Finite Group Databasebeta

← #14780629

Subgroups — #14780629

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×#67002C211yesmaximal, characteristic, complemented
2C2×#10623361C211yesmaximal, characteristic, complemented
3C2×#10622846C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622847C211yesmaximal, characteristic, complemented
6#13069617C214yesmaximal, complemented
7#13069612C214yesmaximal, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C2×C11×#537C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C22×C11×#41C2211yescharacteristic
12C23×D44C2211yescharacteristic
13C11×#537—24no—
14C11×#537—24no—
15C2×C11×C22⋊Q8—21no—
16C2×C11×C22⋊Q8C2212yescomplemented
17C2×C11×#121—21no—
18C2×C11×#121—22no—
19C2×C11×#121C2212yescomplemented
20C22×C11×C4⋊C4C2211yescharacteristic
21#10623361—24no—
22#10623361—24no—
23C2×#67002—24no—
24C2×#67002—24no—
25C2×#67002—24no—
26C2×#67000—21no—
27C22×#4325C2212yes—
28C2×#66993—21no—
29C2×#66990—22no—
30C22×#4323C2212yes—
31C2×#66983C2214yes—
32C2×#66979C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C23×C11⋊C8C2211yescharacteristic
35#10622847—24no—
36#10622846—24no—
37C2×#66899C2212yescomplemented
38C2×#66896C2212yescomplemented
39C2×C22⋊(C11⋊C8)C2214yescomplemented
40C2×#66873—24no—
41C2×#66873C2214yes—
42#10622167C2214yescomplemented
43C24×D11—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—
50C2×C11×#41—22no—
51C2×C11×#41—22no—
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—22no—
55C2×C11×#41D414yescomplemented
56C22×Q8×C11D411yescharacteristic
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11—22no—
60C22×D4×C11D412yes—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2312yes—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—24no—
68C22×D44—22no—
69C22×D44—22no—
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—21no—
73C22×D44—22no—
74C22×D44D414yescomplemented
75C22×D44C2312yes—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8—24no—
79C11×#121—216no—
80C11×#121—28no—
81C11×#121—24no—
82C11×#121—24no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4D414yescomplemented
87C2×C11×C4⋊C4C2312yes—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C22⋊Dic11—21no—
91#67002—232no—
92#67000—28no—
93C2×#4325—24no—
94C2×#4325—24no—
95C2×#4325—24no—
96#66993—28no—
97#66990—216no—
98C2×#4323—24no—
99C2×#4323—24no—
100C2×#4323—24no—
101#66983—28no—
102#66983—28no—
103C2×(C2×D11)⋊C4—24no—
104#66979—22no—
105#66979D414yescomplemented
106C2×C4⋊Dic11C2312yes—
107C2×C4×Dic11—21no—
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#66899—24no—
117#66896—24no—
118C22⋊(C11⋊C8)—28no—
119#66873—28no—
120#23393—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11C2×D412yes—
123C24×C11C2×D411yescharacteristic
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—42no—
127C23×D11—42no—
128C23×D11—82no—
129C23×D11—82no—
130C11×#41—28no—
131C11×#41—28no—
132C11×#41—44no—
133C11×#41—44no—
134C11×#41—44no—
135C11×#41—44no—
136C11×#41—44no—
137C11×#41—44no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—21no—
142C2×Q8×C11—21no—
143C2×Q8×C11—21no—
144C2×Q8×C11—21no—
145C2×Q8×C11—21no—
146C2×Q8×C11C2×D412yes—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—28no—
152C2×D4×C11—22no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—42no—
161C2×D4×C11—42no—
162C2×D4×C11—84no—
163C2×D4×C11C2×D412yes—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—24no—
167C22×C4×C11—24no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—42no—
175C22×C4×C11—42no—
176C22×C4×C11—82no—
177C22×C4×C11C2×D412yes—
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D412yes—
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×D412yes—
184C22×C4×C11#4112yes—
185C22×C4×C11C2411yescharacteristic
186C2×C22⋊D11—216no—
187C2×C22⋊D11—84no—
188C2×C22⋊D11—84no—
189C22×Dic11—22no—
190C2×D44—24no—
191C2×D44—28no—
192C2×D44—28no—
193C2×D44—22no—
194C2×D44—22no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44—22no—
198C2×D44—42no—
199C2×D44—44no—
200C2×D44—42no—
201C2×D44—44no—
