Finite Group Databasebeta

← #14755049

Subgroups — #14755049

Order 2816.

1842 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×#10623041C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic, complemented
3C2×#10622746C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5C2×#10622742C211yesmaximal, characteristic, complemented
6#13068937C212yesmaximal, complemented
7#13068932C212yesmaximal, complemented
8#13068927C212yesmaximal, complemented
9#13068922C212yesmaximal, complemented
10C2×#10622167C211yesmaximal, characteristic, complemented
11C11×#1736C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C22×#4339C2211yescharacteristic
14C22×C11×M16C2211yescharacteristic
15C2×C11×#117C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C2×#66983—22no—
18C22×C4⋊Dic11C2211yescharacteristic
19C23×C11⋊C8C2211yescharacteristic
20#10623054—24no—
21#10623054—24no—
22#10623041—24no—
23#10623041C418yescomplemented
24C2×#66950—21no—
25C2×#66950C2212yes—
26C2×#66948—21no—
27C2×#66948C2212yes—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×(C22⋊D11)⋊C4—22no—
31C2×C4×D44—21no—
32C2×C4×Dic22—21no—
33#10622746—24no—
34#10622742—24no—
35C2×#66885C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×(C2×D11)⋊C8C2212yes—
38C2×#66880C2212yes—
39#10622615—24no—
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C11×#340C2212yes—
45C11×#340C2212yes—
46#10622167C2212yes—
47#10622167C2212yes—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C22×C22⋊D11D412yes—
52C23×Dic11—21no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339—22no—
58C2×#4339—22no—
59C2×#4339—22no—
60C2×#4339—22no—
61C2×#4339—22no—
62C2×#4339C2×C414yes—
63C2×#4339C2×C414yescomplemented
64C2×#4339D414yes—
65C22×D44—22no—
66C22×D44D411yescharacteristic
67C22×D44C2311yescharacteristic
68C22×C4×D11—21no—
69C22×C4×D11—22no—
70C22×C4×D11C2312yes—
71C22×Dic22D411yescharacteristic
72C22×Dic22C2311yescharacteristic
73C2×C11×M16—22no—
74C2×C11×M16—22no—
75C2×C11×M16—22no—
76C22×C8×C11C2312yes—
77C11×#117—22no—
78C11×#117D414yescomplemented
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4C2×C414yescomplemented
82C2×C11×C4⋊C4C2312yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C42×C11—21no—
87#66983—216no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11D414yescomplemented
95C2×C4⋊Dic11C2312yes—
96C2×Dic11⋊C4—22no—
97C2×C4×Dic11—22no—
98C22×C11⋊C8—22no—
99C22×C11⋊C8—22no—
100C22×C11⋊C8—22no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66950—24no—
104#66950—28no—
105#66950C2×C418yescomplemented
106#66948—28no—
107#66948—24no—
108#66948C2×C418yescomplemented
109#66945—24no—
110#66945—24no—
111C4⋊C4×D11—24no—
112C4⋊C4×D11—24no—
113(C22⋊D11)⋊C4—216no—
114C4×D44—28no—
115C4×Dic22—28no—
116#66885—24no—
117(C2×D11)⋊C8—24no—
118(C2×D11)⋊C8—24no—
119#66880—24no—
120#66874—22no—
121#66874—22no—
122#66873—22no—
123#66873—22no—
124#20915—111nomaximal, Sylow
125C24×C11C2×D411yescharacteristic
126C23×D11—21no—
127C23×D11C2×D412yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—81no—
133C22×C4×C11—81no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—24no—
144C2×C22⋊D11—24no—
145C2×C22⋊D11—42no—
146C2×C22⋊D11—42no—
147C2×C22⋊D11C22⋊C418yes—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—21no—
151C22×Dic11—81no—
152C22×Dic11—81no—
153C22×Dic11C2×D412yes—
154#4339—28no—
155#4339—28no—
156#4339—28no—
