Finite Group Databasebeta

← #14720233

Subgroups — #14720233

Order 2816.

1292 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2#13077244C211yesmaximal, characteristic, complemented
3D11×#423C211yesmaximal, characteristic, complemented
4#13067054C214yesmaximal, complemented
5#13067045C211yesmaximal, characteristic, complemented
6#13067042C211yesmaximal, characteristic, complemented
7#13067040C211yesmaximal, characteristic, complemented
8#13067002C214yesmaximal, complemented
9C11×#1487C211yesmaximal, characteristic, complemented
10C22×#4343C411yescharacteristic
11C2×C4×Q8×C11C2211yescharacteristic
12C2×Q8×Dic11C411yescharacteristic
13C2×M16×D11—21no—
14C4×#4343—21no—
15C4×#4343—21no—
16C4×#4343—21no—
17C4×#4343—21no—
18C4×#4343C412yes—
19C4×#4343C412yes—
20C4×#4343C2212yes—
21C4×#4343C2212yes—
22C2×#66946—21no—
23C2×#66946C411yescharacteristic
24C2×#66945—21no—
25C2×#66945C411yescharacteristic
26C2×C4×D44—21no—
27C2×C4×D44C2211yescharacteristic
28C2×C42×D11—21no—
29C2×C42×D11C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C11×#423C2211yescharacteristic
32#10622731—21no—
33#10622538C2211yescharacteristic
34#10622537C2211yescharacteristic
35#10622450—21no—
36#10622450—21no—
37#10622450C2212yescomplemented
38#10622448—21no—
39D11×C4⋊C8—21no—
40D11×C4⋊C8C2212yescomplemented
41#10622339—21no—
42#10622332—21no—
43C4×#4313C2212yescomplemented
44#10622298C2212yescomplemented
45C11×Q8⋊C8C2214yescomplemented
46Q8⋊(C11⋊C8)C2214yescomplemented
47#10622121C2214yescomplemented
48#10622097C2214yescomplemented
49C22×Q8×C11C2×C411yescharacteristic
50C2×#4343—28no—
51C2×#4343—21no—
52C2×#4343—21no—
53C2×#4343C2×C412yes—
54C2×#4343C2×C412yes—
55C22×D44—21no—
56C22×D44C2×C411yescharacteristic
57C22×C4×D11—21no—
58C22×C4×D11—21no—
59C22×C4×D11—21no—
60C22×C4×D11C2×C411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C2×C11×M16—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11—21no—
66C4×Q8×C11C2×C412yes—
67C4×Q8×C11C2312yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72Q8×Dic11—21no—
73Q8×Dic11—21no—
74Q8×Dic11C2×C412yes—
75Q8×Dic11C2×C412yes—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11C2×C411yescharacteristic
81C2×C4×Dic11—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11D411yescharacteristic
85C2×C4×Dic11D411yescharacteristic
86C2×#4318—21no—
87M16×D11—44no—
88C2×#4313—22no—
89C2×#4313—22no—
90C2×C8×D11—22no—
91#66946—22no—
92#66946—22no—
93#66946—22no—
94#66946—22no—
95#66946—21no—
96#66946—21no—
97#66946C2×C412yes—
98#66946C2×C412yes—
99#66945—21no—
100#66945—21no—
101#66945—22no—
102#66945—22no—
103#66945—22no—
104#66945—22no—
105#66945C2×C412yes—
106#66945C2×C412yes—
107C4×D44—22no—
108C4×D44—22no—
109C4×D44—22no—
110C4×D44—22no—
111C4×D44—21no—
112C4×D44—21no—
113C4×D44C2×C412yes—
114C4×D44C2312yes—
115C42×D11—22no—
116C42×D11—22no—
117C42×D11—22no—
118C42×D11—22no—
119C42×D11C2×C411yescharacteristic
