Finite Group Databasebeta

← #14759608

Subgroups — #14759608

Order 2816.

1354 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66954C211yesmaximal, characteristic, complemented
2#13077832C211yesmaximal, characteristic
3C2×#10622757C212yesmaximal, complemented
4#13068946C212yesmaximal, complemented
5#13068919C211yesmaximal, characteristic, complemented
6#13068890C212yesmaximal, complemented
7#13068820C211yesmaximal, characteristic, complemented
8#13068559C211yesmaximal, characteristic, complemented
9#13068455C212yesmaximal, 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
18C2×#66954—21no—
19C2×#66954—21no—
20C2×#66954—28no—
21C2×#66954C2212yes—
22C2×#66954C2212yes—
23C22×#4313—21no—
24C22×C8×D11—21no—
25C11×#435—21no—
26C11×#435—21no—
27C8×D4×C11—21no—
28C8×D4×C11—21no—
29C11×#424C2211yescharacteristic, complemented
30C11×#408C2211yescharacteristic, complemented
31C11×#407C2211yescharacteristic
32C11×#405C2211yescharacteristic, complemented
33C2×#66901C2212yescomplemented
34C4×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622757—28no—
37C2×#66889C2212yes—
38C2×#66889C2212yes—
39C2×#66886C2212yescomplemented
40C2×C8×Dic11C2212yescomplemented
41#10622663C411yescharacteristic, complemented
42#10622660C412yescomplemented
43#10622659C411yescharacteristic, complemented
44#10622653C411yescharacteristic, complemented
45#10622650C412yescomplemented
46#10622649C411yescharacteristic, complemented
47#10622615C2212yes—
48#10622196C2212yescomplemented
49#10622188C2212yescomplemented
50#10622170C2212yescomplemented
51C2×C11×#41C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C2×#4339—21no—
55C2×#4339—21no—
56C2×#4339—24no—
57C2×#4339—24no—
58C2×#4339C2×C412yes—
59C2×#4339C2312yes—
60C22×D44C2×C411yescharacteristic
61C22×C4×D11—21no—
62C22×Dic22C2×C411yescharacteristic
63C11×#131—24no—
64C2×C11×M16—21no—
65C2×C11×M16C2311yescharacteristic
66C2×C11×M16C2311yescharacteristic
67C22×C8×C11—24no—
68C22×C8×C11—21no—
69C22×C8×C11D411yescharacteristic
70C22×C8×C11D411yescharacteristic
71C22×C8×C11D411yescharacteristic
72C22×C8×C11D411yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#123—21no—
76C11×C22⋊Q8C2×C411yescharacteristic
77C11×C22⋊Q8C2×C411yescharacteristic
78C11×#121C2×C411yescharacteristic
79C11×#121C2×C411yescharacteristic
80C11×#120—21no—
81C4×D4×C11—21no—
82C4×D4×C11—21no—
83C11×#117C2311yescharacteristic
84C2×C22⋊Dic11—21no—
85#67003—24no—
86#67003—24no—
87C2×#4326C2×C412yes—
88C2×#4325C2×C412yes—
89C2×#4324C2×C412yes—
90C2×#4323C2×C412yes—
91C2×C4×Dic11C2312yes—
92C2×#4318—21no—
93C2×#4318—24no—
94C2×#4318C2312yes—
95C22×C11⋊C8—21no—
96C22×C11⋊C8C2312yes—
97#66954—28no—
98#66954—28no—
99#66954—24no—
100#66954—24no—
101#66954—24no—
102#66954D418yescomplemented
103C2×#4313—28no—
104C2×#4313—22no—
105C2×#4313—22no—
106C2×C8×D11—28no—
107C2×C8×D11—22no—
108C2×C8×D11—22no—
109C11×C4⋊C8—21no—
110C11×C4⋊C8—21no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C11×C22⋊C8—21no—
115C11×#97—21no—
116C4×C8×C11—21no—
117#66901—24no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120C22⋊(C11⋊C8)C2×C412yes—
121C22⋊(C11⋊C8)C2×C411yescharacteristic
122#66889—24no—
123#66889—24no—
124#66886—24no—
125C8×Dic11—24no—
126#66874C2×C412yes—
127#66874C2×C412yes—
128#66873C2×C412yes—
129#66873C2×C412yes—
130#21466—111nomaximal, Sylow
131C24×C11#4111yescharacteristic
132C23×D11—21no—
133C11×#41—22no—
134C11×#41—22no—
135C2×Q8×C11C22×C411yescharacteristic
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11C22×C411yescharacteristic
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11#4111yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C2×C22⋊D11—28no—
150C2×C22⋊D11—22no—
151C2×C22⋊D11—22no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154#4339—24no—
155#4339—28no—
156#4339—24no—
157#4339—24no—
158#4339—24no—
159#4339—22no—
160#4339—22no—
161#4339C2×D414yes—
162#4339#4114yes—
163C2×D44—24no—
164C2×D44—21no—
165C2×D44C22×C412yes—
166C2×C4×D11—24no—
167C2×C4×D11—24no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×Dic22—24no—
171C2×Dic22—21no—