202C2×D44C2×D414yes—
203C11×C4⋊C4—28no—
204C11×C4⋊C4—24no—
205C11×C4⋊C4—22no—
206C11×C4⋊C4C2×D414yes—
207C11×C22⋊C4—28no—
208C11×C22⋊C4—28no—
209C22⋊Dic11—24no—
210#4325—216no—
211#4323—216no—
212(C2×D11)⋊C4—216no—
213C4⋊Dic11—22no—
214C4⋊Dic11C2×D414yes—
215C4×Dic11—24no—
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×#537D1111yescharacteristic, complemented
226C2×#535—111no—
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—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—24no—
240C23×C11—24no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11#12012yes—
246C23×C11#12012yes—
247C23×C11#12112yes—
248C23×C11C22×D411yescharacteristic
249C22×D11—24no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11—48no—
255C22×D11—88no—
256C22×D11—84no—
257C22×D11—84no—
258C22×D11—88no—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—41no—
262Q8×C11—41no—
263Q8×C11—44no—
264D4×C11—22no—
265D4×C11—22no—
266D4×C11—48no—
267D4×C11—48no—
268D4×C11—41no—
269D4×C11—41no—
270D4×C11—44no—
271D4×C11—88no—
272C2×C4×C11—22no—
273C2×C4×C11—24no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—44no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—42no—
283C2×C4×C11—42no—
284C2×C4×C11—48no—
285C2×C4×C11—84no—
286C2×C4×C11#12014yes—
287C2×C4×C11#12012yes—
288C2×C4×C11#12012yes—
289C2×C4×C11#12114yes—
290C2×C4×C11#12114yes—
291C2×C4×C11#12112yes—
292C2×C4×C11#12714yes—
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C22⋊D11—816no—
300C2×Dic11—24no—
301C2×Dic11—42no—
302C2×Dic11—42no—
303D44—24no—
304D44—24no—
305D44—42no—
306D44—42no—
307D44—48no—
308C11⋊C8—24no—
309C11⋊C8—42no—
310C22×#41C2×D1111yescharacteristic
311C22×#41C2×D1111yescharacteristic
312C23×D4—111no—
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—24no—
321#537—24no—
322#535—224no—
323#535—224no—
324C2×#127—221no—
325C2×#124—221no—
326C2×C22⋊Q8—21no—
327C2×C22⋊Q8C2×D1112yescomplemented
328C2×#121—21no—
329C2×#121—22no—
330C2×#121—114no—
331C2×#121C2×D1112yescomplemented
332C2×#120—222no—
333C2×#117—111no—
334C22×C4⋊C4C2×D1111yescharacteristic
335#416—224no—
336C2×#103—112no—
337C2×#102—112no—
338C2×#102—114no—
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—42no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—44no—
354C22×C11—44no—
355C22×C11—82no—
356C22×C11—82no—
357C22×C11#39214yes—
358C22×C11C2×#12011yescharacteristic
359C22×C11C2×#12011yescharacteristic
360C22×C11C2×#12111yescharacteristic
361C22×C11#57612yes—
362C22×C11#57712yes—
363C2×D11—44no—
364C2×D11—48no—
365C2×D11—816no—
366C2×D11—82no—
367C2×D11—82no—
368C2×D11—84no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—44no—
372C4×C11#39214yes—
373C4×C11C2×#12011yescharacteristic
374C4×C11C2×#12111yescharacteristic
375C4×C11C2×#12111yescharacteristic
376C4×C11C2×#12711yescharacteristic
377Dic11—44no—
378C25—221no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41—22no—
382C2×#41—22no—
383C2×#41—22no—
384C2×#41—22no—
385C2×#41—22no—
386C2×#41—22no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41C22⋊D1114yescomplemented
391C22×Q8C22⋊D1111yescharacteristic
392C22×Q8C22×D1111yescharacteristic
393C22×D4—21no—
394C22×D4—22no—
395C22×D4—114no—
396C22×D4—112no—
397C22×D4—224no—
398C22×D4—222no—
399C22×D4—222no—
400C22×D4—222no—
401C22×D4—222no—
402C22×D4—222no—
403C22×D4—221no—
404C22×D4C22⋊D1112yes—
405C22×D4C22⋊D1111yescharacteristic
406C22×D4C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
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—228no—
427#124—228no—
428C22⋊Q8—28no—
429C22⋊Q8—24no—
430C22⋊Q8—24no—
431#121—216no—
432#121—28no—
433#121—24no—
434#121—24no—
435#121—228no—
436#121—228no—
437#120—2216no—
438#117—114no—
439#117—222no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—22no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4—112no—
444C2×C4⋊C4C22⋊D1114yescomplemented
445C2×C4⋊C4C22×D1112yes—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—224no—
450C2×C42—221no—
451#103—224no—
452#102—224no—
453#102—228no—
454C22⋊C8—228no—
455C2×C11—24no—
