Finite Group Databasebeta

← #14785927

Subgroups — #14785927

Order 2816.

1690 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2C2×#10622830C211yesmaximal, characteristic, complemented
3C22×#66896C211yesmaximal, characteristic, complemented
4#13069752C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069042C211yesmaximal, characteristic, complemented
7#13068967C212yesmaximal, complemented
8#13068934C212yesmaximal, complemented
9#13068909C211yesmaximal, characteristic, complemented
10#13068700C211yesmaximal, characteristic, complemented
11C11×#2408C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C22×#4341—21no—
14C2×C11×#121C2212yes—
15C2×C11×#120—21no—
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2212yes—
18C2×#66983C2211yescharacteristic
19C2×#66983C2211yescharacteristic, complemented
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22C23×C11⋊C8C2211yescharacteristic
23#10623086—24no—
24#10623086—24no—
25C2×#66950—21no—
26C2×#66939—21no—
27C2×#66939—21no—
28C2×C4×D44C2211yescharacteristic, complemented
29C2×#66922C2211yescharacteristic, complemented
30C11×#394—21no—
31C11×#392—21no—
32C11×#390C2212yes—
33C11×#380C2211yescharacteristic
34C11×#379—21no—
35#10622830—24no—
36C2×#66896—24no—
37C2×#66896C2212yes—
38C2×#66896C2212yes—
39C2×#66896C2212yes—
40C2×C22⋊(C11⋊C8)C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2212yescomplemented
42C2×#66873C2212yescomplemented
43#10622167C2212yescomplemented
44#10622167C2212yescomplemented
45#10622167C2212yescomplemented
46#10622162C2212yescomplemented
47C25×C11—21no—
48C22×D4×C11—24no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—21no—
53C22×D4×C11—42no—
54C22×D4×C11D411yescharacteristic
55C22×D4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—21no—
59C22×C22⋊D11—21no—
60C23×Dic11—21no—
61C23×Dic11—21no—
62C2×#4341—28no—
63C2×#4341—44no—
64C2×#4341—44no—
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×Dic22—21no—
68C11×#121—24no—
69C11×#121—42no—
70C11×#120—44no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2312yes—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—22no—
77C2×C11×C22⋊C4—22no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4D411yescharacteristic
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4323—24no—
83C2×#4323—24no—
84C2×#4323—42no—
85#66983—22no—
86#66983—22no—
87#66983—22no—
88#66983D414yescomplemented
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11D414yescomplemented
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C22×C11⋊C8—22no—
103C22×C11⋊C8—42no—
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2312yes—
106#66950—28no—
107#66939—28no—
108#66939—28no—
109C4×D44—22no—
110C4×D44—22no—
111#66922—22no—
112#66922—22no—
113C11×#95—21no—
114#66896—24no—
115#66896—24no—
116#66896—24no—
117C22⋊(C11⋊C8)—22no—
118C22⋊(C11⋊C8)—42no—
119#66873—42no—
120#23960—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—44no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—42no—
126C24×C11—82no—
127C24×C11C2×D411yescharacteristic
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—28no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—48no—
139C2×D4×C11—44no—
140C2×D4×C11—44no—
141C2×D4×C11—44no—
142C2×D4×C11—44no—
143C2×D4×C11—42no—
144C2×D4×C11—82no—
145C2×D4×C11D814yescomplemented
146C2×D4×C11#4114yescomplemented
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2411yescharacteristic
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—42no—
164C2×C22⋊D11—42no—
165C2×C22⋊D11—42no—
166C2×C22⋊D11—42no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—42no—
173C22×Dic11—42no—
174C22×Dic11—42no—
175C22×Dic11—42no—
176#4341—432no—
177C2×D44—21no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44C2×D412yes—
181C2×C4×D11—24no—
182C2×C4×D11—42no—
183C2×C4×D11—42no—
184C2×Dic22—24no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C4⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—44no—
193C11×C22⋊C4—42no—
194C11×C22⋊C4—44no—
195C11×C22⋊C4—82no—
196C42×C11—21no—
197C42×C11—21no—
198#4323—48no—
199(C2×D11)⋊C4—24no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—24no—
202C4⋊Dic11—24no—
203C4⋊Dic11—24no—
204C4⋊Dic11—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11C2×D412yes—
209C4⋊Dic11C2×D412yes—
210C4⋊Dic11C2×D412yes—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—44no—
