Finite Group Databasebeta

← #14720721

Subgroups — #14720721

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082209C211yesmaximal, characteristic
2#13077184C211yesmaximal, characteristic, complemented
3#13067082C212yesmaximal, complemented
4#13067068C211yesmaximal, characteristic, complemented
5#13067056C212yesmaximal, complemented
6#13067046C211yesmaximal, characteristic, complemented
7#13067030C212yesmaximal, complemented
8#13067016C211yesmaximal, characteristic, complemented
9#13067004C212yesmaximal, complemented
10C2×#10622094C211yesmaximal, characteristic, complemented
11C11×#2965C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623363—21no—
14C2×#67001—21no—
15#10623116C411yescharacteristic
16#10623099—21no—
17#10623098C411yescharacteristic
18#10623096C412yes—
19#10623090—21no—
20#10623084C411yescharacteristic
21#10623083C412yes—
22#10623073C411yescharacteristic
23#10623071—22no—
24#10623059—22no—
25#10623053—21no—
26#10623010C2212yes—
27#10623008C2211yescharacteristic
28C4×#4339C2212yes—
29C2×C4×Dic22C2211yescharacteristic
30C11×#446—21no—
31C11×#436—21no—
32C11×#435—22no—
33C11×#431C2211yescharacteristic
34C11×#431C2212yes—
35C4×C11×M16C2212yes—
36C2×C4×C8×C11C2211yescharacteristic
37#10622612—21no—
38#10622612—22no—
39#10622537C2211yescharacteristic
40#10622537C2212yes—
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2212yes—
43#10622097C2212yes—
44#10622097C2212yes—
45#10622097C2212yes—
46#10622097C2212yes—
47#10622094C2211yescharacteristic
48#10622094C2212yes—
49#10622094C2212yes—
50#10622094C2211yescharacteristic
51#10622094C2211yescharacteristic
52#10622094C2211yescharacteristic
53C2×C11×#41D411yescharacteristic
54C2×#4339—21no—
55C2×#4339C2×C412yes—
56C22×Dic22C2×C411yescharacteristic
57C2×C11×M16—22no—
58C22×C8×C11—21no—
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C412yes—
63C4×D4×C11D412yes—
64C4×D4×C11D411yescharacteristic
65C11×#117D411yescharacteristic
66C11×#117D412yes—
67C2×C42×C11C2311yescharacteristic
68C2×C42×C11C2312yes—
69#67001—44no—
70#67000—21no—
71#66997—21no—
72#66993—21no—
73#66992—22no—
74#66992—22no—
75#66989—21no—
76#66983—21no—
77#66983C2×C412yes—
78#66983C2×C412yes—
79#66982—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—22no—
82C4×C22⋊D11—22no—
83#66979C2×C412yes—
84C2×C4⋊Dic11C2×C411yescharacteristic
85#66977C2×C412yes—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×#4318—22no—
89C2×#4318—21no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—21no—
92#66951—22no—
93#66949—22no—
94#66947—22no—
95#66946—21no—
96#66946—21no—
97#66942—22no—
98#66940—21no—
99#66940—21no—
100#66938—22no—
101#66937—22no—
102#66936—22no—
103(C22⋊D11)⋊C4—22no—
104(C22⋊D11)⋊C4—22no—
105#66932—22no—
106#66929—22no—
107#66928—21no—
108#66928C2×C412yes—
109#66927C2×C411yescharacteristic
110C4×D44—21no—
111C4×D44C2×C412yes—
112C4×D44C2312yes—
113#66925—22no—
114#66925—22no—
115C42×D11—22no—
116#66923C2×C412yes—
117#66922C2×C411yescharacteristic
118C4×Dic22—21no—
119C4×Dic22—21no—
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22C2×C411yescharacteristic
122C4×Dic22C2×C412yes—
123C4×Dic22C2311yescharacteristic
124C4×Dic22C2311yescharacteristic
125C11×C4⋊C8—22no—
126C11×C4⋊C8—21no—
127C11×C22⋊C8—21no—
128C11×C22⋊C8—22no—
129C11×#97—22no—
130C4×C8×C11—21no—
131C4×C8×C11C2311yescharacteristic