120C42×D11C2×C411yescharacteristic
121C42×D11D411yescharacteristic
122C42×D11D411yescharacteristic
123C42×D11D411yescharacteristic
124C42×D11D411yescharacteristic
125C42×D11C2311yescharacteristic
126C42×D11C2311yescharacteristic
127C11×C4⋊C8—21no—
128C11×C4⋊C8—21no—
129C11×C4⋊C8C2312yes—
130C11×C22⋊C8—21no—
131C4×C8×C11C2312yes—
132C22⋊(C11⋊C8)—21no—
133(C2×D11)⋊C8—22no—
134#66879—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137Dic11⋊C8—22no—
138C4⋊(C11⋊C8)—21no—
139C4⋊(C11⋊C8)—21no—
140C4⋊(C11⋊C8)C2312yes—
141C4×C11⋊C8C2312yes—
142#17451—111nomaximal, Sylow
143C23×D11—21no—
144C23×D11C22⋊C411yescharacteristic
145C2×Q8×C11—24no—
146C2×Q8×C11—21no—
147C2×Q8×C11C22×C412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11C22×C411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11C22⋊C411yescharacteristic
155C22×Dic11C22⋊C411yescharacteristic
156C22×Dic11C22⋊C411yescharacteristic
157#4343—28no—
158#4343—28no—
159#4343—24no—
160#4343—24no—
161#4343—24no—
162#4343M1618yescomplemented
163C2×D44—28no—
164C2×D44—24no—
165C2×D44—22no—
166C2×D44—22no—
167C2×D44—21no—
168C2×D44C22×C412yes—
169C2×C4×D11—28no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—24no—
173C2×C4×D11—22no—
174C2×C4×D11—22no—
175C2×C4×D11—22no—
176C2×C4×D11—22no—
177C2×C4×D11—22no—
178C2×C4×D11—22no—
179C2×C4×D11—42no—
180C2×C4×D11—44no—
181C2×C4×D11—42no—
182C2×C4×D11—42no—
183C2×C4×D11C22⋊C411yescharacteristic
184C2×C4×D11C22⋊C411yescharacteristic
185C2×C4×D11C22⋊C411yescharacteristic
186C2×C4×D11C22⋊C411yescharacteristic
187C2×C4×D11C22⋊C411yescharacteristic
188C2×C4×D11C22⋊C411yescharacteristic
189C2×C4×D11C22×C411yescharacteristic
190C2×C4×D11C22×C411yescharacteristic
191C2×C4×D11C2×D411yescharacteristic
192C2×C4×D11C2×D411yescharacteristic
193C2×C4×D11C2×D411yescharacteristic
194C2×C4×D11C2×D411yescharacteristic
195C11×M16—42no—
196C2×C8×C11—22no—
197C2×C8×C11—22no—
198C11×C4⋊C4—22no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C22×C412yes—
202C42×C11—22no—
203C42×C11—22no—
204C42×C11C22×C411yescharacteristic
205C42×C11C2×D411yescharacteristic
206C42×C11C2×D411yescharacteristic
207C42×C11C2411yescharacteristic
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)⋊C4—22no—
214C4⋊Dic11—22no—
215C4⋊Dic11—22no—
216C4⋊Dic11—21no—
217C4⋊Dic11C22×C412yes—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221C4×Dic11—22no—
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×Dic11C2×D411yescharacteristic
231C4×Dic11C2×D411yescharacteristic
232C4×Dic11C2×D411yescharacteristic
233C4×Dic11C2×D411yescharacteristic
234#4318—42no—
235C2×C11⋊C8—22no—
236C2×C11⋊C8—22no—
237#4313—44no—
238#4313—44no—
239C8×D11—44no—
240C2×C4×#41—111no—
241#2920—111no—
242C2×#423—111no—
243#1489—114no—
244#1487—111no—
245#1487D1111yescharacteristic, complemented
246#1486—111no—
247#1486—111no—
248#1477—114no—
249C23×C11C2×C22⋊C411yescharacteristic
