Finite Group Databasebeta

← #14788818

Subgroups — #14788818

Order 2816.

1566 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622696C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic, complemented
3C2×#10622851C212yesmaximal, complemented
4C4×#66983C211yesmaximal, characteristic, complemented
5#13069852C212yesmaximal, complemented
6#13069693C212yesmaximal, complemented
7#13069544C211yesmaximal, characteristic, complemented
8#13069540C211yesmaximal, characteristic, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068556C212yesmaximal, complemented
11C2×C11×#532C211yesmaximal, characteristic, complemented
12C22×C11×#41C2212yes—
13C11×#532—24no—
14C11×#532—24no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#124C2212yes—
18C2×C11×#121—21no—
19C2×C11×#121—21no—
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11—21no—
22C22×C42×C11C2211yescharacteristic
23C22×#4325C2212yes—
24C22×#4323C2212yes—
25C2×#66983C2211yescharacteristic
26C2×C4×C22⋊D11—21no—
27C2×C4×D44C2211yescharacteristic
28#10622851—28no—
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32C2×#66896C2212yes—
33C2×#66896C2212yes—
34C2×#66896C2212yes—
35#10622826—21no—
36#10622825C2211yescharacteristic
37C2×C22⋊(C11⋊C8)C2212yes—
38#10622696—24no—
39#10622685—24no—
40#10622553—21no—
41#10622552C2211yescharacteristic
42C4×(C2×D11)⋊C4—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622162C2212yes—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—24no—
51C2×C11×#41—24no—
52C2×C11×#41—42no—
53C2×C11×#41—42no—
54C22×Q8×C11C2312yes—
55C22×D4×C11—22no—
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11C2312yes—
59C23×C4×C11—22no—
60C23×C4×C11D411yescharacteristic
61C23×C4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8D414yescomplemented
68C11×#127—22no—
69C11×#127D414yescomplemented
70C11×#124—24no—
71C11×#124—24no—
72C11×#121—28no—
73C11×#121—28no—
74C4×D4×C11—28no—
75C4×D4×C11—28no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—22no—
81C2×C42×C11—22no—
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×#4325—24no—
88C2×#4325—24no—
89C2×#4325—42no—
90C2×#4323—24no—
91C2×#4323—24no—
92C2×#4323—42no—
93#66983—22no—
94#66983D414yescomplemented
95C4×C22⋊D11—44no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C22×C11⋊C8C2312yes—
106C22×C11⋊C8C2312yes—
107C4×D44—22no—
108C4×D44—22no—
109#66899—24no—
110#66899—24no—
111#66899—42no—
112#66896—24no—
113#66896—24no—
114#66896—42no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—24no—
119C4⋊(C11⋊C8)—22no—
120C4⋊(C11⋊C8)—22no—
121#24210—111nomaximal, Sylow
122C24×C11—22no—
123C24×C11C2×D411yescharacteristic
124C23×D11—21no—
125C11×#41—48no—
126C11×#41—48no—
127C11×#41—48no—
128C11×#41—48no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2×D414yes—
135C2×D4×C11—28no—
136C2×D4×C11—24no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11C2×D414yes—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—28no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—41no—
161C22×C4×C11—41no—
162C22×C4×C11—44no—
163C22×C4×C11—44no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11#4112yes—
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—42no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44C2×D412yes—
184C2×C4×D11—42no—
185C2×C4×D11—42no—
186C2×C4×D11—42no—
187C11×C4⋊C4—24no—
188C11×C4⋊C4—24no—
189C11×C22⋊C4—28no—
190C11×C22⋊C4—28no—
191C42×C11—22no—
192C42×C11—22no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11C2×D412yes—
196C42×C11C2×D412yes—
197C22⋊Dic11—42no—
198#4325—48no—
199#4323—48no—
200(C2×D11)⋊C4—24no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—42no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11C2×D412yes—
210Dic11⋊C4—42no—
211C4×Dic11—42no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8—22no—
214C2×C11⋊C8—22no—
215C2×C11⋊C8—22no—
216C2×C11⋊C8—22no—
217C2×C11⋊C8—22no—
218C2×#532D1111yescharacteristic, complemented
219C2×#461—111no—
220C2×#459—111no—
221C2×#449—112no—
222C4×#121—111no—
223#2042—112no—
224#2012—112no—
