Finite Group Databasebeta

← #14780631

Subgroups — #14780631

Order 2816.

2206 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66985C211yesmaximal, characteristic, complemented
2C2×#10623364C211yesmaximal, characteristic, complemented
3C2×#10622615C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069619C214yesmaximal, complemented
7#13069612C214yesmaximal, complemented
8#13068337C211yesmaximal, characteristic, complemented
9C2×C11×#535C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C22×#4339C2211yescharacteristic
13C11×#535—24no—
14C11×#535—24no—
15C2×C11×#127—21no—
16C2×C11×#124—21no—
17C2×C11×#121C2214yes—
18C2×C11×#120—22no—
19C2×C11×#117C2211yescharacteristic
20#10623364—24no—
21#10623364—24no—
22C2×#66999—21no—
23C2×#66992—22no—
24C2×#66991—21no—
25C22×#4324C2212yes—
26C2×#66985—24no—
27C2×#66985—24no—
28C2×#66985—24no—
29C22×#4323C2212yes—
30C2×#66983C2212yescomplemented
31C22×C4⋊Dic11C2211yescharacteristic
32C2×#66977C2212yescomplemented
33C22×#4318C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35#10622847—24no—
36C2×#66896—24no—
37C2×#66896C2214yes—
38C2×C22⋊(C11⋊C8)C2214yescomplemented
39#10622615—24no—
40C2×#66874C2212yescomplemented
41C2×#66873C2212yescomplemented
42#10622167C2214yescomplemented
43C25×C11—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41—22no—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11—22no—
58C22×D4×C11D411yescharacteristic
59C22×D4×C11D412yes—
60C22×D4×C11D414yescomplemented
61C22×D4×C11C2312yes—
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C22×C22⋊D11—22no—
66C23×Dic11—21no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339D414yescomplemented
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×Dic22C2311yescharacteristic
76C11×#127—28no—
77C11×#124—28no—
78C11×#121—28no—
79C11×#121—28no—
80C11×#120—216no—
81C11×#117—22no—
82C11×#117D414yescomplemented
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—24no—
86C2×C42×C11—21no—
87C2×C22⋊Dic11—22no—
88#66999—28no—
89#66992—216no—
90#66991—28no—
91C2×#4324—24no—
92C2×#4324—24no—
93C2×#4324—24no—
94#66985—232no—
95C2×#4323—24no—
96C2×#4323—24no—
97C2×#4323—24no—
98#66983—24no—
99#66983—24no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11D414yescomplemented
104C2×C4⋊Dic11C2312yes—
105#66977—24no—
106#66977—24no—
107C2×Dic11⋊C4—22no—
108C2×#4318—22no—
109C2×#4318—22no—
110C2×#4318D414yescomplemented
111C22×C11⋊C8—22no—
112C22×C11⋊C8—22no—
113C22×C11⋊C8—22no—
114C22×C11⋊C8C2312yes—
115C22×C11⋊C8C2312yes—
116#66896—28no—
117C22⋊(C11⋊C8)—28no—
118#66874—24no—
119#66873—24no—
120#23393—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—24no—
123C24×C11—42no—
124C24×C11—42no—
125C24×C11—82no—
126C24×C11—82no—
127C24×C11C2×D412yes—
128C24×C11C2×D411yescharacteristic
129C23×D11—21no—
130C11×#41—44no—
131C11×#41—44no—
132C11×#41—44no—
133C11×#41—44no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—24no—
139C2×D4×C11—24no—
140C2×D4×C11—216no—
141C2×D4×C11—28no—
142C2×D4×C11—22no—
143C2×D4×C11—24no—
144C2×D4×C11—22no—
145C2×D4×C11—28no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—42no—
153C2×D4×C11—44no—
154C2×D4×C11—42no—
155C2×D4×C11—44no—
156C2×D4×C11—84no—
157C2×D4×C11—84no—
158C2×D4×C11C2×D414yes—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2×D412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11#4112yes—