132C4×C8×C11C2311yescharacteristic
133C4×C8×C11C2312yes—
134C4⋊(C11⋊C8)—21no—
135C4⋊(C11⋊C8)—22no—
136C4⋊(C11⋊C8)—21no—
137C4⋊(C11⋊C8)—22no—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140C4⋊(C11⋊C8)C2312yes—
141#17515—111nomaximal, Sylow
142C11×#41—22no—
143C11×#41—22no—
144C2×Q8×C11C22⋊C411yescharacteristic
145C2×D4×C11C22⋊C411yescharacteristic
146C2×D4×C11C22⋊C412yes—
147C22×C4×C11C22×C412yes—
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C2×C22⋊D11—22no—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—22no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158#4339—24no—
159#4339—42no—
160#4339—42no—
161#4339—42no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44C22×C412yes—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×Dic22—22no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—41no—
172C2×Dic22C22×C411yescharacteristic
173C2×Dic22C22×C411yescharacteristic
174C11×M16—44no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—22no—
178C2×C8×C11—42no—
179C11×C4⋊C4C22⋊C411yescharacteristic
180C11×C4⋊C4C22⋊C411yescharacteristic
181C11×C4⋊C4C22⋊C412yes—
182C11×C4⋊C4C22⋊C412yes—
183C11×C22⋊C4C22⋊C412yes—
184C11×C22⋊C4C22⋊C412yes—
185C11×C22⋊C4C22⋊C412yes—
186C42×C11C22×C411yescharacteristic
187C42×C11C22×C412yes—
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D412yes—
190C42×C11C2×D411yescharacteristic
191C42×C11C2×D412yes—
192C42×C11C2411yescharacteristic
193C22⋊Dic11—22no—
194C22⋊Dic11—22no—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199(C2×D11)⋊C4—22no—
200(C2×D11)⋊C4—22no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C22×C411yescharacteristic
204C4⋊Dic11C22×C411yescharacteristic
205C4⋊Dic11C22×C412yes—
206Dic11⋊C4—21no—
207Dic11⋊C4—21no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—21no—
213Dic11⋊C4—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220#4318—44no—
221#4318—42no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—44no—
226C2×C11⋊C8—42no—
227#3480—111no—
228#2965D1111yescharacteristic, complemented
229#2906—111no—
230#1495—112no—
231#1492—111no—
232#1489—112no—
233#1487—111no—
234#1483—112no—
235#1480—111no—
236#1477—112no—
237C2×Q8⋊C8—111no—
238C23×C11C2×C22⋊C412yes—
239C23×C11C2×C22⋊C411yescharacteristic
240C22×D11—22no—
241Q8×C11—22no—
242D4×C11—24no—
243D4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—41no—
251C2×C4×C11—42no—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C412yes—
254C2×C4×C11C2×C22⋊C411yescharacteristic
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11AGL(1,ℤ/8)12yes—
259C2×C4×C11#13712yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C22⋊D11—44no—
264C22⋊D11—44no—
265C22⋊D11—82no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—42no—
272C2×Dic11—81no—
273D44—22no—
274D44—22no—
275D44—42no—
276D44—81no—
277C4×D11—44no—
278C4×D11—42no—
279C4×D11—42no—
280C4×D11—82no—
281Dic22—21no—
282Dic22—21no—
283Dic22—21no—
284Dic22—42no—
285Dic22—42no—
286Dic22#13112yescomplemented
287C8×C11—22no—
288C8×C11—41no—
289C8×C11—42no—
290C11⋊C8—41no—
291C11⋊C8—42no—
292C11⋊C8—41no—
293C2×#131—221no—
294#559—111no—
295#559—221no—
296#557—111no—
297#556—111no—
298#556—221no—
299#553—112no—
300#553—222no—
301#550—111no—
302#548—112no—
303#532—111no—
304#532—221no—
305#529—112no—
306#529—222no—
307C4×#41—112no—
308C4×#41—221no—
