Finite Group Databasebeta

← #14720011

Subgroups — #14720011

Order 2816.

944 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×#10623112C211yesmaximal, characteristic
2#13077275C212yesmaximal, complemented
3#13066986C212yesmaximal, complemented
4#13066970C212yesmaximal, complemented
5#13066963C212yesmaximal
6#13066949C211yesmaximal, characteristic, complemented
7#13066944C211yesmaximal, characteristic, complemented
8#13066940C211yesmaximal, characteristic, complemented
9#13066929C211yesmaximal, characteristic, complemented
10D11×#324C211yesmaximal, characteristic, complemented
11C11×#1467C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999C411yescharacteristic
14C2×#66999C411yescharacteristic
15#10623112—22no—
16#10623112—22no—
17#10623112—22no—
18#10623112—22no—
19C2×#66947C411yescharacteristic
20C2×#66947C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66942C411yescharacteristic
24C2×#66942C2211yescharacteristic
25C2×#66929C411yescharacteristic
26C2×#66929C2211yescharacteristic
27C2×C4×D44C411yescharacteristic
28C2×#66925C411yescharacteristic
29C2×#66925C2211yescharacteristic
30C2×#66923C411yescharacteristic
31C11×#432C2212yes—
32#10622538C2212yes—
33#10622453—22no—
34#10622452—22no—
35#10622339C2212yes—
36D11×C22⋊C8C2212yes—
37#10622332C2212yes—
38#10622331C2212yes—
39#10622322—22no—
40#10622321—22no—
41C11×#324C2211yescharacteristic
42C11×#324C2211yescharacteristic
43C11×#324C2212yes—
44#10622166C2211yescharacteristic
45#10622166C2211yescharacteristic
46#10622166C2212yes—
47#10622107C2212yes—
48#10622107C2212yes—
49#10622106C2212yes—
50#10622106C2212yes—
51C22×Q8×C11C2×C411yescharacteristic
52C22×D44C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2311yescharacteristic
57C4×Q8×C11—22no—
58C4×Q8×C11—22no—
59C2×C11×C4⋊C4C2×C411yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C42×C11C2×C411yescharacteristic
63C2×C42×C11C2×C411yescharacteristic
64C2×C42×C11C2311yescharacteristic
65#66999—22no—
66#66999—22no—
67#66999—22no—
68#66999—22no—
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×(C2×D11)⋊C4C2×C411yescharacteristic
73C2×(C2×D11)⋊C4C2×C411yescharacteristic
74C2×(C2×D11)⋊C4C2×C411yescharacteristic
75C2×(C2×D11)⋊C4C2×C411yescharacteristic
76C2×(C2×D11)⋊C4C2311yescharacteristic
77C2×C4⋊Dic11C2×C411yescharacteristic
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2311yescharacteristic
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×#4313—22no—
93C2×C8×D11—22no—
94#66947—22no—
95#66947—22no—
96#66947—22no—
97#66947—22no—
98#66945—22no—
99#66945—22no—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—22no—
102#66942—22no—
103#66942—22no—
104#66942—22no—
105#66942—22no—
106#66929—22no—
107#66929—22no—
108#66929—22no—
109#66929—22no—
110C4×D44—21no—
111C4×D44—21no—
112C4×D44—21no—
113C4×D44—21no—
114#66925—21no—
115#66925—21no—
116#66925—21no—
117#66925—21no—
118#66925D412yes—
119#66925D412yes—
120#66925D412yes—
121#66925D412yes—
122#66923—22no—
123#66923—22no—
124C11×C4⋊C8—22no—
125C11×C22⋊C8C2312yes—
126C11×C22⋊C8C2312yes—
127C11×#97—22no—
128C22⋊(C11⋊C8)C2312yes—
129C22⋊(C11⋊C8)C2312yes—
130(C2×D11)⋊C8—22no—
131(C2×D11)⋊C8—22no—
132#66879—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C4⋊(C11⋊C8)—22no—
137C4×C11⋊C8—22no—
138#17417—111nomaximal, Sylow
139C23×D11C22×C411yescharacteristic
140C23×D11C22×C411yescharacteristic
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—41no—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C22×C411yescharacteristic
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—42no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—41no—
169C2×C4×D11—41no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11C2×D412yes—
173C2×C4×D11C2×D412yes—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11C2×D412yes—
184C42×C11C2×D412yes—
185(C2×D11)⋊C4—22no—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—21no—
188(C2×D11)⋊C4—21no—
189(C2×D11)⋊C4—21no—
190(C2×D11)⋊C4—21no—
191(C2×D11)⋊C4—22no—
