Finite Group Databasebeta

← #14780855

Subgroups — #14780855

Order 2816.

2290 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67002C211yesmaximal, characteristic, complemented
2C23×#4323C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13071196C211yesmaximal, characteristic, complemented
6#13069693C214yesmaximal, complemented
7#13069687C214yesmaximal, complemented
8#13068313C211yesmaximal, characteristic, complemented
9C2×C11×#535C211yesmaximal, characteristic, complemented
10C22×C11×#41C2211yescharacteristic
11C23×D4×C11C2211yescharacteristic
12C23×D44C2211yescharacteristic
13C11×#535—24no—
14C11×#535—24no—
15C2×C11×#127C2212yescomplemented
16C2×C11×#124C2212yescomplemented
17C2×C11×#121—22no—
18C2×C11×#120—22no—
19C2×C11×#117C2211yescharacteristic
20C2×#67002—24no—
21C2×#67002—24no—
22C2×#67002—24no—
23C22×#4325C2212yescomplemented
24C22×#4323—24no—
25C22×#4323—24no—
26C22×#4323—24no—
27C22×#4323C2214yes—
28C22×#4323C2212yescomplemented
29C2×#66979C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C23×C11⋊C8C2211yescharacteristic
32#10622846—24no—
33C2×#66899C2212yescomplemented
34#10622828—24no—
35C2×#66896C2212yescomplemented
36C2×#66896C2214yescomplemented
37#10622601—22no—
38#10622568—22no—
39#10622552C2214yescomplemented
40#10622162C2214yescomplemented
41C25×C11—21no—
42C24×D11—21no—
43C2×C11×#41—22no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41D414yes—
49C22×Q8×C11C2311yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—22no—
56C22×D4×C11—24no—
57C22×D4×C11—22no—
58C22×D4×C11D414yes—
59C22×D4×C11C2312yes—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×D44—22no—
64C22×D44—22no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—22no—
69C22×D44D414yescomplemented
70C22×D44C2312yes—
71C11×#127—24no—
72C11×#127—24no—
73C11×#124—24no—
74C11×#124—24no—
75C11×#121—216no—
76C11×#120—216no—
77C11×#117—22no—
78C11×#117—22no—
79C2×C11×C4⋊C4D412yes—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4D412yes—
82C2×C42×C11C2312yes—
83C2×C22⋊Dic11—21no—
84#67002—232no—
85C2×#4325—24no—
86C2×#4325—24no—
87C2×#4325—24no—
88C2×#4323—232no—
89C2×#4323—28no—
90C2×#4323—24no—
91C2×#4323—28no—
92C2×#4323—24no—
93C2×#4323—28no—
94C2×#4323—24no—
95C2×(C2×D11)⋊C4—28no—
96#66979—22no—
97#66979—22no—
98C2×C4⋊Dic11C2312yes—
99C2×C4×Dic11—21no—
100C2×#4318—22no—
101C2×#4318—22no—
102C2×#4318D414yescomplemented
103C22×C11⋊C8—22no—
104C22×C11⋊C8—22no—
105C22×C11⋊C8D414yescomplemented
106C22×C11⋊C8C2312yes—
107C22×C11⋊C8C2312yes—
108#66899—24no—
109#66896—28no—
110#66896—24no—
111#23422—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—24no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11—84no—
118C24×C11C2×D411yescharacteristic
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—42no—
122C23×D11—42no—
123C23×D11—84no—
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—44no—
127C11×#41—44no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11C2×D412yes—
134C2×D4×C11—24no—
135C2×D4×C11—216no—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—28no—
139C2×D4×C11—22no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—44no—