225#1982—111no—
226#1981—111no—
227#1797—111no—
228#1788—112no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—24no—
236C23×C11—42no—
237C23×C11—42no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11#12112yes—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251Q8×C11—24no—
252Q8×C11—24no—
253Q8×C11—42no—
254Q8×C11—42no—
255D4×C11—24no—
256D4×C11—24no—
257D4×C11—48no—
258D4×C11—416no—
259D4×C11—42no—
260D4×C11—42no—
261D4×C11—48no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—24no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—21no—
277C2×C4×C11—44no—
278C2×C4×C11—416no—
279C2×C4×C11—42no—
280C2×C4×C11—42no—
281C2×C4×C11—44no—
282C2×C4×C11#12012yes—
283C2×C4×C11#12012yes—
284C2×C4×C11#12112yes—
285C2×C4×C11#13512yes—
286C2×C4×C11AGL(1,ℤ/8)12yes—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C22⋊D11—48no—
294C2×Dic11—22no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303D44—22no—
304D44—22no—
305D44—41no—
306D44—41no—
307C4×D11—84no—
308C11⋊C8—42no—
309C11⋊C8—42no—
310C22×#41C2×D1112yes—
311C22×SD16—112no—
312C22×D8—112no—
313#532—24no—
314#532—24no—
315C2×C4⋊Q8C2×D1111yescharacteristic
316C2×#127C2×D1111yescharacteristic
317C2×#124C2×D1112yes—
318C2×#121—21no—
319C2×#121—21no—
320C2×#121—111no—
321C2×C4×D4—21no—
322C2×C4×D4—21no—
323C2×C4×D4—111no—
324C2×C4×D4—221no—
325C22×C42C2×D1111yescharacteristic
326#461—224no—
327#459—224no—
328#449—228no—
329C2×C4⋊C8—111no—
330C2×C4⋊C8—111no—
331C2×#103—112no—
332C2×#103—112no—
333C2×#103—112no—
334C2×#102—112no—
335C2×#102—112no—
336C2×#102—112no—
337C2×C22⋊C8—112no—
338#390—111no—
339#389—111no—
340#388—221no—
341#386—221no—
342#380—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—221no—
345#336—112no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—44no—
354C22×C11—44no—
355C22×C11—44no—
356C22×C11—82no—
357C22×C11—82no—
358C22×C11—82no—
359C22×C11—82no—
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11#53511yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57511yescharacteristic
366C22×C11#57511yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—44no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11#44914yescomplemented
380C4×C11D4211yescharacteristic
381C4×C11D4211yescharacteristic
382C4×C11#54611yescharacteristic
383C4×C11#54611yescharacteristic
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387C2×#41—24no—
388C2×#41—24no—
389C2×#41—24no—
390C2×#41—24no—
391C2×#41—42no—
392C2×#41—42no—
393C22×Q8C22×D1112yes—
394C22×D4—22no—
395C22×D4—21no—
396C22×D4—21no—
397C22×D4—111no—
398C22×D4—221no—
399C22×D4C22×D1112yes—
400C23×C4—22no—
401C23×C4—221no—
402C23×C4C22⋊D1111yescharacteristic
403C23×C4C22⋊D1111yescharacteristic
404C23×C4C22×D1111yescharacteristic
405C2×SD16—224no—
406C2×SD16—224no—
407C2×SD16—442no—
408C2×D8—224no—
409C2×D8—224no—
410C2×D8—442no—
411C22×C8—112no—
412C22×C8—112no—
413C4⋊Q8—22no—
414C4⋊Q8C22⋊D1114yescomplemented
415#127—22no—
416#127C22⋊D1114yescomplemented
417#124—24no—
418#124—24no—
419#121—28no—
420#121—28no—
421#121—114no—
422#121—222no—
423C4×D4—28no—
424C4×D4—28no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—444no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—111no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—221no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—221no—
444C2×C42C22⋊D1111yescharacteristic
445C2×C42C22⋊D1111yescharacteristic
446C2×C42C22×D1111yescharacteristic
447C2×C42C22×D1111yescharacteristic
448C4⋊C8—222no—
449C4⋊C8—222no—
450#103—224no—
451#103—224no—
452#103—442no—
453#102—224no—
454#102—224no—
455#102—442no—
456C22⋊C8—224no—
457#95—221no—
458#95—221no—
459#95—221no—
460C2×C11—42no—
461C2×C11—84no—
462C2×C11#240811yescharacteristic
463C2×C11C2×#44911yescharacteristic
464C2×C11#300511yescharacteristic
465C2×C11#303511yescharacteristic
466C2×C11#303611yescharacteristic
467C2×C11#321211yescharacteristic
468C2×C11#321411yescharacteristic
469D11—82no—
470C24—22no—
471C24—221no—
472C24C2×C22⋊D1111yescharacteristic
473#41—48no—