174C22×C4×C11C2411yescharacteristic
175C2×C22⋊D11—28no—
176C2×C22⋊D11—24no—
177C2×C22⋊D11—42no—
178C2×C22⋊D11—42no—
179C2×C22⋊D11—84no—
180C22×Dic11—24no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—82no—
184#4339—28no—
185#4339—28no—
186#4339—44no—
187#4339—44no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44C2×D412yes—
194C2×C4×D11—24no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×Dic22—21no—
198C2×Dic22—21no—
199C2×Dic22—21no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22C2×D412yes—
203C11×C4⋊C4—22no—
204C11×C4⋊C4C2×D414yes—
205C11×C22⋊C4—216no—
206C11×C22⋊C4—24no—
207C42×C11—24no—
208C22⋊Dic11—28no—
209#4324—216no—
210#4323—216no—
211(C2×D11)⋊C4—28no—
212C4⋊Dic11—24no—
213C4⋊Dic11—22no—
214C4⋊Dic11C2×D414yes—
215Dic11⋊C4—28no—
216#4318—28no—
217C2×C11⋊C8—22no—
218C2×C11⋊C8—22no—
219C2×C11⋊C8—22no—
220C2×C11⋊C8—22no—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—44no—
223C2×C11⋊C8C2×D414yes—
224C22×AGL(1,ℤ/8)—111no—
225C2×#537—111no—
226C2×#535D1111yescharacteristic, complemented
227C2×#416—111no—
228C22×#102—111no—
229C2×#408—111no—
230#2000—114no—
231#1999—114no—
232#1736—111no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—44no—
244C23×C11—44no—
245C23×C11—48no—
246C23×C11—88no—
247C23×C11—84no—
248C23×C11—84no—
249C23×C11—88no—
250C23×C11#12012yes—
251C23×C11#12012yes—
252C23×C11#12112yes—
253C23×C11C22×D411yescharacteristic
254C22×D11—22no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—42no—
258C22×D11—42no—
259Q8×C11—44no—
260D4×C11—24no—
261D4×C11—24no—
262D4×C11—48no—
263D4×C11—42no—
264D4×C11—42no—
265D4×C11—48no—
266D4×C11—44no—
267D4×C11—816no—
268C2×C4×C11—22no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—42no—
278C2×C4×C11#12014yes—
279C2×C4×C11#12012yes—
280C2×C4×C11#12012yes—
281C2×C4×C11#12114yes—
282C2×C4×C11#12114yes—
283C2×C4×C11#12112yes—
284C2×C4×C11#12714yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C22⋊D11—48no—
292C22⋊D11—88no—
293C2×Dic11—22no—
294C2×Dic11—24no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—44no—
298C2×Dic11—84no—
299D44—22no—
300D44—22no—
301D44—41no—
302D44—41no—
303C4×D11—48no—
304Dic22—22no—
305Dic22—22no—
306Dic22—41no—
307Dic22—41no—
308C11⋊C8—24no—
309C11⋊C8—42no—
310C22×#41—111no—
311C22×#41C2×D1111yescharacteristic
312C23×D4C2×D1111yescharacteristic
313C2×AGL(1,ℤ/8)—224no—
314C2×AGL(1,ℤ/8)—224no—
315C2×AGL(1,ℤ/8)—224no—
316C22×SD16—112no—
317C22×D8—112no—
318C22×M16—111no—
319C23×C8—111no—
320#537—224no—
321#537—224no—
322#535—24no—
323#535—24no—
324C2×#127—21no—
325C2×#124—21no—
326C2×C22⋊Q8—112no—
327C2×C22⋊Q8—221no—
328C2×#121—112no—
329C2×#121—221no—
330C2×#121—222no—
331C2×#121C2×D1114yes—
332C2×#120—22no—
333C2×#117C2×D1111yescharacteristic
334C22×C4⋊C4—111no—
335#416—224no—
336C2×#103—112no—
337C2×#102—114no—
338C2×#102—112no—
339C2×#102—224no—
340#408—224no—
341C2×C22⋊C8—114no—
342#340—114no—
343C22×C11—22no—
344C22×C11—22no—
345C22×C11—24no—
346C22×C11—24no—
347C22×C11—42no—
348C22×C11—44no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—44no—
352C22×C11—48no—
353C22×C11—44no—
354C22×C11—816no—
355C22×C11—82no—
356C22×C11—82no—
357C22×C11—84no—
358C22×C11#39214yes—
359C22×C11C2×#12011yescharacteristic