152C2×D4×C11—42no—
153C2×D4×C11—44no—
154C2×D4×C11—42no—
155C2×D4×C11—88no—
156C2×D4×C11C2×D414yes—
157C2×D4×C11C2×D412yes—
158C22×C4×C11—21no—
159C22×C4×C11—24no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C22×Dic11—22no—
172C2×D44—28no—
173C2×D44—28no—
174C2×D44—24no—
175C2×D44—22no—
176C2×D44—22no—
177C2×D44—22no—
178C2×D44—22no—
179C2×D44—22no—
180C2×D44—42no—
181C2×D44—44no—
182C2×D44—44no—
183C2×D44—42no—
184C2×D44C2×D414yes—
185C11×C4⋊C4—24no—
186C11×C22⋊C4—216no—
187C11×C22⋊C4—24no—
188C42×C11—22no—
189C42×C11—22no—
190C22⋊Dic11—42no—
191#4325—216no—
192#4323—232no—
193#4323—216no—
194(C2×D11)⋊C4—88no—
195C4⋊Dic11—22no—
196C4⋊Dic11—22no—
197C4×Dic11—42no—
198#4318—28no—
199C2×C11⋊C8—28no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8C2×D414yes—
205C2×C11⋊C8C2×D414yes—
206C22×AGL(1,ℤ/8)—111no—
207C23×D8—111no—
208C2×#535D1111yescharacteristic, complemented
209C2×#418—111no—
210C2×#416—111no—
211#2309—111no—
212#2012—114no—
213#2011—114no—
214#1729—111no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—41no—
219C23×C11—42no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—88no—
226C23×C11—88no—
227C23×C11—88no—
228C23×C11#12012yes—
229C23×C11#12112yes—
230C23×C11#12712yes—
231C23×C11C22×D411yescharacteristic
232C22×D11—24no—
233C22×D11—42no—
234C22×D11—42no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—88no—
238C22×D11—88no—
239C22×D11—88no—
240Q8×C11—22no—
241Q8×C11—22no—
242Q8×C11—41no—
243Q8×C11—41no—
244D4×C11—24no—
245D4×C11—22no—
246D4×C11—24no—
247D4×C11—22no—
248D4×C11—48no—
249D4×C11—42no—
250D4×C11—41no—
251D4×C11—42no—
252D4×C11—41no—
253D4×C11—48no—
254D4×C11—816no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—28no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—48no—
261C2×C4×C11#12014yes—
262C2×C4×C11#12014yes—
263C2×C4×C11#12012yes—
264C2×C4×C11#12112yes—
265C2×C4×C11#12114yes—
266C2×C4×C11#12114yes—
267C2×C4×C11#12712yes—
268C2×C4×C11C22×D411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×D411yescharacteristic
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×Dic11—42no—
275C2×Dic11—44no—
276D44—24no—
277D44—24no—
278D44—42no—
279D44—42no—
280D44—48no—
281C11⋊C8—24no—
282C11⋊C8—24no—
283C22×#41C2×D1111yescharacteristic
284C23×D4—111no—
285C23×D4C2×D1111yescharacteristic
286C2×AGL(1,ℤ/8)—224no—
287C2×AGL(1,ℤ/8)—224no—
288C2×AGL(1,ℤ/8)—224no—
289C22×SD16—112no—
290C22×D8—114no—
291C22×D8—112no—
292C22×D8—224no—
293C22×D8—224no—
294C22×D8—224no—
295C22×M16—111no—
296C23×C8—111no—
297#535—24no—
298#535—24no—
299C2×#127C2×D1112yescomplemented
300C2×#124C2×D1112yescomplemented
301C2×#121—22no—
302C2×#120—22no—
303C2×#117—111no—
304C2×#117C2×D1111yescharacteristic
305#418—224no—
306#416—224no—
307C2×#103—112no—
308C2×#102—112no—
309C2×#102—114no—
310#390—114no—
311#390—222no—
312#379—222no—
313#336—114no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—48no—
321C22×C11—816no—
322C22×C11—82no—
323C22×C11—84no—
324C22×C11—82no—
325C22×C11—84no—
326C22×C11#39214yes—
327C22×C11C2×#12011yescharacteristic
328C22×C11C2×#12111yescharacteristic
