Finite Group Databasebeta

← #14720248

Subgroups — #14720248

Order 2816.

1222 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67042C211yesmaximal, characteristic
2#13077734C211yesmaximal, characteristic, complemented
3#13077577C211yesmaximal, characteristic, complemented
4#13067057C212yesmaximal, complemented
5#13067054C212yesmaximal, complemented
6#13067049C212yesmaximal, complemented
7#13067039C212yesmaximal, complemented
8#13067008C211yesmaximal, characteristic, complemented
9#13066998C211yesmaximal, characteristic, complemented
10C2×#10622121C211yesmaximal, characteristic, complemented
11C11×#1477C211yesmaximal, characteristic, complemented
12C2×#67042C411yescharacteristic
13C4×C11×#41C2211yescharacteristic
14#10623358C411yescharacteristic
15#10623105C412yes—
16C4×#4343C2212yes—
17#10623076—22no—
18#10623076C412yes—
19C4×D4×D11—22no—
20C4×D4×D11C2212yes—
21#10623054—21no—
22#10623054C411yescharacteristic
23#10623052—21no—
24#10623052C411yescharacteristic
25C4×#4339—21no—
26C4×#4339C2211yescharacteristic
27C2×C4×D44—21no—
28C2×C4×D44C2211yescharacteristic
29C11×#431C2211yescharacteristic, complemented
30C2×C11×C4⋊C8C2211yescharacteristic, complemented
31#10622724—22no—
32#10622538C2211yescharacteristic, complemented
33C2×C4×C11⋊C8C2211yescharacteristic, complemented
34#10622451—21no—
35#10622451—21no—
36#10622450C2212yescomplemented
37#10622448C2212yescomplemented
38#10622444—21no—
39#10622444—21no—
40#10622343—22no—
41C4×#4313C2212yescomplemented
42#10622298C2212yescomplemented
43C11×Q8⋊C8C2212yescomplemented
44C11×D4⋊C8C2212yescomplemented
45Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
46Q8⋊(C11⋊C8)C2211yescharacteristic, complemented
47D4⋊(C11⋊C8)C2211yescharacteristic, complemented
48D4⋊(C11⋊C8)C2211yescharacteristic, complemented
49#10622121C2212yescomplemented
50#10622121C2212yescomplemented
51#10622097C2212yescomplemented
52#10622097C2212yescomplemented
53C2×C11×#41C2×C411yescharacteristic
54#67042—24no—
55#67042—24no—
56C2×#4343C2×C412yes—
57C2×D4×D11—22no—
58C2×D4×D11C2×C412yes—
59C2×#4339—21no—
60C2×#4339C2×C411yescharacteristic
61C22×D44—21no—
62C22×D44C2×C411yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—22no—
65C22×C8×C11—21no—
66C4×Q8×C11C2×C411yescharacteristic
67C4×Q8×C11C2311yescharacteristic
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C4×D4×C11C2×C411yescharacteristic
71C4×D4×C11C2311yescharacteristic
72C11×#117—21no—
73C11×#117C2×C411yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76Q8×Dic11C2×C412yes—
77D4×Dic11—22no—
78D4×Dic11C2×C412yes—
79C4×C22⋊D11—22no—
80C4×C22⋊D11—22no—
81C4×C22⋊D11D412yes—
82C4×C22⋊D11D412yes—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85#66979—21no—
86#66979C2×C411yescharacteristic
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2×C411yescharacteristic
89C22×C11⋊C8—21no—
90C2×#4313—22no—
91C2×#4313—22no—
92#66946—22no—
93#66946—22no—
94#66946C2×C412yes—
95#66946C2×C412yes—
96#66945—22no—
97#66945C2×C412yes—
98C4⋊C4×D11—22no—
99C4⋊C4×D11C2×C412yes—
100(C22⋊D11)⋊C4—22no—
101(C22⋊D11)⋊C4—22no—
102(C22⋊D11)⋊C4—22no—
103C22⋊C4×D11—22no—
104C22⋊C4×D11—22no—
105C22⋊C4×D11—22no—
106C4×D44—21no—
107C4×D44—22no—
108C4×D44—21no—
109C4×D44—21no—
110C4×D44—22no—
111C4×D44—21no—
112C4×D44—21no—
113C4×D44C2×C412yes—
114C4×D44D411yescharacteristic
115C4×D44D411yescharacteristic
116C4×D44C2312yes—
117#66925—22no—
118#66925C2×C412yes—
119C42×D11—22no—
120C42×D11C2312yes—
121C4×Dic22—21no—
122C4×Dic22D411yescharacteristic
