Finite Group Databasebeta

← #14720263

Subgroups — #14720263

Order 2816.

1138 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×#67043C211yesmaximal, characteristic
2#13077733C211yesmaximal, characteristic, complemented
3#13067064C212yesmaximal, complemented
4#13067056C212yesmaximal, complemented
5#13067051C212yesmaximal, complemented
6#13067046C212yesmaximal, complemented
7#13067012C211yesmaximal, characteristic, complemented
8#13067004C211yesmaximal, characteristic, complemented
9#13066999C211yesmaximal, characteristic, complemented
10C2×#10622094C211yesmaximal, characteristic, complemented
11C11×#2965C211yesmaximal, characteristic, complemented
12C2×#67043C411yescharacteristic
13C4×C11×#41C2211yescharacteristic
14#10623358C411yescharacteristic
15#10623103—21no—
16C4×Q8×D11—21no—
17#10623077—22no—
18#10623077—21no—
19C4×#4341—22no—
20C4×#4341—21no—
21#10623054C412yes—
22#10623054C411yescharacteristic
23#10623047C412yes—
24#10623047C411yescharacteristic
25C4×#4339C2212yes—
26C4×#4339C2211yescharacteristic
27C2×C4×Dic22C2211yescharacteristic
28C2×C4×Dic22C2212yes—
29C11×#446—21no—
30C11×#436—21no—
31C11×#435—22no—
32C11×#431C2211yescharacteristic
33C11×#431C2212yes—
34C4×C11×M16C2212yes—
35C2×C4×C8×C11C2211yescharacteristic
36#10622637—21no—
37#10622625—21no—
38#10622624—22no—
39#10622539C2212yes—
40#10622538C2211yescharacteristic
41#10622537C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622097C2211yescharacteristic
44#10622097C2212yes—
45#10622097C2211yescharacteristic
46#10622094C2212yes—
47#10622094C2212yes—
48#10622094C2211yescharacteristic
49#10622094C2212yes—
50#10622094C2212yes—
51#10622094C2212yes—
52#10622094C2211yescharacteristic
53C2×C11×#41C2×C411yescharacteristic
54#67043—24no—
55#67043—24no—
56C2×Q8×D11—21no—
57C2×#4341—22no—
58C2×#4341—21no—
59C2×#4339C2×C412yes—
60C2×#4339C2×C411yescharacteristic
61C22×Dic22C2×C412yes—
62C22×Dic22C2×C411yescharacteristic
63C2×C11×M16—22no—
64C22×C8×C11—21no—
65C4×Q8×C11D411yescharacteristic
66C4×Q8×C11D411yescharacteristic
67C4×D4×C11D412yes—
68C4×D4×C11D411yescharacteristic
69C4×D4×C11D412yes—
70C4×D4×C11D411yescharacteristic
71C11×#117C2×C412yes—
72C11×#117C2×C411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2312yes—
75Q8×Dic11—21no—
76D4×Dic11—22no—
77D4×Dic11—21no—
78C4×C22⋊D11—21no—
79C4×C22⋊D11—22no—
80C4×C22⋊D11—21no—
81C4×C22⋊D11—22no—
82#66979C2×C412yes—
83#66979C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C412yes—
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—22no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11—22no—
90C2×#4318—22no—
91C22×C11⋊C8—21no—
92#66945—22no—
93#66945—21no—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—21no—
96#66940—22no—
97#66940—21no—
98#66940—22no—
99#66940—21no—
100(C22⋊D11)⋊C4—22no—
101(C22⋊D11)⋊C4—22no—
102(C22⋊D11)⋊C4—22no—
103#66930—22no—
104#66930—22no—