218C2×#547—111no—
219C2×#447—111no—
220C22×#102—111no—
221#2408D1111yescharacteristic, complemented
222#2023—112no—
223#1999—112no—
224#1893—111no—
225#1879—112no—
226#1874—112no—
227#1869—111no—
228#1823—111no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—21no—
232C23×C11—22no—
233C23×C11—21no—
234C23×C11—22no—
235C23×C11—24no—
236C23×C11—48no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—88no—
244C23×C11—88no—
245C23×C11—84no—
246C23×C11—84no—
247C23×C11#12012yes—
248C23×C11C2×D812yes—
249C23×C11C2×D812yes—
250C23×C11AGL(1,ℤ/8)12yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—22no—
253C22×D11—42no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—42no—
257D4×C11—28no—
258D4×C11—24no—
259D4×C11—24no—
260D4×C11—48no—
261D4×C11—42no—
262D4×C11—42no—
263D4×C11—88no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11—42no—
279C2×C4×C11—42no—
280C2×C4×C11#12012yes—
281C2×C4×C11C2×D812yes—
282C2×C4×C11C22×D411yescharacteristic
283C2×C4×C11C22×D411yescharacteristic
284C2×C4×C11C2×#4112yes—
285C2×C4×C11H(5,𝔽2)12yes—
286C22⋊D11—48no—
287C22⋊D11—48no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—48no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—48no—
299D44—24no—
300D44—41no—
301D44—41no—
302C4×D11—48no—
303Dic22—48no—
304C11⋊C8—42no—
305C11⋊C8—42no—
306C22×#41—221no—
307C23×D4C2×D1111yescharacteristic
308C22×D8—112no—
309C23×C8—111no—
310#547—224no—
311#547—224no—
312C2×C4⋊Q8—111no—
313C2×#123—221no—
314C2×#123—221no—
315C2×C22⋊Q8—221no—
316C2×#121—111no—
317C2×#121—111no—
318C2×#121C2×D1112yes—
319C2×#120—21no—
320C2×C4×D4—111no—
321C2×C4×D4C2×D1111yescharacteristic
322C22×C4⋊C4—111no—
323C22×C4⋊C4—111no—
324#447—224no—
325C2×#102—112no—
326C2×#102—112no—
327C2×#102—112no—
328C2×#102—112no—
329C2×#102—224no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—112no—
332#394—21no—
333#392—21no—
334#390C2×D1112yes—
335#380C2×D1111yescharacteristic
336#379—21no—
337#340—112no—
338#340—112no—
339#340—112no—
340#336—112no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—24no—
344C22×C11—24no—
345C22×C11—22no—
346C22×C11—24no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—42no—
350C22×C11—44no—
351C22×C11—44no—
352C22×C11—44no—
353C22×C11—816no—
354C22×C11—82no—
355C22×C11—82no—
356C22×C11—82no—
357C22×C11—82no—
358C22×C11#44714yes—
359C22×C11C2×#12011yescharacteristic
360C22×C11#54612yes—
361C22×C11C22×D811yescharacteristic
362C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C11#57712yes—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—82no—
368C2×D11—82no—
369C4×C11—22no—
370C4×C11—22no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11—82no—
374C4×C11#52511yescharacteristic
375C4×C11#53511yescharacteristic
376C4×C11#54612yes—
377Dic11—42no—
378Dic11—42no—
379Dic11—42no—
380C25—21no—
381C2×#41—228no—
382C2×#41—444no—
383C2×#41—444no—
384C22×Q8—221no—
385C22×D4—24no—
386C22×D4—22no—
387C22×D4—22no—
388C22×D4—22no—
389C22×D4—21no—
390C22×D4—42no—
391C22×D4—111no—
392C22×D4—221no—
393C22×D4—221no—
394C22×D4C22⋊D1111yescharacteristic
395C22×D4C22×D1112yes—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C2×D8—224no—
402C2×D8—224no—
403C2×D8—442no—
404C22×C8—112no—
405C22×C8—112no—
406C22×C8—222no—
407C22×C8—442no—
408C4⋊Q8—222no—
409C4⋊Q8—222no—
410#123—228no—
411#123—228no—
412C22⋊Q8—228no—
413#121—24no—
414#121—42no—
415#121—114no—
416#121—222no—
417#121—222no—
418#121—222no—
419#120—44no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—222no—
423C4×D4—222no—
424C2×C4⋊C4—114no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—222no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4C22⋊D1111yescharacteristic
435C2×C4⋊C4C22×D1112yes—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—22no—
438C2×C22⋊C4—22no—
439C2×C22⋊C4—22no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4C22⋊D1111yescharacteristic
444C2×C22⋊C4C22⋊D1111yescharacteristic
445C2×C42C22×D1111yescharacteristic
446#102—224no—
447#102—224no—
448#102—224no—
449#102—442no—
450C22⋊C8—222no—
451C22⋊C8—442no—
452#95—21no—
453C2×C11—24no—
454C2×C11—42no—
455C2×C11—84no—
456C2×C11#240411yescharacteristic
457C2×C11C2×#44711yescharacteristic
458C2×C11#301011yescharacteristic
459C2×C11#329412yes—
460C2×C11#330612yes—
461D11—82no—
462C24—22no—
463C24—44no—