172C2×Dic22C22×C412yes—
173C11×M16—22no—
174C11×M16—22no—
175C11×M16—42no—
176C2×C8×C11—22no—
177C2×C8×C11—22no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11—22no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—42no—
184C2×C8×C11C2×D414yes—
185C2×C8×C11C2×D411yescharacteristic
186C2×C8×C11C2×D411yescharacteristic
187C2×C8×C11C2×D411yescharacteristic
188C2×C8×C11C2×D411yescharacteristic
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4C22×C411yescharacteristic
192C11×C4⋊C4C22×C411yescharacteristic
193C11×C22⋊C4—21no—
194C11×C22⋊C4—21no—
195C11×C22⋊C4—21no—
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C42×C11—21no—
199C22⋊Dic11—24no—
200#4326—24no—
201#4325—24no—
202#4324—24no—
203#4323—24no—
204C4×Dic11—22no—
205C4×Dic11—22no—
206#4318—24no—
207#4318—22no—
208#4318C2×D414yes—
209C2×C11⋊C8—24no—
210C2×C11⋊C8—22no—
211C2×C11⋊C8—22no—
212C2×C11⋊C8—22no—
213C2×C11⋊C8C22×C412yes—
214C2×C11⋊C8C22×C412yes—
215#4313—28no—
216#4313—28no—
217C8×D11—28no—
218C8×D11—28no—
219C22×#131—111no—
220#3002—111no—
221C2×#443—112no—
222#2929D1111yescharacteristic, complemented
223#1876—112no—
224#1871—111no—
225#1866—112no—
226#1855—111no—
227#1789—111no—
228#1764—112no—
229C8×C22⋊C4—111no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—21no—
233C23×C11—41no—
234C23×C11C4×D411yescharacteristic
235C23×C11C4×D411yescharacteristic
236C23×C11C2×#4111yescharacteristic
237C22×D11—24no—
238C22×D11—22no—
239C22×D11—42no—
240C22×D11—42no—
241Q8×C11—22no—
242D4×C11—22no—
243D4×C11—42no—
244D4×C11—42no—
245D4×C11—42no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4112yes—
264C22⋊D11—28no—
265C22⋊D11—24no—
266C22⋊D11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272D44—24no—
273D44—22no—
274D44C4×D414yes—
275C4×D11—28no—
276C4×D11—24no—
277C4×D11—24no—
278Dic22—24no—
279Dic22—22no—
280Dic22C4×D414yes—
281C8×C11—21no—
282C8×C11—21no—
283C8×C11—41no—
284C8×C11—41no—
285C8×C11#12012yes—
286C8×C11#12012yes—
287C11⋊C8—22no—
288C11⋊C8—22no—
289C11⋊C8—24no—
290C22×#41—111no—
291C2×#135—112no—
292C2×#131—112no—
293C2×#131—112no—
294C2×#131—228no—
295C2×#131—221no—
296C2×#131—221no—
297C2×#131C2×D1111yescharacteristic, complemented
298C22×M16—111no—
299C22×M16—221no—
300C23×C8—221no—
301C23×C8C2×D1111yescharacteristic
302#525C2×D1111yescharacteristic
303#452—112no—
304#451—111no—
305#450—111no—
306#449—112no—
307#448—111no—
308#447—111no—
309#443—228no—
310#435—21no—
311#435—21no—
312C8×D4—21no—
313C8×D4—21no—
314C2×#108—112no—
315#424C2×D1111yescharacteristic, complemented
316C2×#104—112no—
317C2×#104—112no—
318C2×#104—112no—
319#416—112no—
320#408C2×D1111yescharacteristic, complemented
321#407C2×D1111yescharacteristic
322C2×C22⋊C8—111no—
323#405C2×D1111yescharacteristic, complemented
324C2×C4×C8—112no—
325C4×C22⋊C4—111no—
326#341—112no—
327#339—112no—
328#336—112no—
329C22×C11—21no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—44no—
337C22×C11—41no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11#44312yescomplemented
341C22×C11C2×C4×D411yescharacteristic
342C22×C11#52512yes—
343C2×D11—24no—
344C2×D11—48no—
345C2×D11—42no—
346C2×D11—42no—
347C4×C11—21no—
348C4×C11—21no—
349C4×C11—41no—
350C4×C11—41no—
351C4×C11—41no—
352C4×C11C2×C4×D412yes—
353C4×C11C2×#12011yescharacteristic
354C4×C11#52511yescharacteristic
355Dic11—24no—
356Dic11—44no—
357C2×#41—112no—
358C2×#41—112no—
359C2×#41—224no—
360C2×#41—224no—
361C2×#41—221no—
362C2×#41—221no—
363C2×#41C22×D1111yescharacteristic
364C22×Q8—111no—
365C22×D4—111no—
366C22×D4—221no—
367C23×C4—221no—
368C23×C4C22×D1111yescharacteristic
369#135—224no—
370#135—224no—
371C2×Q16—112no—
372C2×SD16—112no—
373C2×SD16—112no—
374C2×D8—112no—
375#131—24no—
376#131—118no—
377#131—224no—
378#131—224no—
379#131—228no—
380#131—228no—
381#131—224no—
382C2×M16—21no—
383C2×M16—112no—
384C2×M16—228no—
385C2×M16—224no—
386C2×M16—221no—
387C2×M16—222no—
388C2×M16—222no—
389C2×M16C22×D1111yescharacteristic
390C2×M16C22×D1111yescharacteristic
391C22×C8—24no—
392C22×C8—21no—
393C22×C8—112no—
394C22×C8—228no—
395C22×C8—221no—
396C22×C8—222no—
