Finite Group Databasebeta

← #14720759

Subgroups — #14720759

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082231C211yesmaximal, characteristic
2C4×#67001C211yesmaximal, characteristic, complemented
3#13067074C212yesmaximal, complemented
4#13067070C211yesmaximal, characteristic, complemented
5#13067062C212yesmaximal, complemented
6#13067053C211yesmaximal, characteristic, complemented
7#13067036C211yesmaximal, characteristic, complemented
8#13067027C212yesmaximal, complemented
9#13066996C211yesmaximal, characteristic, complemented
10C2×#10622122C212yesmaximal, complemented
11C11×#2990C211yesmaximal, characteristic, complemented
12C4×C11×#41C2211yescharacteristic
13#10623355—21no—
14C2×#67001—21no—
15#10623115C411yescharacteristic
16#10623109—21no—
17#10623098C411yescharacteristic
18#10623086C411yescharacteristic
19#10623083C412yes—
20#10623072C412yes—
21#10623069—22no—
22D4×Dic22C411yescharacteristic
23C4×#4341—21no—
24#10623064—21no—
25#10623062—22no—
26#10623010C2212yes—
27C4×#4339C2211yescharacteristic
28#10623001C2211yescharacteristic
29C2×C4×Dic22C2212yes—
30C11×#446—21no—
31C11×#435—22no—
32C8×D4×C11—21no—
33C11×#432C2212yes—
34C11×#431C2211yescharacteristic
35C11×#423C2211yescharacteristic
36C2×C11×C4⋊C8C2212yes—
37#10622610—22no—
38#10622610—21no—
39C4×#4318C2212yes—
40C4×#4318C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42C2×C4×C11⋊C8C2212yes—
43#10622122C2212yes—
44#10622122C2212yes—
45#10622122C2212yes—
46#10622122C2212yes—
47#10622122C2211yescharacteristic
48#10622122C2212yes—
49#10622122C2211yescharacteristic
50#10622121C2211yescharacteristic
51#10622121C2212yes—
52#10622121C2211yescharacteristic
53C2×C11×#41D411yescharacteristic
54C2×#4341—21no—
55C2×#4339C2×C411yescharacteristic
56C22×Dic22C2×C412yes—
57C2×C11×M16—21no—
58C22×C8×C11—22no—
59C4×Q8×C11C2×C411yescharacteristic
60C4×Q8×C11D411yescharacteristic
61C4×D4×C11C2×C411yescharacteristic
62C4×D4×C11C2×C412yes—
63C4×D4×C11D411yescharacteristic
64C4×D4×C11D412yes—
65C11×#117D412yes—
66C11×#117D411yescharacteristic
67C2×C42×C11C2312yes—
68C2×C42×C11C2311yescharacteristic
69#67001—28no—
70#66999—21no—
71#66997—21no—
72#66992—22no—
73#66988—22no—
74D4×Dic11—21no—
75#66983C2×C412yes—
76#66982—22no—
77C4×C22⋊D11—21no—
78C4×C22⋊D11—21no—
79C4×C22⋊D11—22no—
80#66979—21no—
81#66979C2×C411yescharacteristic
82C2×C4⋊Dic11C2×C412yes—
83#66977—21no—
84#66977C2×C412yes—
85#66977C2×C412yes—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—22no—
88C2×#4318—22no—
89C2×#4318—21no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—21no—
92#66951—22no—
93#66950—21no—
94#66949—22no—
95#66945—21no—
96#66942—22no—
97#66942—22no—
98#66941—21no—
99#66940—21no—
100#66939—22no—
101#66938—22no—
102(C22⋊D11)⋊C4—22no—
103#66932—22no—
104#66931—22no—
105#66930—22no—
106#66929—22no—
107#66928C2×C412yes—
108C4×D44C2×C411yescharacteristic
109C4×D44C2311yescharacteristic
110#66925—21no—
111#66925—22no—
112C42×D11—21no—
113#66923—21no—
114#66923C2×C412yes—
115#66922C2×C411yescharacteristic
116#66922C2×C411yescharacteristic
117C4×Dic22—22no—
118C4×Dic22—22no—
119C4×Dic22—21no—
120C4×Dic22C2×C412yes—
121C4×Dic22C2×C412yes—
122C4×Dic22C2×C411yescharacteristic
123C4×Dic22C2311yescharacteristic
124C4×Dic22C2312yes—
125C11×C4⋊C8—22no—
126C11×C4⋊C8—21no—
127C11×C4⋊C8C2311yescharacteristic
