Finite Group Databasebeta

← #14770675

Subgroups — #14770675

Order 2816.

1058 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082211C211yesmaximal, characteristic
2#13071094C211yesmaximal, characteristic, complemented
3#13069535C212yesmaximal, complemented
4#13069535C211yesmaximal, characteristic, complemented
5#13069447C212yesmaximal, complemented
6#13069443C211yesmaximal, characteristic, complemented
7#13068633C211yesmaximal, characteristic, complemented
8#13068633C212yesmaximal, complemented
9#13068429C212yesmaximal, complemented
10C4×#66889C211yesmaximal, characteristic, complemented
11Q8×C11×M16C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13#10623348—21no—
14#10623116C411yescharacteristic, complemented
15#10623116C412yescomplemented
16#10623115C412yescomplemented
17#10623115C411yescharacteristic, complemented
18#10623111—21no—
19#10623111—22no—
20#10623108C411yescharacteristic, complemented
21C4×#4343—21no—
22#10623101C411yescharacteristic, complemented
23#10623045—22no—
24#10623045—21no—
25#10623008C2211yescharacteristic
26#10623008C2212yes—
27C4×#4339C2211yescharacteristic
28C4×#4339C2212yes—
29C11×#446—21no—
30C11×#446—22no—
31C8×Q8×C11—21no—
32C11×#423C2211yescharacteristic
33C11×#423C2212yes—
34C4×C11×M16C2211yescharacteristic
35C4×C11×M16C2212yes—
36#10622843—21no—
37C2×#66889C2212yes—
38C2×#66889C2211yescharacteristic
39C2×#66889C2211yescharacteristic
40C2×#66889C2212yes—
41C2×#66889C2212yes—
42C2×#66889C2212yes—
43C2×#66889C2212yes—
44#10622598—21no—
45#10622594—22no—
46C4×C4⋊Dic11C2212yes—
47C4×C4⋊Dic11C2211yescharacteristic
48#10622545C2212yes—
49C42×Dic11C2211yescharacteristic
50#10622193C2211yescharacteristic
51#10622193C2212yes—
52#10622193C2211yescharacteristic
53C22×Q8×C11D411yescharacteristic
54C2×#4343—21no—
55C2×#4339C2311yescharacteristic
56C2×#4339C2312yes—
57C2×C11×M16C2312yes—
58C2×C11×M16C2311yescharacteristic
59C2×C11×M16C2311yescharacteristic
60C4×Q8×C11C2×C411yescharacteristic
61C4×Q8×C11C2×C411yescharacteristic
62C4×Q8×C11C2×C412yes—
63C4×Q8×C11D411yescharacteristic
64C4×Q8×C11D411yescharacteristic
65C4×Q8×C11D412yes—
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C42×C11C2311yescharacteristic
69C2×C42×C11C2312yes—
70#67000—21no—
71#67000—22no—
72#66999—21no—
73#66999—22no—
74Q8×Dic11—21no—
75#66983—21no—
76#66983—22no—
77#66983—21no—
78#66983—22no—
79C4×C22⋊D11—21no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11—21no—
82C4×C22⋊D11—22no—
83#66979C2311yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C2×C4×Dic11C2312yes—
90C2×C4×Dic11C2311yescharacteristic
91#66951—22no—
92#66951—22no—
93#66951—22no—
94#66948—22no—
95#66948—21no—
96#66947—22no—
97#66947—22no—
98#66947—22no—
99#66946—22no—
100#66946—21no—
101#66945—22no—
102#66945—21no—
103#66943—22no—
104#66943—21no—
105#66928C2×C412yes—
106#66928C2×C412yes—
107#66928C2×C412yes—
108#66927C2×C411yescharacteristic
109#66927C2×C412yes—
110C4×D44—21no—
111C4×D44—22no—
112C4×D44—22no—
113C4×D44—21no—
114C4×D44C2×C411yescharacteristic
115C4×D44C2×C412yes—