105#66930—22no—
106C4×D44C2×C412yes—
107C4×D44C2×C411yescharacteristic
108C4×D44C2311yescharacteristic
109#66925—21no—
110#66925—22no—
111C42×D11—21no—
112C42×D11—22no—
113C4×Dic22—21no—
114C4×Dic22—22no—
115C4×Dic22—21no—
116C4×Dic22—22no—
117C4×Dic22C2×C412yes—
118C4×Dic22C2×C412yes—
119C4×Dic22C2×C412yes—
120C4×Dic22C2×C412yes—
121C4×Dic22C2×C411yescharacteristic
122C4×Dic22C2312yes—
123C4×Dic22C2311yescharacteristic
124C11×C4⋊C8—22no—
125C11×C4⋊C8—21no—
126C11×C22⋊C8—21no—
127C11×C22⋊C8—22no—
128C11×#97—22no—
129C4×C8×C11—21no—
130C4×C8×C11C2311yescharacteristic
131C4×C8×C11C2311yescharacteristic
132C4×C8×C11C2312yes—
133C22⋊(C11⋊C8)—21no—
134C22⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—21no—
136C4⋊(C11⋊C8)—22no—
137C4⋊(C11⋊C8)C2312yes—
138C4⋊(C11⋊C8)C2311yescharacteristic
139C4⋊(C11⋊C8)C2311yescharacteristic
140#66867—22no—
141C4×C11⋊C8—21no—
142#17454—111nomaximal, Sylow
143C11×#41—22no—
144C11×#41—22no—
145C2×Q8×C11C22⋊C411yescharacteristic
146C2×D4×C11C22⋊C412yes—
147C2×D4×C11C22⋊C411yescharacteristic
148C22×C4×C11C22×C412yes—
149C22×C4×C11C22×C411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D412yes—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C2×C22⋊D11—22no—
155C2×C22⋊D11—21no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160Q8×D11—28no—
161#4341—216no—
162#4341—28no—
163#4339—24no—
164#4339—24no—
165#4339—22no—
166#4339M1614yescomplemented
167C2×D44C22×C411yescharacteristic
168C2×C4×D11—22no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—22no—
172C2×C4×D11—21no—
173C2×Dic22—24no—
174C2×Dic22—24no—
175C2×Dic22—22no—
176C2×Dic22—21no—
177C2×Dic22—22no—
178C2×Dic22M1614yescomplemented
179C2×Dic22C22×C411yescharacteristic
180C2×Dic22C22×C412yes—
181C11×M16—44no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—22no—
185C2×C8×C11—42no—
186C11×C4⋊C4C22⋊C412yes—
187C11×C4⋊C4C22⋊C411yescharacteristic
188C11×C4⋊C4C22⋊C412yes—
189C11×C4⋊C4C22⋊C411yescharacteristic
190C11×C22⋊C4C22⋊C412yes—
191C11×C22⋊C4C22⋊C412yes—
192C11×C22⋊C4C22⋊C412yes—
193C42×C11C22×C411yescharacteristic
194C42×C11C22×C412yes—
195C42×C11C2×D411yescharacteristic
196C42×C11C2×D412yes—
197C42×C11C2×D411yescharacteristic
198C42×C11C2×D412yes—
199C42×C11C2411yescharacteristic
200C22⋊Dic11—22no—
201C22⋊Dic11—21no—
202(C2×D11)⋊C4—21no—
203(C2×D11)⋊C4—22no—
204(C2×D11)⋊C4—21no—
205C4⋊Dic11—22no—
206C4⋊Dic11—21no—
207C4⋊Dic11C22×C411yescharacteristic
208C4⋊Dic11C22×C412yes—
209C4⋊Dic11C22×C411yescharacteristic
210Dic11⋊C4—22no—
211Dic11⋊C4—22no—
212Dic11⋊C4—22no—
213Dic11⋊C4—21no—
214Dic11⋊C4—22no—
215Dic11⋊C4—22no—
216Dic11⋊C4—21no—
217C4×Dic11—22no—
218C4×Dic11—22no—
219C4×Dic11—22no—
220C4×Dic11—21no—
221C4×Dic11—22no—
222C4×Dic11—22no—
223C4×Dic11—21no—
224C4×Dic11—22no—
225C4×Dic11—21no—
226#4318—82no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—22no—
230C2×C11⋊C8—81no—
