Finite Group Databasebeta

← #14759605

Subgroups — #14759605

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×#67001C211yesmaximal, characteristic, complemented
2#13077834C211yesmaximal, characteristic
3C2×#10622437C212yesmaximal, complemented
4#13077306C211yesmaximal, characteristic, complemented
5#13068941C212yesmaximal, complemented
6#13068916C211yesmaximal, characteristic, complemented
7#13068889C212yesmaximal, complemented
8#13068820C211yesmaximal, characteristic, complemented
9#13068454C212yesmaximal, complemented
10C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#1789C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C2×#67003C2212yes—
14C2×#67001—28no—
15C2×#67001—21no—
16C2×#67001—21no—
17C2×#67001C2212yes—
18C2×#67001C2212yes—
19#10623322C2211yescharacteristic
20C22×#4318—21no—
21C22×#4318C2211yescharacteristic
22C23×C11⋊C8—21no—
23C23×C11⋊C8C2211yescharacteristic
24C2×#66960C2211yescharacteristic, complemented
25C2×C11×#104C2212yes—
26C2×C11×#104C2212yes—
27C11×#407C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29#10622852C412yescomplemented
30#10622851C412yescomplemented
31#10622846C2212yes—
32#10622841C411yescharacteristic, complemented
33#10622840C411yescharacteristic, complemented
34#10622831C411yescharacteristic, complemented
35#10622830C411yescharacteristic, complemented
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37#10622742C2211yescharacteristic, complemented
38C2×#66886C2212yescomplemented
39#10622735C2211yescharacteristic, complemented
40#10622732C2211yescharacteristic, complemented
41C2×#66869C2212yescomplemented
42C2×C4×C11⋊C8C2212yescomplemented
43#10622437—28no—
44#10622343—21no—
45#10622343—21no—
46(C22⋊D11)⋊C8—21no—
47(C22⋊D11)⋊C8—21no—
48#10622196C2212yescomplemented
49#10622162C2212yescomplemented
50#10622161C2212yescomplemented
51C2×C11×#41—24no—
52C2×C11×#41—24no—
53C2×C11×#41—21no—
54C2×C11×#41—21no—
55C2×C11×#41C2×C412yes—
56C2×C11×#41C2312yes—
57C22×Q8×C11C2×C411yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×#4339C2311yescharacteristic
63C2×C11×M16C2311yescharacteristic
64C2×C11×M16C2311yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11C2312yes—
67#67006—21no—
68#67003—24no—
69#67003—24no—
70#67001—28no—
71#67001—28no—
72#67001—24no—
73#67001—24no—
74#67001—24no—
75#67001D418yescomplemented
76C2×#4326C2×C412yes—
77C2×#4325C2×C412yes—
78C2×#4324C2×C412yes—
79C2×#4323C2×C412yes—
80#66983C2×C411yescharacteristic
81#66983C2×C411yescharacteristic
82#66982—21no—
83C4×C22⋊D11—21no—
84C4×C22⋊D11—21no—
85#66979C2311yescharacteristic
86#66977C2×C411yescharacteristic
87#66977C2×C411yescharacteristic
88C2×#4318—28no—
89C2×#4318—21no—
90C2×#4318—24no—
91C2×#4318—22no—
92C2×#4318—22no—
93C2×#4318C2312yes—
94C22×C11⋊C8—28no—
95C22×C11⋊C8—21no—
96C22×C11⋊C8—22no—
97C22×C11⋊C8—22no—
98C22×C11⋊C8—24no—
99C22×C11⋊C8D411yescharacteristic
100C22×C11⋊C8D411yescharacteristic
101C22×C11⋊C8D411yescharacteristic
102C22×C11⋊C8D411yescharacteristic
103C22×C11⋊C8C2312yes—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66960—24no—
107C2×#4313—21no—
108C2×C8×D11—21no—
109C11×#104—24no—
110C11×#104—24no—
111C11×C22⋊C8—21no—
112C11×C22⋊C8—21no—
113C11×#95—21no—
114#66899C2×C412yes—
115#66899C2×C412yes—
116#66896C2×C412yes—
117#66896C2×C412yes—
118C22⋊(C11⋊C8)C2×C411yescharacteristic
119C22⋊(C11⋊C8)C2×C411yescharacteristic