250C22×D11—24no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—41no—
255C22×D11—42no—
256C22×D11—42no—
257C22×D11C2×C22⋊C411yescharacteristic
258C22×D11C2×C22⋊C411yescharacteristic
259Q8×C11—24no—
260Q8×C11—22no—
261Q8×C11C2×M1614yescomplemented
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—41no—
267C2×C4×C11—42no—
268C2×C4×C11C2×C22⋊C411yescharacteristic
269C2×C4×C11C2×C22⋊C411yescharacteristic
270C2×C4×C11C2×C22⋊C411yescharacteristic
271C2×C4×C11AGL(1,ℤ/8)12yes—
272C2×C4×C11#13712yes—
273C2×C4×C11C23×C411yescharacteristic
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C22×D411yescharacteristic
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—42no—
281C2×Dic11C2×C22⋊C411yescharacteristic
282C2×Dic11C2×C22⋊C411yescharacteristic
283C2×Dic11C2×C22⋊C411yescharacteristic
284C2×Dic11C2×C22⋊C411yescharacteristic
285C2×Dic11C2×C22⋊C411yescharacteristic
286C2×Dic11C2×C22⋊C411yescharacteristic
287D44—28no—
288D44—24no—
289D44—28no—
290D44—22no—
291D44C2×M1614yescomplemented
292C4×D11—28no—
293C4×D11—22no—
294C4×D11—22no—
295C4×D11—21no—
296C4×D11—21no—
297C4×D11—21no—
298C4×D11—21no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—28no—
302C4×D11—22no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—41no—
306C4×D11—41no—
307C4×D11—44no—
308C4×D11—42no—
309C4×D11—42no—
310C4×D11—44no—
311C4×D11—44no—
312C4×D11C2×M1614yes—
313C8×C11—42no—
314C8×C11—42no—
315C11⋊C8—42no—
316C11⋊C8—42no—
317C22×#41—111no—
318C22×M16—221no—
319C4×#41—112no—
320C4×#41—112no—
321C4×#41—112no—
322C4×#41—112no—
323C4×#41—221no—
324C4×#41—221no—
325C4×#41—221no—
326C4×#41—221no—
327C2×C4×Q8—111no—
328C2×C4×Q8C2×D1111yescharacteristic
329C2×C4×D4—111no—
330C2×C4×D4—111no—
331C2×C4×D4—221no—
332C2×C4×D4—221no—
333C2×#117—111no—
334C2×#117—221no—
335C22×C42—111no—
336C22×C42—221no—
337#432—221no—
338#432—221no—
339#431—111no—
340#431—112no—
341#431C2×D1111yescharacteristic
342#423—111no—
343#423—112no—
344#423—221no—
345#423—221no—
346#423—221no—
347#423C2×D1111yescharacteristic
348C2×C4⋊C8—112no—
349C2×C4⋊C8—221no—
350#407—221no—
351C4×M16—112no—
352Q8⋊C8—114no—
353Q8⋊C8C2×D1114yescomplemented
354D4⋊C8—114no—
355D4⋊C8—114no—
356C22×C11—21no—
357C22×C11—21no—
358C22×C11#41712yes—
359C22×C11C22×C22⋊C411yescharacteristic
360C2×D11—21no—
361C2×D11—21no—
362C2×D11—24no—
363C2×D11—21no—
364C2×D11—21no—
365C2×D11—21no—
366C2×D11—44no—
367C2×D11—48no—
368C2×D11—42no—
369C2×D11—42no—
370C2×D11#40712yes—
371C4×C11—24no—
372C4×C11—21no—
373C4×C11—21no—
374C4×C11—21no—
375C4×C11—42no—
376C4×C11#41712yes—
377C4×C11C22×M1612yes—
378C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
379C4×C11C2×#13711yescharacteristic
380Dic11—21no—
381Dic11—21no—
382Dic11—21no—
383Dic11—21no—
384Dic11—42no—
385Dic11#40712yes—
386Dic11#42112yes—
387C2×#41—112no—
388C2×#41—112no—
389C2×#41—221no—
390C2×#41—221no—
391C2×#41—228no—
392C22×Q8C4×D1111yescharacteristic
393C22×D4—111no—
394C22×D4—221no—