123C4×Dic22D411yescharacteristic
124C11×C4⋊C8—21no—
125C11×C4⋊C8—21no—
126C11×C4⋊C8C2312yes—
127C11×C22⋊C8—21no—
128C4×C8×C11C2312yes—
129C22⋊(C11⋊C8)—21no—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133#66879—22no—
134Dic11⋊C8—22no—
135Dic11⋊C8—22no—
136C4⋊(C11⋊C8)C2311yescharacteristic
137C4⋊(C11⋊C8)C2311yescharacteristic
138C4×C11⋊C8—21no—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142#17453—111nomaximal, Sylow
143C23×D11—21no—
144C23×D11—22no—
145C11×#41—22no—
146C11×#41M1614yescomplemented
147C2×Q8×C11C22×C411yescharacteristic
148C2×D4×C11—21no—
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C2×C22⋊D11—22no—
157C2×C22⋊D11C22⋊C412yes—
158C22×Dic11—22no—
159C22×Dic11—21no—
160#4343—24no—
161#4343—24no—
162D4×D11—216no—
163D4×D11—24no—
164D4×D11—24no—
165#4339—28no—
166#4339—22no—
167#4339—22no—
168C2×D44—28no—
169C2×D44—22no—
170C2×D44—21no—
171C2×D44—22no—
172C2×D44C22⋊C411yescharacteristic
173C2×D44M1614yescomplemented
174C2×D44C22×C412yes—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—22no—
180C2×C4×D11—22no—
181C2×C4×D11—81no—
182C2×C4×D11—81no—
183C2×C4×D11—82no—
184C2×C4×D11—82no—
185C2×C4×D11C22×C412yes—
186C2×C4×D11C2×D412yes—
187C2×C4×D11C2×D412yes—
188C2×Dic22C22⋊C411yescharacteristic
189C2×C8×C11—22no—
190C2×C8×C11—22no—
191C2×C8×C11—81no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4C22×C411yescharacteristic
195C11×C4⋊C4C22×C411yescharacteristic
196C11×C22⋊C4—21no—
197C11×C22⋊C4—21no—
198C11×C22⋊C4—21no—
199C42×C11—21no—
200C42×C11—21no—
201C42×C11—21no—
202C42×C11C22×C411yescharacteristic
203C42×C11C2×D411yescharacteristic
204C42×C11C2×D411yescharacteristic
205C42×C11C2411yescharacteristic
206C22⋊Dic11—22no—
207C22⋊Dic11C22⋊C412yes—
208(C2×D11)⋊C4—22no—
209(C2×D11)⋊C4—22no—
210(C2×D11)⋊C4—22no—
211(C2×D11)⋊C4—22no—
212(C2×D11)⋊C4—22no—
213(C2×D11)⋊C4C22⋊C412yes—
214(C2×D11)⋊C4C22⋊C412yes—
215C4⋊Dic11—22no—
216C4⋊Dic11—21no—
217C4⋊Dic11C22⋊C411yescharacteristic
218C4⋊Dic11C22⋊C411yescharacteristic
219C4⋊Dic11C22×C412yes—
220Dic11⋊C4—22no—
221Dic11⋊C4C22⋊C412yes—
222Dic11⋊C4C22⋊C412yes—
223C4×Dic11—22no—
224C4×Dic11—22no—
225C4×Dic11C22×C412yes—
226C4×Dic11C2×D412yes—
227C4×Dic11C2×D412yes—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—42no—
233#4313—44no—
234#4313—82no—
235C4×H(5,𝔽2)—111no—
236#2989—111no—
237#2965—111no—
238#1490—112no—
239#1489—112no—
240#1488—112no—
241#1486—112no—
242#1478—111no—
243#1477D1111yescharacteristic, complemented
244#1476—111no—
245C2×D4⋊C8—111no—
246C23×C11—21no—
247C23×C11C2×C22⋊C411yescharacteristic
248C22×D11—22no—
249C22×D11—28no—
250C22×D11—24no—
251C22×D11—82no—
252C22×D11—82no—
253C22×D11—81no—
254C22×D11—81no—
255C22×D11C2×C22⋊C412yes—
256Q8×C11—21no—
257Q8×C11C2×M1612yes—
258D4×C11—24no—
259D4×C11—21no—
260D4×C11C2×M1612yes—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—24no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—81no—
271C2×C4×C11C2×C22⋊C411yescharacteristic
272C2×C4×C11C2×C22⋊C411yescharacteristic
273C2×C4×C11C2×C22⋊C411yescharacteristic
274C2×C4×C11C2×M1612yes—
275C2×C4×C11C2×M1612yes—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C22⋊D11—28no—
280C22⋊D11—24no—
281C2×Dic11—22no—
282C2×Dic11—82no—
283C2×Dic11—81no—
284C2×Dic11C2×C22⋊C412yes—
285C2×Dic11C2×C22⋊C412yes—
286C2×Dic11C2×C22⋊C412yes—
287D44—28no—
288D44—22no—
289D44—22no—
290D44—24no—
291D44C2×M1614yes—
292C4×D11—28no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—22no—
297C4×D11—42no—
298C4×D11—42no—