192(C2×D11)⋊C4—22no—
193(C2×D11)⋊C4C22⋊C411yescharacteristic
194(C2×D11)⋊C4C22⋊C411yescharacteristic
195(C2×D11)⋊C4C22⋊C411yescharacteristic
196(C2×D11)⋊C4C22⋊C411yescharacteristic
197(C2×D11)⋊C4C22⋊C412yes—
198(C2×D11)⋊C4C22⋊C412yes—
199C4⋊Dic11—22no—
200C4⋊Dic11—22no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203Dic11⋊C4—22no—
204Dic11⋊C4—22no—
205Dic11⋊C4—21no—
206Dic11⋊C4—21no—
207Dic11⋊C4—22no—
208Dic11⋊C4—22no—
209Dic11⋊C4—21no—
210Dic11⋊C4—21no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4C22⋊C412yes—
214Dic11⋊C4C22⋊C412yes—
215Dic11⋊C4C22⋊C412yes—
216Dic11⋊C4C22⋊C412yes—
217C4×Dic11—21no—
218C4×Dic11—21no—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C2×C11⋊C8—22no—
222C2×C11⋊C8—22no—
223#4313—44no—
224C8×D11—44no—
225C2×#552—111no—
226#2924—112no—
227#1473—112no—
228#1470—112no—
229#1468—112no—
230#1467D1111yescharacteristic, complemented
231#1464—111no—
232#1463—111no—
233#1461—111no—
234#1458—111no—
235C2×#324—111no—
236C23×C11C23×C411yescharacteristic
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—22no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11C2×C22⋊C411yescharacteristic
247C22×D11C2×C22⋊C411yescharacteristic
248Q8×C11—44no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11C2×C22⋊C411yescharacteristic
263C2×C4×C11C2×C22⋊C411yescharacteristic
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11#13112yes—
266C2×C4×C11C22×D412yes—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11C2×C22⋊C411yescharacteristic
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C412yes—
281C2×Dic11C2×C22⋊C412yes—
282D44—42no—
283D44—42no—
284C4×D11—24no—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—42no—
288C4×D11—42no—
289C4×D11—42no—
290C4×D11—42no—
291C4×D11—42no—
292C8×C11—42no—
293C8×C11—42no—
294C11⋊C8—42no—
295C11⋊C8—42no—
296#552—222no—
297#552—222no—
298#552—222no—
299#552—222no—
300C2×#126—111no—
301C2×#126—111no—
302C2×#125—111no—
303C2×#125—111no—
304C2×#125—111no—
305C2×#123—111no—
306C2×#123—111no—
307C2×C22⋊Q8—111no—
308C2×C22⋊Q8—111no—
309C2×C4×Q8C2×D1111yescharacteristic
310C2×C4×D4—111no—
311C2×#117—111no—
312C2×#117—111no—
313C2×#117—111no—
314C22×C4⋊C4—111no—
315#433—222no—
316#433—222no—
317#432—112no—
318#432C2×D1112yes—
319#431—112no—
320#431—112no—
321#424—222no—
322#407—112no—
323C2×C22⋊C8—112no—
324#405—222no—
325#324—111no—
326#324—111no—
327#324—112no—
328#324—112no—
329#324—112no—
330#324C2×D1111yescharacteristic
331#324C2×D1111yescharacteristic
332#324C2×D1112yes—
333#323—112no—
334#323—112no—
335C22×C11—21no—
336C22×C11—21no—
337C22×C11C22×C22⋊C411yescharacteristic
338C22×C11C2×#13111yescharacteristic
339C22×C11#56811yescharacteristic
340C2×D11—21no—
341C2×D11—21no—
342C2×D11—21no—
343C2×D11—21no—
344C2×D11—21no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—41no—
348C2×D11—41no—
349C2×D11—41no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11#41012yes—
353C4×C11—22no—
354C4×C11—22no—
355C4×C11—22no—
356C4×C11—21no—
357C4×C11—21no—
358C4×C11—41no—
359C4×C11—41no—
360C4×C11—41no—
361Dic11—21no—
362Dic11—21no—
363Dic11—22no—
364Dic11—22no—
365Dic11—41no—
366Dic11—41no—
367Dic11—41no—
368C22×Q8C4×D1111yescharacteristic
369C22×D4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—111no—
374C2×M16—222no—
375C22×C8—222no—
376#126—222no—
377#126—222no—
378#126—222no—
379#126—222no—
380#125—222no—
381#125—222no—
382#125—222no—
383#125—222no—
384#125—222no—
385#125—222no—
386#123—222no—
387#123—222no—
388#123—222no—
389#123—222no—
390C22⋊Q8—222no—
391C22⋊Q8—222no—
392C22⋊Q8—222no—
393C22⋊Q8—222no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×D4—221no—
397C4×D4—221no—
398C4×D4—221no—
399C4×D4—221no—
400#117—112no—
401#117—112no—
402#117—112no—
403#117—112no—
404#117—221no—
405#117—221no—
406#117—221no—
407#117—221no—
408#117—222no—
409#117—222no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4C4×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C22⋊C4—111no—
429C2×C22⋊C4—111no—
