes—
594C2×C4#6700212yes—
595C2×C4#6700312yes—
596C2×C4#6700612yes—
597C2×C4#6700612yes—
598C2×C4C2×D4×D1111yescharacteristic
599C2×C4C2×#434111yescharacteristic
600C2×C4#6703712yes—
601C2×C4C22×C22⋊D1112yes—
602C8—442no—
603C8—442no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—44no—
612C22—44no—
613C22—44no—
614C22—82no—
615C22—82no—
616C22—82no—
617C22—82no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—881no—
622C22—881no—
623C22—881no—
624C22—881no—
625C22C2×#6699111yescharacteristic
626C22#1062333611yescharacteristic
627C22C2×#6700211yescharacteristic
628C22C2×#6700311yescharacteristic
629C22#1062335311yescharacteristic
630C22#1062335311yescharacteristic
631C22C2×#6700611yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—22no—
636C4—22no—
637C4—44no—
638C4—442no—
639C4—881no—
640C4—881no—
641C4D4×C22⋊D1112yes—
642C4#1062333712yes—
643C2—42no—
644C2—84no—
645C2—882no—
646C2#1307196611yescharacteristic
647C2#1307783411yescharacteristic
648C2#1307786811yescharacteristic
649C2#1307806511yescharacteristic
650C2#1307807611yescharacteristic
651C2#1307954911yescharacteristic
652C2#1307965311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11#24214
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622670C2semidirect
2. C2×#10622851C2semidirect
3. C4×#66983C2semidirect
4. #13069859C2semidirect
5. #13069847C2semidirect
6. #13069699C2semidirect
7. #13069687C2semidirect
8. #13069549C2semidirect
9. #13068596C2semidirect
10. #13068556C2semidirect
11. C2×C11×#532C2semidirect
67. C11×#124D4semidirect
89. #66983D4semidirect
203. C2×#532D11semidirect
391. #124C22⋊D11semidirect
528. C11#24214semidirect

Maximal subgroups

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

subgroupindex
C2×#106226702
C2×#106228512
C4×#669832
#130698592
#130698472
#130696992
#130696872
#130695492
#130685962
#130685562
C2×C11×#5322
#2421411