397C22×C8—222no—
398C22×C8C22⋊D1111yescharacteristic
399C22×C8C22⋊D1111yescharacteristic
400C22×C8C22⋊D1111yescharacteristic
401C22×C8C22⋊D1111yescharacteristic
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404#123—21no—
405C22⋊Q8C4×D1111yescharacteristic
406C22⋊Q8C4×D1111yescharacteristic
407#121C4×D1111yescharacteristic
408#121C4×D1111yescharacteristic
409#120—21no—
410C4×D4—21no—
411C4×D4—21no—
412#117C22×D1111yescharacteristic
413C2×C22⋊C4—221no—
414C2×C42—112no—
415#108—224no—
416C4⋊C8—21no—
417C4⋊C8—21no—
418#104—224no—
419#104—224no—
420#104—224no—
421#103—112no—
422#103—112no—
423#102—112no—
424#102—112no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C22⋊C8—112no—
432#97—21no—
433C4×C8—21no—
434C4×C8—224no—
435#95—221no—
436C2×C11—22no—
437C2×C11—22no—
438C2×C11—41no—
439C2×C11—81no—
440C2×C11C4×#12011yescharacteristic
441C2×C11C2×#44311yescharacteristic
442C2×C11#295511yescharacteristic
443D11—44no—
444C24—221no—
445C24#433911yescharacteristic
446#41—22no—
447#41—22no—
448#41—114no—
449#41—114no—
450#41—224no—
451#41—224no—
452#41—224no—
453#41—228no—
454#41—224no—
455#41—222no—
456#41—222no—
457C2×Q8—112no—
458C2×Q8—224no—
459C2×Q8—221no—
460C2×Q8C2×C4×D1111yescharacteristic
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—112no—
465C2×D4—224no—
466C2×D4—228no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—221no—
470C2×D4C2×C4×D1111yescharacteristic
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—221no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4#433911yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486Q16—224no—
487SD16—224no—
488SD16—224no—
489D8—224no—
490M16—22no—
491M16—22no—
492M16—42no—
493M16—114no—
494M16—228no—
495M16—224no—
496M16—222no—
497M16—228no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—42no—
506C2×C8—112no—
507C2×C8—112no—
508C2×C8—228no—
509C2×C8—224no—
510C2×C8—222no—
511C2×C8—222no—
512C2×C8—222no—
513C2×C8—228no—
514C2×C8D4×D1114yes—
515C2×C8C2×C22⋊D1111yescharacteristic
516C2×C8C2×C22⋊D1111yescharacteristic
517C2×C8C2×C22⋊D1111yescharacteristic
518C2×C8C2×C22⋊D1111yescharacteristic
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4C2×C4×D1111yescharacteristic
522C4⋊C4C2×C4×D1111yescharacteristic
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—224no—
529C42—21no—
530C42—222no—
531C42—222no—
532C11#2146611yescharacteristic, complemented, Sylow
533C23—22no—
534C23—22no—
535C23—21no—
536C23—41no—
537C23—224no—
538C23—222no—
539C23—442no—
540C23—442no—
541C23C4×C22⋊D1111yescharacteristic
542C23C4×C22⋊D1111yescharacteristic
543C23C2×#433911yescharacteristic
544Q8—22no—
545Q8—114no—
546Q8—224no—
547Q8—222no—
548D4—22no—
549D4—42no—
550D4—42no—
551D4—42no—
552D4—114no—
553D4—224no—
554D4—228no—
555D4—224no—
556D4—224no—
557D4—222no—
558C2×C4—22no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—228no—
571C2×C4—224no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4C4×C22⋊D1111yescharacteristic
579C2×C4C4×C22⋊D1111yescharacteristic
580C2×C4C22×C4×D1111yescharacteristic
581C2×C4C2×D4×D1112yes—
582C2×C4#41×D1112yes—
583C2×C4C22×C22⋊D1111yescharacteristic
584C8—21no—
585C8—21no—
586C8—41no—
587C8—41no—
588C8—224no—
589C8—222no—
590C8—222no—
591C8#6699012yes—
592C8#6699012yes—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—44no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—224no—
605C22—448no—
606C22—442no—
607C22—442no—
608C22#1062275712yescomplemented
609C22#1062307812yes—
610C22C2×C4×C22⋊D1111yescharacteristic
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—224no—
617C4—444no—
618C4C4×D4×D1112yes—
619C4C2×#6699011yescharacteristic
620C4#1062335911yescharacteristic
621C2—22no—
622C2—22no—
623C2—41no—
624C2—81no—
625C2—444no—
626C2C4×#6699011yescharacteristic
627C2C2×#1062275711yescharacteristic
628C2#1307751711yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2929C2
socleC22×C11C2×C4×D4
prime radical#13077832C2
cosocleC22×C4×C11C24
hypercenter#2929D11
hypocenterC11#21466
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C8 ◁ C23×C8 ◁ #2929