464C24—42no—
465C24—42no—
466C24—42no—
467C24—82no—
468C24—221no—
469C24C2×C22⋊D1111yescharacteristic
470C24C2×C22⋊D1111yescharacteristic
471#41—4432no—
472C2×Q8—224no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—28no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—48no—
484C2×D4—44no—
485C2×D4—44no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4—82no—
490C2×D4—112no—
491C2×D4—224no—
492C2×D4—224no—
493C2×D4—221no—
494C2×D4—222no—
495C2×D4—222no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—442no—
500C2×D4#432314yescomplemented
501C2×D4#434114yescomplemented
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—224no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4D4×D1112yes—
522C22×C4D4×D1112yes—
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1111yescharacteristic
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C23×D1111yescharacteristic
528D8—448no—
529C2×C8—222no—
530C2×C8—222no—
531C2×C8—222no—
532C2×C8—222no—
533C2×C8—222no—
534C2×C8—222no—
535C2×C8—444no—
536C4⋊C4—22no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—112no—
540C4⋊C4—112no—
541C4⋊C4—112no—
542C4⋊C4—224no—
543C4⋊C4—224no—
544C4⋊C4—224no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—44no—
551C22⋊C4—42no—
552C22⋊C4—44no—
553C22⋊C4—82no—
554C22⋊C4—224no—
555C22⋊C4—224no—
556C22⋊C4—224no—
557C42—21no—
558C42—21no—
559C11#2396011yescharacteristic, complemented, Sylow
560C23—22no—
561C23—22no—
562C23—21no—
563C23—22no—
564C23—21no—
565C23—22no—
566C23—24no—
567C23—48no—
568C23—42no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23—88no—
575C23—88no—
576C23—84no—
577C23—84no—
578C23—222no—
579C23—441no—
580C23—442no—
581C23—441no—
582C23—442no—
583C23C2×#432312yes—
584C23C2×#432312yes—
585C23#6699012yes—
586C23#6700212yes—
587C23C22×C22⋊D1111yescharacteristic
588Q8—448no—
589D4—28no—
590D4—24no—
591D4—24no—
592D4—48no—
593D4—42no—
594D4—42no—
595D4—88no—
596D4—224no—
597D4—448no—
598D4—448no—
599D4—441no—
600D4—441no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—41no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—448no—
621C2×C4—448no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—448no—
629C2×C4C2×#432312yes—
630C2×C4#6699012yes—
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4C2×D4×D1111yescharacteristic
633C2×C4C2×#434112yes—
634C2×C4#6703712yes—
635C8—442no—
636C8—442no—
637C22—24no—
638C22—22no—
639C22—24no—
640C22—22no—
641C22—22no—
642C22—24no—
643C22—42no—
644C22—41no—
645C22—41no—
646C22—44no—
647C22—44no—
648C22—44no—
649C22—816no—
650C22—82no—
651C22—82no—
652C22—82no—
653C22—82no—
654C22—442no—
655C22—442no—
656C22—442no—
657C22—882no—
658C22—882no—
659C22#1062264914yes—
660C22C22×#432311yescharacteristic
661C22C2×#6699011yescharacteristic
662C22#1062333712yes—
663C22C2×#6700211yescharacteristic
664C22#1062336712yes—
665C4—22no—
666C4—22no—
667C4—41no—
668C4—41no—
669C4—82no—
670C4—442no—
671C4—442no—
672C4—442no—
673C4#1062311711yescharacteristic
674C4#1062312212yes—
675C4#1062312311yescharacteristic
676C2—24no—
677C2—42no—
678C2—84no—
679C2—882no—
680C2#1307193211yescharacteristic
681C2C2×#1062264911yescharacteristic
682C2#1307790011yescharacteristic
683C2#1308042912yes—
684C2#1308057712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2408C2
socleC23×C11C22×D4
hypercenter#2408D11
hypocenterC11#23960
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. C2×#10622830C2semidirect
3. C22×#66896C2semidirect
4. #13069752C2semidirect
5. #13069612C2semidirect
6. #13069042C2semidirect
7. #13068967C2semidirect
8. #13068934C2semidirect
9. #13068909C2semidirect
10. #13068700C2semidirect
11. C11×#2408C2semidirect
19. C2×#66983C22semidirect
21. C22×C4⋊Dic11C22semidirect
28. C2×C4×D44C22semidirect
29. C2×#66922C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×#66873C22semidirect
43. #10622167C22semidirect
44. #10622167C22semidirect
45. #10622167C22semidirect
46. #10622162C22semidirect
88. #66983D4semidirect
98. C2×C4⋊Dic11D4semidirect
145. C2×D4×C11D8semidirect
146. C2×D4×C11#41semidirect
221. #2408D11semidirect
500. C2×D4#4323semidirect
501. C2×D4#4341semidirect
559. C11#23960semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106228302
C22×#668962
#130697522
#130696122
#130690422
#130689672
#130689342
#130689092
#130687002
C11×#24082
#2396011