Finite Group Databasebeta

← #14765168

Subgroups — #14765168

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077832C211yesmaximal, characteristic
2C2×#10622723C211yesmaximal, characteristic, complemented
3#13069503C212yesmaximal, complemented
4#13069319C212yesmaximal, complemented
5#13069264C212yesmaximal, complemented
6#13068943C212yesmaximal, complemented
7#13068919C211yesmaximal, characteristic, complemented
8#13068820C211yesmaximal, characteristic, complemented
9#13068559C211yesmaximal, characteristic, complemented
10C8×C22⋊Dic11C211yesmaximal, characteristic, complemented
11C11×#2929C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#131C2211yescharacteristic, complemented
14C23×C8×C11C2211yescharacteristic
15C11×#525C2211yescharacteristic
16C2×#67003C2212yes—
17C22×#4318C2211yescharacteristic
18C11×#435—21no—
19C11×#435—21no—
20C8×D4×C11—21no—
21C8×D4×C11—21no—
22C11×#424C2211yescharacteristic, complemented
23C11×#408C2211yescharacteristic, complemented
24C11×#407C2211yescharacteristic
25C11×#405C2211yescharacteristic, complemented
26C2×#66901C2212yescomplemented
27C4×C22⋊Dic11C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×#66889C2212yes—
30C2×#66889C2212yes—
31C2×#66886C2212yescomplemented
32#10622723—21no—
33#10622723—21no—
34#10622723C2212yes—
35#10622723C2212yes—
36C2×(C2×D11)⋊C8—21no—
37C2×(C2×D11)⋊C8—21no—
38C2×C8×Dic11C2212yescomplemented
39#10622663C411yescharacteristic, complemented
40#10622660C412yescomplemented
41#10622659C411yescharacteristic, complemented
42#10622653C411yescharacteristic, complemented
43#10622650C412yescomplemented
44#10622649C411yescharacteristic, complemented
45#10622615C2212yes—
46#10622196C2212yescomplemented
47#10622188C2212yescomplemented
48#10622170C2212yescomplemented
49C2×C11×#41C2311yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×C22⋊D11—21no—
52C2×#4339—21no—
53C2×#4339—21no—
54C2×#4339—42no—
55C2×#4339—42no—
56C2×#4339C2×C412yes—
57C2×#4339C2312yes—
58C22×D44C2×C411yescharacteristic
59C22×C4×D11—21no—
60C22×Dic22C2×C411yescharacteristic
61C11×#131—42no—
62C2×C11×M16—21no—
63C2×C11×M16C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C22×C8×C11—21no—
66C22×C8×C11—42no—
67C22×C8×C11D411yescharacteristic
68C22×C8×C11D411yescharacteristic
69C22×C8×C11D411yescharacteristic
70C22×C8×C11D411yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#123—21no—
74C11×C22⋊Q8C2×C411yescharacteristic
75C11×C22⋊Q8C2×C411yescharacteristic
76C11×#121C2×C411yescharacteristic
77C11×#121C2×C411yescharacteristic
78C11×#120—21no—
79C4×D4×C11—21no—
80C4×D4×C11—21no—
81C11×#117C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83#67003—42no—
84#67003—42no—
85C2×#4326C2×C412yes—
86C2×#4325C2×C412yes—
87C2×#4324C2×C412yes—
88C2×#4323C2×C412yes—
89C2×C4×Dic11C2312yes—
90C2×#4318—21no—
91C2×#4318—42no—
92C2×#4318C2312yes—
93C22×C11⋊C8—21no—
94C22×C11⋊C8C2312yes—
95C11×C4⋊C8—21no—
96C11×C4⋊C8—21no—
97C11×C22⋊C8—21no—
98C11×C22⋊C8—21no—
99C11×C22⋊C8—21no—
100C11×C22⋊C8—21no—
101C11×#97—21no—
102C4×C8×C11—21no—
103#66901—42no—
104C11⋊#95—21no—
105C22⋊(C11⋊C8)C2×C411yescharacteristic
106C22⋊(C11⋊C8)C2×C412yes—
107C22⋊(C11⋊C8)C2×C411yescharacteristic
108#66889—42no—
109#66889—42no—
110#66886—42no—
111(C2×D11)⋊C8—22no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—22no—
114(C2×D11)⋊C8—22no—
115C8×Dic11—42no—
116#66874C2×C412yes—
117#66874C2×C412yes—
118#66873C2×C412yes—
119#66873C2×C412yes—
120#22060—111nomaximal, Sylow
121C24×C11#4111yescharacteristic
122C23×D11—21no—
123C11×#41—22no—
124C11×#41—22no—
125C2×Q8×C11C22×C411yescharacteristic
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11C22×C411yescharacteristic
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4111yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—22no—
140C2×C22⋊D11—22no—
141C2×C22⋊D11—44no—
142C22×Dic11—21no—
143C22×Dic11—22no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—22no—
148#4339—42no—
149#4339—42no—
150#4339—44no—
151#4339—42no—
152#4339—42no—
153C2×D44—21no—
154C2×D44—42no—
155C2×D44C22×C412yes—
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×Dic22—21no—
161C2×Dic22—42no—
162C2×Dic22C22×C412yes—
