Finite Group Databasebeta

← #14719622

Subgroups — #14719622

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#117C211yesmaximal, characteristic
2#13077246C212yesmaximal, complemented
3#13066950C211yesmaximal, characteristic, complemented
4#13066948C212yesmaximal, complemented
5#13066944C212yesmaximal, complemented
6#13066941C212yesmaximal
7#13066929C212yesmaximal, complemented
8#13066927C212yesmaximal, complemented
9C11×#1464C211yesmaximal, characteristic, complemented
10C23×C4×D11C411yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C411yescharacteristic
13D11×#117—22no—
14D11×#117—22no—
15D11×#117—22no—
16D11×#117—22no—
17C2×#66945C411yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×C4⋊C4×D11C411yescharacteristic
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C22⋊C4×D11C411yescharacteristic
22C2×C22⋊C4×D11C2211yescharacteristic
23C2×#66930C411yescharacteristic
24C2×#66930C2211yescharacteristic
25C2×#66925C411yescharacteristic
26C2×#66925C2211yescharacteristic
27C2×C42×D11C411yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C11×#432C2212yescomplemented
30#10622539C2212yescomplemented
31#10622450—22no—
32#10622446—22no—
33#10622339C2214yes—
34#10622331C2214yescomplemented
35#10622320—22no—
36#10622318—22no—
37C11×#324C2212yescomplemented
38C11×#323C2212yes—
39#10622166C2212yescomplemented
40#10622163C2212yes—
41#10622107C2214yescomplemented
42#10622106C2214yes—
43C24×D11C2×C411yescharacteristic
44C23×C4×C11C2×C411yescharacteristic
45C23×Dic11C2×C411yescharacteristic
46C22×C4×D11—24no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—21no—
50C22×C4×D11—21no—
51C22×C4×D11—24no—
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2×C411yescharacteristic
59C22×C4×D11C2311yescharacteristic
60C11×#117—22no—
61C11×#117—22no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2311yescharacteristic
66C2×C42×C11C2×C411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11C2×C411yescharacteristic
69C2×C22⋊Dic11C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2311yescharacteristic
74#66979—22no—
75#66979—22no—
76C2×C4⋊Dic11C2×C411yescharacteristic
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2311yescharacteristic
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×#4313—24no—
89#66945—22no—
90#66945—22no—
91#66945—22no—
92#66945—22no—
93C4⋊C4×D11—22no—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11—22no—
97C22⋊C4×D11—22no—
98C22⋊C4×D11—22no—
99C22⋊C4×D11—22no—
100C22⋊C4×D11—22no—
101#66930—22no—
102#66930—22no—
103#66930—22no—
104#66930—22no—
105#66925—22no—
106#66925—22no—
107#66925—22no—
108#66925—22no—
109C42×D11—21no—
110C42×D11—21no—
111C42×D11—21no—
112C42×D11—21no—
113C42×D11D412yes—
114C42×D11D412yes—
115C42×D11D412yes—
116C42×D11D412yes—
117C11×C4⋊C8—22no—
118C11×C22⋊C8C2314yes—
119C11×#97—22no—
120C22⋊(C11⋊C8)C2314yes—
121(C2×D11)⋊C8—24no—
122Dic11⋊C8—24no—
123C8×Dic11—24no—
124C4⋊(C11⋊C8)—22no—
125#66867—22no—
126#17357—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11—22no—
129C23×D11—21no—
130C23×D11—21no—
131C23×D11—22no—
132C23×D11—42no—
133C23×D11—42no—
134C23×D11C22×C411yescharacteristic
135C23×D11C22×C411yescharacteristic
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11M1614yescomplemented
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11—28no—
159C2×C4×D11—28no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—22no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—22no—
177C2×C4×D11—42no—
178C2×C4×D11—42no—
179C2×C4×D11—42no—
180C2×C4×D11—42no—
181C2×C4×D11C22⋊C411yescharacteristic
182C2×C4×D11C22⋊C411yescharacteristic
183C2×C4×D11C22⋊C411yescharacteristic
184C2×C4×D11C22⋊C411yescharacteristic
185C2×C4×D11C22⋊C412yes—
186C2×C4×D11C22⋊C412yes—
187C2×C4×D11M1614yescomplemented
188C2×C4×D11C2×D412yes—
189C2×C4×D11C2×D412yes—
190C2×C8×C11—24no—
191C11×C4⋊C4—22no—
192C11×C4⋊C4—22no—
193C11×C22⋊C4—22no—
194C11×C22⋊C4—22no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11C2×D412yes—
198C42×C11C2×D412yes—
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201(C2×D11)⋊C4—22no—
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205C4⋊Dic11—22no—
206C4⋊Dic11—22no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—22no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11C22⋊C412yes—