231C4×2−1+4—111no—
232#2989—111no—
233#2965D1111yescharacteristic, complemented
234#1491—112no—
235#1489—112no—
236#1488—112no—
237#1487—112no—
238#1479—111no—
239#1477—111no—
240#1476—111no—
241C2×Q8⋊C8—111no—
242C23×C11C2×C22⋊C412yes—
243C23×C11C2×C22⋊C411yescharacteristic
244C22×D11—21no—
245Q8×C11—22no—
246D4×C11—24no—
247D4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—21no—
253C2×C4×C11—22no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11C2×C22⋊C411yescharacteristic
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C2×C22⋊C411yescharacteristic
259C2×C4×C11C2×C22⋊C412yes—
260C2×C4×C11C2×C22⋊C412yes—
261C2×C4×C11C2×C22⋊C411yescharacteristic
262C2×C4×C11C2×M1612yes—
263C2×C4×C11C2×M1612yes—
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×D411yescharacteristic
267C22⋊D11—28no—
268C22⋊D11—24no—
269C2×Dic11—28no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—21no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—81no—
277C2×Dic11—82no—
278D44—21no—
279D44C2×M1612yes—
280C4×D11—28no—
281C4×D11—24no—
282C4×D11—41no—
283C4×D11—41no—
284C4×D11—81no—
285C4×D11—82no—
286Dic22—28no—
287Dic22—22no—
288Dic22—21no—
289Dic22—24no—
290Dic22C2×M1612yes—
291Dic22C2×M1614yes—
292C8×C11—22no—
293C8×C11—41no—
294C8×C11—42no—
295C11⋊C8—42no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C2×2−1+4—111no—
299#520—111no—
300#520—111no—
301#520—112no—
302#520—222no—
303#520—221no—
304#519—111no—
305#519—112no—
306#519—221no—
307C4×#41—111no—
308C4×#41—112no—
309C4×#41—222no—
310C4×#41—221no—
311C4×#41C2×D1111yescharacteristic
312C2×C4×Q8—111no—
313C2×C4×Q8—112no—
314C2×C4×Q8—221no—
315#446—21no—
316#446—221no—
317#436—21no—
318#436—221no—
319#435—22no—
320#435—222no—
321#432—112no—
322#431—111no—
323#431C2×D1111yescharacteristic
324#431C2×D1112yes—
325#423—112no—
326C2×C4⋊C8—111no—
327C4×M16C2×D1112yes—
328C2×C4×C8C2×D1111yescharacteristic
329Q8⋊C8—112no—
330Q8⋊C8—112no—
331Q8⋊C8—111no—
332Q8⋊C8—111no—
333Q8⋊C8—112no—
334Q8⋊C8—112no—
335Q8⋊C8—112no—
336D4⋊C8—111no—
337D4⋊C8—111no—
338D4⋊C8—112no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11#40712yes—
345C22×C11C22×C22⋊C411yescharacteristic
346C2×D11—22no—
347C2×D11—41no—
348C2×D11—41no—
349C4×C11—22no—
350C4×C11—21no—
351C4×C11—22no—
352C4×C11—21no—
353C4×C11—21no—
354C4×C11—22no—
355C4×C11#40712yes—
356C4×C11C22×M1611yescharacteristic
357C4×C11C22×M1611yescharacteristic
358C4×C11#57711yescharacteristic
359C4×C11#57811yescharacteristic
360Dic11—22no—
361Dic11—24no—
362Dic11—41no—
363Dic11—42no—
364Dic11—41no—
3652−1+4—224no—
3662−1+4—224no—
367C2×#41—111no—
368C2×#41—112no—
369C2×#41—221no—
370C2×#41—222no—
371C2×#41C4×D1111yescharacteristic
372C22×Q8—111no—
373C22×Q8—112no—
374C22×Q8—221no—
375C2×M16—22no—
376C2×M16—222no—
377C22×C8—21no—
378C22×C8—221no—
379C4×Q8—112no—
380C4×Q8—112no—
381C4×Q8—112no—
382C4×Q8—111no—
