Finite Group Databasebeta

← #14770681

Subgroups — #14770681

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
2Q8×#4318C211yesmaximal, characteristic, complemented
3#13069534C211yesmaximal, characteristic, complemented
4#13069534C212yesmaximal, complemented
5#13069448C212yesmaximal, complemented
6#13069444C211yesmaximal, characteristic, complemented
7#13068637C211yesmaximal, characteristic, complemented
8#13068637C212yesmaximal, complemented
9#13068427C212yesmaximal, complemented
10C4×#66869C211yesmaximal, characteristic, complemented
11C11×#2295C211yesmaximal, 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×#391—21no—
30C11×#389—21no—
31C11×#387—22no—
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C4⋊C4C2212yes—
34C11×#376C2212yes—
35C43×C11C2211yescharacteristic
36#10622637—21no—
37#10622637—22no—
38Q8×C11⋊C8—21no—
39C2×#66869C2212yes—
40C2×#66869C2211yescharacteristic
41C2×#66869C2211yescharacteristic
42C2×#66869C2212yes—
43C2×#66869C2212yes—
44C2×#66869C2212yes—
45C2×#66869C2212yes—
46#10622537C2211yescharacteristic
47#10622537C2212yes—
48C4×#4318C2211yescharacteristic
49C4×#4318C2212yes—
50#10622161C2211yescharacteristic
51#10622161C2212yes—
52#10622161C2211yescharacteristic
53C22×Q8×C11D411yescharacteristic
54C2×#4343—21no—
55C2×#4339C2311yescharacteristic
56C2×#4339C2312yes—
57C4×Q8×C11C2×C411yescharacteristic
58C4×Q8×C11C2×C411yescharacteristic
59C4×Q8×C11C2×C412yes—
60C4×Q8×C11D411yescharacteristic
61C4×Q8×C11D411yescharacteristic
62C4×Q8×C11D412yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D412yes—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C42×C11—21no—
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×C42×C11C2312yes—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2312yes—
74#67000—21no—
75#67000—22no—
76#66999—21no—
77#66999—22no—
78Q8×Dic11—21no—
79#66983—21no—
80#66983—22no—
81#66983—21no—
82#66983—22no—
83C4×C22⋊D11—21no—
84C4×C22⋊D11—22no—
85C4×C22⋊D11—21no—
86C4×C22⋊D11—22no—
87#66979C2311yescharacteristic
88C2×#4318C2311yescharacteristic
89C2×#4318C2312yes—
90C2×#4318C2311yescharacteristic
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×#95—22no—
129C11×#95—22no—
130C11×#95—21no—
131C11×#95—22no—
132#66869—24no—
133#66869—22no—
134#66869—22no—
135#66869—24no—
136#66869—42no—
137#66869—42no—
138#66869—42no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)—22no—
141C4⋊(C11⋊C8)—22no—
142C4⋊(C11⋊C8)—21no—
143#66867—22no—
144#66867—21no—
145C4×C11⋊C8—21no—
146C4×C11⋊C8—22no—
147#22551—111nomaximal, Sylow
148C2×Q8×C11—42no—
149C2×Q8×C11C22⋊C411yescharacteristic
150C2×Q8×C11C22⋊C411yescharacteristic
151C2×Q8×C11C22⋊C412yes—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—21no—
161C2×C22⋊D11—22no—
162#4343—44no—
163#4339—22no—
164#4339—21no—
165#4339—21no—
166#4339—22no—
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×C4⋊C4—42no—
186C11×C4⋊C4—44no—
187C11×C4⋊C4C22⋊C412yes—
188C11×C4⋊C4C22⋊C411yescharacteristic
189C11×C4⋊C4C22⋊C412yes—
190C11×C4⋊C4C22⋊C411yescharacteristic
191C11×C4⋊C4C22⋊C412yes—
192C11×C4⋊C4C22⋊C412yes—
193C11×C4⋊C4C22⋊C412yes—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—22no—
197C42×C11—21no—
198C42×C11—22no—
199C42×C11—42no—
200C42×C11—42no—
201C42×C11C22×C412yes—
202C42×C11C22×C411yescharacteristic
203C42×C11C22×C411yescharacteristic
204C42×C11C22×C412yes—
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D412yes—
207C42×C11C2×D412yes—
208C42×C11C2×D411yescharacteristic