395C23×C4—111no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—221no—
399C23×C4—221no—
400C23×C4—221no—
401C2×M16—21no—
402C2×M16—222no—
403C2×M16—222no—
404C2×M16—221no—
405C2×M16—444no—
406C22×C8—222no—
407C4×Q8—21no—
408C4×Q8—21no—
409C4×Q8—112no—
410C4×Q8—112no—
411C4×Q8—221no—
412C4×Q8—221no—
413C4×Q8C4×D1112yes—
414C4×Q8C22×D1112yes—
415C4×D4—112no—
416C4×D4—112no—
417C4×D4—112no—
418C4×D4—112no—
419C4×D4—222no—
420C4×D4—222no—
421C4×D4—222no—
422C4×D4—222no—
423C4×D4—221no—
424C4×D4—221no—
425C4×D4—222no—
426C4×D4—222no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—221no—
430C4×D4—221no—
431#117—112no—
432#117—112no—
433#117—222no—
434#117—222no—
435#117—222no—
436#117—222no—
437#117—221no—
438#117—221no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—111no—
441C2×C4⋊C4—221no—
442C2×C4⋊C4C4×D1111yescharacteristic
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊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—222no—
461C2×C42—222no—
462C2×C42—221no—
463C2×C42—221no—
464C2×C42C22×D1111yescharacteristic
465C4⋊C8—21no—
466C4⋊C8—21no—
467C4⋊C8—112no—
468C4⋊C8—222no—
469C4⋊C8—222no—
470C4⋊C8—222no—
471C4⋊C8—221no—
472C4⋊C8—221no—
473C4⋊C8C22×D1112yes—
474C22⋊C8—21no—
475C22⋊C8—222no—
476C22⋊C8—221no—
477#97—222no—
478C4×C8—112no—
479C4×C8C22×D1112yes—
480C2×C11—22no—
481C2×C11C2×#40711yescharacteristic
482C2×C11C2×#41711yescharacteristic
483C2×C11C2×#42111yescharacteristic
484D11—22no—
485D11—41no—
486D11—44no—
487C24—111no—
488C24—221no—
489#41—118no—
490#41—224no—
491#41—224no—
492#41—228no—
493#41—228no—
494#41—224no—
495C2×Q8—24no—
496C2×Q8—21no—
497C2×Q8C2×C4×D1112yes—
498C2×D4—112no—
499C2×D4—224no—
500C2×D4—222no—
501C2×D4—222no—
502C2×D4—228no—
503C2×D4—221no—
504C22×C4—21no—
505C22×C4—21no—
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—111no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—111no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—224no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—228no—
527C22×C4—222no—
528C22×C4—222no—
529C22×C4—221no—
530C22×C4—222no—
531C22×C4—222no—
532C22×C4—442no—
533C22×C4—444no—
534C22×C4—442no—
535C22×C4—442no—
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4D4×D1111yescharacteristic
538C22×C4D4×D1111yescharacteristic
539M16—42no—
540M16—444no—
541M16—444no—
542M16—442no—
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—222no—
546C2×C8—222no—
547C2×C8—444no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—22no—
551C4⋊C4—112no—
552C4⋊C4—222no—
553C4⋊C4—222no—
554C4⋊C4—221no—
555C4⋊C4C2×C4×D1112yes—
556C22⋊C4—222no—
557C22⋊C4—222no—
558C22⋊C4—222no—
559C22⋊C4—222no—
560C22⋊C4—222no—
561C22⋊C4—222no—
562C42—22no—
563C42—22no—
564C42—111no—
565C42—111no—
566C42—111no—
567C42—111no—
568C42—111no—
569C42—111no—
570C42—111no—
571C42—111no—
572C42—111no—
573C42—111no—
574C42—111no—
575C42—111no—
576C42—222no—
577C42—222no—
578C42—222no—