299C4×D11—42no—
300C4×D11—82no—
301C4×D11—82no—
302C4×D11—82no—
303C4×D11—82no—
304Dic22—22no—
305C8×C11—42no—
306C8×C11—42no—
307C11⋊C8—22no—
308C11⋊C8—41no—
309C11⋊C8—41no—
310C11⋊C8—41no—
311C2×H(5,𝔽2)—111no—
312#520—111no—
313#520—111no—
314#520—112no—
315#520—221no—
316#518—112no—
317#518—111no—
318#518—221no—
319#518—222no—
320C4×#41—111no—
321C4×#41—112no—
322C4×#41—221no—
323C4×#41C2×D1111yescharacteristic
324C2×C4×D4—112no—
325C2×C4×D4—111no—
326C2×C4×D4—221no—
327C2×C4×D4—222no—
328#446—221no—
329#446—221no—
330#436—221no—
331#436—221no—
332#435—222no—
333#435—222no—
334#432—112no—
335#431—112no—
336#431—111no—
337#431C2×D1111yescharacteristic, complemented
338#423—112no—
339C2×C4⋊C8C2×D1111yescharacteristic, complemented
340C4×M16—112no—
341C2×C4×C8—111no—
342Q8⋊C8—111no—
343Q8⋊C8—111no—
344Q8⋊C8C2×D1112yescomplemented
345D4⋊C8—111no—
346D4⋊C8—111no—
347D4⋊C8—112no—
348D4⋊C8—112no—
349D4⋊C8—112no—
350D4⋊C8—112no—
351D4⋊C8C2×D1112yescomplemented
352C22×C11—21no—
353C22×C11—21no—
354C22×C11—22no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11#40712yes—
358C22×C11C22×C22⋊C411yescharacteristic
359C2×D11—24no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—42no—
364C2×D11—42no—
365C2×D11—84no—
366C2×D11—88no—
367C4×C11—22no—
368C4×C11—21no—
369C4×C11—21no—
370C4×C11—21no—
371C4×C11—41no—
372C4×C11—41no—
373C4×C11#40712yes—
374C4×C11C22×M1611yescharacteristic
375C4×C11C22×M1611yescharacteristic
376C4×C11#57611yescharacteristic
377C4×C11#57711yescharacteristic
378Dic11—22no—
379Dic11—22no—
380Dic11—22no—
381Dic11—42no—
382H(5,𝔽2)—224no—
383H(5,𝔽2)—224no—
384C2×#41—111no—
385C2×#41—112no—
386C2×#41—221no—
387C2×#41C4×D1111yescharacteristic
388C22×D4—112no—
389C22×D4—111no—
390C22×D4—221no—
391C22×D4—222no—
392C23×C4—222no—
393C23×C4—221no—
394C2×M16—222no—
395C2×M16—222no—
396C22×C8—21no—
397C22×C8—221no—
398C4×Q8—111no—
399C4×Q8—111no—
400C4×Q8—112no—
401C4×Q8—221no—
402C4×Q8C4×D1111yescharacteristic
403C4×Q8C22×D1111yescharacteristic
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—112no—
407C4×D4—112no—
408C4×D4—112no—
409C4×D4—112no—
410C4×D4—112no—
411C4×D4—112no—
412C4×D4—111no—
413C4×D4—111no—
414C4×D4—112no—
415C4×D4—222no—
416C4×D4—221no—
417C4×D4—221no—
418C4×D4—222no—
419C4×D4—221no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—222no—
424C4×D4—222no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4—221no—
429C4×D4—221no—
430C4×D4C4×D1111yescharacteristic
431C4×D4C22×D1111yescharacteristic
432#117—21no—
433#117—111no—
434#117—112no—
435#117—112no—
436#117—222no—
437#117—222no—
438#117—221no—
439#117C4×D1111yescharacteristic
440C2×C4⋊C4—111no—
441C2×C4⋊C4—112no—
442C2×C4⋊C4—222no—
443C2×C4⋊C4—221no—
444C2×C22⋊C4—222no—
445C2×C22⋊C4—222no—
446C2×C22⋊C4—222no—
447C2×C22⋊C4—222no—
448C2×C22⋊C4—221no—
449C2×C42—21no—
450C2×C42—112no—
451C2×C42—222no—
452C2×C42C22×D1111yescharacteristic
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—111no—
456C4⋊C8—111no—
457C4⋊C8—222no—
458C4⋊C8—222no—
459C4⋊C8C22×D1112yes—
460C22⋊C8—21no—
461C22⋊C8—222no—
462C22⋊C8—222no—
463C22⋊C8—221no—
464#97—222no—
465#97—222no—
466C4×C8—111no—
467C4×C8—111no—
468C4×C8—221no—
469C4×C8—221no—
470C4×C8C22×D1112yes—
471C2×C11—22no—
472C2×C11—42no—
473C2×C11C2×#40711yescharacteristic
474C2×C11#289711yescharacteristic
475C2×C11#290111yescharacteristic
476D11—42no—
477D11—44no—
478C24—222no—
479C24—221no—
480#41—22no—
481#41—228no—
482#41—224no—
483#41—224no—
484#41—222no—
485#41—222no—
486#41#431314yescomplemented
