Finite Group Databasebeta

← #14720959

Subgroups — #14720959

Order 2816.

1194 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081911C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13067138C214yesmaximal, complemented
5#13067117C214yesmaximal, complemented
6#13067116C211yesmaximal, characteristic, complemented
7#13067114C211yesmaximal, characteristic, complemented
8#13067111C211yesmaximal, characteristic, complemented
9C11×#1502C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11#10623359—21no—
12#41×Dic11—21no—
13#10623259C411yescharacteristic, complemented
14#10623259C411yescharacteristic, complemented
15#10623247C411yescharacteristic, complemented
16#10623247C411yescharacteristic, complemented
17#10623211—21no—
18#10623211—21no—
19#10623137—21no—
20#10623137C2212yes—
21#10623131—21no—
22#10623131C2212yes—
23#10623088—21no—
24#10623088C412yescomplemented
25C4×#4341—21no—
26C4×#4341C412yescomplemented
27C2×C4⋊C4×D11—21no—
28C2×C42×D11—21no—
29C2×C42×D11C2211yescharacteristic
30#10623001C2211yescharacteristic
31C11×#431C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4⋊C4×Dic11—21no—
34C4×C4⋊Dic11C2211yescharacteristic
35C4×Dic11⋊C4—21no—
36#10622538C2211yescharacteristic
37#10622450—21no—
38#10622448—21no—
39#10622339C2212yes—
40#10622332C2212yes—
41C4×#4313—21no—
42#10622298—21no—
43D11×#95C2212yes—
44#10622262C2212yes—
45C11×#327C2214yes—
46#10622175C2214yes—
47#10622105C2214yes—
48#10622090C2214yes—
49C2×C11×#41—21no—
50C2×#4341—21no—
51C2×#4341C2×C412yes—
52C22×C4×D11—22no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C11×C4⋊Q8C2×C411yescharacteristic, complemented
57C11×#127C2×C411yescharacteristic, complemented
58C11×#124—21no—
59C11×#121—21no—
60C11×#121C2312yes—
61C4×D4×C11—21no—
62C4×D4×C11C2×C412yescomplemented
63C2×C11×C4⋊C4—21no—
64C2×C42×C11—21no—
65C2×C42×C11C2311yescharacteristic
66#66999—21no—
67#66999—21no—
68Q8×Dic11—21no—
69Q8×Dic11—21no—
70#66991—21no—
71#66991—21no—
72#66991—21no—
73#66991C2×C412yes—
74#66990—22no—
75#66989—21no—
76#66989C2×C412yescomplemented
77#66988—22no—
78D4×Dic11—22no—
79D4×Dic11—22no—
80D4×Dic11—21no—
81D4×Dic11—21no—
82D4×Dic11—21no—
83D4×Dic11C2×C412yescomplemented
84C4×C22⋊D11—22no—
85C4×C22⋊D11—22no—
86#66979—21no—
87#66979—22no—
88C2×C4⋊Dic11—21no—
89#66977—21no—
90#66977C2312yes—
91C2×Dic11⋊C4—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—22no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C2×#4313—22no—
99#66950—21no—
100#66950C2×C412yes—
101#66945—21no—
102#66945C2×C412yes—
103C4⋊C4×D11—28no—
104#66943—21no—
105#66943C2×C412yescomplemented
106#66940—21no—
107#66940C2×C412yescomplemented
108#66936—22no—
109#66936—22no—
110(C22⋊D11)⋊C4—22no—
111(C22⋊D11)⋊C4—22no—
112#66932—22no—
113#66932—22no—
114#66930—22no—
115#66930—22no—
116C42×D11—44no—
117C42×D11C2×C411yescharacteristic
118C42×D11C2×C411yescharacteristic
119C42×D11C2×C411yescharacteristic
120C42×D11C2×C411yescharacteristic
121C42×D11D411yescharacteristic
122C42×D11D411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11D411yescharacteristic
125#66923—21no—
126#66922C2×C411yescharacteristic, complemented
127#66922C2×C411yescharacteristic, complemented
128C4×Dic22—21no—
129C4×Dic22C2×C412yescomplemented
130C11×C4⋊C8—21no—
131C11×C22⋊C8C2312yes—
132C4×C8×C11—21no—
133C11×#95C2312yes—
134C11⋊#95—22no—
135C11⋊#95C2312yes—
136C22⋊(C11⋊C8)C2312yes—
137(C2×D11)⋊C8—22no—
138#66879—22no—
139Dic11⋊C8—22no—
140C4⋊(C11⋊C8)—21no—
141C4×C11⋊C8—21no—
142#17546—111nomaximal, Sylow
143C23×D11C2×D411yescharacteristic
144C11×#41—42no—
145C11×#41—42no—
