Finite Group Databasebeta

← #14719679

Subgroups — #14719679

Order 2816.

1350 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623076C211yesmaximal, characteristic
2#13077644C212yesmaximal, complemented
3#13066957C211yesmaximal, characteristic, complemented
4#13066951C212yesmaximal, complemented
5#13066948C212yesmaximal, complemented
6#13066941C212yesmaximal, complemented
7#13066931C212yesmaximal, complemented
8D11×#323C212yesmaximal, complemented
9C11×#1466C211yesmaximal, characteristic, complemented
10C22×D4×D11C411yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×D4×Dic11C411yescharacteristic
13C2×C4×C22⋊D11C411yescharacteristic
14C2×C4×C22⋊D11C411yescharacteristic
15C22×(C2×D11)⋊C4C411yescharacteristic
16C22×(C2×D11)⋊C4C411yescharacteristic
17#10623076—24no—
18#10623076—24no—
19C2×#66946C411yescharacteristic
20C2×#66945C411yescharacteristic
21C2×(C22⋊D11)⋊C4C2211yescharacteristic
22C2×(C22⋊D11)⋊C4C2211yescharacteristic
23C2×C22⋊C4×D11C2211yescharacteristic
24C2×C22⋊C4×D11C2211yescharacteristic
25C2×C4×D44C2211yescharacteristic
26C2×#66925C2211yescharacteristic
27C11×#432C2212yescomplemented
28#10622539C2212yescomplemented
29#10622449—24no—
30#10622339C2214yescomplemented
31D11×C22⋊C8C2214yescomplemented
32#10622319—24no—
33C11×#323C2212yescomplemented
34C11×#323C2212yescomplemented
35#10622163C2212yescomplemented
36#10622163C2212yescomplemented
37#10622107C2214yescomplemented
38#10622106C2214yes—
39C24×D11C2×C411yescharacteristic
40C24×D11C2×C411yescharacteristic
41C22×D4×C11C2×C411yescharacteristic
42C23×C4×C11C2×C411yescharacteristic
43C23×C4×C11C2×C411yescharacteristic
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×D11C2311yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C22⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4C2311yescharacteristic
62C2×C42×C11C2311yescharacteristic
63C2×C22⋊Dic11C2×C411yescharacteristic
64C2×C22⋊Dic11C2×C411yescharacteristic
65D4×Dic11—24no—
66C4×C22⋊D11—22no—
67C4×C22⋊D11—22no—
68C4×C22⋊D11—22no—
69C4×C22⋊D11—22no—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
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×C4⋊Dic11C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2311yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2×C411yescharacteristic
88C2×#4313—24no—
89C2×C8×D11—24no—
90#66946—24no—
91#66945—24no—
92(C22⋊D11)⋊C4—24no—
93(C22⋊D11)⋊C4—24no—
94C22⋊C4×D11—24no—
95C22⋊C4×D11—24no—
96C4×D44D414yes—
97C4×D44D414yes—
98#66925—22no—
99#66925—22no—
100C11×C4⋊C8—22no—
101C11×C22⋊C8C2314yes—
102C11×#97—22no—
103C22⋊(C11⋊C8)C2314yes—
104(C2×D11)⋊C8—24no—
105(C2×D11)⋊C8—24no—
106C4⋊(C11⋊C8)—22no—
107#66867—22no—
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—21no—
130C22×C4×C11—21no—
131C22×C4×C11—81no—
132C22×C4×C11—81no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
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⋊D11M1614yescomplemented
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×D44C22⋊C414yes—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—81no—
163C2×C4×D11—81no—
164C2×C4×D11—81no—
165C2×C4×D11—81no—
166C2×C4×D11C2×D414yes—
167C2×C4×D11C2×D414yes—
168C2×C8×C11—24no—
169C11×C4⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C42×C11C2×D412yes—
173C42×C11C2×D412yes—
174C22⋊Dic11—22no—
175C22⋊Dic11—22no—
176(C2×D11)⋊C4—22no—
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—22no—
183(C2×D11)⋊C4C22⋊C412yes—
184(C2×D11)⋊C4C22⋊C412yes—
185(C2×D11)⋊C4C22⋊C412yes—
186(C2×D11)⋊C4C22⋊C412yes—
187C4⋊Dic11C22⋊C414yes—
188Dic11⋊C4—21no—
189Dic11⋊C4—21no—
190Dic11⋊C4—22no—
191C4×Dic11—22no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194C2×C11⋊C8—24no—
195#4313—84no—
196C8×D11—84no—
197C2×#518—111no—
198#2973—112no—
199#1466—111no—
200#1466D1111yescharacteristic, complemented
201#1465—112no—
202#1464—112no—
