Finite Group Databasebeta

← #14752797

Subgroups — #14752797

Order 2816.

1106 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622741C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic
3C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic
4C8×Dic11⋊C4C211yesmaximal, characteristic, complemented
5#13068477C211yesmaximal, characteristic, complemented
6#13068470C211yesmaximal, characteristic, complemented
7#13068401C211yesmaximal, characteristic, complemented
8#13068400C211yesmaximal, characteristic, complemented
9#13068398C211yesmaximal, characteristic, complemented
10C22⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C4×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
12#13068360C211yesmaximal, characteristic, complemented
13#13068309C211yesmaximal, characteristic, complemented
14#13068308C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20C22×#4313C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C2×(C22⋊D11)⋊C4C412yes—
23C2×C42×D11C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622741C418yescomplemented
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×C8×Dic11C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36C2×C8×Dic11C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38C22⋊C4×Dic11C412yes—
39C4×(C2×D11)⋊C4C2211yescharacteristic
40C4×Dic11⋊C4C2211yescharacteristic
41C42×Dic11C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44#10622342C418yescomplemented
45#10622279C412yes—
46#10622262C412yes—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11C2×C411yescharacteristic
59C23×Dic11C2×C412yes—
60C22×C4×D11C2×C412yes—
61C22×C4×D11C2311yescharacteristic
62C2×C11×M16—41no—
63C2×C11×M16—41no—
64C2×C11×M16C2×C414yescomplemented
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4C2×C412yes—
70C2×C42×C11C2311yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11C2×C411yescharacteristic
73C4×C22⋊D11C2×C414yes—
74C4×C22⋊D11C2×C414yes—
75C2×(C2×D11)⋊C4C2×C412yes—
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C412yes—
79C2×C4×Dic11—41no—
80C2×C4×Dic11—41no—
81C2×C4×Dic11C2×C412yes—
82C2×C4×Dic11C2×C412yes—
83C2×C4×Dic11C2×C412yes—
84C2×C4×Dic11C2×C412yes—
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×#4318—41no—
89C2×#4318—41no—
90C2×#4318C2×C414yescomplemented
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×#4313—41no—
96C2×#4313—41no—
97C2×#4313—41no—
98C2×#4313—41no—
99C2×#4313C2×C414yescomplemented
100C2×#4313C2×C414yescomplemented
101(C22⋊D11)⋊C4—28no—
102C42×D11—41no—
103C42×D11—41no—
104C11×C22⋊C8C2×C414yescomplemented
105C11×#97—41no—
106C4×C8×C11—41no—
107C11×#95C2×C412yes—
108C11⋊#95C2×C412yes—
109C11⋊#95C2×C412yes—
110C22⋊(C11⋊C8)C2×C414yescomplemented
111(C2×D11)⋊C8C2×C414yescomplemented
112(C2×D11)⋊C8C2×C414yescomplemented
113Dic11⋊C8C2×C414yescomplemented
114Dic11⋊C8C2×C414yescomplemented
115C8×Dic11—41no—
116C8×Dic11—41no—
117C8×Dic11C2×C414yescomplemented
118C8×Dic11C2×C414yescomplemented
119#66867—41no—
120C4×C11⋊C8—41no—
121#20567—111nomaximal, Sylow
122C24×C11C22×C411yescharacteristic
123C23×D11C22×C411yescharacteristic
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C412yes—
131C22×C4×C11C22×C412yes—
132C22×C4×C11C22×C412yes—
133C22×C4×C11C2411yescharacteristic
134C2×C22⋊D11—24no—
135C2×C22⋊D11C4214yes—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—42no—
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C412yes—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C411yescharacteristic
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11—21no—
149C2×C4×D11—21no—
150C2×C4×D11—42no—
151C2×C4×D11C22×C412yes—
152C2×C4×D11C22×C412yes—
153C11×M16—44no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C2×C8×C11C22×C412yes—
164C2×C8×C11C22×C412yes—
165C2×C8×C11C22×C412yes—
166C11×C22⋊C4—24no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C22⋊Dic11C4214yes—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4C4214yes—
174Dic11⋊C4C4214yes—