146C2×Q8×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164#4341—44no—
165#4341—44no—
166C2×C4×D11—24no—
167C2×C4×D11—28no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—42no—
171C2×C4×D11—44no—
172C2×C4×D11—44no—
173C2×C4×D11C22⋊C411yescharacteristic
174C2×C4×D11C22⋊C411yescharacteristic
175C2×C4×D11C22⋊C411yescharacteristic
176C2×C4×D11C22⋊C411yescharacteristic
177C2×C4×D11C22⋊C411yescharacteristic
178C2×C4×D11C22⋊C411yescharacteristic
179C2×C4×D11C22⋊C411yescharacteristic
180C2×C4×D11C22⋊C411yescharacteristic
181C2×C4×D11C22×C411yescharacteristic
182C2×C4×D11C22×C411yescharacteristic
183C2×C4×D11C2×D411yescharacteristic
184C2×C4×D11C2×D411yescharacteristic
185C2×Dic22—21no—
186C2×Dic22C22×C412yes—
187C2×C8×C11—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4C22×C412yes—
191C11×C22⋊C4—22no—
192C11×C22⋊C4—22no—
193C42×C11—42no—
194C42×C11C22×C411yescharacteristic
195C42×C11C22×C411yescharacteristic
196C42×C11C2×D411yescharacteristic
197C42×C11C2×D411yescharacteristic
198C22⋊Dic11—22no—
199C22⋊Dic11—22no—
200C22⋊Dic11—22no—
201C22⋊Dic11—22no—
202C22⋊Dic11—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205C4⋊Dic11—24no—
206C4⋊Dic11—22no—
207C4⋊Dic11—22no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11C22×C412yes—
212Dic11⋊C4—28no—
213Dic11⋊C4—22no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—22no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—44no—
221C4×Dic11—42no—
222C4×Dic11C22⋊C411yescharacteristic
223C4×Dic11C22⋊C411yescharacteristic
224C4×Dic11C22⋊C411yescharacteristic
225C4×Dic11C22⋊C411yescharacteristic
226C4×Dic11C22⋊C411yescharacteristic
227C4×Dic11C22⋊C411yescharacteristic
228C4×Dic11C22⋊C411yescharacteristic
229C4×Dic11C22⋊C411yescharacteristic
230C4×Dic11C22×C411yescharacteristic
231C4×Dic11C22×C411yescharacteristic
232C4×Dic11C2×D411yescharacteristic
233C4×Dic11C2×D411yescharacteristic
234C2×C11⋊C8—22no—
235#4313—44no—
236#3444—111no—
237#2920—111no—
238C2×C4×C4⋊C4—111no—
239#1509—114no—
240#1504—114no—
241#1503—111no—
242#1503—111no—
243#1502—111no—
244#1502D1111yescharacteristic, complemented
245C23×C11—22no—
246C23×C11C22×D411yescharacteristic
247C22×D11—21no—
248C22×D11—21no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11C2×C22⋊C411yescharacteristic
252C22×D11C2×C22⋊C411yescharacteristic
253Q8×C11—42no—
254D4×C11—42no—
255D4×C11—42no—
256D4×C11—42no—
257D4×C11—42no—
258D4×C11—42no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—41no—
263C2×C4×C11—42no—
264C2×C4×C11—42no—
265C2×C4×C11—44no—
266C2×C4×C11C2×C22⋊C411yescharacteristic
267C2×C4×C11C2×C22⋊C411yescharacteristic
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11AGL(1,ℤ/8)12yes—
271C2×C4×C11#13712yes—
272C2×C4×C11C23×C411yescharacteristic
273C2×C4×C11C22×D411yescharacteristic
274C22⋊D11—44no—
275C22⋊D11—44no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—44no—
284C2×Dic11—42no—
285C2×Dic11—42no—
286C2×Dic11—44no—
287C2×Dic11C2×C22⋊C411yescharacteristic
288C2×Dic11C2×C22⋊C411yescharacteristic
289C2×Dic11C2×C22⋊C411yescharacteristic
290C2×Dic11C2×C22⋊C411yescharacteristic
291C2×Dic11C2×C22⋊C411yescharacteristic
292C2×Dic11C2×C22⋊C411yescharacteristic
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—22no—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—416no—
305C4×D11#10414yes—
306Dic22—42no—
307Dic22—42no—
308C8×C11—42no—
309C11⋊C8—42no—
310#533—111no—
311#533—111no—
312#533—111no—
313#532—111no—
314#532—111no—
315#532C2×D1111yescharacteristic
316#529—112no—
317#529—112no—
318#529—221no—
319#529—221no—
320#529—221no—
321#529—221no—
322#525—112no—
323#525—221no—
324#525—221no—
325C4×#41—112no—
326C4×#41—221no—