128C11×C4⋊C8C2312yes—
129C11×C4⋊C8C2311yescharacteristic
130C11×C22⋊C8—21no—
131C11×C22⋊C8—22no—
132C11×#97—22no—
133C4×C8×C11—21no—
134#66867—22no—
135#66867—21no—
136C4×C11⋊C8—22no—
137C4×C11⋊C8—21no—
138C4×C11⋊C8C2311yescharacteristic
139C4×C11⋊C8C2311yescharacteristic
140C4×C11⋊C8C2312yes—
141#17519—111nomaximal, Sylow
142C11×#41—24no—
143C2×Q8×C11C22⋊C411yescharacteristic
144C2×D4×C11C22⋊C412yes—
145C2×D4×C11C22⋊C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C2×C22⋊D11—22no—
153C2×C22⋊D11—21no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156#4341—44no—
157#4339—22no—
158#4339—41no—
159C2×D44C22×C411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×Dic22—24no—
164C2×Dic22—22no—
165C2×Dic22—21no—
166C2×Dic22—42no—
167C2×Dic22C22×C412yes—
168C2×Dic22C22×C411yescharacteristic
169C11×M16—81no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—22no—
173C2×C8×C11—82no—
174C11×C4⋊C4C22⋊C411yescharacteristic
175C11×C4⋊C4C22⋊C411yescharacteristic
176C11×C4⋊C4C22⋊C412yes—
177C11×C4⋊C4C22⋊C412yes—
178C11×C22⋊C4C22⋊C412yes—
179C11×C22⋊C4C22⋊C412yes—
180C11×C22⋊C4C22⋊C412yes—
181C42×C11C22×C412yes—
182C42×C11C22×C411yescharacteristic
183C42×C11C2×D412yes—
184C42×C11C2×D411yescharacteristic
185C42×C11C2×D411yescharacteristic
186C42×C11C2×D412yes—
187C42×C11C2411yescharacteristic
188C22⋊Dic11—22no—
189C22⋊Dic11—21no—
190C22⋊Dic11—22no—
191(C2×D11)⋊C4—21no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4—22no—
194(C2×D11)⋊C4—22no—
195(C2×D11)⋊C4—21no—
196C4⋊Dic11—22no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11C22×C411yescharacteristic
201C4⋊Dic11C22×C412yes—
202C4⋊Dic11C22×C411yescharacteristic
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—22no—
206Dic11⋊C4—21no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—21no—
211Dic11⋊C4—22no—
212C4×Dic11—22no—
213C4×Dic11—22no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—22no—
218#4318—28no—
219#4318—24no—
220C2×C11⋊C8—28no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—22no—
224C2×C11⋊C8—21no—
225#3482—111no—
226#2990D1111yescharacteristic, complemented
227C4×#131—111no—
228#1494—112no—
229#1493—111no—
230#1491—112no—
231#1489—111no—
232#1485—111no—
233#1483—112no—
234#1476—111no—
235C2×Q8⋊C8—112no—
236C23×C11C2×C22⋊C411yescharacteristic
237C23×C11C2×C22⋊C412yes—
238C22×D11—21no—
239Q8×C11—22no—
240D4×C11—24no—
241D4×C11#10414yes—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11C2×C22⋊C412yes—
253C2×C4×C11C2×C22⋊C411yescharacteristic
254C2×C4×C11C2×C22⋊C412yes—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C23×C411yescharacteristic
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C22×D411yescharacteristic
261C22⋊D11—42no—
262C22⋊D11—44no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—44no—
269C2×Dic11—44no—
270D44—21no—
271D44—21no—
272C4×D11—42no—
273C4×D11—41no—
274C4×D11—41no—
275C4×D11—42no—
276Dic22—21no—
277Dic22—22no—
278Dic22—22no—
279Dic22—44no—
280Dic22—42no—
281Dic22#13112yescomplemented
282C8×C11—41no—
283C8×C11—42no—
284C8×C11—41no—
285C11⋊C8—22no—
286C11⋊C8—24no—
287C11⋊C8—22no—
288C2×#131—221no—
289#557—111no—
290#556—111no—
291#556—221no—
292#552—112no—
293#552—222no—
294D4×Q8—111no—
295#548—112no—
296#547—111no—
297#547—221no—
298#533—111no—
299#533—221no—
300#529—112no—
301#529—222no—
302C4×#41—111no—
303C4×#41—221no—