175Dic11⋊C4M1618yescomplemented
176C4×Dic11—24no—
177C4×Dic11—24no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—42no—
183C4×Dic11—42no—
184C4×Dic11C22×C412yes—
185C4×Dic11C22×C412yes—
186#4318—44no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197C2×C11⋊C8C22×C412yes—
198C2×C11⋊C8C22×C412yes—
199#4313—44no—
200#4313—44no—
201C2×#436—111no—
202C2×#436—111no—
203C42×D4—111no—
204C8×C4⋊C4—111no—
205C8×C4⋊C4—111no—
206#1767—111no—
207#1753—111no—
208#1753—111no—
209#1753—111no—
210#1753D1111yescharacteristic, complemented
211C4×C22⋊C8—111no—
212C4×C22⋊C8—111no—
213#1744—111no—
214#1728—111no—
215#1728—111no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11C2×C4212yes—
221C23×C11C23×C411yescharacteristic
222C22×D11—21no—
223C22×D11—21no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11C2×C4212yes—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11C2×C4212yes—
239C2×C4×C11C2×M1614yes—
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C112−1+411yescharacteristic
246C22⋊D11—28no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—48no—
255C2×Dic11C2×C4212yes—
256C2×Dic11C2×C4212yes—
257C2×Dic11C2×C4212yes—
258C2×Dic11C2×M1614yes—
259C2×Dic11C2×M1614yes—
260C2×Dic11#13114yes—
261C4×D11—22no—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—48no—
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—22no—
269C8×C11—22no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C22×M16—111no—
275C22×M16—111no—
276C22×M16—111no—
277C22×M16C2×D1111yescharacteristic
278C2×C4×D4—111no—
279C2×C4×D4—112no—
280C22×C42—111no—
281C22×C42—111no—
282#436—118no—
283#436—118no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×C22⋊C8—111no—
287C2×C22⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×#97—111no—
291C2×#97C2×D1111yescharacteristic
292C2×C4×C8—111no—
293C2×C4×C8—111no—
294C2×C4×C8—111no—
295C2×C4×C8—111no—
296C2×C4×C8—111no—
297C2×C4×C8C2×D1111yescharacteristic
298C4×C4⋊C4—111no—
299C4×C4⋊C4—112no—
300C4×C22⋊C4—112no—
301C4×C22⋊C4—111no—
302C4×C22⋊C4—112no—
303C4×C22⋊C4C2×D1111yescharacteristic
304C43—111no—
305#336—111no—
306#336—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336C2×D1111yescharacteristic
314#336C2×D1111yescharacteristic
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11C22×C4211yescharacteristic
321C22×C11#51811yescharacteristic
322C22×C11#52011yescharacteristic
323C22×C11C22×M1612yes—
324C22×C11C2×#13112yes—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—42no—
329C2×D11—42no—
330C4×C11—24no—
331C4×C11—22no—
332C4×C11—42no—
333C4×C11#51811yescharacteristic
334C4×C11#51811yescharacteristic
335C4×C11#52011yescharacteristic
336C4×C11#52011yescharacteristic
337Dic11—22no—
338Dic11—24no—
339Dic11—24no—
340Dic11—22no—
341Dic11C4×M1614yes—
342C22×D4—111no—
343C23×C4—111no—
344C23×C4—112no—
345C23×C4—112no—
346C23×C4C22×D1111yescharacteristic
347C2×M16—41no—
348C2×M16—41no—
349C2×M16—114no—
350C2×M16—114no—
351C2×M16—114no—
352C2×M16—441no—
353C2×M16—441no—
354C2×M16—441no—
355C2×M16—441no—
356C2×M16—441no—
357C2×M16—441no—
358C2×M16C4×D1114yescomplemented
359C22×C8—111no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1111yescharacteristic
367C4×D4—114no—
368C4×D4—114no—
369C4×D4—228no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—112no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4—111no—
374C2×C22⋊C4—112no—
375C2×C22⋊C4C4×D1112yes—
376C2×C42—111no—
377C2×C42—112no—
378C2×C42—112no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—112no—
382C2×C42—112no—
383C2×C42—441no—
384C2×C42—441no—
385C2×C42—441no—
386C2×C42—441no—
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389C4⋊C8—114no—
390C4⋊C8—114no—
391C22⋊C8—114no—
392C22⋊C8—114no—
393C22⋊C8—114no—
394C22⋊C8C4×D1114yescomplemented
395#97—41no—
396#97—441no—
397C4×C8—41no—
398C4×C8—114no—
399C4×C8—114no—
400C4×C8—441no—
401C4×C8—441no—
402C4×C8—441no—
403#95—112no—
404#95—112no—
405#95C4×D1112yes—
406C2×C11—42no—
