Finite Group Databasebeta

← #14720161

Subgroups — #14720161

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#67040C211yesmaximal, characteristic
2#13077724C211yesmaximal, characteristic, complemented
3#13077572C211yesmaximal, characteristic, complemented
4#13067009C212yesmaximal, complemented
5#13067004C211yesmaximal, characteristic, complemented
6#13067002C212yesmaximal, complemented
7#13066997C212yesmaximal, complemented
8#13066996C211yesmaximal, characteristic, complemented
9C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
10D11×Q8⋊C8C212yesmaximal, complemented
11C11×#1479C211yesmaximal, characteristic, complemented
12C2×#67040C411yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14#10623343C411yescharacteristic
15#10623105—21no—
16#10623105C412yes—
17C4×#4343—21no—
18C4×#4343C2212yes—
19#10623103—21no—
20#10623103C412yes—
21C4×Q8×D11—21no—
22C4×Q8×D11C2212yes—
23#10623035—22no—
24#10623035C411yescharacteristic
25#10623035C411yescharacteristic
26C4×#4339—22no—
27C4×#4339C2211yescharacteristic
28C4×#4339C2211yescharacteristic
29C11×#431C2211yescharacteristic
30C11×#431C2211yescharacteristic
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622447—21no—
34#10622446C2212yes—
35D11×C4⋊C8C2212yes—
36#10622443—21no—
37(C22⋊D11)⋊C8—22no—
38(C22⋊D11)⋊C8—22no—
39C8×D44—21no—
40#10622298C2212yes—
41C4×C8×D11C2212yes—
42C8×Dic22—21no—
43C11×Q8⋊C8C2212yes—
44C11×Q8⋊C8C2212yes—
45Q8⋊(C11⋊C8)C2212yes—
46Q8⋊(C11⋊C8)C2212yes—
47#10622122C2211yescharacteristic
48#10622122C2211yescharacteristic
49#10622121C2211yescharacteristic
50#10622121C2211yescharacteristic
51#10622097C2212yes—
52#10622094C2212yes—
53C22×Q8×C11C2×C411yescharacteristic
54#67040—24no—
55#67040C818yescomplemented
56C2×#4343—21no—
57C2×#4343C2×C412yes—
58C2×Q8×D11—21no—
59C2×Q8×D11C2×C412yes—
60C2×#4339—22no—
61C2×#4339C2×C411yescharacteristic
62C2×#4339C2×C411yescharacteristic
63C4×Q8×C11—21no—
64C4×Q8×C11—21no—
65C4×Q8×C11C2×C412yes—
66C4×Q8×C11C2312yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71Q8×Dic11—21no—
72Q8×Dic11—21no—
73Q8×Dic11C2×C412yes—
74Q8×Dic11C2×C412yes—
75C4×C22⋊D11—21no—
76C4×C22⋊D11—21no—
77C4×C22⋊D11—22no—
78C4×C22⋊D11—22no—
79C4×C22⋊D11D412yes—
80C4×C22⋊D11D412yes—
81#66979—22no—
82#66979C2×C411yescharacteristic
83#66979C2×C411yescharacteristic
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C2×C8×D11—22no—
87C2×C8×D11—22no—
88#66946—21no—
89#66946—22no—
90#66946—22no—
91#66946C2×C412yes—
92#66945—22no—
93#66945—21no—
94#66945—22no—
95#66945C2×C412yes—
96C4⋊C4×D11—22no—
97C4⋊C4×D11—21no—
98C4⋊C4×D11—22no—
99C4⋊C4×D11C2×C412yes—
100#66940—21no—
101#66940—22no—
102#66940—22no—
103#66940C2×C412yes—
104C4×D44—22no—
105C4×D44—22no—
106C4×D44C2×C411yescharacteristic
107C4×D44D411yescharacteristic
108C4×D44D411yescharacteristic
109C4×D44C2311yescharacteristic
110#66925—21no—
111#66925—22no—
112#66925—22no—
113#66925C2×C412yes—
114C42×D11—22no—
115C42×D11—21no—
116C42×D11—22no—
117C42×D11C2312yes—
118C4×Dic22—22no—
119C4×Dic22—22no—
120C4×Dic22C2×C411yescharacteristic
121C4×Dic22D411yescharacteristic
122C4×Dic22D411yescharacteristic
123C4×Dic22C2311yescharacteristic
124C11×C4⋊C8—21no—
125C11×C4⋊C8C2311yescharacteristic
126C11×C4⋊C8C2311yescharacteristic
127C11×C22⋊C8—21no—
128C11×C22⋊C8—21no—
129C4×C8×C11—21no—
130C4×C8×C11C2312yes—
131(C2×D11)⋊C8—22no—
132(C2×D11)⋊C8—22no—
133Dic11⋊C8—22no—
134Dic11⋊C8—22no—
135C8×Dic11—22no—
136C8×Dic11—22no—
137C4⋊(C11⋊C8)—21no—
138C4⋊(C11⋊C8)C2312yes—