309C4×#41C2×D1111yescharacteristic
310C2×C4×Q8—111no—
311#446—21no—
312#436—21no—
313#435—22no—
314#431C2×D1112yes—
315#431C2×D1111yescharacteristic
316#424—221no—
317#424—222no—
318#423—111no—
319#423—112no—
320C2×C4⋊C8—111no—
321C2×C4⋊C8—112no—
322C4×M16C2×D1112yes—
323C2×C4×C8C2×D1111yescharacteristic
324Q8⋊C8—111no—
325Q8⋊C8—111no—
326Q8⋊C8—111no—
327Q8⋊C8—111no—
328Q8⋊C8—112no—
329Q8⋊C8—112no—
330D4⋊C8—112no—
331D4⋊C8—112no—
332D4⋊C8—112no—
333D4⋊C8—112no—
334C22×C11—21no—
335C22×C11—21no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11#41712yes—
340C22×C11C22×C22⋊C411yescharacteristic
341C2×D11—42no—
342C2×D11—42no—
343C2×D11—42no—
344C4×C11—21no—
345C4×C11—22no—
346C4×C11—22no—
347C4×C11—21no—
348C4×C11—22no—
349C4×C11—21no—
350C4×C11#41712yes—
351C4×C11C2×#13111yescharacteristic
352C4×C11#56811yescharacteristic
353C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
354C4×C11C2×#13711yescharacteristic
355Dic11—22no—
356Dic11—41no—
357Dic11—42no—
358Dic11—41no—
359Dic11—41no—
360C2×#41—112no—
361C2×#41—221no—
362C2×#41D4411yescharacteristic
363C22×Q8—111no—
364#131—444no—
365C2×M16—22no—
366C2×M16—222no—
367C2×M16—221no—
368C22×C8—21no—
369C22×C8—222no—
370C22×C8—221no—
371C4⋊Q8—111no—
372C4⋊Q8—221no—
373#127—111no—
374#127—221no—
375#126—222no—
376#126—222no—
377#126—222no—
378#125—112no—
379#125—222no—
380#124—112no—
381#124—221no—
382#124—221no—
383#124—222no—
384#124—221no—
385#123—222no—
386#123—222no—
387#123—222no—
388C22⋊Q8—112no—
389C22⋊Q8—222no—
390#121—112no—
391#121—112no—
392#121—222no—
393#121—222no—
394#121—221no—
395#121—222no—
396C4×Q8—111no—
397C4×Q8—111no—
398C4×Q8—112no—
399C4×Q8—111no—
400C4×Q8—111no—
401C4×Q8—221no—
402C4×Q8—221no—
403C4×Q8—221no—
404C4×Q8—221no—
405C4×Q8C4×D1111yescharacteristic
406C4×Q8C22⋊D1111yescharacteristic
407C4×D4—112no—
408C4×D4—112no—
409C4×D4—222no—
410C4×D4—222no—
411C4×D4—222no—
412C4×D4—221no—
413C4×D4—221no—
414C4×D4—222no—
415C4×D4—222no—
416C4×D4—221no—
417C4×D4C4×D1112yes—
418C4×D4C4×D1111yescharacteristic
419C4×D4C22⋊D1112yes—
420C4×D4C22⋊D1111yescharacteristic
421#117—112no—
422#117—222no—
423#117—222no—
424#117D4411yescharacteristic
425#117D4412yes—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C42—221no—
429C2×C42—222no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1112yes—
432C4⋊C8—22no—
433C4⋊C8—21no—
434C4⋊C8—111no—
435C4⋊C8—112no—
436C4⋊C8—111no—
437C4⋊C8—222no—
438C4⋊C8—221no—
439C4⋊C8—222no—
440C4⋊C8—221no—
441C22⋊C8—21no—
442C22⋊C8—22no—
443#97—22no—
444C4×C8—21no—
445C4×C8C22×D1111yescharacteristic
446C4×C8C22×D1111yescharacteristic
447C4×C8C22×D1112yes—
448C2×C11—22no—
449C2×C11—42no—
450C2×C11#288011yescharacteristic
451C2×C11C2×#41711yescharacteristic
452C2×C11#290111yescharacteristic
453D11—82no—
454#41—22no—
455#41—22no—
456#41—224no—
457#41—442no—
458#41—442no—
459#41—442no—
460C2×Q8—111no—
461C2×Q8—111no—
462C2×Q8—222no—
463C2×Q8—221no—
464C2×Q8—221no—
465C2×Q8—441no—
466C2×Q8(C2×D11)⋊C411yescharacteristic
467C2×D4—112no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—222no—
471C2×D4—221no—
472C2×D4—221no—
473C2×D4(C2×D11)⋊C412yes—
474C2×D4(C2×D11)⋊C411yescharacteristic
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×C4×D1112yes—
482C22×C4C2×D4412yes—
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×C22⋊D1111yescharacteristic