120C22⋊(C11⋊C8)C2×C412yes—
121#66886—24no—
122(C2×D11)⋊C8—21no—
123(C2×D11)⋊C8—21no—
124#66879—21no—
125Dic11⋊C8—21no—
126Dic11⋊C8—21no—
127C8×Dic11—21no—
128#66869—24no—
129C4×C11⋊C8—24no—
130#21466—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11#4111yescharacteristic
133C11×#41—24no—
134C11×#41—28no—
135C11×#41—24no—
136C11×#41—24no—
137C11×#41—24no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41C2×D414yes—
141C11×#41#4114yes—
142C2×Q8×C11—24no—
143C2×Q8×C11—21no—
144C2×Q8×C11C22×C412yes—
145C2×D4×C11—28no—
146C2×D4×C11—22no—
147C2×D4×C11—22no—
148C2×D4×C11—24no—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—21no—
166C2×C22⋊D11—21no—
167C2×C22⋊D11—21no—
168#4339—22no—
169#4339—22no—
170C2×D44C22×C411yescharacteristic
171C2×C4×D11—21no—
172C2×Dic22C22×C411yescharacteristic
173C11×M16—22no—
174C11×M16—22no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C11×C22⋊C4—24no—
178C42×C11—22no—
179C42×C11—22no—
180C22⋊Dic11—21no—
181C22⋊Dic11—21no—
182C22⋊Dic11—21no—
183#4326—24no—
184#4325—24no—
185#4324—24no—
186#4323—24no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189C4⋊Dic11C22×C411yescharacteristic
190C4⋊Dic11C22×C411yescharacteristic
191Dic11⋊C4—21no—
192Dic11⋊C4—21no—
193C4×Dic11—21no—
194#4318—28no—
195#4318—24no—
196#4318—28no—
197#4318—22no—
198#4318C2×D414yes—
199C2×C11⋊C8—24no—
200C2×C11⋊C8—28no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—28no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—22no—
208C2×C11⋊C8—22no—
209C2×C11⋊C8—22no—
210C2×C11⋊C8C22×C412yes—
211C2×C11⋊C8C22×C412yes—
212C2×C11⋊C8C2×D411yescharacteristic
213C2×C11⋊C8C2×D411yescharacteristic
214C2×C11⋊C8C2×D414yes—
215C2×C11⋊C8C2×D411yescharacteristic
216C2×C11⋊C8C2×D411yescharacteristic
217#4313—42no—
218C8×D11—42no—
219C22×#131—111no—
220#3002—111no—
221C2×#443—112no—
222#2929—111no—
223#1876—112no—
224#1871—111no—
225#1866—112no—
226#1855—111no—
227#1789D1111yescharacteristic, complemented
228#1764—112no—
229C8×C22⋊C4—111no—
230C23×C11—24no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—41no—
235C23×C11—42no—
236C23×C11—42no—
237C23×C11C4×D411yescharacteristic
238C23×C11C4×D411yescharacteristic
239C23×C11C2×#4111yescharacteristic
240C22×D11—21no—
241Q8×C11—24no—
242Q8×C11—22no—
243Q8×C11C4×D414yes—
244D4×C11—28no—
245D4×C11—24no—
246D4×C11—24no—
247D4×C11—24no—
248D4×C11—22no—
249D4×C11C4×D414yes—
250C2×C4×C11—24no—
251C2×C4×C11—28no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—24no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—24no—
261C2×C4×C11—21no—
262C2×C4×C11—24no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11C4×D411yescharacteristic
266C2×C4×C11C4×D411yescharacteristic
267C2×C4×C11C23×C411yescharacteristic
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4112yes—
271C22⋊D11—42no—
272C22⋊D11—42no—
273C22⋊D11—42no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277D44—22no—
278C4×D11—41no—
279C4×D11—41no—
280Dic22—22no—
281C8×C11—41no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—22no—
285C11⋊C8—21no—
286C11⋊C8—24no—
287C11⋊C8—21no—
288C11⋊C8#12012yes—
289C11⋊C8#12012yes—
290C22×#41C2×D1111yescharacteristic
291C2×#135—112no—
292C2×#131—112no—
293C2×#131—112no—
294C2×#131—111no—
295C2×#131—221no—
296C2×#131—221no—
297C2×#131—228no—
298C22×M16—111no—
299C22×M16—221no—
300C23×C8—111no—
301C23×C8—221no—