209C42×C11#4112yescomplemented
210C22⋊Dic11—21no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4—22no—
214(C2×D11)⋊C4—21no—
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—
220(C2×D11)⋊C4—22no—
221C4⋊Dic11—22no—
222C4⋊Dic11—21no—
223C4⋊Dic11—22no—
224C4⋊Dic11—21no—
225C4⋊Dic11C22×C411yescharacteristic
226C4⋊Dic11C22×C411yescharacteristic
227Dic11⋊C4—22no—
228Dic11⋊C4—21no—
229Dic11⋊C4—21no—
230Dic11⋊C4—22no—
231C4×Dic11—22no—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—22no—
235C4×Dic11—21no—
236#4318—22no—
237#4318—21no—
238#4318—22no—
239#4318—21no—
240#4318—21no—
241#4318#4112yescomplemented
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—22no—
245#3480—111no—
246Q8×M16—111no—
247#2295D1111yescharacteristic, complemented
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—22no—
264C2×C4×C11—22no—
265C2×C4×C11—41no—
266C2×C4×C11—42no—
267C2×C4×C11—42no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—42no—
273C2×C4×C11—42no—
274C2×C4×C11—42no—
275C2×C4×C11C2×C22⋊C412yes—
276C2×C4×C11C2×C22⋊C411yescharacteristic
277C2×C4×C11C2×C22⋊C412yes—
278C2×C4×C11C2×C22⋊C412yes—
279C2×C4×C11C2×C22⋊C411yescharacteristic
280C2×C4×C11C2×C22⋊C411yescharacteristic
281C2×C4×C11C2×C22⋊C412yes—
282C2×C4×C11C2×C22⋊C411yescharacteristic
283C2×C4×C11C23×C411yescharacteristic
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×C4×C112−1+411yescharacteristic
289C22⋊D11—42no—
290C22⋊D11—41no—
291C22⋊D11—41no—
292C22⋊D11—42no—
293C2×Dic11—21no—
294C2×Dic11—21no—
295C2×Dic11—22no—
296C2×Dic11—21no—
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—
317C11⋊C8—22no—
318C11⋊C8—41no—
319C11⋊C8—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—221no—
338#446—222no—
339C8×Q8—221no—
340#423—111no—
341#423—112no—
342C2×#104—112no—
343C2×#104—111no—
344C2×#104—111no—
345C2×#104—112no—
346C2×#104—112no—
347C2×#104—112no—
348C2×#104—112no—
349C4×M16—111no—
350C4×M16—112no—
351#391—21no—
352#389—21no—
353#387—22no—
354C4×C4⋊C4C2×D1111yescharacteristic
355C4×C4⋊C4C2×D1112yes—
356#376C2×D1112yes—
357C43C2×D1111yescharacteristic
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—42no—
380C4×C11—42no—
381C4×C11—82no—
382C4×C11#42112yes—
383C4×C11C4×#4111yescharacteristic
384C4×C11#52011yescharacteristic
385C4×C11#54811yescharacteristic
386C4×C11#55011yescharacteristic
387Dic11—42no—
388Dic11—41no—
389Dic11—41no—
390Dic11—41no—
391C2×#41—111no—
392C2×#41—112no—
393C2×#41—221no—
394C22×Q8C22⋊D1111yescharacteristic
395C2×M16—111no—
396C2×M16—111no—
397C2×M16—112no—
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×Q8D4411yescharacteristic
432C4×Q8D4411yescharacteristic
433C4×Q8D4412yes—
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—22no—
454C2×C4⋊C4—21no—
455C2×C4⋊C4C22⋊D1112yes—
456C2×C4⋊C4C22⋊D1111yescharacteristic
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—221no—
460C2×C42—222no—
461C2×C42C22×D1111yescharacteristic
462C2×C42C22×D1112yes—
463C2×C42C22×D1111yescharacteristic
464C2×C42C22×D1111yescharacteristic
465C2×C42C22×D1112yes—
466C4⋊C8—221no—
467C4⋊C8—222no—
468C4⋊C8—222no—
469C4⋊C8—221no—
470#104—222no—
471#104—224no—
472#104—224no—
473#104—222no—
474#104—442no—
475#104—442no—
476#104—442no—
477#97—222no—
478#97—221no—
479C4×C8—221no—
480C4×C8—222no—
481#95—22no—
482#95—22no—
483#95—21no—
484#95—22no—
485C2×C11—21no—
486C2×C11—21no—
487C2×C11#234111yescharacteristic
488C2×C11C2×#42111yescharacteristic
489C2×C11#290111yescharacteristic
490D11—82no—
491D11—81no—