474#41—48no—
475#41—48no—
476#41—48no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8C2×C22⋊D1114yes—
483C2×D4—28no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—44no—
494C2×D4—44no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—112no—
498C2×D4—224no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4C2×C22⋊D1114yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4D4×D1112yes—
528C22×C4#434112yes—
529C22×C4C2×C22⋊D1111yescharacteristic
530C22×C4C2×C22⋊D1111yescharacteristic
531C22×C4C2×C22⋊D1111yescharacteristic
532C22×C4C2×C22⋊D1111yescharacteristic
533C22×C4C2×C22⋊D1111yescharacteristic
534C22×C4C23×D1111yescharacteristic
535SD16—448no—
536D8—448no—
537C2×C8—222no—
538C2×C8—222no—
539C2×C8—222no—
540C2×C8—222no—
541C2×C8—222no—
542C2×C8—222no—
543C4⋊C4—24no—
544C4⋊C4—24no—
545C4⋊C4—112no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—442no—
552C22⋊C4—28no—
553C22⋊C4—28no—
554C22⋊C4—224no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C42—22no—
560C42—22no—
561C42—21no—
562C42—21no—
563C42—442no—
564C42C2×C22⋊D1112yes—
565C42C2×C22⋊D1112yes—
566C11#2421011yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—24no—
574C23—42no—
575C23—42no—
576C23—42no—
577C23—42no—
578C23—42no—
579C23—42no—
580C23—222no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23#6699112yes—
588C23C22×C22⋊D1111yescharacteristic
589Q8—24no—
590Q8—24no—
591Q8—42no—
592Q8—42no—
593D4—24no—
594D4—24no—
595D4—48no—
596D4—416no—
597D4—42no—
598D4—42no—
599D4—48no—
600D4—222no—
601D4—222no—
602D4—448no—
603D4—441no—
604D4—441no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—24no—
620C2×C4—44no—
621C2×C4—416no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—44no—
625C2×C4—222no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—884no—
635C2×C4#6699112yes—
636C2×C4#6700212yes—
637C2×C4#6700312yes—
638C2×C4#6700612yes—
639C2×C4#6700612yes—
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4C2×#434111yescharacteristic
642C2×C4#6703711yescharacteristic
643C2×C4#6703711yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C2×C4C22×C22⋊D1111yescharacteristic
646C8—442no—
647C8—442no—
648C22—22no—
649C22—22no—
650C22—22no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—44no—
656C22—44no—
657C22—44no—
658C22—82no—
659C22—82no—
660C22—82no—
661C22—82no—
662C22—442no—
663C22—442no—
664C22—442no—
665C22—881no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22C2×#6699111yescharacteristic
670C22#1062333611yescharacteristic
671C22C2×#6700211yescharacteristic
672C22C2×#6700311yescharacteristic
673C22#1062335311yescharacteristic
674C22#1062335311yescharacteristic
675C22C2×#6700611yescharacteristic
676C4—22no—
677C4—22no—
678C4—41no—
679C4—44no—
680C4—41no—
681C4—442no—
682C4—881no—
683C4—881no—
684C4#1062285114yescomplemented
685C4D4×C22⋊D1111yescharacteristic
686C4D4×C22⋊D1111yescharacteristic
687C4#1062333711yescharacteristic
688C4#1062333711yescharacteristic
689C2—42no—
690C2—84no—
691C2—882no—
692C2#1307196611yescharacteristic
693C2C2×#1062285111yescharacteristic
694C2#1307785811yescharacteristic
695C2#1307806511yescharacteristic
696C2#1307807611yescharacteristic
697C2#1307959211yescharacteristic
698C2#1307961111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11#24210
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×#10622696C2semidirect
2. C2×#10622685C2semidirect
3. C2×#10622851C2semidirect
4. C4×#66983C2semidirect
5. #13069852C2semidirect
6. #13069693C2semidirect
7. #13069544C2semidirect
8. #13069540C2semidirect
9. #13068596C2semidirect
10. #13068556C2semidirect
11. C2×C11×#532C2semidirect
67. C11×C4⋊Q8D4semidirect
69. C11×#127D4semidirect
94. #66983D4semidirect
218. C2×#532D11semidirect
379. C4×C11#449semidirect
414. C4⋊Q8C22⋊D11semidirect
416. #127C22⋊D11semidirect
566. C11#24210semidirect
684. C4#10622851semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×#106226852
C2×#106228512
C4×#669832
#130698522
#130696932
#130695442
#130695402
#130685962
#130685562
C2×C11×#5322
#2421011