302#525—111no—
303#452—112no—
304#451—111no—
305#450—111no—
306#449—112no—
307#448—111no—
308#447—111no—
309#443—228no—
310#435—221no—
311#435—221no—
312C8×D4—221no—
313C8×D4—221no—
314C2×#108—112no—
315#424—111no—
316C2×#104—112no—
317C2×#104C2×D1112yes—
318C2×#104C2×D1112yes—
319#416—112no—
320#408—111no—
321#407C2×D1111yescharacteristic
322C2×C22⋊C8—111no—
323#405—111no—
324C2×C4×C8—112no—
325C4×C22⋊C4C2×D1111yescharacteristic
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—24no—
337C22×C11—44no—
338C22×C11—48no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11#44312yescomplemented
342C22×C11C2×C4×D411yescharacteristic
343C22×C11#52512yes—
344C2×D11—41no—
345C2×D11—41no—
346C2×D11—41no—
347C4×C11—21no—
348C4×C11—24no—
349C4×C11—21no—
350C4×C11—44no—
351C4×C11C2×C4×D412yes—
352C4×C11C2×#12011yescharacteristic
353C4×C11#52511yescharacteristic
354Dic11—41no—
355Dic11—41no—
356Dic11—41no—
357C2×#41—24no—
358C2×#41—24no—
359C2×#41—21no—
360C2×#41—21no—
361C2×#41—111no—
362C2×#41C4×D1112yes—
363C2×#41C22×D1112yes—
364C22×Q8C4×D1111yescharacteristic
365C22×D4—21no—
366C22×D4C4×D1111yescharacteristic
367C23×C4—21no—
368C23×C4C22×D1111yescharacteristic
369#135—224no—
370#135—224no—
371C2×Q16—112no—
372C2×SD16—112no—
373C2×SD16—112no—
374C2×D8—112no—
375#131—118no—
376#131—224no—
377#131—224no—
378#131—224no—
379#131—228no—
380#131—228no—
381#131—224no—
382C2×M16—112no—
383C2×M16—221no—
384C2×M16—222no—
385C2×M16—222no—
386C2×M16—224no—
387C2×M16—228no—
388C2×M16—221no—
389C2×M16C22×D1111yescharacteristic
390C2×M16C22×D1111yescharacteristic
391C22×C8—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—112no—
398C22×C8—221no—
399C22×C8—224no—
400C22×C8—222no—
401C22×C8—222no—
402C22×C8—228no—
403C22×C8—221no—
404#123—221no—
405C22⋊Q8—111no—
406C22⋊Q8—111no—
407#121—111no—
408#121—111no—
409#120—221no—
410C4×D4—221no—
411C4×D4—221no—
412#117—111no—
413C2×C22⋊C4—21no—
414C2×C42C22×D1112yes—
415#108—224no—
416C4⋊C8—221no—
417C4⋊C8—221no—
418#104—24no—
419#104—24no—
420#104—224no—
421#103—112no—
422#103—112no—
423#102—112no—
424#102—112no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—111no—
428C22⋊C8—111no—
429C22⋊C8—112no—
430C22⋊C8—221no—
431C22⋊C8—221no—
432#97—221no—
433C4×C8—224no—
434C4×C8—221no—
435#95—21no—
436C2×C11—22no—
437C2×C11—22no—
438C2×C11—41no—
439C2×C11—44no—
440C2×C11C4×#12011yescharacteristic
441C2×C11C2×#44311yescharacteristic
442C2×C11#295511yescharacteristic
443D11—81no—
444C24—21no—
445C24#434111yescharacteristic
446#41—24no—
447#41—28no—
448#41—24no—
449#41—24no—
450#41—24no—
451#41—22no—
452#41—22no—
453#41—222no—
454#41—222no—
455#41D4×D1114yes—
456#41#434114yes—
457C2×Q8—24no—
458C2×Q8—21no—
459C2×Q8—111no—
460C2×Q8C2×C4×D1112yes—
461C2×D4—28no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—24no—
465C2×D4—21no—
466C2×D4—111no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4C2×C4×D1112yes—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—221no—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4#434111yescharacteristic
485C22×C4C23×D1111yescharacteristic
486Q16—224no—
487SD16—224no—
488SD16—224no—
489D8—224no—
490M16—22no—
491M16—22no—
492M16—114no—
493M16—228no—
494M16—228no—
495M16—224no—
496M16—222no—
497M16—442no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—114no—
501C2×C8—111no—
502C2×C8—111no—