487C2×Q8—111no—
488C2×Q8C2×C4×D1111yescharacteristic
489C2×D4—21no—
490C2×D4—112no—
491C2×D4—111no—
492C2×D4—114no—
493C2×D4—112no—
494C2×D4—222no—
495C2×D4—228no—
496C2×D4—222no—
497C2×D4—224no—
498C2×D4—2216no—
499C2×D4—224no—
500C2×D4—221no—
501C2×D4—222no—
502C2×D4C2×C4×D1111yescharacteristic
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—112no—
507C22×C4—112no—
508C22×C4—112no—
509C22×C4—222no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—222no—
513C22×C4—222no—
514C22×C4—221no—
515C22×C4—222no—
516C22×C4—222no—
517C22×C4—881no—
518C22×C4—881no—
519C22×C4—882no—
520C22×C4—882no—
521C22×C4C2×C4×D1111yescharacteristic
522C22×C4D4×D1111yescharacteristic
523C22×C4D4×D1111yescharacteristic
524M16—444no—
525M16—882no—
526C2×C8—22no—
527C2×C8—22no—
528C2×C8—81no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—442no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—112no—
537C4⋊C4—111no—
538C4⋊C4—112no—
539C4⋊C4—111no—
540C4⋊C4—112no—
541C4⋊C4—222no—
542C4⋊C4—222no—
543C4⋊C4—221no—
544C4⋊C4C2×C4×D1111yescharacteristic
545C4⋊C4C2×C4×D1111yescharacteristic
546C22⋊C4—21no—
547C22⋊C4—21no—
548C22⋊C4—21no—
549C22⋊C4—112no—
550C22⋊C4—112no—
551C22⋊C4—112no—
552C22⋊C4—222no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—222no—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—112no—
562C42—112no—
563C42—112no—
564C42—222no—
565C42—222no—
566C42C2×C4×D1111yescharacteristic
567C42D4×D1111yescharacteristic
568C42D4×D1111yescharacteristic
569C42C23×D1111yescharacteristic
570C11#1745311yescharacteristic, complemented, Sylow
571C23—21no—
572C23—112no—
573C23—228no—
574C23—222no—
575C23—224no—
576C23—881no—
577C23—881no—
578C23—882no—
579C23—882no—
580C23C22⋊C4×D1111yescharacteristic
581Q8—21no—
582Q8—222no—
583Q8C2×#431312yes—
584D4—24no—
585D4—21no—
586D4—114no—
587D4—228no—
588D4—228no—
589D4—224no—
590D4—222no—
591D4—224no—
592D4—222no—
593D4C2×#431312yes—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—24no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—81no—
604C2×C4—112no—
605C2×C4—112no—
606C2×C4—112no—
607C2×C4—228no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—882no—
617C2×C4—882no—
618C2×C4—882no—
619C2×C4—882no—
620C2×C4—882no—
621C2×C4—881no—
622C2×C4C22⋊C4×D1111yescharacteristic
623C2×C4C22⋊C4×D1111yescharacteristic
624C2×C4C22⋊C4×D1111yescharacteristic
625C2×C4C2×#431312yes—
626C2×C4M16×D1112yes—
627C2×C4C22×C4×D1111yescharacteristic
628C2×C4C2×D4×D1111yescharacteristic
629C2×C4C2×D4×D1111yescharacteristic
630C8—42no—
631C8—42no—
632C8—222no—
633C8—441no—
634C8—441no—
635C8—441no—
636C22—21no—
637C22—21no—
638C22—22no—
639C22—41no—
640C22—41no—
641C22—224no—
642C22—222no—
643C22—222no—
644C22—222no—
645C22—442no—
646C22—442no—
647C22—884no—
648C22—888no—
649C22#1062233912yes—
650C22C2×C22⋊C4×D1111yescharacteristic
651C4—22no—
652C4—21no—
653C4—21no—
654C4—21no—
655C4—41no—
656C4—41no—
657C4—222no—
658C4—222no—
659C4—222no—
660C4—442no—
661C4#1062233912yes—
662C4C22×#431311yescharacteristic
663C4C2×M16×D1111yescharacteristic
664C4#1062330511yescharacteristic
665C4#1062330911yescharacteristic
666C2—22no—
667C2—42no—
668C2—442no—
669C2—444no—
670C2C2×#1062233911yescharacteristic
671C2#1307714011yescharacteristic
672C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1477C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#67042C4
cosocleC42×C11C24
hypercenter#1477D11
hypocenterC11#17453
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1477