116C4×D44C2×C411yescharacteristic
117C4×D44C2×C412yes—
118#66925—22no—
119#66925—21no—
120C42×D11—21no—
121C42×D11—22no—
122#66922C2×C411yescharacteristic
123#66922C2×C412yes—
124C4×Dic22C2×C411yescharacteristic
125C4×Dic22C2×C412yes—
126C4×Dic22C2×C411yescharacteristic
127C4×Dic22C2×C412yes—
128C11×C4⋊C8—21no—
129C11×C4⋊C8—22no—
130C11×C4⋊C8—22no—
131C11×C4⋊C8—21no—
132C11×#97—22no—
133C11×#97—21no—
134C4×C8×C11—21no—
135C4×C8×C11—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—21no—
140#66889—22no—
141#66889—24no—
142#66889—24no—
143#66889—22no—
144#66889—42no—
145#66889—42no—
146#66889—42no—
147#22551—111nomaximal, Sylow
148C2×Q8×C11—42no—
149C2×Q8×C11C22⋊C411yescharacteristic
150C2×Q8×C11C22⋊C411yescharacteristic
151C2×Q8×C11C22⋊C412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D412yes—
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—21no—
158C2×C22⋊D11—22no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162#4343—44no—
163#4339—21no—
164#4339—22no—
165#4339—22no—
166#4339—21no—
167#4339—22no—
168#4339—21no—
169#4339—21no—
170#4339—22no—
171C2×D44—22no—
172C2×D44—21no—
173C2×D44—22no—
174C2×D44—21no—
175C2×D44C22×C411yescharacteristic
176C2×D44C22×C412yes—
177C2×C4×D11—22no—
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—22no—
181C2×C4×D11—21no—
182C2×C4×D11—22no—
183C2×Dic22C22×C411yescharacteristic
184C2×Dic22C22×C412yes—
185C11×M16—22no—
186C11×M16—21no—
187C11×M16—22no—
188C11×M16—21no—
189C11×M16—21no—
190C11×M16#4112yescomplemented
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—22no—
194C11×C4⋊C4C22⋊C412yes—
195C11×C4⋊C4C22⋊C411yescharacteristic
196C11×C4⋊C4C22⋊C412yes—
197C11×C4⋊C4C22⋊C411yescharacteristic
198C11×C4⋊C4C22⋊C412yes—
199C11×C4⋊C4C22⋊C412yes—
200C11×C4⋊C4C22⋊C412yes—
201C42×C11C22×C412yes—
202C42×C11C22×C411yescharacteristic
203C42×C11C22×C411yescharacteristic
204C42×C11C22×C412yes—
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D412yes—
207C42×C11C2×D412yes—
208C42×C11C2×D411yescharacteristic
209C22⋊Dic11—21no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—21no—
214(C2×D11)⋊C4—22no—
215(C2×D11)⋊C4—22no—
216(C2×D11)⋊C4—22no—
217(C2×D11)⋊C4—22no—
218(C2×D11)⋊C4—22no—
219(C2×D11)⋊C4—22no—
220C4⋊Dic11—22no—
221C4⋊Dic11—21no—
222C4⋊Dic11—22no—
223C4⋊Dic11—21no—
224C4⋊Dic11—42no—
225C4⋊Dic11—44no—
226C4⋊Dic11C22×C411yescharacteristic
227C4⋊Dic11C22×C411yescharacteristic
228Dic11⋊C4—22no—
229Dic11⋊C4—21no—
230Dic11⋊C4—21no—
231Dic11⋊C4—22no—
232C4×Dic11—22no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—22no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C4×Dic11—22no—
239C4×Dic11—21no—
240C4×Dic11—22no—
241C4×Dic11—21no—
242C4×Dic11—42no—
243C4×Dic11—42no—
244C4×Dic11#4112yescomplemented
245#3480—111no—
246Q8×M16D1111yescharacteristic, complemented
247#2295—111no—
248#1980—111no—
249#1980—112no—
250#1963—112no—
251#1962—111no—
252#1806—111no—
253#1806—112no—
254#1759—112no—
255C4×#104—111no—
256C23×C11C22×D411yescharacteristic
257C22×D11—22no—
258C22×D11—21no—
259Q8×C11—22no—