503C2×C8—112no—
504C2×C8—112no—
505C2×C8—111no—
506C2×C8—111no—
507C2×C8—222no—
508C2×C8—222no—
509C2×C8—222no—
510C2×C8—222no—
511C2×C8—228no—
512C2×C8—224no—
513C2×C8—228no—
514C2×C8—222no—
515C2×C8—222no—
516C2×C8—222no—
517C2×C8—222no—
518C2×C8—442no—
519C4⋊C4—111no—
520C4⋊C4—111no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C22⋊C4—24no—
524C22⋊C4—221no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C22⋊C4—221no—
528C22⋊C4—221no—
529C42—22no—
530C42—22no—
531C42—221no—
532C11#2146611yescharacteristic, complemented, Sylow
533C23—24no—
534C23—22no—
535C23—22no—
536C23—22no—
537C23—41no—
538C23—42no—
539C23—42no—
540C23—221no—
541C23(C22⋊D11)⋊C411yescharacteristic
542C23(C22⋊D11)⋊C411yescharacteristic
543C23C2×#434111yescharacteristic
544Q8—24no—
545Q8—22no—
546Q8—222no—
547Q8(C22⋊D11)⋊C414yes—
548D4—28no—
549D4—24no—
550D4—24no—
551D4—24no—
552D4—22no—
553D4—222no—
554D4—442no—
555D4—442no—
556D4—442no—
557D4(C22⋊D11)⋊C414yes—
558C2×C4—24no—
559C2×C4—28no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—24no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—24no—
569C2×C4—21no—
570C2×C4—24no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4(C22⋊D11)⋊C411yescharacteristic
579C2×C4(C22⋊D11)⋊C411yescharacteristic
580C2×C4C22×C4×D1111yescharacteristic
581C2×C4C2×D4×D1112yes—
582C2×C4C2×D4×D1111yescharacteristic
583C2×C4C2×#434112yes—
584C8—41no—
585C8—41no—
586C8—112no—
587C8—112no—
588C8—222no—
589C8—222no—
590C8—221no—
591C8—221no—
592C8—224no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—24no—
599C22—21no—
600C22—21no—
601C22—44no—
602C22—48no—
603C22—42no—
604C22—42no—
605C22—441no—
606C22—441no—
607C22—441no—
608C22#1062243712yescomplemented
609C22C2×(C22⋊D11)⋊C411yescharacteristic
610C22#1062311712yes—
611C4—21no—
612C4—24no—
613C4—21no—
614C4—44no—
615C4—441no—
616C4—441no—
617C4—441no—
618C4C2×(C22⋊D11)⋊C412yes—
619C4#1062311711yescharacteristic
620C4D11×#12011yescharacteristic
621C2—22no—
622C2—22no—
623C2—41no—
624C2—44no—
625C2—881no—
626C2#1307111511yescharacteristic
627C2C2×#1062243711yescharacteristic
628C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C2×C4×D4
prime radical#13077834C2
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#21466
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. C22×#67001C2semidirect
3. C2×#10622437C2semidirect
4. #13077306C2semidirect
5. #13068941C2semidirect
6. #13068916C2semidirect
7. #13068889C2semidirect
8. #13068820C2semidirect
9. #13068454C2semidirect
10. C22⋊C4×C11⋊C8C2semidirect
11. C11×#1789C2semidirect
24. C2×#66960C22semidirect
29. #10622852C4semidirect
30. #10622851C4semidirect
32. #10622841C4semidirect
33. #10622840C4semidirect
34. #10622831C4semidirect
35. #10622830C4semidirect
37. #10622742C22semidirect
38. C2×#66886C22semidirect
39. #10622735C22semidirect
40. #10622732C22semidirect
41. C2×#66869C22semidirect
42. C2×C4×C11⋊C8C22semidirect
48. #10622196C22semidirect
49. #10622162C22semidirect
50. #10622161C22semidirect
75. #67001D4semidirect
227. #1789D11semidirect
341. C22×C11#443semidirect
532. C11#21466semidirect
608. C22#10622437semidirect

Maximal subgroups

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

subgroupindex
C22×#670012
#130778342
C2×#106224372
#130773062
#130689412
#130689162
#130688892
#130688202
#130684542
C22⋊C4×C11⋊C82
C11×#17892
#2146611