383C4×Q8—112no—
384C4×Q8—112no—
385C4×Q8—111no—
386C4×Q8—221no—
387C4×Q8—222no—
388C4×Q8—221no—
389C4×Q8—222no—
390C4×Q8—221no—
391C4×Q8—221no—
392C4×Q8—222no—
393C4×Q8—221no—
394C4×Q8—222no—
395C4×Q8D4411yescharacteristic
396C4×Q8C22⋊D1111yescharacteristic
397C4×D4—111no—
398C4×D4—112no—
399C4×D4—111no—
400C4×D4—222no—
401C4×D4—221no—
402C4×D4—221no—
403C4×D4—222no—
404C4×D4—221no—
405C4×D4—222no—
406C4×D4—222no—
407C4×D4—222no—
408C4×D4—222no—
409C4×D4D4412yes—
410C4×D4D4411yescharacteristic
411C4×D4C22⋊D1112yes—
412C4×D4C22⋊D1111yescharacteristic
413#117—112no—
414#117—111no—
415#117—222no—
416#117—221no—
417#117—222no—
418#117—222no—
419#117—222no—
420#117—221no—
421#117—222no—
422#117C4×D1112yes—
423#117C4×D1111yescharacteristic
424C2×C4⋊C4—112no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—221no—
430C2×C42—221no—
431C2×C42—222no—
432C2×C42—221no—
433C2×C42—222no—
434C2×C42C22×D1111yescharacteristic
435C2×C42C22×D1112yes—
436C4⋊C8—22no—
437C4⋊C8—21no—
438C4⋊C8—112no—
439C4⋊C8—111no—
440C4⋊C8—111no—
441C4⋊C8—221no—
442C4⋊C8—222no—
443C22⋊C8—21no—
444C22⋊C8—22no—
445C22⋊C8—221no—
446C22⋊C8—222no—
447#97—22no—
448#97—222no—
449C4×C8—21no—
450C4×C8—221no—
451C4×C8C22×D1111yescharacteristic
452C4×C8C22×D1111yescharacteristic
453C4×C8C22×D1112yes—
454C2×C11—22no—
455C2×C11—42no—
456C2×C11C2×#40711yescharacteristic
457C2×C11#289811yescharacteristic
458C2×C11#290111yescharacteristic
459D11—42no—
460#41—22no—
461#41—22no—
462#41—114no—
463#41—224no—
464#41—224no—
465#41—2216no—
466#41—228no—
467#41—222no—
468C2×Q8—114no—
469C2×Q8—112no—
470C2×Q8—111no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8—228no—
474C2×Q8—222no—
475C2×Q8—222no—
476C2×Q8—221no—
477C2×Q8(C2×D11)⋊C411yescharacteristic
478C2×D4—111no—
479C2×D4—222no—
480C2×D4—221no—
481C2×D4(C2×D11)⋊C412yes—
482C2×D4(C2×D11)⋊C411yescharacteristic
483C22×C4—222no—
484C22×C4—221no—
485C22×C4—222no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—222no—
492C22×C4C2×C4×D1112yes—
493C22×C4C2×C4×D1111yescharacteristic
494C22×C4C2×D4411yescharacteristic
495C22×C4C2×D4412yes—
496C22×C4C2×C22⋊D1111yescharacteristic
497C22×C4C2×C22⋊D1112yes—
498M16—44no—
499M16—882no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—22no—
503C2×C8—42no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—222no—
507C2×C8—881no—
508C4⋊C4—111no—
509C4⋊C4—112no—
510C4⋊C4—111no—
511C4⋊C4—222no—
512C4⋊C4—221no—
513C4⋊C4—222no—
514C4⋊C4—222no—
515C4⋊C4—222no—
516C4⋊C4—221no—
517C4⋊C4—222no—
518C4⋊C4—222no—
519C4⋊C4—221no—
520C4⋊C4(C2×D11)⋊C412yes—
521C4⋊C4(C2×D11)⋊C411yescharacteristic
522C4⋊C4(C2×D11)⋊C412yes—
523C4⋊C4(C2×D11)⋊C411yescharacteristic
524C22⋊C4—222no—
525C22⋊C4—221no—
526C22⋊C4—221no—
527C22⋊C4—222no—
528C22⋊C4—221no—
529C22⋊C4(C2×D11)⋊C412yes—
530C22⋊C4(C2×D11)⋊C412yes—
531C22⋊C4(C2×D11)⋊C412yes—
532C42—222no—
533C42—221no—
534C42—221no—