Complements

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

NH ≅ G/Ntype
2. #13077734C2semidirect
3. #13077577C2semidirect
4. #13067057C2semidirect
5. #13067054C2semidirect
6. #13067049C2semidirect
7. #13067039C2semidirect
8. #13067008C2semidirect
9. #13066998C2semidirect
10. C2×#10622121C2semidirect
11. C11×#1477C2semidirect
29. C11×#431C22semidirect
30. C2×C11×C4⋊C8C22semidirect
32. #10622538C22semidirect
33. C2×C4×C11⋊C8C22semidirect
36. #10622450C22semidirect
37. #10622448C22semidirect
41. C4×#4313C22semidirect
42. #10622298C22semidirect
43. C11×Q8⋊C8C22semidirect
44. C11×D4⋊C8C22semidirect
45. Q8⋊(C11⋊C8)C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. D4⋊(C11⋊C8)C22semidirect
48. D4⋊(C11⋊C8)C22semidirect
49. #10622121C22semidirect
50. #10622121C22semidirect
51. #10622097C22semidirect
52. #10622097C22semidirect
146. C11×#41M16semidirect
173. C2×D44M16semidirect
243. #1477D11semidirect
337. #431C2×D11semidirect
339. C2×C4⋊C8C2×D11semidirect
344. Q8⋊C8C2×D11semidirect
351. D4⋊C8C2×D11semidirect
486. #41#4313semidirect
570. C11#17453semidirect

Maximal subgroups

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

subgroupindex
C4×#670422
#130777342
#130775772
#130670572
#130670542
#130670492
#130670392
#130670082
#130669982
C2×#106221212
C11×#14772
#1745311