Finite Group Databasebeta

← #14719582

Subgroups — #14719582

Order 2816.

1314 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
1C2×#10623053C211yesmaximal, characteristic
2D11×#431C212yesmaximal, complemented
3#13066938C212yesmaximal, complemented
4#13066935C212yesmaximal, complemented
5#13066933C212yesmaximal, complemented
6#13066931C212yesmaximal, complemented
7#13066930C211yesmaximal, characteristic, complemented
8#13066928C212yesmaximal, complemented
9C11×#1458C211yesmaximal, characteristic, complemented
10C22×#4339C411yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C4×Dic11C411yescharacteristic
13#10623053—22no—
14#10623053—22no—
15#10623053—22no—
16#10623053—22no—
17C2×#66946C411yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×#66940C411yescharacteristic
20C2×#66940C2211yescharacteristic
21C2×(C22⋊D11)⋊C4C411yescharacteristic
22C2×(C22⋊D11)⋊C4C411yescharacteristic
23C2×(C22⋊D11)⋊C4C2211yescharacteristic
24C2×(C22⋊D11)⋊C4C2211yescharacteristic
25C2×#66925C411yescharacteristic
26C2×#66925C2211yescharacteristic
27C2×C42×D11C411yescharacteristic
28C2×C42×D11C2211yescharacteristic
29C11×#431C2212yes—
30#10622538C2212yes—
31#10622446—22no—
32D11×C4⋊C8—22no—
33D11×C22⋊C8C2214yes—
34#10622331C2214yes—
35#10622298—22no—
36C4×C8×D11—22no—
37C11×#324C2212yes—
38C11×#323C2212yes—
39#10622166C2212yes—
40#10622163C2212yes—
41#10622107C2214yes—
42#10622106C2214yes—
43C23×C4×C11C2×C411yescharacteristic
44C22×C22⋊D11C2×C411yescharacteristic
45C22×C22⋊D11C2×C411yescharacteristic
46C23×Dic11C2×C411yescharacteristic
47C23×Dic11C2×C411yescharacteristic
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—24no—
51C2×#4339C818yescomplemented
52C22×D44C2×C411yescharacteristic
53C22×C4×D11C2×C411yescharacteristic
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11C2×C411yescharacteristic
57C22×C4×D11C2×C411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×Dic22C2×C411yescharacteristic
60C11×#117—22no—
61C11×#117—22no—
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2311yescharacteristic
66C2×C42×C11C2×C411yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4C2×C411yescharacteristic
69C2×(C2×D11)⋊C4C2×C411yescharacteristic
70C2×(C2×D11)⋊C4C2×C411yescharacteristic
71C2×(C2×D11)⋊C4C2311yescharacteristic
72C2×Dic11⋊C4C2×C411yescharacteristic
73C2×Dic11⋊C4C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×Dic11⋊C4C2311yescharacteristic
76C2×C4×Dic11—21no—
77C2×C4×Dic11—21no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2×C411yescharacteristic
85C2×C4×Dic11C2×C411yescharacteristic
86C2×C4×Dic11C2×C411yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C2×C8×D11—24no—
89#66946—22no—
90#66946—22no—
91#66946—22no—
92#66946—22no—
93#66940—22no—
94#66940—22no—
95#66940—22no—
96#66940—22no—
97(C22⋊D11)⋊C4—22no—
98(C22⋊D11)⋊C4—22no—
99(C22⋊D11)⋊C4—22no—
100(C22⋊D11)⋊C4—22no—
101(C22⋊D11)⋊C4—22no—
102(C22⋊D11)⋊C4—22no—
103(C22⋊D11)⋊C4—22no—
104(C22⋊D11)⋊C4—22no—
105#66925—22no—
106#66925—22no—
107#66925—22no—
108#66925—22no—
109C42×D11—21no—
110C42×D11—21no—
111C42×D11—21no—
112C42×D11—21no—
113C42×D11D412yes—
114C42×D11D412yes—
115C42×D11D412yes—
116C42×D11D412yes—
117C11×C4⋊C8—22no—
118C11×C22⋊C8C2314yes—
119C4×C8×C11—22no—
120C22⋊(C11⋊C8)C2314yes—
121(C2×D11)⋊C8—24no—