157#4339—28no—
158#4339—28no—
159#4339—28no—
160#4339—44no—
161#4339—44no—
162C2×D44—28no—
163C2×D44—22no—
164C2×D44—22no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—82no—
171C2×D44—82no—
172C2×D44C22⋊C414yes—
173C2×D44C22×C412yes—
174C2×C4×D11—28no—
175C2×C4×D11—24no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—42no—
181C2×C4×D11—42no—
182C2×C4×D11—82no—
183C2×C4×D11—82no—
184C2×C4×D11C22×C414yes—
185C2×C4×D11C2×D414yes—
186C2×Dic22—22no—
187C2×Dic22—22no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22—21no—
193C2×Dic22C22⋊C414yes—
194C2×Dic22C22×C412yes—
195C11×M16—44no—
196C2×C8×C11—22no—
197C2×C8×C11—22no—
198C2×C8×C11—22no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—22no—
203C11×C4⋊C4C22×C414yes—
204C11×C4⋊C4C2×D412yes—
205C11×C4⋊C4C2×D412yes—
206C11×C22⋊C4—24no—
207C42×C11—24no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—28no—
211C4⋊Dic11—28no—
212C4⋊Dic11—24no—
213C4⋊Dic11—22no—
214C4⋊Dic11C2×D414yes—
215Dic11⋊C4—28no—
216C4×Dic11—28no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—44no—
224C2×#537—111no—
225C2×#520—111no—
226C2×#417—111no—
227C2×#416—111no—
228C2×#408—111no—
229#1875—112no—
230#1874—112no—
231#1873—112no—
232#1872—112no—
233#1736D1111yescharacteristic, complemented
234C2×#340—111no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C2×C22⋊C412yes—
240C23×C11#12012yes—
241C23×C11#12312yes—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11C2×C22⋊C414yes—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—84no—
267C2×C4×C11C2×C22⋊C412yes—
268C2×C4×C11C4×D414yes—
269C2×C4×C11C4×D414yes—
270C2×C4×C11#12012yes—
271C2×C4×C11#12114yes—
272C2×C4×C11#12114yes—
273C2×C4×C11#12312yes—
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C22⋊D11—216no—
281C22⋊D11—48no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—84no—
291C2×Dic11C2×C22⋊C414yes—
292D44—22no—
293D44—22no—
294D44—28no—
295D44—41no—
296D44—41no—
297D44—88no—
298C4×D11—24no—
299C4×D11—24no—
300C4×D11—24no—
301C4×D11—24no—
302C4×D11—48no—
303C4×D11—88no—
304Dic22—28no—
305Dic22—22no—
306Dic22—22no—
307Dic22—41no—
308Dic22—41no—
309C8×C11—42no—
310C11⋊C8—41no—
311C11⋊C8—41no—
312C22×#41—111no—
313C22×#41—111no—
314C22×M16C2×D1111yescharacteristic
315C23×C8—111no—
316#537—118no—
317#537—224no—
318C2×C22⋊Q8—112no—
319C2×C22⋊Q8—221no—
320C2×#121—112no—
321C2×#121—221no—
322C2×#121—222no—
323#520—224no—
324#520—224no—
325C2×C4×Q8—221no—
326C2×C4×D4—221no—
327C2×C4×D4—222no—
328C2×#117—112no—
329C2×#117C2×D1111yescharacteristic
330C22×C4⋊C4—111no—
331C22×C4⋊C4—112no—
332C22×C4⋊C4C2×D1111yescharacteristic
333#417—224no—
334#416—224no—
335C2×#103—112no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#102—112no—
339C2×#102—111no—
340C2×#102—111no—
341#408—224no—
342C2×C22⋊C8—112no—
343C2×C22⋊C8—112no—
344#340—112no—
345#340—112no—
346#340C2×D1112yes—
347#340C2×D1112yes—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11#38614yes—
355C22×C11C22×C22⋊C411yescharacteristic
356C22×C11C2×#12011yescharacteristic
357C22×C11C2×#12311yescharacteristic
358C22×C11#57611yescharacteristic
359C22×C11#57711yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57811yescharacteristic
362C2×D11—24no—
363C2×D11—24no—
364C2×D11—24no—
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
371C2×D11—42no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C4×C11—44no—