327C4×#41—221no—
328C22×C4⋊C4—221no—
329C22×C42—111no—
330C22×C42—221no—
331#432—112no—
332#432—221no—
333#431—111no—
334#431—221no—
335#431C2×D1111yescharacteristic
336#423—221no—
337#407—112no—
338C4×M16—221no—
339C4×C4⋊C4—111no—
340C4×C4⋊C4—112no—
341C4×C4⋊C4—221no—
342C4×C4⋊C4—221no—
343C4×C4⋊C4C2×D1111yescharacteristic
344C2×#95—112no—
345#328—114no—
346#328—114no—
347#327—114no—
348#327C2×D1114yes—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11C22×C22⋊C411yescharacteristic
355C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C11C2×#13711yescharacteristic
357C2×D11—24no—
358C2×D11—24no—
359C2×D11—21no—
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—21no—
363C2×D11#41012yes—
364C2×D11C2×#10412yes—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—44no—
369C4×C11—42no—
370C4×C11#41712yes—
371C4×C11#41712yes—
372C4×C11C2×#10412yes—
373Dic11—21no—
374Dic11—21no—
375Dic11—21no—
376Dic11—21no—
377Dic11—21no—
378Dic11—44no—
379Dic11—42no—
380Dic11—42no—
381Dic11C2×#10412yes—
382C2×#41—21no—
383C2×#41—112no—
384C2×#41—221no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—222no—
389C2×M16—222no—
390C4⋊Q8—111no—
391C4⋊Q8—111no—
392C4⋊Q8C4×D1111yescharacteristic, complemented
393#127C4×D1111yescharacteristic, complemented
394#126—222no—
395#126—222no—
396#125—112no—
397#125—221no—
398#125—221no—
399#124—21no—
400#124—112no—
401#124—221no—
402#123—222no—
403#123—222no—
404#123—222no—
405C22⋊Q8—112no—
406C22⋊Q8—112no—
407C22⋊Q8—221no—
408C22⋊Q8—221no—
409C22⋊Q8—221no—
410C22⋊Q8—221no—
411#121—21no—
412#121—112no—
413#121—221no—
414#121—221no—
415#121—221no—
416#121C22×D1112yes—
417#120—222no—
418C4×Q8—112no—
419C4×Q8—112no—
420C4×Q8—221no—
421C4×Q8—221no—
422C4×Q8—221no—
423C4×Q8—221no—
424C4×D4—21no—
425C4×D4—112no—
426C4×D4—221no—
427C4×D4—221no—
428C4×D4—221no—
429C4×D4—222no—
430C4×D4—222no—
431C4×D4—222no—
432C4×D4—222no—
433C4×D4—222no—
434C4×D4—222no—
435C4×D4C4×D1112yescomplemented
436#117—112no—
437#117—222no—
438#117—222no—
439#117—222no—
440#117—221no—
441#117—221no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—228no—
444C2×C4⋊C4—222no—
445C2×C4⋊C4—221no—
446C2×C42—21no—
447C2×C42—111no—
448C2×C42—111no—
449C2×C42—111no—
450C2×C42—111no—
451C2×C42—111no—
452C2×C42—111no—
453C2×C42—111no—
454C2×C42—111no—
455C2×C42—111no—
456C2×C42—111no—
457C2×C42—111no—
458C2×C42—222no—
459C2×C42—222no—
460C2×C42—221no—
461C2×C42—444no—
462C2×C42C22×D1111yescharacteristic
463C4⋊C8—21no—
464C4⋊C8—222no—
465C4⋊C8—221no—
466C22⋊C8—112no—
467C22⋊C8—222no—
468C22⋊C8C22×D1112yes—
469#97—222no—
470C4×C8—21no—
471C4×C8—221no—
472#95—112no—
473#95—222no—
474#95C22×D1112yes—
475C2×C11—21no—
476C2×C11—21no—
477C2×C11—82no—
478C2×C11C2×#41011yescharacteristic
479C2×C11C2×#41711yescharacteristic
480C2×C11C22×#10411yescharacteristic
481D11—22no—
482D11—22no—
483C24—111no—
484#41—42no—
485#41—42no—
486#41—444no—
487#41—444no—
488C2×Q8—21no—
489C2×Q8—112no—
490C2×Q8—221no—
491C2×D4—22no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—222no—
495C2×D4—222no—
496C2×D4C2×C4×D1112yes—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—111no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—111no—
505C22×C4—111no—
506C22×C4—111no—
507C22×C4—111no—
508C22×C4—111no—
509C22×C4—111no—
510C22×C4—111no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—224no—
515C22×C4—228no—
516C22×C4—222no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—442no—
522C22×C4—444no—
523C22×C4—444no—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527M16—444no—
528C2×C8—22no—
529C2×C8—222no—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—112no—