139C4×C11⋊C8—21no—
140C4×C11⋊C8C2311yescharacteristic
141C4×C11⋊C8C2311yescharacteristic
142#17439—111nomaximal, Sylow
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11C2×C814yescomplemented
146C2×Q8×C11C22×C412yes—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C2×C22⋊D11—21no—
153C2×C22⋊D11C22⋊C412yes—
154#4343—28no—
155#4343—24no—
156#4343C2×C818yescomplemented
157Q8×D11—24no—
158Q8×D11—28no—
159Q8×D11C2×C818yescomplemented
160#4339—216no—
161#4339—22no—
162#4339C2×C814yes—
163#4339C2×C814yescomplemented
164#4339M1614yes—
165C2×D44—22no—
166C2×D44C22⋊C411yescharacteristic
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11—22no—
171C2×C4×D11—22no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11C22×C412yes—
176C2×C4×D11C2×D412yes—
177C2×C4×D11C2×D412yes—
178C2×Dic22—22no—
179C2×Dic22C22⋊C411yescharacteristic
180C2×Dic22C22×C411yescharacteristic
181C2×C8×C11—21no—
182C2×C8×C11—22no—
183C2×C8×C11—21no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—22no—
187C11×C4⋊C4C22×C412yes—
188C42×C11—22no—
189C42×C11—22no—
190C42×C11C22×C411yescharacteristic
191C42×C11C2×D411yescharacteristic
192C42×C11C2×D411yescharacteristic
193C42×C11C2411yescharacteristic
194C22⋊Dic11—21no—
195C22⋊Dic11C22⋊C412yes—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—21no—
199(C2×D11)⋊C4—21no—
200(C2×D11)⋊C4C22⋊C412yes—
201(C2×D11)⋊C4C22⋊C412yes—
202C4⋊Dic11—22no—
203C4⋊Dic11—22no—
204C4⋊Dic11C22⋊C411yescharacteristic
205C4⋊Dic11C22⋊C411yescharacteristic
206C4⋊Dic11C22×C411yescharacteristic
207C4⋊Dic11C22×C411yescharacteristic
208Dic11⋊C4—22no—
209Dic11⋊C4—22no—
210Dic11⋊C4—21no—
211Dic11⋊C4—21no—
212Dic11⋊C4C22⋊C412yes—
213Dic11⋊C4C22⋊C412yes—
214C4×Dic11—22no—
215C4×Dic11—22no—
216C4×Dic11—22no—
217C4×Dic11—22no—
218C4×Dic11—21no—
219C4×Dic11—21no—
220C4×Dic11—21no—
221C4×Dic11C22×C412yes—
222C4×Dic11C2×D412yes—
223C4×Dic11C2×D412yes—
224C2×C11⋊C8—21no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—22no—
227C2×C11⋊C8—42no—
228C2×C11⋊C8—81no—
229C8×D11—44no—
230C8×D11—82no—
231C4×2−1+4—111no—
232#2988—111no—
233C8×#41—111no—
234#1479—112no—
235#1479D1111yescharacteristic, complemented
236#1477—111no—
237#1477—112no—
238#1476—111no—
239#1476—112no—
240C2×Q8⋊C8—112no—
241C2×Q8⋊C8—111no—
242C23×C11C2×C22⋊C411yescharacteristic
243C22×D11—21no—
244C22×D11C2×C22⋊C412yes—
245Q8×C11—22no—
246Q8×C11—24no—
247Q8×C11C22×C814yes—
248C2×C4×C11—22no—
249C2×C4×C11—24no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—41no—
254C2×C4×C11—81no—
255C2×C4×C11C2×C22⋊C411yescharacteristic
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C411yescharacteristic
258C2×C4×C11C22×C812yes—
259C2×C4×C11C2×M1612yes—
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C22⋊D11—24no—
264C22⋊D11C22⋊C818yes—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11C2×C22⋊C412yes—
269C2×Dic11C2×C22⋊C412yes—
270C2×Dic11C2×C22⋊C412yes—
271D44—28no—
272D44—21no—
273D44C22⋊C814yes—
274D44C22×C812yes—
275C4×D11—28no—
276C4×D11—22no—
277C4×D11—22no—
278C4×D11—24no—
279C4×D11—28no—
280C4×D11—42no—
281C4×D11—41no—
282C4×D11—41no—
283C4×D11—82no—
284C4×D11—81no—
285C4×D11—82no—
286C4×D11C22×C814yes—
287C4×D11C2×M1614yes—
288Dic22—21no—
289Dic22—28no—
290Dic22C22⋊C814yes—
291Dic22C22×C812yes—
292C8×C11—42no—
293C8×C11—41no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—41no—
297C11⋊C8—42no—
298C2×2−1+4—111no—
299#520—111no—
300#520—112no—
301#520—111no—
302#520—222no—
303#520—221no—
304#519—111no—
305#519—112no—