360C22×C11C2×#12011yescharacteristic
361C22×C11C2×#12111yescharacteristic
362C22×C11#57612yes—
363C22×C11#57712yes—
364C2×D11—42no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—82no—
368C2×D11—82no—
369C4×C11—42no—
370C4×C11—44no—
371C4×C11#39214yes—
372C4×C11C2×#12011yescharacteristic
373C4×C11C2×#12111yescharacteristic
374C4×C11C2×#12111yescharacteristic
375C4×C11C2×#12711yescharacteristic
376Dic11—42no—
377Dic11—44no—
378C25—21no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—22no—
385C2×#41—114no—
386C2×#41—222no—
387C2×#41—222no—
388C2×#41—222no—
389C2×#41—222no—
390C2×#41—222no—
391C22×Q8—111no—
392C22×Q8C22⋊D1111yescharacteristic
393C22×D4—24no—
394C22×D4—22no—
395C22×D4—22no—
396C22×D4—22no—
397C22×D4—22no—
398C22×D4—21no—
399C22×D4—22no—
400C22×D4—111no—
401C22×D4—221no—
402C22×D4—222no—
403C22×D4C22⋊D1112yes—
404C22×D4C22⋊D1111yescharacteristic
405C22×D4C22⋊D1114yescomplemented
406C22×D4C22×D1112yes—
407C23×C4—221no—
408C23×C4—221no—
409C23×C4C22×D1112yes—
410C23×C4C22×D1111yescharacteristic
411AGL(1,ℤ/8)—2232no—
412C2×SD16—224no—
413C2×SD16—224no—
414C2×SD16—224no—
415C2×D8—224no—
416C2×D8—224no—
417C2×D8—224no—
418C2×M16—114no—
419C2×M16—222no—
420C2×M16—222no—
421C22×C8—112no—
422C22×C8—112no—
423C22×C8—222no—
424C22×C8—222no—
425C22×C8—222no—
426#127—28no—
427#124—28no—
428C22⋊Q8—224no—
429C22⋊Q8—224no—
430C22⋊Q8—228no—
431#121—28no—
432#121—28no—
433#121—224no—
434#121—224no—
435#121—228no—
436#121—2216no—
437#120—216no—
438#117—22no—
439#117C22⋊D1114yescomplemented
440C2×C4⋊C4—114no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—222no—
445C2×C4⋊C4C22×D1112yes—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—222no—
449C2×C22⋊C4—222no—
450C2×C42—21no—
451#103—224no—
452#102—228no—
453#102—224no—
454C22⋊C8—228no—
455C2×C11—24no—
456C2×C11—82no—
457C2×C11—84no—
458C2×C11C2×#39211yescharacteristic
459C2×C11#300811yescharacteristic
460C2×C11#301011yescharacteristic
461C2×C11#301212yes—
462C2×C11#306212yes—
463D11—82no—
464C24—22no—
465C24—24no—
466C24—42no—
467C24—42no—
468C24—82no—
469C24—82no—
470C24—221no—
471C24C2×C22⋊D1112yes—
472C24C2×C22⋊D1111yescharacteristic
473#41—44no—
474#41—44no—
475#41—44no—
476#41—44no—
477#41—228no—
478#41—228no—
479#41—444no—
480#41—444no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—112no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—216no—
494C2×D4—28no—
495C2×D4—22no—
496C2×D4—28no—
497C2×D4—22no—
498C2×D4—24no—
499C2×D4—22no—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—22no—
503C2×D4—22no—
504C2×D4—22no—
505C2×D4—42no—
506C2×D4—44no—
507C2×D4—42no—
508C2×D4—44no—
509C2×D4—84no—
510C2×D4—84no—
511C2×D4—112no—
512C2×D4—224no—
513C2×D4—228no—
514C2×D4—221no—
515C2×D4—221no—
516C2×D4—221no—
517C2×D4—221no—
518C2×D4—221no—
519C2×D4—442no—
520C2×D4—442no—
521C2×D4—884no—
522C2×D4C2×C22⋊D1114yes—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—222no—
531C22×C4—221no—
532C22×C4—224no—
533C22×C4—224no—
534C22×C4—442no—
535C22×C4—442no—
536C22×C4—882no—
537C22×C4D4×D1112yes—
538C22×C4D4×D1112yes—
539C22×C4D4×D1112yes—
540C22×C4#434112yes—
541C22×C4C2×C22⋊D1112yes—
542C22×C4C2×C22⋊D1111yescharacteristic
543C22×C4C2×C22⋊D1112yes—
544C22×C4C2×C22⋊D1112yes—
545C22×C4C23×D1111yescharacteristic
546SD16—2216no—
547D8—2216no—