122Dic11⋊C8—24no—
123C8×Dic11—24no—
124C4⋊(C11⋊C8)—22no—
125C4×C11⋊C8—22no—
126#17349—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C23×D11C22×C411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—22no—
133C22×C4×C11C2×C814yescomplemented
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C2×C22⋊D11—22no—
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11—22no—
144C2×C22⋊D11C2×C814yes—
145C2×C22⋊D11C2×C814yescomplemented
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
157C22×Dic11C22×C411yescharacteristic
158#4339—216no—
159#4339—216no—
160C2×D44—22no—
161C2×D44—22no—
162C2×D44C2×C814yes—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—22no—
170C2×C4×D11—42no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11C22⋊C412yes—
175C2×C4×D11C22⋊C412yes—
176C2×C4×D11C22⋊C412yes—
177C2×C4×D11C22⋊C412yes—
178C2×C4×D11C2×C814yes—
179C2×C4×D11C2×C814yescomplemented
180C2×C4×D11M1614yes—
181C2×C4×D11C2×D412yes—
182C2×C4×D11C2×D412yes—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22C2×C814yescomplemented
186C2×C8×C11—24no—
187C11×C4⋊C4—22no—
188C11×C4⋊C4—22no—
189C11×C22⋊C4—22no—
190C11×C22⋊C4—22no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11C2×D412yes—
194C42×C11C2×D412yes—
195(C2×D11)⋊C4—22no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—22no—
199Dic11⋊C4—22no—
200Dic11⋊C4—22no—
201Dic11⋊C4—22no—
202Dic11⋊C4—22no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—21no—
208C4×Dic11—21no—
209C4×Dic11—21no—
210C4×Dic11—21no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11C22⋊C411yescharacteristic
214C4×Dic11C22⋊C411yescharacteristic
215C4×Dic11C22⋊C411yescharacteristic
216C4×Dic11C22⋊C411yescharacteristic
217C4×Dic11C22⋊C412yes—
218C4×Dic11C22⋊C412yes—
219C4×Dic11C2×D412yes—
220C4×Dic11C2×D412yes—
221C2×C11⋊C8—24no—
222C8×D11—48no—
223C2×C4×#41—111no—
224C2×#431—112no—
225#1461—112no—
226#1460—112no—
227#1459—112no—
228#1459—112no—
229#1458—112no—
230#1458—111no—
231#1458D1111yescharacteristic, complemented
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×C812yes—
237C23×C11C23×C411yescharacteristic
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11C2×C22⋊C412yes—
245C22×D11C22×C812yes—
246C22×D11C22×C812yes—
247C22×D11C2×M1612yes—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11C2×C22⋊C412yes—
259C2×C4×C11C2×C22⋊C411yescharacteristic
260C2×C4×C11C2×C22⋊C411yescharacteristic
261C2×C4×C11C22×C812yes—
262C2×C4×C11C22×C812yes—
263C2×C4×C11C2×M1612yes—
264C2×C4×C11C22×D412yes—
265C22⋊D11—28no—
266C22⋊D11—28no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11C2×C22⋊C411yescharacteristic
280C2×Dic11C2×C22⋊C411yescharacteristic
281C2×Dic11C2×C22⋊C412yes—
282C2×Dic11C2×C22⋊C411yescharacteristic
283C2×Dic11C2×C22⋊C411yescharacteristic
284C2×Dic11C22×C812yes—
285C2×Dic11C22×C812yes—
286C2×Dic11C2×M1612yes—
287D44—28no—
288C4×D11—24no—
289C4×D11—24no—
290C4×D11—24no—
291C4×D11—24no—
292C4×D11—42no—
293C4×D11—42no—
294C4×D11—42no—
295C4×D11—42no—
296C4×D11—42no—
297C4×D11—42no—
298C4×D11C22⋊C818yes—
299C4×D11C22⋊C818yes—
300Dic22—28no—
301C8×C11—44no—
302C11⋊C8—44no—
303C22×#41—111no—
304C4×#41—222no—
305C4×#41—222no—
306C4×#41—222no—
307C4×#41—222no—
308C2×C4×Q8—111no—
309C2×C4×Q8—111no—
310C2×C4×D4—111no—
311C2×C4×D4—111no—
312C2×C4×D4—111no—