163C11×M16—22no—
164C11×M16—22no—
165C11×M16—42no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—42no—
175C2×C8×C11C2×D411yescharacteristic
176C2×C8×C11C2×D411yescharacteristic
177C2×C8×C11C2×D411yescharacteristic
178C2×C8×C11C2×D411yescharacteristic
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11—21no—
189C22⋊Dic11—24no—
190#4326—42no—
191#4325—42no—
192#4324—42no—
193#4323—42no—
194C4×Dic11—22no—
195C4×Dic11—22no—
196#4318—22no—
197#4318—22no—
198#4318—42no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—42no—
203C2×C11⋊C8C22×C412yes—
204C2×C11⋊C8C22×C412yes—
205#3002—111no—
206#2929D1111yescharacteristic, complemented
207C2×#408—111no—
208#1974—112no—
209#1937—112no—
210#1929—112no—
211#1876—112no—
212#1871—111no—
213#1855—111no—
214#1789—111no—
215C8×C22⋊C4—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—41no—
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C22×D11—22no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227Q8×C11—22no—
228D4×C11—22no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—42no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11H(5,𝔽2)12yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C22⋊D11—44no—
251C22⋊D11—42no—
252C22⋊D11—42no—
253C2×Dic11—24no—
254C2×Dic11—22no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258D44—22no—
259D44—22no—
260D44—42no—
261C4×D11—44no—
262C4×D11—42no—
263C4×D11—42no—
264Dic22—22no—
265Dic22—22no—
266Dic22—42no—
267C8×C11—21no—
268C8×C11—21no—
269C8×C11—21no—
270C8×C11—21no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—22no—
274C11⋊C8—22no—
275C11⋊C8—42no—
276C22×#41—111no—
277C2×#135—112no—
278C2×#131C2×D1111yescharacteristic, complemented
279C22×M16—111no—
280C23×C8C2×D1111yescharacteristic
281#525C2×D1111yescharacteristic
282#452—112no—
283#451—111no—
284#450—111no—
285#449—112no—
286#448—111no—
287#447—111no—
288#435—21no—
289#435—21no—
290C8×D4—21no—
291C8×D4—21no—
292C2×#108—112no—
293#424C2×D1111yescharacteristic, complemented
294C2×#104—112no—
295C2×#104—112no—
296C2×#104—112no—
297#416—112no—
298#408—112no—
299#408—112no—
300#408—221no—
301#408—221no—
302#408C2×D1111yescharacteristic, complemented
303#407C2×D1111yescharacteristic
304C2×C22⋊C8—111no—
305C2×C22⋊C8—221no—
306C2×C22⋊C8—221no—
307#405C2×D1111yescharacteristic, complemented
308C2×C4×C8—112no—
309C4×C22⋊C4—111no—
310#341—112no—
311#339—112no—
312#336—112no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11#44312yes—
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#53812yes—
327C2×D11—42no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—84no—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11#51812yes—
337C4×C11#53411yescharacteristic
338C4×C11#53511yescharacteristic
339Dic11—44no—
340Dic11—42no—
341C2×#41—112no—
342C2×#41—112no—
343C2×#41—221no—
344C2×#41—221no—
345C2×#41—442no—
346C2×#41—442no—
347C2×#41C22×D1111yescharacteristic
348C22×Q8—111no—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
352C23×C4C22×D1111yescharacteristic
353#135—442no—
354#135—442no—
355C2×Q16—112no—
356C2×SD16—112no—
357C2×SD16—112no—
358C2×D8—112no—
359#131—42no—
360C2×M16—21no—
361C2×M16—112no—
362C2×M16—221no—
363C2×M16—442no—
364C2×M16C22×D1111yescharacteristic
365C2×M16C22×D1111yescharacteristic
366C22×C8—21no—
367C22×C8—42no—
368C22×C8—112no—
369C22×C8—221no—
370C22×C8C22⋊D1111yescharacteristic
371C22×C8C22⋊D1111yescharacteristic
372C22×C8C22⋊D1111yescharacteristic
373C22×C8C22⋊D1111yescharacteristic
374C22×C8C22×D1111yescharacteristic
375C22×C8C22×D1111yescharacteristic
376#123—21no—
377C22⋊Q8C4×D1111yescharacteristic
378C22⋊Q8C4×D1111yescharacteristic
379#121C4×D1111yescharacteristic
380#121C4×D1111yescharacteristic
381#120—21no—
382C4×D4—21no—
383C4×D4—21no—
384#117C22×D1111yescharacteristic
385C2×C22⋊C4—221no—
386C2×C42—112no—
387#108—442no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390#104—442no—
391#104—442no—
392#104—442no—
393#103—112no—
394#103—112no—
395#102—112no—
396#102—112no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—21no—
400C22⋊C8—21no—
401C22⋊C8—111no—
402C22⋊C8—111no—
403C22⋊C8—112no—
404C22⋊C8—222no—
405C22⋊C8—222no—
406C22⋊C8—222no—
