Finite Group Databasebeta

← #14719677

Subgroups — #14719677

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623076C211yesmaximal, characteristic
2#13077643C212yesmaximal, complemented
3#13066955C212yesmaximal, complemented
4#13066954C211yesmaximal, characteristic, complemented
5#13066949C212yesmaximal, complemented
6#13066942C212yesmaximal, complemented
7#13066933C212yesmaximal, complemented
8D11×#323C212yesmaximal, complemented
9C11×#1465C211yesmaximal, characteristic, complemented
10C22×D4×D11C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C22×(C2×D11)⋊C4C411yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17#10623076—24no—
18#10623076—24no—
19C2×#66946C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×(C22⋊D11)⋊C4C411yescharacteristic
22C2×(C22⋊D11)⋊C4C2211yescharacteristic
23C2×C22⋊C4×D11C411yescharacteristic
24C2×C22⋊C4×D11C2211yescharacteristic
25C2×C4×D44C411yescharacteristic
26C2×#66925C411yescharacteristic
27C11×#407C2212yescomplemented
28#10622820C2212yescomplemented
29#10622740—24no—
30#10622341—24no—
31D11×C22⋊C8C2214yescomplemented
32#10622332C2214yescomplemented
33C11×#324C2212yescomplemented
34C11×#323C2212yescomplemented
35#10622166C2212yescomplemented
36#10622163C2212yescomplemented
37#10622106C2214yes—
38#10622106C2214yescomplemented
39C24×D11C2×C411yescharacteristic
40C24×D11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C22⋊D11C2×C411yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C23×Dic11C2×C411yescharacteristic
48C2×D4×D11—24no—
49C2×D4×D11—24no—
50C2×D4×D11—24no—
51C22×D44C2×C411yescharacteristic
52C22×C4×D11C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C2×C11×M16—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4C2×C411yescharacteristic
62C2×C11×C22⋊C4C2311yescharacteristic
63C2×C42×C11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C411yescharacteristic
65C2×C22⋊Dic11C2×C411yescharacteristic
66D4×Dic11—24no—
67C4×C22⋊D11—22no—
68C4×C22⋊D11—22no—
69C4×C22⋊D11D414yes—
70C4×C22⋊D11D414yes—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2×C411yescharacteristic
77C2×(C2×D11)⋊C4C2×C411yescharacteristic
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2311yescharacteristic
82C2×(C2×D11)⋊C4C2311yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C2×#4318—22no—
90C2×C8×D11—24no—
91#66946—24no—
92#66945—24no—
93(C22⋊D11)⋊C4—24no—
94(C22⋊D11)⋊C4—24no—
95C22⋊C4×D11—24no—
96C22⋊C4×D11—24no—
97C4×D44—22no—
98C4×D44—22no—
99#66925—22no—
100#66925—22no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8C2314yes—
103C22⋊(C11⋊C8)—22no—
104C22⋊(C11⋊C8)C2314yes—
105(C2×D11)⋊C8—24no—
106#66879—24no—
107Dic11⋊C8—24no—
108#17367—111nomaximal, Sylow
109C24×C11C22×C411yescharacteristic
110C24×C11C22×C411yescharacteristic
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—81no—
117C23×D11—81no—
118C23×D11—81no—
119C23×D11—81no—
120C23×D11M1614yescomplemented
121C23×D11C22×C411yescharacteristic
122C23×D11C22×C411yescharacteristic
123C23×D11C22×C411yescharacteristic
124C2×D4×C11—22no—
125C2×D4×C11—22no—
126C2×D4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—81no—
130C22×C4×C11—81no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2411yescharacteristic
138C2×C22⋊D11—22no—
139C2×C22⋊D11—22no—
140C2×C22⋊D11—22no—
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11C22⋊C414yes—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—81no—
147C22×Dic11—81no—
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153D4×D11—232no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44M1614yescomplemented
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11—81no—
166C2×C4×D11—81no—
167C2×C4×D11C2×D414yes—
168C11×M16—82no—
169C2×C8×C11—24no—
170C11×C4⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C42×C11—21no—
174C42×C11—21no—
175C22⋊Dic11—22no—
176C22⋊Dic11C22⋊C414yes—
177(C2×D11)⋊C4—22no—
178(C2×D11)⋊C4—22no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—21no—
181(C2×D11)⋊C4—21no—
182(C2×D11)⋊C4—21no—
183(C2×D11)⋊C4—21no—