313C2×C4×D4—111no—
314C2×C4×D4—111no—
315C2×C4×D4—111no—
316C2×#117—111no—
317C2×#117—111no—
318C2×#117C2×D1111yescharacteristic
319C22×C42—111no—
320C22×C42—111no—
321C22×C42—111no—
322#431—112no—
323#431—114no—
324#431—222no—
325#431—222no—
326#431C2×D1112yes—
327C2×C4⋊C8—222no—
328C2×C22⋊C8—114no—
329C2×C4×C8—222no—
330#324—112no—
331#324—114no—
332#324C2×D1112yes—
333#323—112no—
334#323—114no—
335#323C2×D1112yes—
336C22×C11—21no—
337C22×C11—21no—
338C22×C11—22no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C22×C22⋊C411yescharacteristic
344C22×C11C23×C811yescharacteristic
345C22×C11C22×M1611yescharacteristic
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—22no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—41no—
353C2×D11—41no—
354C2×D11—42no—
355C2×D11C2×C22⋊C814yes—
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11C2×C22⋊C812yes—
362C4×C11C2×C22⋊C812yes—
363Dic11—22no—
364Dic11—21no—
365Dic11—21no—
366Dic11—41no—
367Dic11—41no—
368Dic11C2×C22⋊C814yes—
369Dic11#41012yes—
370Dic11#41312yes—
371C2×#41—118no—
372C2×#41—222no—
373C2×#41—222no—
374C2×#41—224no—
375C22×Q8—111no—
376C22×D4—111no—
377C22×D4—111no—
378C22×D4—111no—
379C23×C4—111no—
380C23×C4—111no—
381C23×C4—111no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4C4×D1111yescharacteristic
388C22×C8—224no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—222no—
393C4×D4—222no—
394C4×D4—222no—
395C4×D4—222no—
396C4×D4—222no—
397C4×D4—222no—
398C4×D4—222no—
399C4×D4—222no—
400C4×D4—222no—
401C4×D4—222no—
402C4×D4—222no—
403C4×D4—222no—
404C4×D4—222no—
405#117—22no—
406#117—22no—
407#117—222no—
408#117—222no—
409#117—222no—
410#117—222no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4C4×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C22⋊C4—111no—
418C2×C22⋊C4—111no—
419C2×C22⋊C4—111no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4C4×D1111yescharacteristic
422C2×C22⋊C4C22×D1111yescharacteristic
423C2×C42—111no—
424C2×C42—111no—
425C2×C42—111no—
426C2×C42—112no—
427C2×C42—112no—
428C2×C42—112no—
429C2×C42—112no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—111no—
435C2×C42—221no—
436C2×C42—221no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42—221no—
443C2×C42C4×D1111yescharacteristic
444C2×C42C22×D1111yescharacteristic
445C4⋊C8—22no—
446C4⋊C8—224no—
447C4⋊C8—222no—
448C22⋊C8—114no—
449C22⋊C8—224no—
450C22⋊C8C22×D1114yes—
451C4×C8—22no—
452C4×C8—224no—
453C4×C8—222no—
454C2×C11—21no—
455C2×C11—21no—
456C2×C11—42no—
457C2×C11C22×C22⋊C811yescharacteristic
458C2×C11C2×#41011yescharacteristic
459C2×C11C2×#41311yescharacteristic
460D11—24no—
461D11—42no—
462C24—111no—
463C24—111no—
464C24C2×C4×D1111yescharacteristic
465#41—2216no—
466#41—2216no—
467C2×Q8—114no—
468C2×Q8—222no—
469C2×Q8—222no—
470C2×D4—114no—
471C2×D4—114no—
472C2×D4—114no—
473C2×D4—222no—
474C2×D4—222no—
475C2×D4—222no—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—222no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—111no—
483C22×C4—112no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—111no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—112no—
491C22×C4—114no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4C8×D1114yescomplemented
515C22×C4C2×C4×D1111yescharacteristic
516C22×C4C2×C4×D1111yescharacteristic