456C2×C11—82no—
457C2×C11—82no—
458C2×C11C2×#39211yescharacteristic
459C2×C11#300811yescharacteristic
460C2×C11#301011yescharacteristic
461C2×C11#301212yes—
462C2×C11#306212yes—
463D11—84no—
464C24—21no—
465C24—222no—
466C24—224no—
467C24—442no—
468C24—442no—
469C24—882no—
470C24—882no—
471C24C2×C22⋊D1112yes—
472C24C2×C22⋊D1111yescharacteristic
473#41—28no—
474#41—28no—
475#41—44no—
476#41—44no—
477#41—44no—
478#41—44no—
479#41—44no—
480#41—44no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8C2×C22⋊D1112yes—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—24no—
493C2×D4—24no—
494C2×D4—28no—
495C2×D4—22no—
496C2×D4—22no—
497C2×D4—22no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—84no—
506C2×D4—114no—
507C2×D4—2216no—
508C2×D4—228no—
509C2×D4—224no—
510C2×D4—228no—
511C2×D4—222no—
512C2×D4—222no—
513C2×D4—222no—
514C2×D4—222no—
515C2×D4—222no—
516C2×D4—444no—
517C2×D4—442no—
518C2×D4—444no—
519C2×D4—442no—
520C2×D4—884no—
521C2×D4—884no—
522C2×D4C2×C22⋊D1112yes—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—42no—
534C22×C4—42no—
535C22×C4—82no—
536C22×C4—222no—
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—28no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—114no—
560C4⋊C4—222no—
561C4⋊C4C2×C22⋊D1114yes—
562C22⋊C4—28no—
563C22⋊C4—28no—
564C22⋊C4—2216no—
565C22⋊C4—224no—
566C42—224no—
567C11#2339311yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—22no—
571C23—22no—
572C23—24no—
573C23—24no—
574C23—22no—
575C23—22no—
576C23—41no—
577C23—41no—
578C23—42no—
579C23—42no—
580C23—224no—
581C23—442no—
582C23—448no—
583C23—444no—
584C23—444no—
585C23—442no—
586C23—888no—
587C23—888no—
588C23—884no—
589C23—884no—
590C23#6699012yes—
591C23#6699212yes—
592C23#6700612yes—
593C23C22×C22⋊D1111yescharacteristic
594Q8—22no—
595Q8—22no—
596Q8—41no—
597Q8—41no—
598Q8—44no—
599D4—22no—
600D4—22no—
601D4—48no—
602D4—48no—
603D4—41no—
604D4—41no—
605D4—44no—
606D4—88no—
607D4—224no—
608D4—224no—
609D4—442no—
610D4—442no—
611D4—448no—
612D4—8816no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—44no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—48no—
626C2×C4—84no—
627C2×C4—224no—
628C2×C4—442no—
629C2×C4—442no—
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—42no—
653C22—42no—
654C22—44no—
655C22—42no—
656C22—42no—
657C22—82no—
658C22—82no—
659C22—448no—
660C22—444no—
661C22—8816no—
662C22—884no—
663C22—882no—
664C22—882no—
665C22#1062283614yes—
666C22C2×#6699011yescharacteristic
667C22C2×#6699211yescharacteristic
668C22#1062336612yes—
669C22#1062336812yes—
670C22C2×#6700611yescharacteristic
671C4—44no—
672C4—42no—
673C4—42no—
674C4—444no—
675C4#1062283614yes—
676C4C2×#6699011yescharacteristic
677C4C2×#6699111yescharacteristic
678C4C2×#6699211yescharacteristic
679C4C2×#6699311yescharacteristic
680C2—24no—
681C2—82no—
682C2—82no—
683C2—884no—
684C2C2×#1062283611yescharacteristic
685C2#1307788411yescharacteristic
686C2#1307790211yescharacteristic
687C2#1307791712yes—
688C2#1307829812yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#537C2
socleC23×C11C22×D4
hypercenterC2×#537D11
hypocenterC11#23393
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C22×#67002C2semidirect
2. C2×#10623361C2semidirect
3. C2×#10622846C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622847C2semidirect
6. #13069617C2semidirect
7. #13069612C2semidirect
8. #13068335C2semidirect
9. C2×C11×#537C2semidirect
16. C2×C11×C22⋊Q8C22semidirect
19. C2×C11×#121C22semidirect
37. C2×#66899C22semidirect
38. C2×#66896C22semidirect
39. C2×C22⋊(C11⋊C8)C22semidirect
42. #10622167C22semidirect
55. C2×C11×#41D4semidirect
74. C22×D44D4semidirect
86. C2×C11×C4⋊C4D4semidirect
105. #66979D4semidirect
110. C2×#4318D4semidirect
225. C2×#537D11semidirect
327. C2×C22⋊Q8C2×D11semidirect
331. C2×#121C2×D11semidirect
390. C2×#41C22⋊D11semidirect
444. C2×C4⋊C4C22⋊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×#670022
C2×#106233612
C2×#106228462
C22×#668732
C2×#106228472
#130696172
#130696122
#130683352
C2×C11×#5372
#2339311