304C4×#41C2×D1111yescharacteristic
305C2×C4×Q8—112no—
306#446—21no—
307#435—22no—
308C8×D4—21no—
309#432C2×D1112yes—
310#431C2×D1111yescharacteristic
311#423C2×D1111yescharacteristic
312C2×C4⋊C8C2×D1112yes—
313#405—222no—
314#405—221no—
315C4×M16—112no—
316C4×M16—111no—
317C2×C4×C8—112no—
318C2×C4×C8—111no—
319Q8⋊C8—111no—
320Q8⋊C8—112no—
321Q8⋊C8—112no—
322Q8⋊C8—112no—
323Q8⋊C8—111no—
324Q8⋊C8—112no—
325Q8⋊C8—112no—
326D4⋊C8—111no—
327D4⋊C8—111no—
328D4⋊C8—112no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—21no—
332C22×C11—21no—
333C22×C11—21no—
334C22×C11C2×#10414yes—
335C22×C11C22×C22⋊C411yescharacteristic
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C4×C11—22no—
340C4×C11—21no—
341C4×C11—22no—
342C4×C11—21no—
343C4×C11—21no—
344C4×C11—22no—
345C4×C11C2×#10412yes—
346C4×C11C2×#13111yescharacteristic
347C4×C11#56811yescharacteristic
348C4×C11#57711yescharacteristic
349C4×C11#57811yescharacteristic
350Dic11—22no—
351Dic11—42no—
352Dic11—41no—
353Dic11—42no—
354Dic11—41no—
355C2×#41—111no—
356C2×#41—221no—
357C2×#41D4411yescharacteristic
358C22×Q8—112no—
359#131—228no—
360C2×M16—21no—
361C2×M16—222no—
362C2×M16—221no—
363C22×C8—22no—
364C22×C8—222no—
365C22×C8—221no—
366C4⋊Q8—111no—
367C4⋊Q8—111no—
368C4⋊Q8—221no—
369C4⋊Q8—221no—
370#126—222no—
371#126—222no—
372#126—222no—
373#125—112no—
374#125—222no—
375#125—222no—
376#125—221no—
377#124—112no—
378#124—222no—
379#123—222no—
380#123—222no—
381#123—222no—
382C22⋊Q8—112no—
383C22⋊Q8—112no—
384C22⋊Q8—221no—
385C22⋊Q8—221no—
386C22⋊Q8—221no—
387C22⋊Q8—222no—
388C22⋊Q8—222no—
389#121—112no—
390#121—222no—
391C4×Q8—112no—
392C4×Q8—112no—
393C4×Q8—111no—
394C4×Q8—111no—
395C4×Q8—112no—
396C4×Q8—221no—
397C4×Q8—222no—
398C4×Q8—222no—
399C4×Q8—221no—
400C4×Q8C4×D1111yescharacteristic
401C4×Q8C22⋊D1111yescharacteristic
402C4×D4—111no—
403C4×D4—111no—
404C4×D4—221no—
405C4×D4—221no—
406C4×D4—221no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4C4×D1111yescharacteristic
410C4×D4C4×D1112yes—
411C4×D4C22⋊D1111yescharacteristic
412C4×D4C22⋊D1112yes—
413#117—111no—
414#117—221no—
415#117—221no—
416#117—222no—
417#117—221no—
418#117—222no—
419#117D4412yes—
420#117D4411yescharacteristic
421C2×C4⋊C4—112no—
422C2×C4⋊C4—222no—
423C2×C42—222no—
424C2×C42—221no—
425C2×C42C22×D1112yes—
426C2×C42C22×D1111yescharacteristic
427C4⋊C8—22no—
428C4⋊C8—21no—
429C4⋊C8C22×D1111yescharacteristic
430C4⋊C8C22×D1112yes—
431C4⋊C8C22×D1111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—22no—
434#97—22no—
435#97—221no—
436#97—222no—
437C4×C8—21no—
438C4×C8—111no—
439C4×C8—111no—
440C4×C8—112no—
441C4×C8—221no—
442C4×C8—222no—
443C2×C11—24no—
444C2×C11—41no—
445C2×C11#288011yescharacteristic
446C2×C11#289811yescharacteristic
447C2×C11C22×#10411yescharacteristic
448D11—81no—
449#41—24no—
450#41—222no—
451#41—441no—
452#41—444no—
453C2×Q8—111no—
454C2×Q8—112no—
455C2×Q8—224no—
456C2×Q8—222no—
457C2×Q8—221no—
458C2×Q8—442no—
459C2×Q8(C2×D11)⋊C411yescharacteristic
460C2×D4—111no—
461C2×D4—222no—
462C2×D4—221no—
463C2×D4(C2×D11)⋊C412yes—
464C2×D4(C2×D11)⋊C411yescharacteristic
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4C2×C4×D1112yes—
471C22×C4C2×C4×D1111yescharacteristic
472C22×C4C2×D4412yes—
473C22×C4C2×D4411yescharacteristic
474C22×C4C2×C22⋊D1112yes—
475C22×C4C2×C22⋊D1111yescharacteristic
476M16—81no—