548M16—228no—
549C2×C8—114no—
550C2×C8—222no—
551C2×C8—222no—
552C2×C8—222no—
553C2×C8—222no—
554C2×C8—222no—
555C2×C8—444no—
556C4⋊C4—22no—
557C4⋊C4—114no—
558C4⋊C4—228no—
559C4⋊C4—224no—
560C4⋊C4—222no—
561C4⋊C4C2×C22⋊D1114yes—
562C22⋊C4—216no—
563C22⋊C4—24no—
564C22⋊C4—228no—
565C22⋊C4—228no—
566C42—24no—
567C11#2339311yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—22no—
576C23—42no—
577C23—42no—
578C23—48no—
579C23—44no—
580C23—44no—
581C23—88no—
582C23—88no—
583C23—84no—
584C23—84no—
585C23—222no—
586C23—441no—
587C23—442no—
588C23—442no—
589C23—441no—
590C23#6699012yes—
591C23#6699212yes—
592C23#6700612yes—
593C23C22×C22⋊D1111yescharacteristic
594Q8—44no—
595Q8—222no—
596Q8—222no—
597Q8—441no—
598Q8—441no—
599D4—24no—
600D4—24no—
601D4—48no—
602D4—42no—
603D4—42no—
604D4—48no—
605D4—44no—
606D4—816no—
607D4—222no—
608D4—222no—
609D4—448no—
610D4—441no—
611D4—441no—
612D4—888no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—224no—
624C2×C4—222no—
625C2×C4—441no—
626C2×C4—444no—
627C2×C4—441no—
628C2×C4—448no—
629C2×C4—884no—
630C2×C4#6699014yes—
631C2×C4#6699012yes—
632C2×C4#6699114yes—
633C2×C4#6699214yes—
634C2×C4#6699212yes—
635C2×C4#6699314yes—
636C2×C4#6700612yes—
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4C2×D4×D1111yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C2×C4C2×#434111yescharacteristic
641C2×C4C22×C22⋊D1111yescharacteristic
642C2×C4C22×C22⋊D1111yescharacteristic
643C8—224no—
644C8—442no—
645C22—24no—
646C22—22no—
647C22—22no—
648C22—24no—
649C22—44no—
650C22—42no—
651C22—42no—
652C22—44no—
653C22—48no—
654C22—42no—
655C22—44no—
656C22—816no—
657C22—84no—
658C22—82no—
659C22—82no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—882no—
664C22—882no—
665C22#1062283614yes—
666C22C2×#6699011yescharacteristic
667C22C2×#6699211yescharacteristic
668C22#1062336612yes—
669C22#1062336712yes—
670C22C2×#6700611yescharacteristic
671C4—44no—
672C4—42no—
673C4—444no—
674C4—442no—
675C4#1062283614yes—
676C4C2×#6699011yescharacteristic
677C4C2×#6699111yescharacteristic
678C4C2×#6699211yescharacteristic
679C4C2×#6699311yescharacteristic
680C2—24no—
681C2—82no—
682C2—84no—
683C2—882no—
684C2C2×#1062283611yescharacteristic
685C2#1307788211yescharacteristic
686C2#1307790011yescharacteristic
687C2#1307792012yes—
688C2#1307829212yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11#23393
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#66985C2semidirect
2. C2×#10623364C2semidirect
3. C2×#10622615C2semidirect
4. C22×#66896C2semidirect
5. C2×#10622847C2semidirect
6. #13069619C2semidirect
7. #13069612C2semidirect
8. #13068337C2semidirect
9. C2×C11×#535C2semidirect
30. C2×#66983C22semidirect
32. C2×#66977C22semidirect
38. C2×C22⋊(C11⋊C8)C22semidirect
40. C2×#66874C22semidirect
41. C2×#66873C22semidirect
42. #10622167C22semidirect
60. C22×D4×C11D4semidirect
72. C2×#4339D4semidirect
82. C11×#117D4semidirect
103. C2×C4⋊Dic11D4semidirect
110. C2×#4318D4semidirect
226. C2×#535D11semidirect
405. C22×D4C22⋊D11semidirect
439. #117C22⋊D11semidirect
567. C11#23393semidirect

Maximal subgroups

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

subgroupindex
C22×#669852
C2×#106233642
C2×#106226152
C22×#668962
C2×#106228472
#130696192
#130696122
#130683372
C2×C11×#5352
#2339311