Finite Group Databasebeta

← #14720962

Subgroups — #14720962

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#13081913C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D11C211yesmaximal, characteristic, complemented
4#13067140C214yesmaximal, complemented
5#13067119C214yesmaximal, complemented
6#13067115C211yesmaximal, characteristic, complemented
7#13067112C211yesmaximal, characteristic, complemented
8#13067110C211yesmaximal, characteristic, complemented
9C11×#1503C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11#10623259C411yescharacteristic, complemented
12#10623259C411yescharacteristic, complemented
13#10623256C411yescharacteristic, complemented
14#10623256C411yescharacteristic, complemented
15#10623222—21no—
16#10623222—21no—
17#10623158—21no—
18#10623158C2212yes—
19#10623155—21no—
20#10623155C2212yes—
21#10623111—21no—
22#10623111C412yescomplemented
23C4×#4343—21no—
24C4×#4343C412yescomplemented
25#10623055—21no—
26#10623053—21no—
27C2×C4⋊C4×D11—21no—
28#10623008C2211yescharacteristic
29C2×C42×D11—21no—
30C2×C42×D11C2211yescharacteristic
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×#328C2214yes—
46#10622176C2214yes—
47#10622108C2214yes—
48#10622089C2214yes—
49C2×#4343—21no—
50C2×#4343C2×C412yes—
51C2×#4339—21no—
52C22×C4×D11—22no—
53C22×C4×D11D411yescharacteristic
54C22×C4×D11D411yescharacteristic
55C22×C4×D11C2311yescharacteristic
56C11×C4⋊Q8C2×C411yescharacteristic, complemented
57C11×C4⋊Q8C2×C411yescharacteristic, complemented
58C11×#125—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8C2312yes—
61C4×Q8×C11—21no—
62C4×Q8×C11C2×C412yescomplemented
63C11×#117—21no—
64C2×C11×C4⋊C4—21no—
65C2×C42×C11—21no—
66C2×C42×C11C2311yescharacteristic
67#67000—21no—
68#67000C2×C412yescomplemented
69#66999—21no—
70#66999C2×C412yes—
71Q8×Dic11—21no—
72Q8×Dic11C2×C412yescomplemented
73#66983—21no—
74#66983C2312yes—
75C2×C4⋊Dic11—21no—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C2×#4313—22no—
83#66951—22no—
84#66951—22no—
85#66950—21no—
86#66950—21no—
87#66948—21no—
88#66948—21no—
89#66948—21no—
90#66948C2×C412yes—
91#66947—22no—
92#66947—22no—
93#66946—22no—
94#66946—22no—
95#66946—21no—
96#66946—21no—
97#66946—21no—
98#66946C2×C412yescomplemented
99#66945—21no—
100#66945—22no—
101#66945—22no—
102#66945C2×C412yes—
103C4⋊C4×D11—28no—
104#66943—21no—
105#66943C2×C412yescomplemented
106#66940—21no—
107#66940—21no—
108#66939—22no—
109#66935—22no—
110(C22⋊D11)⋊C4—22no—
111(C22⋊D11)⋊C4—22no—
112#66928—21no—
113#66927C2×C411yescharacteristic, complemented
114C4×D44—22no—
115C4×D44—22no—
116C4×D44—21no—
117C4×D44C2×C412yescomplemented
118#66925—22no—
119C42×D11—22no—
120C42×D11—44no—
121C42×D11C2×C411yescharacteristic
122C42×D11C2×C411yescharacteristic
123C42×D11C2×C411yescharacteristic
124C42×D11C2×C411yescharacteristic
125C42×D11D411yescharacteristic
126C42×D11D411yescharacteristic
127C42×D11D411yescharacteristic
128C42×D11D411yescharacteristic
129#66922C2×C411yescharacteristic, complemented
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
144C2×Q8×C11—21no—
145C2×Q8×C11C22×C412yes—
146C22×C4×C11—22no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—22no—
151C22×Dic11—22no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155#4343—44no—
156#4343—44no—
157#4339—42no—
158#4339—42no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44C22×C412yes—
164C2×C4×D11—24no—
165C2×C4×D11—28no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—42no—
172C2×C4×D11—44no—
173C2×C4×D11—44no—
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×D11C22×C411yescharacteristic
184C2×C4×D11C2×D411yescharacteristic
185C2×C4×D11C2×D411yescharacteristic
186C2×Dic22—21no—
187C2×C8×C11—22no—
188C11×C4⋊C4—24no—
189C11×C4⋊C4—21no—
190C11×C4⋊C4—21no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4C22×C412yes—
195C11×C22⋊C4—22no—
196C42×C11—22no—
197C42×C11—42no—
198C42×C11C22×C411yescharacteristic
199C42×C11C22×C411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202(C2×D11)⋊C4—22no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—22no—
205(C2×D11)⋊C4—22no—
206(C2×D11)⋊C4—22no—
207(C2×D11)⋊C4—22no—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210C4⋊Dic11—24no—
211C4⋊Dic11—22no—
212C4⋊Dic11—22no—
213C4⋊Dic11—21no—
214C4⋊Dic11C22×C412yes—
215Dic11⋊C4—28no—
216Dic11⋊C4—22no—
217Dic11⋊C4—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#1503D1111yescharacteristic, complemented
243#1502—111no—
244#1502—111no—
245C23×C11C22×D411yescharacteristic
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11C2×C22⋊C411yescharacteristic
252C22×D11C2×C22⋊C411yescharacteristic
253Q8×C11—42no—
254Q8×C11—42no—
255C2×C4×C11—22no—
256C2×C4×C11—24no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—41no—
260C2×C4×C11—42no—
261C2×C4×C11—42no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C411yescharacteristic
265C2×C4×C11C2×C22⋊C411yescharacteristic
266C2×C4×C11AGL(1,ℤ/8)12yes—
267C2×C4×C11#13712yes—
268C2×C4×C11C23×C411yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C22⋊D11—42no—
271C22⋊D11—42no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—41no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11C2×C22⋊C411yescharacteristic
281C2×Dic11C2×C22⋊C411yescharacteristic
282C2×Dic11C2×C22⋊C411yescharacteristic
283C2×Dic11C2×C22⋊C411yescharacteristic
284C2×Dic11C2×C22⋊C411yescharacteristic
285C2×Dic11C2×C22⋊C411yescharacteristic