329C22×C11C2×#12711yescharacteristic
330C22×C11#57614yes—
331C2×D11—44no—
332C2×D11—48no—
333C2×D11—816no—
334C2×D11—84no—
335C2×D11—84no—
336C4×C11—42no—
337C4×C11—44no—
338C4×C11#39214yes—
339C4×C11C2×#12011yescharacteristic
340C4×C11C2×#12011yescharacteristic
341C4×C11C2×#12111yescharacteristic
342C4×C11C2×#12111yescharacteristic
343Dic11—82no—
344C25—21no—
345C25—221no—
346C2×#41—22no—
347C2×#41—22no—
348C2×#41—22no—
349C2×#41—22no—
350C2×#41—22no—
351C2×#41C22⋊D1114yes—
352C22×Q8C22×D1111yescharacteristic
353C22×D4—21no—
354C22×D4—22no—
355C22×D4—22no—
356C22×D4—22no—
357C22×D4—22no—
358C22×D4—21no—
359C22×D4—22no—
360C22×D4—24no—
361C22×D4—114no—
362C22×D4—112no—
363C22×D4—222no—
364C22×D4—222no—
365C22×D4—222no—
366C22×D4—222no—
367C22×D4—222no—
368C22×D4—221no—
369C22×D4C22⋊D1114yes—
370C22×D4C22×D1112yes—
371C22×D4C22×D1111yescharacteristic
372C23×C4—21no—
373C23×C4C22×D1111yescharacteristic
374AGL(1,ℤ/8)—2232no—
375C2×SD16—224no—
376C2×SD16—224no—
377C2×SD16—224no—
378C2×D8—228no—
379C2×D8—224no—
380C2×D8—228no—
381C2×D8—224no—
382C2×D8—2232no—
383C2×D8—228no—
384C2×D8—224no—
385C2×M16—114no—
386C2×M16—222no—
387C2×M16—222no—
388C22×C8—114no—
389C22×C8—112no—
390C22×C8—112no—
391C22×C8—222no—
392C22×C8—222no—
393#127—24no—
394#127—24no—
395#124—24no—
396#124—24no—
397#121—216no—
398#120—216no—
399#117—22no—
400#117—22no—
401#117—222no—
402#117—222no—
403C2×C4⋊C4—112no—
404C2×C4⋊C4C22⋊D1112yes—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—228no—
408C2×C22⋊C4C22⋊D1112yes—
409C2×C42—221no—
410C2×C42C22×D1112yes—
411#103—224no—
412#102—224no—
413#102—228no—
414C2×C11—24no—
415C2×C11—82no—
416C2×C11—84no—
417C2×C11C2×#39211yescharacteristic
418C2×C11#300812yes—
419C2×C11#304112yes—
420C2×C11#315512yes—
421D11—84no—
422C24—22no—
423C24—21no—
424C24—24no—
425C24—42no—
426C24—42no—
427C24—84no—
428C24—222no—
429C24—224no—
430C24—442no—
431C24—442no—
432C24—884no—
433C24C2×C22⋊D1111yescharacteristic
434#41—28no—
435#41—28no—
436#41—44no—
437#41—44no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8C2×C22⋊D1112yes—
444C2×D4—24no—
445C2×D4—216no—
446C2×D4—28no—
447C2×D4—28no—
448C2×D4—24no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—22no—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—44no—
462C2×D4—42no—
463C2×D4—44no—
464C2×D4—42no—
465C2×D4—88no—
466C2×D4—114no—
467C2×D4—228no—
468C2×D4—228no—
469C2×D4—224no—
470C2×D4—222no—
471C2×D4—222no—
472C2×D4—222no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—444no—
476C2×D4—444no—
477C2×D4—442no—
478C2×D4—442no—
479C2×D4C2×C22⋊D1114yes—
480C2×D4C2×C22⋊D1112yes—
481C22×C4—21no—
482C22×C4—24no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—222no—
486C22×C4D4×D1112yes—
487C22×C4D4×D1112yes—
488C22×C4D4×D1112yes—
489C22×C4#434112yes—
490C22×C4C2×C22⋊D1114yes—
491C22×C4C2×C22⋊D1112yes—
492C22×C4C2×C22⋊D1112yes—
493C22×C4C2×C22⋊D1111yescharacteristic
494C22×C4C23×D1111yescharacteristic
495SD16—2216no—
496D8—2232no—
497D8—2216no—
498M16—228no—
499C2×C8—114no—
500C2×C8—114no—
501C2×C8—228no—
502C2×C8—222no—
503C2×C8—222no—
504C2×C8—222no—
505C2×C8—222no—
506C4⋊C4—24no—