218C4×Dic11C22⋊C412yes—
219C4×Dic11C22⋊C412yes—
220C4×Dic11C22⋊C412yes—
221C4×Dic11C2×D412yes—
222C4×Dic11C2×D412yes—
223C2×C11⋊C8—24no—
224#4313—48no—
225C22×#117—111no—
226#2920—112no—
227#1464—112no—
228#1464—111no—
229#1464D1111yescharacteristic, complemented
230#1463—112no—
231#1462—112no—
232#1458—112no—
233#1458—112no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11C2×M1612yes—
239C23×C11C23×C411yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—42no—
251C22×D11—42no—
252C22×D11—42no—
253C22×D11—42no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11C2×C22⋊C411yescharacteristic
257C22×D11C2×C22⋊C411yescharacteristic
258C22×D11C2×M1612yes—
259C2×C4×C11—24no—
260C2×C4×C11—24no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C412yes—
274C2×C4×C11C2×M1612yes—
275C2×C4×C11C22×D412yes—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11C2×C22⋊C412yes—
287C2×Dic11C2×C22⋊C412yes—
288C2×Dic11C2×C22⋊C411yescharacteristic
289C2×Dic11C2×C22⋊C411yescharacteristic
290C2×Dic11C2×M1612yes—
291C2×Dic11C2×M1612yes—
292C2×Dic11C2×M1612yes—
293C4×D11—24no—
294C4×D11—24no—
295C4×D11—24no—
296C4×D11—24no—
297C4×D11—24no—
298C4×D11—24no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—22no—
302C4×D11—22no—
303C4×D11—24no—
304C4×D11—24no—
305C4×D11—42no—
306C4×D11—42no—
307C4×D11—42no—
308C4×D11—42no—
309C4×D11—42no—
310C4×D11—42no—
311C8×C11—44no—
312C11⋊C8—44no—
313C24×C4—111no—
314C2×#117—111no—
315C2×#117—111no—
316C2×#117—111no—
317C2×#117—111no—
318C2×#117—111no—
319C2×#117—111no—
320C2×#117—111no—
321C2×#117—222no—
322C2×#117—222no—
323C2×#117—222no—
324C2×#117—222no—
325C2×#117C2×D1111yescharacteristic
326C22×C4⋊C4—111no—
327C22×C4⋊C4—111no—
328C22×C22⋊C4—111no—
329C22×C22⋊C4—111no—
330C22×C42—111no—
331C22×C42—111no—
332#432—112no—
333#432—222no—
334#432C2×D1112yescomplemented
335#431—114no—
336#431—222no—
337#423—222no—
338#407—114no—
339C4×M16—222no—
340#324—112no—
341#324—114no—
342#324C2×D1112yescomplemented
343#323—112no—
344#323—114no—
345#323C2×D1112yes—
346C22×C11—21no—
347C22×C11—21no—
348C22×C11—22no—
349C22×C11—42no—
350C22×C11—42no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11C22×C22⋊C411yescharacteristic
354C22×C11C22×M1611yescharacteristic
355C22×C11C22×M1611yescharacteristic
356C2×D11—24no—
357C2×D11—24no—
358C2×D11—21no—
359C2×D11—21no—
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—22no—
363C2×D11—48no—
364C2×D11—48no—
365C2×D11—42no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—42no—
369C2×D11#41012yes—
370C2×D11#41312yes—
371C4×C11—21no—
372C4×C11—21no—
373C4×C11—22no—
374C4×C11—22no—
375C4×C11—22no—
376C4×C11—41no—
377C4×C11—41no—
378Dic11—22no—
379Dic11—22no—
380Dic11—22no—
381Dic11—41no—
382Dic11—41no—
383Dic11#40712yes—
384Dic11#40712yes—
385C25—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—111no—
395C23×C4—221no—
396C23×C4—221no—
397C23×C4—221no—
398C23×C4—221no—
399C23×C4—224no—
400C23×C4—224no—
401C23×C4C4×D1111yescharacteristic
402C2×M16—224no—
403#117—22no—
404#117—22no—
405#117—222no—
406#117—222no—
407#117—222no—
408#117—222no—
409#117—222no—
410#117—222no—
411#117—222no—
412#117—222no—
413#117—222no—
414#117—222no—
415#117—222no—
416#117—222no—
417#117—222no—
418#117—222no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4C4×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—111no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—222no—
438C2×C22⋊C4—222no—
439C2×C22⋊C4—222no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4C4×D1111yescharacteristic
442C2×C22⋊C4C22×D1111yescharacteristic
443C2×C42—111no—
444C2×C42—111no—
445C2×C42—111no—
446C2×C42—112no—
447C2×C42—112no—
448C2×C42—112no—
449C2×C42—112no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—221no—
454C2×C42—221no—
455C2×C42—221no—
456C2×C42—221no—
457C2×C42C4×D1111yescharacteristic
458C2×C42C22×D1111yescharacteristic
459C4⋊C8—22no—
460C4⋊C8—224no—
461C4⋊C8—222no—
462C22⋊C8—114no—
463C22⋊C8—224no—
464C22⋊C8C22×D1114yes—
465#97—22no—
466#97—222no—
467C4×C8—224no—
468C2×C11—21no—
469C2×C11—21no—
470C2×C11—42no—
471C2×C11C2×#40711yescharacteristic
472C2×C11C2×#41011yescharacteristic
473C2×C11C2×#41311yescharacteristic
474D11—22no—
475D11—22no—