286D44—42no—
287D44—44no—
288D44—44no—
289D44—42no—
290D44—42no—
291C4×D11—22no—
292C4×D11—22no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—41no—
301C4×D11—41no—
302C4×D11—44no—
303C4×D11—416no—
304C4×D11—44no—
305C4×D11—44no—
306C4×D11#10414yes—
307Dic22—42no—
308C8×C11—42no—
309C11⋊C8—42no—
310#533—111no—
311#533—111no—
312#533C2×D1111yescharacteristic
313#532—111no—
314#532—111no—
315#532—111no—
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#328C2×D1114yes—
347#327—114no—
348#327—114no—
349C22×C11—21no—
350C22×C11—21no—
351C22×C11C22×C22⋊C411yescharacteristic
352C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C11C2×#13711yescharacteristic
354C2×D11—24no—
355C2×D11—24no—
356C2×D11—21no—
357C2×D11—21no—
358C2×D11—21no—
359C2×D11—21no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—42no—
363C2×D11#41012yes—
364C2×D11C2×#10412yes—
365C4×C11—21no—
366C4×C11—21no—
367C4×C11—21no—
368C4×C11—44no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11#41712yes—
372C4×C11#41712yes—
373C4×C11C2×#10412yes—
374Dic11—21no—
375Dic11—21no—
376Dic11—21no—
377Dic11—21no—
378Dic11—21no—
379Dic11—44no—
380Dic11—42no—
381Dic11C2×#10412yes—
382C2×#41—112no—
383C2×#41—221no—
384C2×#41—221no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—222no—
389C2×M16—222no—
390C4⋊Q8—111no—
391C4⋊Q8C4×D1111yescharacteristic, complemented
392C4⋊Q8C4×D1111yescharacteristic, complemented
393#127—111no—
394#126—222no—
395#126—222no—
396#125—21no—
397#125—112no—
398#125—221no—
399#124—112no—
400#124—221no—
401#124—221no—
402#123—222no—
403#123—222no—
404#123—222no—
405C22⋊Q8—21no—
406C22⋊Q8—112no—
407C22⋊Q8—221no—
408C22⋊Q8—221no—
409C22⋊Q8—221no—
410C22⋊Q8C22×D1112yes—
411#121—112no—
412#121—112no—
413#121—221no—
414#121—221no—
415#121—221no—
416#121—221no—
417#120—222no—
418C4×Q8—21no—
419C4×Q8—112no—
420C4×Q8—221no—
421C4×Q8—221no—
422C4×Q8—221no—
423C4×Q8C4×D1112yescomplemented
424C4×D4—112no—
425C4×D4—112no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4—221no—
429C4×D4—221no—
430C4×D4—221no—
431C4×D4—222no—
432C4×D4—222no—
433C4×D4—222no—
434C4×D4—222no—
435C4×D4—221no—
436#117—21no—
437#117—112no—
438#117—222no—
439#117—222no—
440#117—222no—
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×C11C2×#41011yescharacteristic
478C2×C11C2×#41711yescharacteristic
479C2×C11C22×#10411yescharacteristic
480D11—22no—
481D11—22no—
482D11—82no—
483C24—111no—
484#41—444no—
485#41—444no—
486#41—442no—
487#41—442no—
488C2×Q8—21no—
489C2×Q8—221no—
490C2×Q8C2×C4×D1112yes—
491C2×D4—112no—
492C2×D4—222no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—221no—
496C2×D4—221no—
497C22×C4—22no—
498C22×C4—111no—
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—224no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—228no—
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—21no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—112no—
537C4⋊C4—222no—
538C4⋊C4—222no—
539C4⋊C4—222no—
540C4⋊C4—222no—
541C4⋊C4—228no—
542C4⋊C4—224no—
543C4⋊C4—221no—
544C4⋊C4C2×C4×D1112yes—
545C22⋊C4—22no—
546C22⋊C4—222no—
547C22⋊C4—222no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C22⋊C4—222no—
551C22⋊C4—222no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C42—22no—
555C42—42no—
556C42—111no—
557C42—111no—
558C42—111no—
559C42—111no—
560C42—111no—
561C42—111no—
562C42—111no—
563C42—111no—
564C42—111no—
565C42—111no—
566C42—111no—
567C42—111no—
568C42—222no—
569C42—222no—
570C42—444no—
571C42—442no—
572C42C2×C4×D1111yescharacteristic
573C42C2×C4×D1111yescharacteristic
574C42D4×D1111yescharacteristic
575C42D4×D1111yescharacteristic
576C11#1754611yescharacteristic, complemented, Sylow
577C23—111no—
578C23—111no—
579C23—222no—
580C23—222no—
581C23—221no—
582C23—221no—
583C23—222no—
584C23C2×D4×D1111yescharacteristic
585Q8—42no—
586Q8—42no—
587Q8—442no—
588D4—442no—
589D4—444no—
590D4—444no—
591D4—442no—
592D4—442no—
593D4—442no—
594D4—442no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
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—441no—
624C2×C4—441no—
625C2×C4—444no—
626C2×C4—444no—
627C2×C4—4416no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—444no—
632C2×C4C22⋊C4×D1111yescharacteristic
633C2×C4C22⋊C4×D1111yescharacteristic
634C2×C4C22⋊C4×D1111yescharacteristic
635C2×C4C22⋊C4×D1111yescharacteristic
636C2×C4#6696712yes—
637C2×C4#6697112yes—
638C2×C4C22×C4×D1111yescharacteristic
639C2×C4C2×D4×D1111yescharacteristic
640C8—42no—
641C8—442no—
642C22—21no—
643C22—21no—
644C22—112no—
645C22—112no—
646C22—224no—
647C22—224no—
648C22—221no—
649C22—221no—
650C22—221no—
651C22—221no—
652C22—442no—
653C22—442no—
654C22—442no—
655C22C2×C22⋊C4×D1111yescharacteristic
656C22C2×#6696711yescharacteristic
657C22C2×#6697111yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—44no—
662C4—42no—
663C4—42no—
664C4—112no—
665C4—221no—
666C4—221no—
667C4—221no—
668C4—221no—
669C4—221no—
670C4—444no—
671C4—442no—
672C4#1062241612yes—
673C4#1062241612yes—
674C4D11×#10412yes—
675C2—21no—
676C2—21no—
677C2—222no—
678C2—222no—
679C2—882no—
680C2D11×#41011yescharacteristic
681C2C2×#1062241611yescharacteristic
682C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1503C2
socleC22×C11C22×C22⋊C4
prime radical#13081913C2
cosocleC22×C4×C11C24
hypercenter#1503D11
hypocenterC11#17546
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1503