535C42—222no—
536C42—222no—
537C42—222no—
538C42—222no—
539C42—222no—
540C42—221no—
541C42C2×C4×D1111yescharacteristic
542C42C2×C4×D1112yes—
543C42C2×D4411yescharacteristic
544C42C2×D4412yes—
545C42C2×C22⋊D1111yescharacteristic
546C42C2×C22⋊D1112yes—
547C42C23×D1111yescharacteristic
548C11#1745411yescharacteristic, complemented, Sylow
549C23—221no—
550C23C2×(C2×D11)⋊C412yes—
551C23C2×(C2×D11)⋊C411yescharacteristic
552Q8—22no—
553Q8—114no—
554Q8—112no—
555Q8—228no—
556Q8—224no—
557Q8—222no—
558Q8—221no—
559D4—24no—
560D4—22no—
561D4—112no—
562D4—228no—
563D4—224no—
564D4—221no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—42no—
573C2×C4—228no—
574C2×C4—228no—
575C2×C4—224no—
576C2×C4—222no—
577C2×C4—221no—
578C2×C4—224no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—221no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—881no—
585C2×C4—882no—
586C2×C4—881no—
587C2×C4—882no—
588C2×C4M16×D1112yes—
589C2×C4M16×D1112yes—
590C2×C4C2×(C2×D11)⋊C411yescharacteristic
591C2×C4C2×(C2×D11)⋊C412yes—
592C2×C4C2×(C2×D11)⋊C411yescharacteristic
593C2×C4C2×(C2×D11)⋊C412yes—
594C2×C4C2×(C2×D11)⋊C412yes—
595C2×C4C2×(C2×D11)⋊C411yescharacteristic
596C2×C4C22×C4×D1111yescharacteristic
597C2×C4C22×D4411yescharacteristic
598C2×C4C22×C22⋊D1111yescharacteristic
599C8—22no—
600C8—41no—
601C8—42no—
602C8—442no—
603C8—441no—
604C8—441no—
605C22—21no—
606C22—21no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—222no—
611C22—441no—
612C22—441no—
613C22#1062273912yes—
614C22C22×(C2×D11)⋊C411yescharacteristic
615C4—22no—
616C4—21no—
617C4—22no—
618C4—21no—
619C4—21no—
620C4—22no—
621C4—224no—
622C4—222no—
623C4—441no—
624C4—442no—
625C4—441no—
626C4#1062273912yes—
627C4C2×M16×D1111yescharacteristic
628C4C2×M16×D1111yescharacteristic
629C4#1062328211yescharacteristic
630C4#1062328411yescharacteristic
631C2—22no—
632C2—42no—
633C2—442no—
634C2C2×#1062273911yescharacteristic
635C2#1307715011yescharacteristic
636C2#1307716411yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2965C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#67043C4
cosocleC42×C11C24
hypercenter#2965D11
hypocenterC11#17454
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2965

Complements

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

NH ≅ G/Ntype
2. #13077733C2semidirect
3. #13067064C2semidirect
4. #13067056C2semidirect
5. #13067051C2semidirect
6. #13067046C2semidirect
7. #13067012C2semidirect
8. #13067004C2semidirect
9. #13066999C2semidirect
10. C2×#10622094C2semidirect
11. C11×#2965C2semidirect
166. #4339M16semidirect
178. C2×Dic22M16semidirect
233. #2965D11semidirect
548. C11#17454semidirect

Maximal subgroups

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

subgroupindex
C4×#670432
#130777332
#130670642
#130670562
#130670512
#130670462
#130670122
#130670042
#130669992
C2×#106220942
C11×#29652
#1745411