203#1462—112no—
204#1459—112no—
205C2×#323—112no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11C2×M1612yes—
215C23×C11C2×M1612yes—
216C23×C11C23×C411yescharacteristic
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—82no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—84no—
234C22×D11—84no—
235C22×D11—84no—
236C22×D11—84no—
237C22×D11C2×C22⋊C412yes—
238C22×D11C2×C22⋊C412yes—
239C22×D11C2×M1612yes—
240C22×D11C2×M1612yes—
241C22×D11C2×M1612yes—
242D4×C11—28no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—81no—
252C2×C4×C11—81no—
253C2×C4×C11—81no—
254C2×C4×C11—81no—
255C2×C4×C11C2×C22⋊C412yes—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C22×D412yes—
259C22⋊D11—28no—
260C22⋊D11—28no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—82no—
270C2×Dic11—82no—
271C2×Dic11C2×C22⋊C412yes—
272C2×Dic11C2×C22⋊C412yes—
273C2×Dic11C2×M1612yes—
274D44—28no—
275C4×D11—28no—
276C4×D11—44no—
277C4×D11—44no—
278C4×D11—82no—
279C4×D11—82no—
280C8×C11—44no—
281C11⋊C8—44no—
282C23×D4—111no—
283#518—224no—
284#518—224no—
285C2×C4×D4—111no—
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×D4C2×D1111yescharacteristic
293C2×#117—111no—
294C2×#117—111no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—111no—
299#435—224no—
300#435—224no—
301#432—112no—
302#432C2×D1112yescomplemented
303#407—114no—
304C2×C22⋊C8—114no—
305#324—114no—
306#323—112no—
307#323—112no—
308#323—114no—
309#323C2×D1112yescomplemented
310#323C2×D1112yescomplemented
311C22×C11—21no—
312C22×C11—21no—
313C22×C11—22no—
314C22×C11—22no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11C22×C22⋊C411yescharacteristic
324C22×C11C22×M1611yescharacteristic
325C22×C11C22×M1611yescharacteristic
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—41no—
338C2×D11—41no—
339C2×D11—42no—
340C2×D11—88no—
341C2×D11—88no—
342C2×D11#40714yes—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—41no—
349Dic11—22no—
350Dic11—22no—
351Dic11—22no—
352Dic11—41no—
353Dic11—41no—
354C25—111no—
355C25—111no—
356C22×D4—111no—
357C22×D4—111no—
358C22×D4—111no—
359C22×D4—224no—
360C22×D4—224no—
361C22×D4—224no—
362C22×D4C4×D1111yescharacteristic
363C23×C4—111no—
364C23×C4—111no—
365C23×C4—111no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4C4×D1111yescharacteristic
371C23×C4C4×D1111yescharacteristic
372C2×M16—224no—
373C22×C8—224no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—114no—
377C4×D4—114no—
378C4×D4—224no—
379C4×D4—224no—
380C4×D4—222no—
381C4×D4—222no—
382C4×D4—222no—
383C4×D4—222no—
384C4×D4—224no—
385C4×D4—224no—
386#117—224no—
387#117—222no—
388#117—222no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4C4×D1111yescharacteristic
393C2×C22⋊C4—111no—
394C2×C22⋊C4—111no—
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—224no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—222no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—222no—
408C2×C22⋊C4—222no—
409C2×C22⋊C4C22×D1111yescharacteristic
410C2×C22⋊C4C22×D1111yescharacteristic
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—111no—
414C2×C42C22×D1111yescharacteristic
415C4⋊C8—22no—
416C4⋊C8—222no—
417C22⋊C8—114no—
418C22⋊C8—224no—
419C22⋊C8—224no—
420C22⋊C8C22×D1114yes—
421#97—22no—
422#97—222no—
423C2×C11—21no—
424C2×C11—21no—
425C2×C11—42no—
426C2×C11—42no—
427C2×C11C2×#40711yescharacteristic
428C2×C11#288311yescharacteristic
429C2×C11#288811yescharacteristic
430D11—24no—
431D11—42no—
432D11—42no—
433C24—111no—
434C24—111no—
435C24—111no—
436C24—114no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—222no—
442C24—881no—
443C24—881no—
444C24—881no—
445C24—881no—
446C24C2×C4×D1111yescharacteristic
447C24C2×C4×D1111yescharacteristic
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—114no—
452C2×D4—114no—
453C2×D4—222no—
454C2×D4—222no—
455C2×D4—222no—
456C2×D4—2232no—