306#519—221no—
307C4×#41—111no—
308C4×#41—112no—
309C4×#41—111no—
310C4×#41—222no—
311C4×#41—221no—
312C2×C4×Q8—112no—
313C2×C4×Q8—221no—
314C2×C4×Q8C2×D1111yescharacteristic
315C8×Q8—221no—
316C8×Q8—221no—
317C8×D4—221no—
318C8×D4—222no—
319C8×D4—222no—
320C8×D4—221no—
321#431—112no—
322#431—112no—
323#431C2×D1111yescharacteristic
324#431C2×D1111yescharacteristic
325C2×C4⋊C8—111no—
326C2×C4⋊C8—112no—
327C2×C4×C8—111no—
328C2×C4×C8—112no—
329Q8⋊C8—112no—
330Q8⋊C8—112no—
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333Q8⋊C8—112no—
334Q8⋊C8C2×D1112yes—
335Q8⋊C8C2×D1112yes—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—112no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11C2×C22⋊C812yes—
342C22×C11C22×C22⋊C411yescharacteristic
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—41no—
347C2×D11—41no—
348C2×D11C2×C22⋊C814yes—
349C4×C11—24no—
350C4×C11—21no—
351C4×C11—21no—
352C4×C11—21no—
353C4×C11—42no—
354C4×C11C2×C22⋊C812yes—
355C4×C11C23×C811yescharacteristic
356C4×C11C22×M1611yescharacteristic
357C4×C11#57711yescharacteristic
358C4×C11#57811yescharacteristic
359Dic11—22no—
360Dic11—22no—
361Dic11—22no—
362Dic11—41no—
363Dic11—41no—
364Dic11C2×C22⋊C814yes—
3652−1+4—118no—
3662−1+4—224no—
367C2×#41—111no—
368C2×#41—112no—
369C2×#41—111no—
370C2×#41—222no—
371C2×#41—221no—
372C22×Q8—112no—
373C22×Q8—221no—
374C22×Q8C4×D1111yescharacteristic
375C22×C8—222no—
376C22×C8—222no—
377C22×C8—221no—
378C22×C8—221no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8—111no—
382C4×Q8—111no—
383C4×Q8—112no—
384C4×Q8—112no—
385C4×Q8—112no—
386C4×Q8—111no—
387C4×Q8—111no—
388C4×Q8—222no—
389C4×Q8—222no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—221no—
393C4×Q8—221no—
394C4×Q8—221no—
395C4×Q8C4×D1112yes—
396C4×Q8C22×D1112yes—
397C4×D4—112no—
398C4×D4—112no—
399C4×D4—112no—
400C4×D4—111no—
401C4×D4—111no—
402C4×D4—111no—
403C4×D4—111no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4—221no—
410C4×D4—222no—
411C4×D4—221no—
412C4×D4—221no—
413#117—111no—
414#117—112no—
415#117—111no—
416#117—112no—
417#117—222no—
418#117—222no—
419#117—222no—
420#117—222no—
421#117—222no—
422#117—221no—
423#117—221no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—112no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4C4×D1111yescharacteristic
430C2×C42—21no—
431C2×C42—112no—
432C2×C42—222no—
433C2×C42—222no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—112no—
438C4⋊C8—222no—
439C4⋊C8—222no—
440C4⋊C8—221no—
441C4⋊C8C22×D1111yescharacteristic
442C4⋊C8C22×D1111yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—222no—
446C22⋊C8—222no—
447C4×C8—21no—
448C4×C8—111no—
449C4×C8—111no—
450C4×C8—222no—
451C4×C8—222no—
452C4×C8—221no—
453C4×C8C22×D1112yes—
454C2×C11—22no—
455C2×C11C22×C22⋊C811yescharacteristic
456C2×C11#289811yescharacteristic
457C2×C11#290111yescharacteristic
458D11—24no—
459D11—42no—
460#41—114no—
461#41—114no—
462#41—118no—
463#41—114no—
464#41—2216no—
465#41—224no—
466#41—228no—
467#41—222no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8—111no—
471C2×Q8—118no—
472C2×Q8—111no—
473C2×Q8—222no—
474C2×Q8—224no—
475C2×Q8—228no—
476C2×Q8C8×D1114yescomplemented
477C2×Q8C2×C4×D1112yes—
478C2×D4—112no—
479C2×D4—111no—
480C2×D4—111no—
481C2×D4—222no—
482C2×D4—221no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—112no—
486C22×C4—112no—
487C22×C4—112no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4C2×C4×D1111yescharacteristic
496C22×C4D4×D1111yescharacteristic