485C22×C4C2×C22⋊D1112yes—
486M16—44no—
487M16—444no—
488M16—442no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—22no—
492C2×C8—42no—
493C2×C8—221no—
494C2×C8—222no—
495C2×C8—221no—
496C2×C8—444no—
497C2×C8—442no—
498C4⋊C4—111no—
499C4⋊C4—111no—
500C4⋊C4—112no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—222no—
505C4⋊C4—222no—
506C4⋊C4—222no—
507C4⋊C4—222no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4(C2×D11)⋊C411yescharacteristic
512C4⋊C4(C2×D11)⋊C411yescharacteristic
513C4⋊C4(C2×D11)⋊C412yes—
514C4⋊C4(C2×D11)⋊C412yes—
515C22⋊C4—222no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—222no—
523C22⋊C4(C2×D11)⋊C412yes—
524C22⋊C4(C2×D11)⋊C412yes—
525C22⋊C4(C2×D11)⋊C412yes—
526C42—222no—
527C42—222no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42C2×C4×D1112yes—
533C42C2×C4×D1111yescharacteristic
534C42C2×D4412yes—
535C42C2×D4411yescharacteristic
536C42C2×C22⋊D1111yescharacteristic
537C42C2×C22⋊D1112yes—
538C42C23×D1111yescharacteristic
539C11#1751511yescharacteristic, complemented, Sylow
540C23—222no—
541C23C2×(C2×D11)⋊C412yes—
542C23C2×(C2×D11)⋊C411yescharacteristic
543Q8—22no—
544Q8—112no—
545Q8—221no—
546Q8—221no—
547Q8—221no—
548Q8—442no—
549Q8—442no—
550D4—24no—
551D4—22no—
552D4—222no—
553D4—222no—
554D4—444no—
555D4—444no—
556D4—442no—
557D4—881no—
558D4—882no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—42no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—222no—
571C2×C4—221no—
572C2×C4—444no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—882no—
577C2×C4—881no—
578C2×C4#6696112yes—
579C2×C4#6696212yes—
580C2×C4C2×(C2×D11)⋊C412yes—
581C2×C4C2×(C2×D11)⋊C412yes—
582C2×C4C2×(C2×D11)⋊C411yescharacteristic
583C2×C4C2×(C2×D11)⋊C412yes—
584C2×C4C2×(C2×D11)⋊C411yescharacteristic
585C2×C4C2×(C2×D11)⋊C411yescharacteristic
586C2×C4C22×C4×D1111yescharacteristic
587C2×C4C22×D4411yescharacteristic
588C2×C4C22×C22⋊D1111yescharacteristic
589C8—22no—
590C8—41no—
591C8—42no—
592C8—441no—
593C8—442no—
594C8—441no—
595C22—21no—
596C22—21no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—442no—
601C22—442no—
602C22—442no—
603C22#1062274612yes—
604C22C22×(C2×D11)⋊C411yescharacteristic
605C4—22no—
606C4—21no—
607C4—22no—
608C4—21no—
609C4—22no—
610C4—21no—
611C4—222no—
612C4—441no—
613C4—442no—
614C4—441no—
615C4—441no—
616C4#1062274612yes—
617C4C2×#6696111yescharacteristic
618C4C2×#6696211yescharacteristic
619C4D11×#13111yescharacteristic
620C4#1062328111yescharacteristic
621C2—22no—
622C2—42no—
623C2—882no—
624C2#1307706311yescharacteristic
625C2C2×#1062274611yescharacteristic
626C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C22×C22⋊C4
prime radical#13082209C2
cosocleC42×C11C24
hypercenter#2965D11
hypocenterC11#17515
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #13077184C2semidirect
3. #13067082C2semidirect
4. #13067068C2semidirect
5. #13067056C2semidirect
6. #13067046C2semidirect
7. #13067030C2semidirect
8. #13067016C2semidirect
9. #13067004C2semidirect
10. C2×#10622094C2semidirect
11. C11×#2965C2semidirect
228. #2965D11semidirect
286. Dic22#131semidirect
539. C11#17515semidirect

Maximal subgroups

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

subgroupindex
#130822092
#130771842
#130670822
#130670682
#130670562
#130670462
#130670302
#130670162
#130670042
C2×#106220942
C11×#29652
#1751511