260Q8×C11—22no—
261Q8×C11—42no—
262C2×C4×C11—22no—
263C2×C4×C11—41no—
264C2×C4×C11—42no—
265C2×C4×C11—42no—
266C2×C4×C11C2×C22⋊C412yes—
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C412yes—
269C2×C4×C11C2×C22⋊C412yes—
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C412yes—
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C23×C411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—42no—
281C22⋊D11—41no—
282C22⋊D11—41no—
283C22⋊D11—42no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—22no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297D44—21no—
298D44—22no—
299D44—21no—
300D44—22no—
301D44—44no—
302D44—42no—
303D44—81no—
304D44—82no—
305C4×D11—44no—
306C4×D11—41no—
307C4×D11—42no—
308C4×D11—41no—
309C4×D11—42no—
310C4×D11—42no—
311C4×D11—81no—
312C4×D11—82no—
313Dic22—21no—
314Dic22—22no—
315Dic22—21no—
316Dic22—22no—
317C8×C11—22no—
318C8×C11—41no—
319C8×C11—42no—
320#559—112no—
321#559—111no—
322#557—111no—
323#556—111no—
324#556—112no—
325#553—222no—
326#553—221no—
327#550—111no—
328#548—221no—
329#532—111no—
330#532—112no—
331#529—221no—
332#529—222no—
333C4×#41—111no—
334C4×#41—112no—
335C4×#41—221no—
336C2×C4×Q8C2×D1111yescharacteristic
337#446—21no—
338#446—22no—
339C8×Q8—21no—
340#423C2×D1111yescharacteristic
341#423C2×D1112yes—
342C2×#104—112no—
343C2×#104—111no—
344C2×#104—111no—
345C2×#104—112no—
346C2×#104—112no—
347C2×#104—112no—
348C2×#104—112no—
349C4×M16C2×D1111yescharacteristic
350C4×M16C2×D1112yes—
351#391—221no—
352#389—221no—
353#387—222no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—112no—
356#376—112no—
357C43—111no—
358#339—111no—
359#339—112no—
360#339—111no—
361C22×C11—21no—
362C22×C11—21no—
363C22×C11C22×C22⋊C411yescharacteristic
364C22×C11#54811yescharacteristic
365C22×C11#55011yescharacteristic
366C2×D11—42no—
367C2×D11—41no—
368C2×D11—42no—
369C2×D11—41no—
370C2×D11—42no—
371C2×D11—41no—
372C4×C11—21no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—21no—
376C4×C11—22no—
377C4×C11—21no—
378C4×C11—22no—
379C4×C11#42112yes—
380C4×C11C4×#4111yescharacteristic
381C4×C11#52011yescharacteristic
382C4×C11#54811yescharacteristic
383C4×C11#55011yescharacteristic
384Dic11—42no—
385Dic11—42no—
386Dic11—42no—
387Dic11—41no—
388Dic11—41no—
389Dic11—41no—
390Dic11—82no—
391C2×#41—111no—
392C2×#41—112no—
393C2×#41—221no—
394C22×Q8D4411yescharacteristic
395C2×M16C22×D1111yescharacteristic
396C2×M16C22×D1112yes—
397C2×M16C22×D1111yescharacteristic
398C4⋊Q8—111no—
399C4⋊Q8—112no—
400#127—111no—
401#127—112no—
402#126—222no—
403#126—222no—
404#126—222no—
405#125—222no—
406#125—221no—
407#124—112no—
408#124—112no—
409#124—112no—
410#124—221no—
411#124—222no—
412#123—222no—
413#123—222no—
414#123—222no—
415C22⋊Q8—221no—
416C22⋊Q8—222no—
417#121—221no—
418#121—222no—
419#121—221no—
420#121—222no—
421#121—222no—
422#121—221no—
423C4×Q8—111no—
424C4×Q8—112no—
425C4×Q8—111no—
426C4×Q8—112no—
427C4×Q8—221no—
428C4×Q8C4×D1111yescharacteristic
429C4×Q8C4×D1111yescharacteristic
430C4×Q8C4×D1112yes—
431C4×Q8C22⋊D1111yescharacteristic