477M16—228no—
478M16—224no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—22no—
482C2×C8—82no—
483C2×C8—228no—
484C2×C8—224no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—222no—
488C4⋊C4—111no—
489C4⋊C4—112no—
490C4⋊C4—111no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—221no—
495C4⋊C4—222no—
496C4⋊C4—221no—
497C4⋊C4—222no—
498C4⋊C4—222no—
499C4⋊C4—221no—
500C4⋊C4—222no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—222no—
504C4⋊C4(C2×D11)⋊C411yescharacteristic
505C4⋊C4(C2×D11)⋊C412yes—
506C4⋊C4(C2×D11)⋊C411yescharacteristic
507C4⋊C4(C2×D11)⋊C412yes—
508C22⋊C4—221no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—221no—
512C22⋊C4—222no—
513C22⋊C4—222no—
514C22⋊C4—222no—
515C22⋊C4—221no—
516C22⋊C4(C2×D11)⋊C412yes—
517C22⋊C4(C2×D11)⋊C412yes—
518C22⋊C4(C2×D11)⋊C412yes—
519C42—221no—
520C42—222no—
521C42—221no—
522C42—222no—
523C42—221no—
524C42—222no—
525C42C2×C4×D1111yescharacteristic
526C42C2×C4×D1112yes—
527C42C2×D4411yescharacteristic
528C42C2×D4412yes—
529C42C2×C22⋊D1111yescharacteristic
530C42C2×C22⋊D1112yes—
531C42C23×D1111yescharacteristic
532C11#1751911yescharacteristic, complemented, Sylow
533C23—221no—
534C23C2×(C2×D11)⋊C411yescharacteristic
535C23C2×(C2×D11)⋊C412yes—
536Q8—22no—
537Q8—112no—
538Q8—221no—
539Q8—222no—
540Q8—222no—
541Q8—444no—
542Q8—442no—
543D4—24no—
544D4—221no—
545D4—221no—
546D4—442no—
547D4—444no—
548D4#6688914yes—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—442no—
565C2×C4—444no—
566C2×C4—444no—
567C2×C4—442no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4C2×(C2×D11)⋊C412yes—
571C2×C4C2×(C2×D11)⋊C411yescharacteristic
572C2×C4C2×(C2×D11)⋊C411yescharacteristic
573C2×C4C2×(C2×D11)⋊C412yes—
574C2×C4C2×(C2×D11)⋊C412yes—
575C2×C4C2×(C2×D11)⋊C411yescharacteristic
576C2×C4C22×C4×D1111yescharacteristic
577C2×C4C22×D4411yescharacteristic
578C2×C4C22×C22⋊D1111yescharacteristic
579C8—41no—
580C8—42no—
581C8—41no—
582C8—222no—
583C8—224no—
584C8—222no—
585C22—22no—
586C22—22no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—441no—
591C22—441no—
592C22—441no—
593C22C2×#6688914yes—
594C22C22×(C2×D11)⋊C411yescharacteristic
595C4—21no—
596C4—22no—
597C4—22no—
598C4—21no—
599C4—21no—
600C4—22no—
601C4—222no—
602C4—442no—
603C4—441no—
604C4—441no—
605C4—442no—
606C4C2×#6688912yes—
607C4D11×#13111yescharacteristic
608C4#1062328111yescharacteristic
609C4#1062336711yescharacteristic
610C4#1062336911yescharacteristic
611C2—24no—
612C2—41no—
613C2—881no—
614C2#1307706311yescharacteristic
615C2#1307714611yescharacteristic
616C2C22×#6688911yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2990C2
socleC22×C11C22×C22⋊C4
prime radical#13082231C2
cosocleC42×C11C24
hypercenter#2990D11
hypocenterC11#17519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. C4×#67001C2semidirect
3. #13067074C2semidirect
4. #13067070C2semidirect
5. #13067062C2semidirect
6. #13067053C2semidirect
7. #13067036C2semidirect
8. #13067027C2semidirect
9. #13066996C2semidirect
10. C2×#10622122C2semidirect
11. C11×#2990C2semidirect
226. #2990D11semidirect
281. Dic22#131semidirect
532. C11#17519semidirect

Maximal subgroups

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

subgroupindex
#130822312
C4×#670012
#130670742
#130670702
#130670622
#130670532
#130670362
#130670272
#130669962
C2×#106221222
C11×#29902
#1751911