377C4×C11—42no—
378C4×C11—42no—
379C4×C11#38614yes—
380C4×C11C2×C4×D411yescharacteristic
381C4×C11C2×C4×D411yescharacteristic
382C4×C11C2×#12111yescharacteristic
383C4×C11C2×#12111yescharacteristic
384Dic11—24no—
385Dic11—44no—
386Dic11—42no—
387C2×#41—114no—
388C2×#41—114no—
389C2×#41—114no—
390C2×#41—222no—
391C2×#41—222no—
392C2×#41—222no—
393C2×#41—222no—
394C2×#41—222no—
395C2×#41—222no—
396C2×#41—222no—
397C2×#41—222no—
398C2×#41—222no—
399C22×Q8—111no—
400C22×Q8—111no—
401C22×D4—112no—
402C22×D4—111no—
403C22×D4—111no—
404C22×D4—222no—
405C22×D4—221no—
406C23×C4—21no—
407C23×C4—112no—
408C23×C4—222no—
409C23×C4—221no—
410C23×C4—221no—
411C23×C4C22×D1111yescharacteristic
412C2×M16—22no—
413C2×M16—22no—
414C2×M16—22no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—222no—
418C22×C8—222no—
419C22×C8—222no—
420C22×C8C22×D1112yes—
421C22⋊Q8—118no—
422C22⋊Q8—224no—
423C22⋊Q8—228no—
424#121—118no—
425#121—224no—
426#121—228no—
427#121—2216no—
428C4×Q8—228no—
429C4×D4—228no—
430C4×D4—2216no—
431#117—22no—
432#117—224no—
433#117—224no—
434#117D4414yescomplemented
435C2×C4⋊C4—21no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—114no—
438C2×C4⋊C4—112no—
439C2×C4⋊C4—224no—
440C2×C4⋊C4—222no—
441C2×C4⋊C4—222no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C4⋊C4—224no—
445C2×C4⋊C4C4×D1114yescomplemented
446C2×C4⋊C4C22×D1112yes—
447C2×C4⋊C4C22×D1111yescharacteristic
448C2×C4⋊C4C22×D1111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—222no—
451C2×C22⋊C4—222no—
452C2×C22⋊C4—222no—
453C2×C42—21no—
454C2×C42—222no—
455#103—224no—
456#103—222no—
457#103—222no—
458#102—224no—
459#102—222no—
460#102—222no—
461C22⋊C8—224no—
462C22⋊C8—224no—
463C2×C11—24no—
464C2×C11C2×#38611yescharacteristic
465C2×C11#289711yescharacteristic
466C2×C11#289811yescharacteristic
467C2×C11#301211yescharacteristic
468C2×C11#301311yescharacteristic
469C2×C11#309811yescharacteristic
470C2×C11#309911yescharacteristic
471D11—44no—
472D11—82no—
473C24—112no—
474C24—221no—
475C24D4×D1111yescharacteristic
476#41—228no—
477#41—228no—
478#41—228no—
479#41—228no—
480#41—228no—
481#41—228no—
482#41—444no—
483#41—444no—
484C2×Q8—114no—
485C2×Q8—112no—
486C2×Q8—222no—
487C2×Q8—222no—
488C2×Q8—221no—
489C2×Q8—221no—
490C2×Q8—221no—
491C2×Q8—221no—
492C2×Q8—221no—
493C2×D4—118no—
494C2×D4—114no—
495C2×D4—112no—
496C2×D4—228no—
497C2×D4—224no—
498C2×D4—224no—
499C2×D4—224no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—442no—
508C2×D4—442no—
509C2×D4—882no—
510C2×D4—882no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—24no—
515C22×C4—81no—
516C22×C4—81no—
517C22×C4—112no—
518C22×C4—114no—
519C22×C4—114no—
520C22×C4—228no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—221no—
527C22×C4—224no—
528C22×C4—224no—
529C22×C4—442no—
530C22×C4—442no—
531C22×C4—882no—
532C22×C4—882no—
533C22×C4—881no—
534C22×C4—881no—
535C22×C4C2×C4×D1112yes—
536C22×C4C2×D4412yes—
537C22×C4#433912yes—
538C22×C4D4×D1111yescharacteristic
539C22×C4D4×D1112yes—
540C22×C4D4×D1112yes—
541C22×C4#434312yes—
542C22×C4C23×D1111yescharacteristic
543M16—44no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—444no—
554C4⋊C4—24no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—114no—
559C4⋊C4—228no—
560C4⋊C4—228no—
561C4⋊C4—224no—
562C4⋊C4—222no—
563C4⋊C4C2×C4×D1114yes—
564C4⋊C4C2×D4412yes—
565C4⋊C4C2×D4412yes—
566C22⋊C4—24no—