432C4×Q8C22⋊D1111yescharacteristic
433C4×Q8C22⋊D1112yes—
434C4×D4—111no—
435C4×D4—112no—
436C4×D4—111no—
437C4×D4—112no—
438C4×D4—221no—
439C4×D4—222no—
440C4×D4—221no—
441C4×D4—222no—
442C4×D4—222no—
443C4×D4—221no—
444C4×D4—221no—
445C4×D4—222no—
446C4×D4—222no—
447C4×D4—221no—
448#117—111no—
449#117—222no—
450#117—221no—
451#117—222no—
452#117—221no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—221no—
455C2×C4⋊C4D4412yes—
456C2×C4⋊C4D4411yescharacteristic
457C2×C42—111no—
458C2×C42—111no—
459C2×C42—112no—
460C2×C42—221no—
461C2×C42—222no—
462C2×C42—221no—
463C2×C42—221no—
464C2×C42C22×D1111yescharacteristic
465C2×C42C22×D1112yes—
466C4⋊C8—21no—
467C4⋊C8—22no—
468C4⋊C8—22no—
469C4⋊C8—21no—
470#104—224no—
471#104—222no—
472#104—222no—
473#104—224no—
474#104—442no—
475#104—442no—
476#104—442no—
477#97—22no—
478#97—21no—
479C4×C8—21no—
480C4×C8—22no—
481#95—222no—
482#95—222no—
483#95—221no—
484#95—222no—
485C2×C11—21no—
486C2×C11—21no—
487C2×C11#234111yescharacteristic
488C2×C11C2×#42111yescharacteristic
489C2×C11#290111yescharacteristic
490D11—82no—
491D11—81no—
492#41—221no—
493#41—222no—
494#41—221no—
495#41—222no—
496#41—222no—
497#41—221no—
498#41—222no—
499#41—221no—
500#41—444no—
501C2×Q8—42no—
502C2×Q8—111no—
503C2×Q8—112no—
504C2×Q8(C2×D11)⋊C411yescharacteristic
505C2×Q8(C2×D11)⋊C411yescharacteristic
506C2×Q8(C2×D11)⋊C412yes—
507C2×D4—111no—
508C2×D4—112no—
509C2×D4—221no—
510C2×D4—222no—
511C2×D4—222no—
512C2×D4—221no—
513C2×D4—222no—
514C2×D4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—222no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—222no—
521C22×C4—221no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4C2×D4411yescharacteristic
525C22×C4C2×D4412yes—
526C22×C4C2×D4411yescharacteristic
527C22×C4C2×D4412yes—
528C22×C4C23×D1111yescharacteristic
529M16—21no—
530M16—22no—
531M16—21no—
532M16—22no—
533M16—21no—
534M16#434312yescomplemented
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—22no—
538C4⋊C4—111no—
539C4⋊C4—111no—
540C4⋊C4—221no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—221no—
544C4⋊C4—222no—
545C4⋊C4—221no—
546C4⋊C4—222no—
547C4⋊C4—221no—
548C4⋊C4—442no—
549C4⋊C4—444no—
550C4⋊C4(C2×D11)⋊C412yes—
551C4⋊C4(C2×D11)⋊C411yescharacteristic
552C4⋊C4(C2×D11)⋊C412yes—
553C4⋊C4(C2×D11)⋊C411yescharacteristic
554C4⋊C4(C2×D11)⋊C412yes—
555C4⋊C4(C2×D11)⋊C412yes—
556C4⋊C4(C2×D11)⋊C412yes—
557C22⋊C4—221no—
558C22⋊C4—222no—
559C22⋊C4—221no—
560C22⋊C4—221no—
561C22⋊C4—222no—
562C22⋊C4—222no—
563C22⋊C4—222no—
564C22⋊C4—222no—
565C22⋊C4—222no—
566C22⋊C4—222no—
567C22⋊C4—222no—
568C42—112no—
569C42—221no—
570C42—222no—
571C42—222no—
572C42—221no—
573C42—221no—
574C42—221no—
575C42—221no—
576C42—222no—
577C42—221no—
578C42—222no—
579C42—442no—
580C42—442no—
581C42C2×C4×D1111yescharacteristic
582C42C2×C4×D1112yes—
583C42C2×C4×D1112yes—
584C42C2×C4×D1111yescharacteristic
585C42C2×C22⋊D1111yescharacteristic
586C42C2×C22⋊D1112yes—
587C42C2×C22⋊D1112yes—
588C42C2×C22⋊D1111yescharacteristic