492#41—222no—
493#41—221no—
494#41—221no—
495#41—222no—
496#41—221no—
497#41—222no—
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—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—222no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4—221no—
523C22×C4—222no—
524C22×C4C2×C22⋊D1111yescharacteristic
525C22×C4C2×C22⋊D1112yes—
526C22×C4C2×C22⋊D1111yescharacteristic
527C22×C4C2×C22⋊D1112yes—
528C22×C4C23×D1111yescharacteristic
529M16—112no—
530M16—221no—
531M16—222no—
532M16—221no—
533M16—222no—
534M16—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—222no—
538C4⋊C4—42no—
539C4⋊C4—44no—
540C4⋊C4—111no—
541C4⋊C4—111no—
542C4⋊C4—221no—
543C4⋊C4—222no—
544C4⋊C4—222no—
545C4⋊C4—221no—
546C4⋊C4—222no—
547C4⋊C4—221no—
548C4⋊C4—222no—
549C4⋊C4—221no—
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—21no—
569C42—21no—
570C42—22no—
571C42—21no—
572C42—22no—
573C42—42no—
574C42—42no—
575C42—221no—
576C42—222no—
577C42—222no—
578C42—221no—
579C42—221no—
580C42C2×C4×D1111yescharacteristic
581C42C2×C4×D1112yes—
582C42C2×C4×D1112yes—
583C42C2×C4×D1111yescharacteristic
584C42C2×D4411yescharacteristic
585C42C2×D4412yes—
586C42C2×D4412yes—
587C42C2×D4411yescharacteristic
588C42#434312yescomplemented
589C11#2255111yescharacteristic, complemented, Sylow
590C23—222no—
591C23—221no—
592C23C22×C22⋊D1111yescharacteristic
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—22no—
614C2×C4—22no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—222no—
628C2×C4—221no—
629C2×C4—444no—
630C2×C4—441no—
631C2×C4—442no—
632C2×C4—441no—
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×C4C22×D4411yescharacteristic
647C2×C4C2×#434311yescharacteristic
648C2×C4#6704011yescharacteristic
649C2×C4#41×D1111yescharacteristic
650C2×C4#6704211yescharacteristic
651C8—222no—
652C8—441no—
653C8—442no—
654C22—21no—
655C22—21no—
656C22—442no—
657C22—441no—
658C22—442no—
659C22—441no—
660C22—442no—
661C22—441no—
662C22C22×(C2×D11)⋊C411yescharacteristic
663C22#1062334811yescharacteristic
664C22#1062336511yescharacteristic
665C4—21no—
666C4—22no—
667C4—22no—
668C4—21no—
669C4—22no—
670C4—21no—
671C4—22no—
672C4—42no—
673C4—42no—
674C4—82no—
675C4—442no—
676C4—441no—
677C4—441no—
678C4—441no—
679C4#1062261812yes—
680C4C4×#434311yescharacteristic
681C4#1062310511yescharacteristic
682C4#1062310711yescharacteristic
683C4#1062310811yescharacteristic
684C2—21no—
685C2—21no—
686C2—882no—
687C2—881no—
688C2#1307145411yescharacteristic
689C2C2×#1062261811yescharacteristic
690C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2295C2
socleC22×C11C22×C22⋊C4
prime radical#13082211C2
cosocleC22×C4×C11C24
hypercenter#2295D11
hypocenterC11#22551
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×Q8 ◁ #2295

Complements

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

NH ≅ G/Ntype
2. Q8×#4318C2semidirect
3. #13069534C2semidirect
4. #13069534C2semidirect
5. #13069448C2semidirect
6. #13069444C2semidirect
7. #13068637C2semidirect
8. #13068637C2semidirect
9. #13068427C2semidirect
10. C4×#66869C2semidirect
11. C11×#2295C2semidirect
14. #10623116C4semidirect
15. #10623116C4semidirect
16. #10623115C4semidirect
17. #10623115C4semidirect
20. #10623108C4semidirect
22. #10623101C4semidirect
209. C42×C11#41semidirect
241. #4318#41semidirect
247. #2295D11semidirect
588. C42#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
Q8×#43182
#130695342
#130694482
#130694442
#130686372
#130684272
C4×#668692
C11×#22952
#2255111