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. C4×C4⋊C4×D11C2semidirect
4. #13067140C2semidirect
5. #13067119C2semidirect
6. #13067115C2semidirect
7. #13067112C2semidirect
8. #13067110C2semidirect
9. C11×#1503C2semidirect
11. #10623259C4semidirect
12. #10623259C4semidirect
13. #10623256C4semidirect
14. #10623256C4semidirect
22. #10623111C4semidirect
24. C4×#4343C4semidirect
56. C11×C4⋊Q8C2×C4semidirect
57. C11×C4⋊Q8C2×C4semidirect
62. C4×Q8×C11C2×C4semidirect
68. #67000C2×C4semidirect
72. Q8×Dic11C2×C4semidirect
98. #66946C2×C4semidirect
105. #66943C2×C4semidirect
113. #66927C2×C4semidirect
117. C4×D44C2×C4semidirect
129. #66922C2×C4semidirect
242. #1503D11semidirect
391. C4⋊Q8C4×D11semidirect
392. C4⋊Q8C4×D11semidirect
423. C4×Q8C4×D11semidirect
576. C11#17546semidirect

Maximal subgroups

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

subgroupindex
#130819132
#130772442
C4×C4⋊C4×D112
#130671402
#130671192
#130671152
#130671122
#130671102
C11×#15032
#1754611