589C11#2255111yescharacteristic, complemented, Sylow
590C23—222no—
591C23—221no—
592C23C22×D4411yescharacteristic
593Q8—22no—
594Q8—22no—
595Q8—42no—
596Q8—221no—
597Q8—222no—
598Q8—221no—
599Q8—222no—
600D4—221no—
601D4—222no—
602D4—221no—
603D4—222no—
604D4—444no—
605D4—441no—
606D4—442no—
607D4—441no—
608D4—442no—
609D4—442no—
610D4—881no—
611D4—882no—
612C2×C4—22no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—222no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—222no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—444no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—442no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—441no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—881no—
636C2×C4—882no—
637C2×C4C2×(C2×D11)⋊C411yescharacteristic
638C2×C4C2×(C2×D11)⋊C412yes—
639C2×C4C2×(C2×D11)⋊C412yes—
640C2×C4C2×(C2×D11)⋊C411yescharacteristic
641C2×C4C2×(C2×D11)⋊C412yes—
642C2×C4C2×(C2×D11)⋊C412yes—
643C2×C4C2×(C2×D11)⋊C411yescharacteristic
644C2×C4C2×(C2×D11)⋊C411yescharacteristic
645C2×C4C22×C4×D1111yescharacteristic
646C2×C4C2×#434311yescharacteristic
647C2×C4#6704011yescharacteristic
648C2×C4#41×D1111yescharacteristic
649C2×C4#6704211yescharacteristic
650C2×C4C22×C22⋊D1111yescharacteristic
651C8—22no—
652C8—41no—
653C8—42no—
654C22—21no—
655C22—21no—
656C22—442no—
657C22—441no—
658C22—442no—
659C22—441no—
660C22—442no—
661C22—441no—
662C22#1062310711yescharacteristic
663C22#1062310811yescharacteristic
664C22C22×(C2×D11)⋊C411yescharacteristic
665C4—21no—
666C4—22no—
667C4—22no—
668C4—21no—
669C4—22no—
670C4—21no—
671C4—22no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4—441no—
676C4—441no—
677C4—441no—
678C4—882no—
679C4#1062275212yes—
680C4C4×#434311yescharacteristic
681C4#1062310511yescharacteristic
682C4#1062334811yescharacteristic
683C4#1062336511yescharacteristic
684C2—21no—
685C2—21no—
686C2—882no—
687C2—881no—
688C2#1307145411yescharacteristic
689C2C2×#1062275211yescharacteristic
690C2#1307716111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingQ8×C11×M16C2
socleC22×C11C22×C22⋊C4
prime radical#13082211C2
cosocleC22×C4×C11C24
hypercenterQ8×M16D11
hypocenterC11#22551
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ Q8×M16

Complements

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

NH ≅ G/Ntype
2. #13071094C2semidirect
3. #13069535C2semidirect
4. #13069535C2semidirect
5. #13069447C2semidirect
6. #13069443C2semidirect
7. #13068633C2semidirect
8. #13068633C2semidirect
9. #13068429C2semidirect
10. C4×#66889C2semidirect
11. Q8×C11×M16C2semidirect
14. #10623116C4semidirect
15. #10623116C4semidirect
16. #10623115C4semidirect
17. #10623115C4semidirect
20. #10623108C4semidirect
22. #10623101C4semidirect
190. C11×M16#41semidirect
244. C4×Dic11#41semidirect
246. Q8×M16D11semidirect
534. M16#4343semidirect
589. C11#22551semidirect

Maximal subgroups

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

subgroupindex
#130822112
#130710942
#130695352
#130694472
#130694432
#130686332
#130684292
C4×#668892
Q8×C11×M162
#2255111