457C2×D4—222no—
458C2×D4—222no—
459C2×D4—222no—
460C2×D4—222no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—81no—
466C22×C4—81no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—881no—
482C22×C4—881no—
483C22×C4—881no—
484C22×C4—881no—
485C22×C4—881no—
486C22×C4—881no—
487C22×C4C2×C4×D1111yescharacteristic
488C22×C4C2×C4×D1111yescharacteristic
489C22×C4C2×C4×D1111yescharacteristic
490C22×C4C2×C4×D1111yescharacteristic
491C22×C4C23×D1111yescharacteristic
492M16—884no—
493C2×C8—24no—
494C2×C8—224no—
495C2×C8—884no—
496C4⋊C4—22no—
497C4⋊C4—114no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—222no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—112no—
504C22⋊C4—112no—
505C22⋊C4—112no—
506C22⋊C4—112no—
507C22⋊C4—222no—
508C22⋊C4—222no—
509C22⋊C4—222no—
510C22⋊C4—222no—
511C22⋊C4—222no—
512C22⋊C4—222no—
513C22⋊C4—221no—
514C22⋊C4—221no—
515C22⋊C4—222no—
516C42—222no—
517C42—222no—
518C42—222no—
519C42D4×D1112yes—
520C42D4×D1112yes—
521C11#1736711yescharacteristic, complemented, Sylow
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528C23—41no—
529C23—41no—
530C23—112no—
531C23—112no—
532C23—112no—
533C23—112no—
534C23—112no—
535C23—228no—
536C23—228no—
537C23—221no—
538C23—221no—
539C23—221no—
540C23—221no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—882no—
548C23—882no—
549C23—882no—
550C23—882no—
551C23—884no—
552C23—884no—
553C23—884no—
554C23—884no—
555C23M16×D1112yes—
556C23M16×D1112yes—
557C23C22×C4×D1111yescharacteristic
558D4—28no—
559D4—228no—
560D4—228no—
561D4—228no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—81no—
571C2×C4—81no—
572C2×C4—81no—
573C2×C4—81no—
574C2×C4—112no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—228no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—444no—
583C2×C4—444no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—882no—
589C2×C4—882no—
590C2×C4—882no—
591C2×C4—882no—
592C2×C4C22⋊C4×D1112yes—
593C2×C4C22⋊C4×D1111yescharacteristic
594C2×C4C22⋊C4×D1111yescharacteristic
595C2×C4C2×D4×D1112yes—
596C8—44no—
597C8—444no—
598C22—21no—
599C22—21no—
600C22—22no—
601C22—22no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—114no—
611C22—222no—
612C22—222no—
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—888no—
626C22—888no—
627C22C2×C22⋊C4×D1111yescharacteristic
628C22C2×M16×D1111yescharacteristic
629C22C2×M16×D1111yescharacteristic
630C4—22no—
631C4—22no—
632C4—21no—
633C4—21no—
634C4—41no—
635C4—41no—
636C4—222no—
637C4—222no—
638C4—222no—
639C4—441no—
640C4—441no—
641C2—21no—
642C2—21no—
643C2—42no—
644C2—42no—
645C2—224no—
646C2—442no—
647C2—442no—
648C2D11×#40711yescharacteristic
649C2#1307707511yescharacteristic
650C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1466C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D4×D11C4
cosocleC22×C4×C11C24
hypercenter#1466D11
hypocenterC11#17367
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1466

Complements

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

NH ≅ G/Ntype
2. #13077644C2semidirect
3. #13066957C2semidirect
4. #13066951C2semidirect
5. #13066948C2semidirect
6. #13066941C2semidirect
7. #13066931C2semidirect
8. D11×#323C2semidirect
9. C11×#1466C2semidirect
27. C11×#432C22semidirect
28. #10622539C22semidirect
30. #10622339C22semidirect
31. D11×C22⋊C8C22semidirect
33. C11×#323C22semidirect
34. C11×#323C22semidirect
35. #10622163C22semidirect
36. #10622163C22semidirect
37. #10622107C22semidirect
120. C23×D11M16semidirect
143. C2×C22⋊D11M16semidirect
200. #1466D11semidirect
302. #432C2×D11semidirect
309. #323C2×D11semidirect
310. #323C2×D11semidirect
521. C11#17367semidirect

Maximal subgroups

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

subgroupindex
C2×#106230762
#130776442
#130669572
#130669512
#130669482
#130669412
#130669312
D11×#3232
C11×#14662
#1736711