533C4⋊C4—222no—
534C4⋊C4—222no—
535C4⋊C4—222no—
536C4⋊C4—222no—
537C4⋊C4—228no—
538C4⋊C4—224no—
539C4⋊C4—222no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—222no—
544C4⋊C4C2×C4×D1112yes—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—222no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C42—42no—
555C42—111no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42—111no—
561C42—111no—
562C42—111no—
563C42—111no—
564C42—111no—
565C42—111no—
566C42—111no—
567C42—222no—
568C42—222no—
569C42—222no—
570C42—444no—
571C42—442no—
572C42C2×C4×D1111yescharacteristic
573C42C2×C4×D1111yescharacteristic
574C42D4×D1111yescharacteristic
575C42D4×D1111yescharacteristic
576C11#1754611yescharacteristic, complemented, Sylow
577C23—22no—
578C23—111no—
579C23—111no—
580C23—222no—
581C23—222no—
582C23—221no—
583C23—221no—
584C23C2×D4×D1111yescharacteristic
585Q8—42no—
586Q8—442no—
587Q8—442no—
588D4—42no—
589D4—42no—
590D4—42no—
591D4—42no—
592D4—42no—
593D4—444no—
594D4—444no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—44no—
602C2×C4—111no—
603C2×C4—114no—
604C2×C4—111no—
605C2×C4—111no—
606C2×C4—111no—
607C2×C4—111no—
608C2×C4—111no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—221no—
615C2×C4—221no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—224no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—4416no—
627C2×C4—444no—
628C2×C4—441no—
629C2×C4—444no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4C22⋊C4×D1111yescharacteristic
633C2×C4C22⋊C4×D1111yescharacteristic
634C2×C4C22⋊C4×D1111yescharacteristic
635C2×C4C22⋊C4×D1111yescharacteristic
636C2×C4#6696412yes—
637C2×C4#6696812yes—
638C2×C4C22×C4×D1111yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C8—42no—
641C8—442no—
642C22—21no—
643C22—21no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22—112no—
648C22—112no—
649C22—224no—
650C22—224no—
651C22—221no—
652C22—221no—
653C22—221no—
654C22—221no—
655C22C2×C22⋊C4×D1111yescharacteristic
656C22C2×#6696411yescharacteristic
657C22C2×#6696811yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—44no—
662C4—42no—
663C4—112no—
664C4—221no—
665C4—221no—
666C4—221no—
667C4—221no—
668C4—221no—
669C4—444no—
670C4—442no—
671C4—442no—
672C4#1062238412yes—
673C4#1062238412yes—
674C4D11×#10412yes—
675C2—21no—
676C2—21no—
677C2—82no—
678C2—222no—
679C2—222no—
680C2D11×#41011yescharacteristic
681C2C2×#1062238411yescharacteristic
682C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1502C2
socleC22×C11C22×C22⋊C4
prime radical#13081911C2
cosocleC22×C4×C11C24
hypercenter#1502D11
hypocenterC11#17546
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. C4×C4⋊C4×D11C2semidirect
4. #13067138C2semidirect
5. #13067117C2semidirect
6. #13067116C2semidirect
7. #13067114C2semidirect
8. #13067111C2semidirect
9. C11×#1502C2semidirect
13. #10623259C4semidirect
14. #10623259C4semidirect
15. #10623247C4semidirect
16. #10623247C4semidirect
24. #10623088C4semidirect
26. C4×#4341C4semidirect
56. C11×C4⋊Q8C2×C4semidirect
57. C11×#127C2×C4semidirect
62. C4×D4×C11C2×C4semidirect
76. #66989C2×C4semidirect
83. D4×Dic11C2×C4semidirect
105. #66943C2×C4semidirect
107. #66940C2×C4semidirect
126. #66922C2×C4semidirect
127. #66922C2×C4semidirect
129. C4×Dic22C2×C4semidirect
244. #1502D11semidirect
392. C4⋊Q8C4×D11semidirect
393. #127C4×D11semidirect
435. C4×D4C4×D11semidirect
576. C11#17546semidirect

Maximal subgroups

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

subgroupindex
#130819112
#130772442
C4×C4⋊C4×D112
#130671382
#130671172
#130671162
#130671142
#130671112
C11×#15022
#1754611