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—111no—
433C2×C22⋊C4—111no—
434C2×C22⋊C4—111no—
435C2×C22⋊C4—111no—
436C2×C42—111no—
437C2×C42—111no—
438C2×C42C4×D1111yescharacteristic
439C2×C42C4×D1111yescharacteristic
440C2×C42C22×D1111yescharacteristic
441C4⋊C8—22no—
442C4⋊C8—222no—
443C4⋊C8—222no—
444C4⋊C8—222no—
445C22⋊C8—112no—
446C22⋊C8—112no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449C22⋊C8C22×D1112yes—
450C22⋊C8C22×D1112yes—
451#97—22no—
452#97—222no—
453C4×C8—222no—
454C4×C8—222no—
455C2×C11—21no—
456C2×C11—21no—
457C2×C11#288011yescharacteristic
458C2×C11C2×#41011yescharacteristic
459C2×C11#288911yescharacteristic
460D11—22no—
461D11—41no—
462D11—81no—
463C24—111no—
464C24—111no—
465C2×Q8—22no—
466C2×Q8—22no—
467C2×Q8—41no—
468C2×D4—221no—
469C2×D4—221no—
470C2×D4—442no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—441no—
488C22×C4—441no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4C2×C4×D1111yescharacteristic
492C22×C4C2×C4×D1111yescharacteristic
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C2×C4×D1111yescharacteristic
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4C2×C4×D1111yescharacteristic
497C22×C4C23×D1111yescharacteristic
498M16—444no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—222no—
502C2×C8—222no—
503C2×C8—444no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—112no—
508C4⋊C4—112no—
509C4⋊C4—112no—
510C4⋊C4—112no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—222no—
516C4⋊C4—221no—
517C4⋊C4—221no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—222no—
524C4⋊C4—222no—
525C22⋊C4—111no—
526C22⋊C4—111no—
527C22⋊C4—111no—
528C22⋊C4—111no—
529C22⋊C4—112no—
530C22⋊C4—112no—
531C22⋊C4—222no—
532C22⋊C4—222no—
533C22⋊C4—221no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C22⋊C4—222no—
538C22⋊C4—222no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—112no—
544C42—112no—
545C42—221no—
546C42—221no—
547C42D4×D1112yes—
548C42D4×D1112yes—
549C11#1741711yescharacteristic, complemented, Sylow
550C23—111no—
551C23—111no—
552C23—222no—
553C23—221no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—441no—
559C23—441no—
560C23—441no—
561C23C22×C4×D1111yescharacteristic
562Q8—44no—
563D4—442no—
564D4—442no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—111no—
579C2×C4—111no—
580C2×C4—112no—
581C2×C4—112no—
582C2×C4—224no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4C22⋊C4×D1111yescharacteristic
602C2×C4C22⋊C4×D1111yescharacteristic
603C2×C4C22⋊C4×D1112yes—
604C2×C4#6696012yes—
605C2×C4C2×D4×D1112yes—
606C8—42no—
607C8—42no—
608C8—442no—
609C8—442no—
610C22—21no—
611C22—21no—
612C22—112no—
613C22—221no—
614C22—221no—
615C22—221no—
616C22—221no—
617C22—221no—
618C22—442no—
619C22—442no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—881no—
624C22—881no—
625C22C2×C22⋊C4×D1111yescharacteristic
626C22C2×#6696011yescharacteristic
627C22#1062327611yescharacteristic
628C4—22no—
629C4—22no—
630C4—22no—
631C4—21no—
632C4—21no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—221no—
637C4—221no—
638C4—222no—
639C4—222no—
640C4—441no—
641C4—441no—
642C4—441no—
643C2—21no—
644C2—21no—
645C2—222no—
646C2—441no—
647C2—881no—
648C2#1307706611yescharacteristic
649C2D11×#41011yescharacteristic
650C2#1307709611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1467C2
socleC22×C11C22×C22⋊C4
prime radicalC22×D44C2×C4
cosocleC22×C4×C11C24
hypercenter#1467D11
hypocenterC11#17417
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
2. #13077275C2semidirect
3. #13066986C2semidirect
4. #13066970C2semidirect
6. #13066949C2semidirect
7. #13066944C2semidirect
8. #13066940C2semidirect
9. #13066929C2semidirect
10. D11×#324C2semidirect
11. C11×#1467C2semidirect
230. #1467D11semidirect
549. C11#17417semidirect

Maximal subgroups

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

subgroupindex
C2×#106231122
#130772752
#130669862
#130669702
#130669632
#130669492
#130669442
#130669402
#130669292
D11×#3242
C11×#14672
#1741711