476D11—42no—
477C24—111no—
478C24—111no—
479C24—221no—
480C24—221no—
481C24—222no—
482C24—222no—
483C24—442no—
484C24—442no—
485C24C2×C4×D1111yescharacteristic
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—111no—
491C22×C4—114no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—112no—
500C22×C4—114no—
501C22×C4—112no—
502C22×C4—112no—
503C22×C4—112no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—222no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—228no—
517C22×C4—228no—
518C22×C4—228no—
519C22×C4—228no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—222no—
527C22×C4—221no—
528C22×C4—221no—
529C22×C4—222no—
530C22×C4—442no—
531C22×C4—442no—
532C22×C4—442no—
533C22×C4—442no—
534C22×C4C2×C4×D1111yescharacteristic
535C22×C4C2×C4×D1111yescharacteristic
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C2×C4×D1111yescharacteristic
538C22×C4C2×C4×D1111yescharacteristic
539C22×C4C23×D1111yescharacteristic
540M16—448no—
541C2×C8—24no—
542C2×C8—224no—
543C4⋊C4—22no—
544C4⋊C4—22no—
545C4⋊C4—222no—
546C4⋊C4—222no—
547C4⋊C4—222no—
548C4⋊C4—222no—
549C4⋊C4—222no—
550C4⋊C4—222no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—222no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C42—21no—
560C42—21no—
561C42—112no—
562C42—112no—
563C42—112no—
564C42—112no—
565C42—112no—
566C42—112no—
567C42—221no—
568C42—221no—
569C42—221no—
570C42—221no—
571C42—221no—
572C42—221no—
573C42D4×D1112yes—
574C42D4×D1112yes—
575C11#1735711yescharacteristic, complemented, Sylow
576C23—21no—
577C23—21no—
578C23—41no—
579C23—41no—
580C23—111no—
581C23—111no—
582C23—112no—
583C23—222no—
584C23—222no—
585C23—224no—
586C23—224no—
587C23—221no—
588C23—221no—
589C23—221no—
590C23—221no—
591C23—441no—
592C23—441no—
593C23—442no—
594C23—442no—
595C23—448no—
596C23—448no—
597C23—442no—
598C23—442no—
599C23M16×D1112yes—
600C23C22×C4×D1111yescharacteristic
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—111no—
614C2×C4—111no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—112no—
619C2×C4—112no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—224no—
625C2×C4—224no—
626C2×C4—224no—
627C2×C4—224no—
628C2×C4—224no—
629C2×C4—224no—
630C2×C4—224no—
631C2×C4—224no—
632C2×C4—224no—
633C2×C4—224no—
634C2×C4—221no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—221no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4—442no—
641C2×C4—442no—
642C2×C4—442no—
643C2×C4—442no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4C22⋊C4×D1111yescharacteristic
649C2×C4C22⋊C4×D1111yescharacteristic
650C2×C4C22⋊C4×D1112yes—
651C2×C4M16×D1112yes—
652C2×C4C2×D4×D1112yes—
653C8—44no—
654C8—444no—
655C22—21no—
656C22—21no—
657C22—22no—
658C22—42no—
659C22—42no—
660C22—41no—
661C22—41no—
662C22—112no—
663C22—112no—
664C22—224no—
665C22—224no—
666C22—221no—
667C22—221no—
668C22—221no—
669C22—221no—
670C22—222no—
671C22—442no—
672C22—442no—
673C22—448no—
674C22—448no—
675C22—441no—
676C22—441no—
677C22C2×C22⋊C4×D1111yescharacteristic
678C22C2×M16×D1111yescharacteristic
679C22C2×M16×D1111yescharacteristic
680C4—21no—
681C4—21no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—41no—
686C4—41no—
687C4—112no—
688C4—112no—
689C4—222no—
690C4—222no—
691C4—222no—
692C4—441no—
693C4—441no—
694C2—21no—
695C2—21no—
696C2—42no—
697C2—222no—
698C2—222no—
699C2—442no—
700C2D11×#40711yescharacteristic
701C2D11×#41011yescharacteristic
702C2D11×#41311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1464C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1464D11
hypocenterC11#17357
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #13077246C2semidirect
3. #13066950C2semidirect
4. #13066948C2semidirect
5. #13066944C2semidirect
7. #13066929C2semidirect
8. #13066927C2semidirect
9. C11×#1464C2semidirect
29. C11×#432C22semidirect
30. #10622539C22semidirect
34. #10622331C22semidirect
37. C11×#324C22semidirect
39. #10622166C22semidirect
41. #10622107C22semidirect
149. C22×Dic11M16semidirect
187. C2×C4×D11M16semidirect
229. #1464D11semidirect
334. #432C2×D11semidirect
342. #324C2×D11semidirect
575. C11#17357semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1172
#130772462
#130669502
#130669482
#130669442
#130669412
#130669292
#130669272
C11×#14642
#1735711