184(C2×D11)⋊C4—22no—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4C22⋊C412yes—
187(C2×D11)⋊C4C22⋊C412yes—
188C4⋊Dic11—22no—
189Dic11⋊C4—22no—
190Dic11⋊C4C22⋊C412yes—
191Dic11⋊C4C22⋊C412yes—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C4×Dic11C2×D414yes—
195#4318—82no—
196C2×C11⋊C8—24no—
197C8×D11—84no—
198C2×#518—111no—
199#2973—112no—
200#1466—112no—
201#1465—111no—
202#1465D1111yescharacteristic, complemented
203#1464—112no—
204#1462—112no—
205#1459—112no—
206C2×#323—112no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C2×C22⋊C412yes—
216C23×C11C2×M1612yes—
217C23×C11C23×C411yescharacteristic
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—28no—
223C22×D11—28no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—84no—
237C22×D11—84no—
238C22×D11C2×C22⋊C412yes—
239C22×D11C2×M1612yes—
240C22×D11C2×M1612yes—
241C22×D11C2×M1612yes—
242C22×D11C2×M1612yes—
243D4×C11—28no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—81no—
255C2×C4×C11—81no—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C2×M1612yes—
259C2×C4×C11C22×D412yes—
260C22⋊D11—28no—
261C22⋊D11—28no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—82no—
271C2×Dic11—82no—
272C2×Dic11C2×C22⋊C412yes—
273C2×Dic11C2×C22⋊C412yes—
274C2×Dic11C2×C22⋊C412yes—
275D44—28no—
276C4×D11—28no—
277C4×D11—44no—
278C4×D11—82no—
279C4×D11—82no—
280C4×D11—82no—
281C8×C11—44no—
282C11⋊C8—44no—
283C23×D4—111no—
284#518—224no—
285#518—224no—
286C2×C4×D4—111no—
287C2×C4×D4—111no—
288C2×C4×D4—111no—
289C2×C4×D4—111no—
290C2×C4×D4—111no—
291C2×C4×D4—111no—
292C2×C4×D4—111no—
293C2×C4×D4C2×D1111yescharacteristic
294C2×#117—111no—
295C2×#117—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—111no—
299C22×C22⋊C4—111no—
300#435—224no—
301#435—224no—
302#432—114no—
303#407—112no—
304#407C2×D1112yescomplemented
305C2×C22⋊C8—114no—
306#324—112no—
307#324C2×D1112yescomplemented
308#323—112no—
309#323—114no—
310#323—114no—
311#323C2×D1112yescomplemented
312C22×C11—21no—
313C22×C11—21no—
314C22×C11—22no—
315C22×C11—22no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11C22×C22⋊C411yescharacteristic
325C22×C11C22×M1611yescharacteristic
326C22×C11C22×M1611yescharacteristic
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—42no—
340C2×D11—42no—
341C2×D11—88no—
342C2×D11—88no—
343C2×D11#40714yes—
344C4×C11—22no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—22no—
348C4×C11—41no—
349C4×C11—41no—
350Dic11—22no—
351Dic11—22no—
352Dic11—22no—
353Dic11—41no—
354Dic11—41no—
355C25—111no—
356C25—111no—
357C22×D4—111no—
358C22×D4—111no—
359C22×D4—111no—
360C22×D4—224no—
361C22×D4—224no—
362C22×D4—224no—
363C22×D4C4×D1111yescharacteristic
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4C4×D1111yescharacteristic
372C23×C4C22×D1111yescharacteristic
373C2×M16—22no—
374C2×M16—222no—
375C22×C8—224no—
376C4×D4—22no—
377C4×D4—22no—
378C4×D4—114no—
379C4×D4—114no—
380C4×D4—222no—
381C4×D4—222no—
382C4×D4—224no—
383C4×D4—224no—
384C4×D4—224no—
385C4×D4—224no—
386C4×D4—222no—
387C4×D4—222no—
388#117—222no—
389#117—222no—
390#117—224no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4C22×D1111yescharacteristic
395C2×C22⋊C4—111no—
396C2×C22⋊C4—111no—
397C2×C22⋊C4—111no—
398C2×C22⋊C4—111no—
399C2×C22⋊C4—111no—
400C2×C22⋊C4—111no—
401C2×C22⋊C4—111no—
402C2×C22⋊C4—111no—
403C2×C22⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4—222no—
410C2×C22⋊C4—222no—
411C2×C22⋊C4C4×D1111yescharacteristic
412C2×C22⋊C4C22×D1111yescharacteristic
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42C4×D1111yescharacteristic
417C4⋊C8—224no—
418C22⋊C8—22no—
419C22⋊C8—114no—
420C22⋊C8—224no—
421C22⋊C8—222no—
422C22⋊C8C22×D1114yes—
423#97—224no—
424C2×C11—21no—
425C2×C11—21no—
426C2×C11—42no—
427C2×C11—42no—
428C2×C11C2×#40711yescharacteristic
429C2×C11#288311yescharacteristic
430C2×C11#288811yescharacteristic
431D11—24no—
432D11—42no—
433D11—42no—
434C24—111no—
435C24—111no—
436C24—111no—
437C24—114no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—222no—