567C22⋊C4—228no—
568C22⋊C4—228no—
569C22⋊C4—228no—
570C42—24no—
571C42—228no—
572C11#2091511yescharacteristic, complemented, Sylow
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—114no—
578C23—222no—
579C23—222no—
580C23—222no—
581C23—222no—
582C23—222no—
583C23—222no—
584C23—222no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23C22⋊C4×D1112yes—
592C23#6693512yes—
593C23#6694712yes—
594C23C2×D4×D1111yescharacteristic
595Q8—228no—
596Q8—222no—
597Q8—222no—
598Q8—441no—
599Q8—441no—
600D4—2216no—
601D4—222no—
602D4—222no—
603D4—228no—
604D4—448no—
605D4—441no—
606D4—441no—
607D4—888no—
608C2×C4—24no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—114no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—224no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—224no—
625C2×C4—222no—
626C2×C4—224no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—448no—
632C2×C4—888no—
633C2×C4—884no—
634C2×C4C4×D4414yes—
635C2×C4C22⋊C4×D1112yes—
636C2×C4#6693512yes—
637C2×C4#6693714yes—
638C2×C4#6694614yes—
639C2×C4#6694712yes—
640C2×C4#6694814yes—
641C2×C4C22×C4×D1111yescharacteristic
642C2×C4C22×D4411yescharacteristic
643C2×C4C2×#433911yescharacteristic
644C2×C4C2×D4×D1111yescharacteristic
645C2×C4C2×D4×D1111yescharacteristic
646C2×C4C2×#434311yescharacteristic
647C8—42no—
648C8—441no—
649C8—441no—
650C22—22no—
651C22—22no—
652C22—22no—
653C22—22no—
654C22—22no—
655C22—22no—
656C22—224no—
657C22—224no—
658C22—224no—
659C22—442no—
660C22—442no—
661C22—442no—
662C22—442no—
663C22—442no—
664C22—442no—
665C22—442no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22—881no—
670C22#1062227814yes—
671C22C2×C22⋊C4×D1111yescharacteristic
672C22C2×#6693511yescharacteristic
673C22C2×#6694711yescharacteristic
674C22#1062330511yescharacteristic
675C22#1062330611yescharacteristic
676C22#1062330911yescharacteristic
677C22#1062331011yescharacteristic
678C4—44no—
679C4—42no—
680C4—42no—
681C4—224no—
682C4—444no—
683C4—442no—
684C4#1062227814yes—
685C4C2×C4×D4411yescharacteristic
686C4C2×#6693711yescharacteristic
687C4C2×#6694611yescharacteristic
688C4C2×#6694811yescharacteristic
689C2—24no—
690C2—444no—
691C2—882no—
692C2C2×#1062227811yescharacteristic
693C2#1307714111yescharacteristic
694C2#1307714811yescharacteristic
695C2#1307792211yescharacteristic
696C2#1307793311yescharacteristic
697C2#1307859811yescharacteristic
698C2#1307860911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC2×#10623041C2
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20915
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C2×#10623054C2semidirect
3. C2×#10622746C2semidirect
4. C2×#10622615C2semidirect
5. C2×#10622742C2semidirect
6. #13068937C2semidirect
7. #13068932C2semidirect
8. #13068927C2semidirect
9. #13068922C2semidirect
10. C2×#10622167C2semidirect
11. C11×#1736C2semidirect
23. #10623041C4semidirect
63. C2×#4339C2×C4semidirect
78. C11×#117D4semidirect
81. C2×C11×C4⋊C4C2×C4semidirect
94. C2×C4⋊Dic11D4semidirect
105. #66950C2×C4semidirect
108. #66948C2×C4semidirect
233. #1736D11semidirect
434. #117D44semidirect
445. C2×C4⋊C4C4×D11semidirect
572. C11#20915semidirect

Maximal subgroups

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

subgroupindex
C2×#106230412
C2×#106230542
C2×#106227462
C2×#106226152
C2×#106227422
#130689372
#130689322
#130689272
#130689222
C2×#106221672
C11×#17362
#2091511