407C2×C11#227511yescharacteristic
408C2×C11C2×C4×M1611yescharacteristic
409C2×C11C4×#13111yescharacteristic
410C2×C11#297412yes—
411C2×C11#299112yes—
412D11—42no—
413C24—111no—
414C24C2×C4×D1111yescharacteristic
415C2×D4—114no—
416C2×D4—224no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—111no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—224no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4C2×C4×D1112yes—
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4C2×C4×D1112yes—
441C22×C4C2×C4×D1112yes—
442C22×C4C2×C4×D1112yes—
443C22×C4C23×D1111yescharacteristic
444M16—44no—
445M16—444no—
446M16—444no—
447M16—444no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8C2×C4×D1112yes—
469C2×C8C2×C4×D1112yes—
470C2×C8C2×C4×D1112yes—
471C2×C8C2×C4×D1112yes—
472C4⋊C4—114no—
473C4⋊C4—118no—
474C22⋊C4—24no—
475C22⋊C4—114no—
476C22⋊C4—114no—
477C22⋊C4—224no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—112no—
483C42—112no—
484C42—224no—
485C42—224no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—442no—
491C42—442no—
492C11#2056711yescharacteristic, complemented, Sylow
493C23—22no—
494C23—22no—
495C23—21no—
496C23—21no—
497C23—112no—
498C23—222no—
499C23—222no—
500C23—221no—
501C23—221no—
502C23C42×D1112yes—
503C23C22×C4×D1111yescharacteristic
504D4—228no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—112no—
517C2×C4—114no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—114no—
521C2×C4—114no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—448no—
534C2×C4—448no—
535C2×C4C42×D1112yes—
536C2×C4M16×D1114yes—
537C2×C4C22×C4×D1111yescharacteristic
538C2×C4C22×C4×D1111yescharacteristic
539C2×C4#6703711yescharacteristic
540C2×C4#6703711yescharacteristic
541C2×C4#6704211yescharacteristic
542C2×C4#6704311yescharacteristic
543C8—22no—
544C8—22no—
545C8—22no—
546C8—22no—
547C8—222no—
548C8—222no—
549C8—222no—
550C8—222no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—42no—
555C22—42no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—442no—
560C22—442no—
561C22C2×C42×D1111yescharacteristic
562C22#1062307611yescharacteristic
563C22#1062307711yescharacteristic
564C22C2×M16×D1112yes—
565C22D11×#13112yes—
566C4—22no—
567C4—24no—
568C4—42no—
569C4—114no—
570C4—222no—
571C4—222no—
572C4—224no—
573C4—224no—
574C4#1062301711yescharacteristic
575C4#1062305411yescharacteristic
576C4#1062307611yescharacteristic
577C4#1062307711yescharacteristic
578C2—42no—
579C2—442no—
580C2#1307097511yescharacteristic
581C2C4×M16×D1111yescharacteristic
582C2#1307703811yescharacteristic
583C2#1307764612yes—
584C2#1307774412yes—
subgroupG/H
center, FrattiniC22×C4C23×D11
commutatorC22×C11C22×C42
FittingC11×#1753C2
socleC23×C11C23×C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#20567
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
4. C8×Dic11⋊C4C2semidirect
5. #13068477C2semidirect
6. #13068470C2semidirect
7. #13068401C2semidirect
8. #13068400C2semidirect
9. #13068398C2semidirect
10. C22⋊C8×Dic11C2semidirect
11. C4×(C2×D11)⋊C8C2semidirect
12. #13068360C2semidirect
13. #13068309C2semidirect
14. #13068308C2semidirect
15. C11×#1753C2semidirect
29. #10622741C4semidirect
44. #10622342C4semidirect
64. C2×C11×M16C2×C4semidirect
90. C2×#4318C2×C4semidirect
99. C2×#4313C2×C4semidirect
100. C2×#4313C2×C4semidirect
104. C11×C22⋊C8C2×C4semidirect
110. C22⋊(C11⋊C8)C2×C4semidirect
111. (C2×D11)⋊C8C2×C4semidirect
112. (C2×D11)⋊C8C2×C4semidirect
113. Dic11⋊C8C2×C4semidirect
114. Dic11⋊C8C2×C4semidirect
117. C8×Dic11C2×C4semidirect
118. C8×Dic11C2×C4semidirect
175. Dic11⋊C4M16semidirect
210. #1753D11semidirect
358. C2×M16C4×D11semidirect
394. C22⋊C8C4×D11semidirect
492. C11#20567semidirect

Maximal subgroups

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

subgroupindex
C2×#106227412
C2×#106223422
C4×(C22⋊D11)⋊C42
C8×Dic11⋊C42
#130684772
#130684702
#130684012
#130684002
#130683982
C22⋊C8×Dic112
C4×(C2×D11)⋊C82
#130683602
#130683092
#130683082
C11×#17532
#2056711