443C24—881no—
444C24—881no—
445C24—881no—
446C24—881no—
447C24C2×C4×D1111yescharacteristic
448C24C2×C4×D1111yescharacteristic
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—114no—
453C2×D4—114no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—222no—
457C2×D4—2232no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—222no—
461C2×D4—222no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—81no—
465C22×C4—81no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—114no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4C2×C4×D1111yescharacteristic
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C2×C4×D1111yescharacteristic
489C22×C4C2×C4×D1111yescharacteristic
490C22×C4D4×D1112yes—
491C22×C4D4×D1112yes—
492C22×C4C23×D1111yescharacteristic
493M16—82no—
494M16—882no—
495C2×C8—24no—
496C2×C8—224no—
497C2×C8—884no—
498C4⋊C4—22no—
499C4⋊C4—112no—
500C4⋊C4—112no—
501C4⋊C4—222no—
502C4⋊C4—222no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—114no—
506C22⋊C4—112no—
507C22⋊C4—112no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—222no—
512C22⋊C4—221no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C22⋊C4—221no—
516C22⋊C4—222no—
517C22⋊C4—222no—
518C42—21no—
519C42—21no—
520C42—114no—
521C42—222no—
522C42—222no—
523C11#1736711yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—112no—
533C23—112no—
534C23—112no—
535C23—112no—
536C23—112no—
537C23—228no—
538C23—228no—
539C23—221no—
540C23—221no—
541C23—221no—
542C23—221no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23—882no—
550C23—882no—
551C23—882no—
552C23—882no—
553C23—884no—
554C23—884no—
555C23—884no—
556C23—884no—
557C23C22⋊C4×D1112yes—
558C23M16×D1112yes—
559C23C22×C4×D1111yescharacteristic
560D4—28no—
561D4—228no—
562D4—228no—
563D4—228no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—81no—
575C2×C4—81no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—228no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—444no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—882no—
590C2×C4—882no—
591C2×C4—882no—
592C2×C4—882no—
593C2×C4—882no—
594C2×C4C22⋊C4×D1111yescharacteristic
595C2×C4C22⋊C4×D1111yescharacteristic
596C2×C4M16×D1112yes—
597C2×C4C2×D4×D1112yes—
598C8—44no—
599C8—444no—
600C22—21no—
601C22—21no—
602C22—22no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—41no—
611C22—41no—
612C22—114no—
613C22—222no—
614C22—222no—
615C22—222no—
616C22—222no—
617C22—442no—
618C22—442no—
619C22—442no—
620C22—442no—
621C22—442no—
622C22—442no—
623C22—441no—
624C22—441no—
625C22—441no—
626C22—441no—
627C22—888no—
628C22—888no—
629C22C2×C22⋊C4×D1111yescharacteristic
630C22C2×M16×D1111yescharacteristic
631C22C2×M16×D1111yescharacteristic
632C4—22no—
633C4—22no—
634C4—21no—
635C4—21no—
636C4—41no—
637C4—41no—
638C4—222no—
639C4—222no—
640C4—222no—
641C4—441no—
642C4—441no—
643C2—21no—
644C2—21no—
645C2—42no—
646C2—42no—
647C2—224no—
648C2—442no—
649C2—442no—
650C2D11×#40711yescharacteristic
651C2#1307707411yescharacteristic
652C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1465C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1465D11
hypocenterC11#17367
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #13077643C2semidirect
3. #13066955C2semidirect
4. #13066954C2semidirect
5. #13066949C2semidirect
6. #13066942C2semidirect
7. #13066933C2semidirect
8. D11×#323C2semidirect
9. C11×#1465C2semidirect
27. C11×#407C22semidirect
28. #10622820C22semidirect
31. D11×C22⋊C8C22semidirect
32. #10622332C22semidirect
33. C11×#324C22semidirect
34. C11×#323C22semidirect
35. #10622166C22semidirect
36. #10622163C22semidirect
38. #10622106C22semidirect
120. C23×D11M16semidirect
156. C2×D44M16semidirect
202. #1465D11semidirect
304. #407C2×D11semidirect
307. #324C2×D11semidirect
311. #323C2×D11semidirect
523. C11#17367semidirect

Maximal subgroups

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

subgroupindex
C2×#106230762
#130776432
#130669552
#130669542
#130669492
#130669422
#130669332
D11×#3232
C11×#14652
#1736711