517C22×C4C2×C4×D1111yescharacteristic
518C22×C4C2×C4×D1111yescharacteristic
519C22×C4C2×C4×D1111yescharacteristic
520C22×C4C23×D1111yescharacteristic
521C2×C8—24no—
522C2×C8—224no—
523C2×C8—448no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—222no—
527C4⋊C4—222no—
528C4⋊C4—222no—
529C4⋊C4—222no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—222no—
533C22⋊C4—222no—
534C22⋊C4—222no—
535C22⋊C4—222no—
536C42—21no—
537C42—21no—
538C42—111no—
539C42—111no—
540C42—112no—
541C42—112no—
542C42—111no—
543C42—111no—
544C42—112no—
545C42—112no—
546C42—221no—
547C42—221no—
548C42—221no—
549C42—221no—
550C42—221no—
551C42—221no—
552C42—221no—
553C42—221no—
554C42—221no—
555C42—221no—
556C42D4×D1112yes—
557C42D4×D1112yes—
558C11#1734911yescharacteristic, complemented, Sylow
559C23—21no—
560C23—21no—
561C23—41no—
562C23—41no—
563C23—112no—
564C23—112no—
565C23—112no—
566C23—112no—
567C23—221no—
568C23—221no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23C2×C8×D1112yes—
574C23C22×C4×D1111yescharacteristic
575Q8—228no—
576D4—228no—
577D4—228no—
578D4—228no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—112no—
590C2×C4—111no—
591C2×C4—111no—
592C2×C4—112no—
593C2×C4—112no—
594C2×C4—118no—
595C2×C4—118no—
596C2×C4—112no—
597C2×C4—111no—
598C2×C4—111no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—442no—
610C2×C4—442no—
611C2×C4—442no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4C22⋊C4×D1112yes—
622C2×C4C22⋊C4×D1111yescharacteristic
623C2×C4C22⋊C4×D1111yescharacteristic
624C2×C4C2×C8×D1112yes—
625C2×C4C2×C8×D1112yes—
626C2×C4M16×D1112yes—
627C2×C4C2×D4×D1112yes—
628C8—44no—
629C8—444no—
630C22—21no—
631C22—21no—
632C22—22no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—41no—
637C22—114no—
638C22—222no—
639C22—222no—
640C22—222no—
641C22—442no—
642C22—442no—
643C22—442no—
644C22—442no—
645C22—441no—
646C22—441no—
647C22C2×C22⋊C4×D1111yescharacteristic
648C22C22×C8×D1111yescharacteristic
649C22C2×M16×D1111yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—41no—
655C4—114no—
656C4—112no—
657C4—112no—
658C4—222no—
659C4—221no—
660C4—221no—
661C4—441no—
662C4—441no—
663C4D11×C22⋊C812yes—
664C4D11×C22⋊C812yes—
665C2—21no—
666C2—21no—
667C2—42no—
668C2—224no—
669C2—442no—
670C2C2×D11×C22⋊C811yescharacteristic
671C2D11×#41011yescharacteristic
672C2D11×#41311yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D11
commutatorC22×C11C23×C8
FrattiniC22×C4C23×D11
FittingC11×#1458C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4339C4
cosocleC22×C4×C11C24
hypercenter#1458D11
hypocenterC11#17349
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. D11×#431C2semidirect
3. #13066938C2semidirect
4. #13066935C2semidirect
5. #13066933C2semidirect
6. #13066931C2semidirect
7. #13066930C2semidirect
8. #13066928C2semidirect
9. C11×#1458C2semidirect
51. C2×#4339C8semidirect
133. C22×C4×C11C2×C8semidirect
145. C2×C22⋊D11C2×C8semidirect
179. C2×C4×D11C2×C8semidirect
185. C2×Dic22C2×C8semidirect
231. #1458D11semidirect
514. C22×C4C8×D11semidirect
558. C11#17349semidirect

Maximal subgroups

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

subgroupindex
C2×#106230532
D11×#4312
#130669382
#130669352
#130669332
#130669312
#130669302
#130669282
C11×#14582
#1734911