Complements

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

NH ≅ G/Ntype
1. C22×#66954C2semidirect
3. C2×#10622757C2semidirect
4. #13068946C2semidirect
5. #13068919C2semidirect
6. #13068890C2semidirect
7. #13068820C2semidirect
8. #13068559C2semidirect
9. #13068455C2semidirect
10. C8×C22⋊Dic11C2semidirect
11. C11×#2929C2semidirect
13. C2×C11×#131C22semidirect
29. C11×#424C22semidirect
30. C11×#408C22semidirect
32. C11×#405C22semidirect
33. C2×#66901C22semidirect
39. C2×#66886C22semidirect
40. C2×C8×Dic11C22semidirect
41. #10622663C4semidirect
42. #10622660C4semidirect
43. #10622659C4semidirect
44. #10622653C4semidirect
45. #10622650C4semidirect
46. #10622649C4semidirect
48. #10622196C22semidirect
49. #10622188C22semidirect
50. #10622170C22semidirect
102. #66954D4semidirect
222. #2929D11semidirect
297. C2×#131C2×D11semidirect
315. #424C2×D11semidirect
320. #408C2×D11semidirect
323. #405C2×D11semidirect
340. C22×C11#443semidirect
532. C11#21466semidirect
608. C22#10622757semidirect

Maximal subgroups

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

subgroupindex
C22×#669542
#130778322
C2×#106227572
#130689462
#130689192
#130688902
#130688202
#130685592
#130684552
C8×C22⋊Dic112
C11×#29292
#2146611