497C22×C4D4×D1111yescharacteristic
498C2×C8—22no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—222no—
504C2×C8—444no—
505C2×C8—442no—
506C2×C8—882no—
507C2×C8—881no—
508C4⋊C4—22no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—112no—
512C4⋊C4—111no—
513C4⋊C4—112no—
514C4⋊C4—111no—
515C4⋊C4—111no—
516C4⋊C4—111no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—222no—
520C4⋊C4—222no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4C2×C4×D1112yes—
524C22⋊C4—112no—
525C22⋊C4—112no—
526C22⋊C4—112no—
527C22⋊C4—222no—
528C22⋊C4—222no—
529C22⋊C4—221no—
530C22⋊C4—221no—
531C22⋊C4—221no—
532C42—22no—
533C42—22no—
534C42—112no—
535C42—112no—
536C42—112no—
537C42—222no—
538C42—222no—
539C42—222no—
540C42—222no—
541C42—221no—
542C42—221no—
543C42—221no—
544C42C2×C4×D1111yescharacteristic
545C42D4×D1111yescharacteristic
546C42D4×D1111yescharacteristic
547C42C23×D1111yescharacteristic
548C11#1743911yescharacteristic, complemented, Sylow
549C23—112no—
550C23—221no—
551C23C22⋊C4×D1111yescharacteristic
552Q8—22no—
553Q8—24no—
554Q8—114no—
555Q8—112no—
556Q8—228no—
557Q8—221no—
558Q8C2×C8×D1114yes—
559D4—118no—
560D4—112no—
561D4—114no—
562D4—228no—
563D4—224no—
564D4—221no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—41no—
571C2×C4—81no—
572C2×C4—112no—
573C2×C4—114no—
574C2×C4—114no—
575C2×C4—112no—
576C2×C4—112no—
577C2×C4—228no—
578C2×C4—228no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—442no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—881no—
589C2×C4—882no—
590C2×C4—882no—
591C2×C4C22⋊C4×D1111yescharacteristic
592C2×C4C22⋊C4×D1111yescharacteristic
593C2×C4C22⋊C4×D1111yescharacteristic
594C2×C4C2×C8×D1112yes—
595C2×C4M16×D1112yes—
596C2×C4C22×C4×D1111yescharacteristic
597C2×C4C2×D4×D1111yescharacteristic
598C2×C4C2×D4×D1111yescharacteristic
599C8—42no—
600C8—41no—
601C8—41no—
602C8—222no—
603C8—441no—
604C8—442no—
605C22—21no—
606C22—21no—
607C22—114no—
608C22—222no—
609C22—222no—
610C22—222no—
611C22—441no—
612C22—441no—
613C22D11×C22⋊C812yes—
614C22C2×C22⋊C4×D1111yescharacteristic
615C4—24no—
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—114no—
621C4—222no—
622C4—222no—
623C4—222no—
624C4—441no—
625C4—441no—
626C4D11×C22⋊C812yes—
627C4C22×C8×D1111yescharacteristic
628C4C2×M16×D1111yescharacteristic
629C4#1062330911yescharacteristic
630C4#1062331011yescharacteristic
631C2—22no—
632C2—224no—
633C2—442no—
634C2C2×D11×C22⋊C811yescharacteristic
635C2#1307714811yescharacteristic
636C2#1307716211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC4×C11C23×C8
FrattiniC42C23×D11
FittingC11×#1479C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#67040C4
cosocleC42×C11C24
hypercenter#1479D11
hypocenterC11#17439
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
2. #13077724C2semidirect
3. #13077572C2semidirect
4. #13067009C2semidirect
5. #13067004C2semidirect
6. #13067002C2semidirect
7. #13066997C2semidirect
8. #13066996C2semidirect
9. C2×Q8⋊(C11⋊C8)C2semidirect
10. D11×Q8⋊C8C2semidirect
11. C11×#1479C2semidirect
55. #67040C8semidirect
145. C2×Q8×C11C2×C8semidirect
156. #4343C2×C8semidirect
159. Q8×D11C2×C8semidirect
163. #4339C2×C8semidirect
235. #1479D11semidirect
476. C2×Q8C8×D11semidirect
548. C11#17439semidirect

Maximal subgroups

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

subgroupindex
C4×#670402
#130777242
#130775722
#130670092
#130670042
#130670022
#130669972
#130669962
C2×Q8⋊(C11⋊C8)2
D11×Q8⋊C82
C11×#14792
#1743911