407C22⋊C8—222no—
408#97—21no—
409C4×C8—21no—
410C4×C8—442no—
411#95—221no—
412C2×C11—22no—
413C2×C11—22no—
414C2×C11—41no—
415C2×C11—81no—
416C2×C11#232111yescharacteristic
417C2×C11C2×#44311yescharacteristic
418C2×C11#295511yescharacteristic
419D11—82no—
420C24—221no—
421C24#433911yescharacteristic
422#41—22no—
423#41—22no—
424#41—222no—
425#41—222no—
426#41—222no—
427#41—222no—
428#41—442no—
429#41—442no—
430#41—444no—
431#41—442no—
432#41—442no—
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—442no—
436C2×Q8C2×C4×D1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—112no—
441C2×D4—222no—
442C2×D4—222no—
443C2×D4—221no—
444C2×D4—442no—
445C2×D4—444no—
446C2×D4C2×C4×D1111yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—221no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—442no—
455C22×C4—442no—
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4#433911yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—442no—
463SD16—442no—
464SD16—442no—
465D8—442no—
466M16—22no—
467M16—22no—
468M16—42no—
469M16—222no—
470M16—222no—
471M16—442no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—42no—
481C2×C8—112no—
482C2×C8—112no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—442no—
487C2×C8C2×C22⋊D1111yescharacteristic
488C2×C8C2×C22⋊D1111yescharacteristic
489C2×C8C2×C22⋊D1111yescharacteristic
490C2×C8C2×C22⋊D1111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4C2×C4×D1111yescharacteristic
494C4⋊C4C2×C4×D1111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—224no—
501C42—21no—
502C42—222no—
503C42—222no—
504C11#2206011yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—21no—
508C23—41no—
509C23—222no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23C4×C22⋊D1111yescharacteristic
514C23C4×C22⋊D1111yescharacteristic
515C23C2×#433911yescharacteristic
516Q8—22no—
517Q8—222no—
518Q8—222no—
519Q8—442no—
520D4—22no—
521D4—42no—
522D4—42no—
523D4—42no—
524D4—222no—
525D4—222no—
526D4—442no—
527D4—444no—
528D4—442no—
529D4—442no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—444no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4C4×C22⋊D1111yescharacteristic
551C2×C4C4×C22⋊D1111yescharacteristic
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4#6703712yes—
554C2×C4#6704212yes—
555C2×C4C22×C22⋊D1111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—222no—
563C8—222no—
564C8—442no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—44no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—442no—
577C22—442no—
578C22—442no—
579C22—884no—
580C22#1062275712yes—
581C22#1062309112yes—
582C22C2×C4×C22⋊D1111yescharacteristic
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—444no—
589C4—442no—
590C4#1062307612yes—
591C4#1062333511yescharacteristic
592C4#1062336111yescharacteristic
593C2—22no—
594C2—22no—
595C2—41no—
596C2—81no—
597C2—882no—
598C2#1307127011yescharacteristic
599C2C2×#1062275711yescharacteristic
600C2#1307751711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2929C2
socleC22×C11C2×C4×D4
prime radical#13077832C2
cosocleC22×C4×C11C24
hypercenter#2929D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. C2×#10622723C2semidirect
3. #13069503C2semidirect
4. #13069319C2semidirect
5. #13069264C2semidirect
6. #13068943C2semidirect
7. #13068919C2semidirect
8. #13068820C2semidirect
9. #13068559C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C11×#2929C2semidirect
13. C2×C11×#131C22semidirect
22. C11×#424C22semidirect
23. C11×#408C22semidirect
25. C11×#405C22semidirect
26. C2×#66901C22semidirect
31. C2×#66886C22semidirect
38. C2×C8×Dic11C22semidirect
39. #10622663C4semidirect
40. #10622660C4semidirect
41. #10622659C4semidirect
42. #10622653C4semidirect
43. #10622650C4semidirect
44. #10622649C4semidirect
46. #10622196C22semidirect
47. #10622188C22semidirect
48. #10622170C22semidirect
206. #2929D11semidirect
278. C2×#131C2×D11semidirect
293. #424C2×D11semidirect
302. #408C2×D11semidirect
307. #405C2×D11semidirect
504. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130778322
C2×#106227232
#130695032
#130693192
#130692642
#130689432
#130689192
#130688202
#130685592
C8×C22⋊Dic112
C11×#29292
#2206011