579C42—222no—
580C42C2×C4×D1111yescharacteristic
581C42D4×D1111yescharacteristic
582C42D4×D1111yescharacteristic
583C42C23×D1111yescharacteristic
584C11#1745111yescharacteristic, complemented, Sylow
585C23—111no—
586C23—111no—
587C23—222no—
588C23—224no—
589C23—222no—
590C23—222no—
591C23—441no—
592C23—442no—
593C23—442no—
594C23C22⋊C4×D1111yescharacteristic
595Q8—24no—
596Q8—22no—
597Q8M16×D1114yescomplemented
598D4—114no—
599D4—228no—
600D4—228no—
601D4—224no—
602D4—222no—
603C2×C4—24no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—111no—
610C2×C4—111no—
611C2×C4—114no—
612C2×C4—111no—
613C2×C4—111no—
614C2×C4—111no—
615C2×C4—111no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—222no—
619C2×C4—228no—
620C2×C4—222no—
621C2×C4—228no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—222no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—444no—
636C2×C4—444no—
637C2×C4—442no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4—444no—
641C2×C4C22⋊C4×D1111yescharacteristic
642C2×C4C22⋊C4×D1111yescharacteristic
643C2×C4C22⋊C4×D1111yescharacteristic
644C2×C4#6696712yes—
645C2×C4#6697112yes—
646C2×C4C22×C4×D1111yescharacteristic
647C2×C4C2×D4×D1111yescharacteristic
648C2×C4C2×D4×D1111yescharacteristic
649C8—42no—
650C8—42no—
651C8—442no—
652C8—442no—
653C22—21no—
654C22—21no—
655C22—112no—
656C22—221no—
657C22—221no—
658C22—224no—
659C22—221no—
660C22—221no—
661C22—221no—
662C22—444no—
663C22—448no—
664C22—442no—
665C22—442no—
666C22#1062241612yes—
667C22C2×C22⋊C4×D1111yescharacteristic
668C4—24no—
669C4—21no—
670C4—21no—
671C4—21no—
672C4—42no—
673C4—112no—
674C4—112no—
675C4—221no—
676C4—221no—
677C4—221no—
678C4—221no—
679C4—442no—
680C4#1062241612yes—
681C4C2×M16×D1112yes—
682C4C2×#6696711yescharacteristic
683C4C2×#6697111yescharacteristic
684C2—22no—
685C2—222no—
686C2—441no—
687C2—444no—
688C2D11×#40711yescharacteristic
689C2C2×#1062241611yescharacteristic
690C2D11×#42111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1487C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4343C4
cosocleC42×C11C24
hypercenter#1487D11
hypocenterC11#17451
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
2. #13077244C2semidirect
3. D11×#423C2semidirect
4. #13067054C2semidirect
5. #13067045C2semidirect
6. #13067042C2semidirect
7. #13067040C2semidirect
8. #13067002C2semidirect
9. C11×#1487C2semidirect
37. #10622450C22semidirect
40. D11×C4⋊C8C22semidirect
43. C4×#4313C22semidirect
44. #10622298C22semidirect
45. C11×Q8⋊C8C22semidirect
46. Q8⋊(C11⋊C8)C22semidirect
47. #10622121C22semidirect
48. #10622097C22semidirect
162. #4343M16semidirect
245. #1487D11semidirect
261. Q8×C11C2×M16semidirect
291. D44C2×M16semidirect
353. Q8⋊C8C2×D11semidirect
584. C11#17451semidirect
597. Q8M16×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
#130772442
D11×#4232
#130670542
#130670452
#130670422
#130670402
#130670022
C11×#14872
#1745111