507C4⋊C4—222no—
508C4⋊C4—222no—
509C22⋊C4—216no—
510C22⋊C4—24no—
511C22⋊C4—442no—
512C22⋊C4—888no—
513C42—22no—
514C42—22no—
515C42—442no—
516C11#2342211yescharacteristic, complemented, Sylow
517C23—24no—
518C23—24no—
519C23—22no—
520C23—41no—
521C23—42no—
522C23—41no—
523C23—42no—
524C23—48no—
525C23—44no—
526C23—48no—
527C23—88no—
528C23—88no—
529C23—88no—
530C23—224no—
531C23—442no—
532C23—448no—
533C23—448no—
534C23—442no—
535C23—888no—
536C23—888no—
537C23—888no—
538C23#6699112yes—
539C23#6699312yes—
540C23#6700612yes—
541C23C22×C22⋊D1111yescharacteristic
542Q8—22no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—24no—
547D4—22no—
548D4—24no—
549D4—22no—
550D4—48no—
551D4—42no—
552D4—41no—
553D4—42no—
554D4—41no—
555D4—48no—
556D4—816no—
557D4—224no—
558D4—224no—
559D4—442no—
560D4—442no—
561D4—448no—
562C2×C4—28no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—48no—
568C2×C4—442no—
569C2×C4—444no—
570C2×C4#6699014yes—
571C2×C4#6699014yes—
572C2×C4#6699112yes—
573C2×C4#6699214yes—
574C2×C4#6699214yes—
575C2×C4#6699312yes—
576C2×C4#6700612yes—
577C2×C4C2×D4×D1111yescharacteristic
578C2×C4C2×D4×D1111yescharacteristic
579C2×C4C2×D4×D1111yescharacteristic
580C2×C4C2×#434111yescharacteristic
581C2×C4C22×C22⋊D1111yescharacteristic
582C2×C4C22×C22⋊D1111yescharacteristic
583C8—224no—
584C8—224no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—44no—
589C22—48no—
590C22—42no—
591C22—44no—
592C22—816no—
593C22—84no—
594C22—82no—
595C22—84no—
596C22—82no—
597C22—448no—
598C22—444no—
599C22—8816no—
600C22—884no—
601C22—884no—
602C22#1062283614yes—
603C22C2×#6699111yescharacteristic
604C22C2×#6699311yescharacteristic
605C22#1062336614yes—
606C22C2×#6700611yescharacteristic
607C4—44no—
608C4—42no—
609C4—882no—
610C4#1062283614yes—
611C4C2×#6699011yescharacteristic
612C4C2×#6699011yescharacteristic
613C4C2×#6699211yescharacteristic
614C4C2×#6699211yescharacteristic
615C2—24no—
616C2—84no—
617C2—82no—
618C2—884no—
619C2C2×#1062283611yescharacteristic
620C2#1307788412yes—
621C2#1307811512yes—
622C2#1307909912yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#535C2
socleC23×C11C22×D4
hypercenterC2×#535D11
hypocenterC11#23422
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C22×#67002C2semidirect
2. C23×#4323C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622846C2semidirect
5. #13071196C2semidirect
6. #13069693C2semidirect
7. #13069687C2semidirect
8. #13068313C2semidirect
9. C2×C11×#535C2semidirect
15. C2×C11×#127C22semidirect
16. C2×C11×#124C22semidirect
23. C22×#4325C22semidirect
28. C22×#4323C22semidirect
33. C2×#66899C22semidirect
35. C2×#66896C22semidirect
36. C2×#66896C22semidirect
39. #10622552C22semidirect
40. #10622162C22semidirect
69. C22×D44D4semidirect
102. C2×#4318D4semidirect
105. C22×C11⋊C8D4semidirect
208. C2×#535D11semidirect
299. C2×#127C2×D11semidirect
300. C2×#124C2×D11semidirect
516. C11#23422semidirect

Maximal subgroups

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

subgroupindex
C22×#670022
C23×#43232
C2×#106228282
C2×#106228462
#130711962
#130696932
#130696872
#130683132
C2×C11×#5352
#2342211