Finite Group Databasebeta

← #14720786

Subgroups — #14720786

Order 2816.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082226C211yesmaximal, characteristic
2#13077741C211yesmaximal, characteristic, complemented
3#13067086C211yesmaximal, characteristic, complemented
4#13067082C211yesmaximal, characteristic, complemented
5#13067077C211yesmaximal, characteristic, complemented
6#13067060C211yesmaximal, characteristic, complemented
7#13067051C211yesmaximal, characteristic, complemented
8#13067042C211yesmaximal, characteristic, complemented
9#13067030C211yesmaximal, characteristic, complemented
10#13067025C211yesmaximal, characteristic, complemented
11#13067016C211yesmaximal, characteristic, complemented
12#13067008C211yesmaximal, characteristic, complemented
13#13067004C211yesmaximal, characteristic, complemented
14C2×#10622097C211yesmaximal, characteristic, complemented
15C11×#2922C211yesmaximal, characteristic, complemented
16C4×C11×#41C2211yescharacteristic
17#10623360—21no—
18#10623116C411yescharacteristic
19#10623111—21no—
20#10623110C411yescharacteristic
21#10623096C411yescharacteristic
22#10623096C411yescharacteristic
23#10623081C411yescharacteristic
24#10623081C411yescharacteristic
25D4×D44C411yescharacteristic
26#10623078—21no—
27#10623078—21no—
28C4×D4×D11—21no—
29#10623074C411yescharacteristic
30#10623061—21no—
31#10623058—21no—
32#10623058—21no—
33#10623010C2211yescharacteristic
34#10623010C2211yescharacteristic
35#10623008C2211yescharacteristic
36C4×#4339C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C11×#433—21no—
40C11×#433—21no—
41C11×#431C2211yescharacteristic, complemented
42C11×#431C2211yescharacteristic, complemented
43C11×#431C2211yescharacteristic, complemented
44C11×#431C2211yescharacteristic, complemented
45C11×#424—21no—
46C11×#408—21no—
47C4×C11×M16C2211yescharacteristic, complemented
48C2×C4×C8×C11C2211yescharacteristic, complemented
49#10622637—21no—
50#10622624—21no—
51#10622624—21no—
52D4×C11⋊C8—21no—
53#10622539C2211yescharacteristic, complemented
54#10622539C2211yescharacteristic, complemented
55#10622538C2211yescharacteristic, complemented
56#10622537C2211yescharacteristic, complemented
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59#10622097C2211yescharacteristic
60#10622097C2211yescharacteristic
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic
63#10622097C2211yescharacteristic, complemented
64#10622097C2211yescharacteristic, complemented
65#10622097C2211yescharacteristic, complemented
66#10622097C2211yescharacteristic, complemented
67#10622097C2211yescharacteristic, complemented
68#10622097C2211yescharacteristic, complemented
69#10622097C2211yescharacteristic, complemented
70#10622097C2211yescharacteristic, complemented
71#10622094C2211yescharacteristic, complemented
72#10622094C2211yescharacteristic, complemented
73#10622094C2211yescharacteristic, complemented
74#10622094C2211yescharacteristic, complemented
75C2×C11×#41D411yescharacteristic
76C2×D4×D11—21no—
77C2×#4339—21no—
78C2×#4339C2×C411yescharacteristic
79C22×D44C2×C411yescharacteristic
80C22×D44C2×C411yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11—21no—
83C2×C11×M16—21no—
84C22×C8×C11—21no—
85C4×Q8×C11C2×C411yescharacteristic
86C4×Q8×C11D411yescharacteristic
87C4×D4×C11C2×C411yescharacteristic
88C4×D4×C11C2×C411yescharacteristic
89C4×D4×C11C2×C411yescharacteristic
90C4×D4×C11D411yescharacteristic
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C11×#117D411yescharacteristic
94C11×#117D411yescharacteristic
95C11×#117D411yescharacteristic
96C2×C42×C11C2311yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C42×C11C2311yescharacteristic
99#67000—21no—
100#66999—21no—
101#66992—21no—
102#66992—21no—
103#66990—21no—
104#66990—21no—
105D4×Dic11—21no—
106#66983—21no—
107#66983C2×C411yescharacteristic
108#66983C2×C411yescharacteristic
109#66983C2×C411yescharacteristic
110#66983C2×C411yescharacteristic
111#66982—21no—
112#66982—21no—
113C4×C22⋊D11—21no—
114C4×C22⋊D11—21no—
115C4×C22⋊D11—21no—
116C4×C22⋊D11—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119#66979C2×C411yescharacteristic
120C2×C4⋊Dic11C2×C411yescharacteristic
121C2×C4⋊Dic11C2×C411yescharacteristic
122#66977C2×C411yescharacteristic
123#66977C2×C411yescharacteristic
124C2×#4318—21no—
125C22×C11⋊C8—21no—
126C22×C11⋊C8—21no—
127#66951—21no—
128#66951—21no—
129#66949—21no—
130#66949—21no—
131#66948—21no—
132#66947—21no—
133#66947—21no—
134#66947—21no—
135#66947—21no—
136#66946—21no—
137C4⋊C4×D11—21no—
138#66943—21no—
139#66937—21no—
140#66937—21no—
141#66936—21no—
142#66936—21no—
143#66935—21no—
144#66935—21no—
145(C22⋊D11)⋊C4—21no—
146(C22⋊D11)⋊C4—21no—
147C22⋊C4×D11—21no—
148C22⋊C4×D11—21no—
149#66931—21no—
150#66931—21no—
151#66929—21no—
152#66929—21no—
153#66928—21no—
154#66928C2×C411yescharacteristic
155#66928C2×C411yescharacteristic
156#66927C2×C411yescharacteristic
157C4×D44—21no—
158C4×D44—21no—
159C4×D44—21no—
160C4×D44—21no—
161C4×D44—21no—
162C4×D44C2×C411yescharacteristic
163C4×D44C2×C411yescharacteristic
164C4×D44C2×C411yescharacteristic
165C4×D44C2×C411yescharacteristic
166C4×D44C2×C411yescharacteristic
167C4×D44C2311yescharacteristic
168C4×D44C2311yescharacteristic
169C4×D44C2311yescharacteristic
170#66925—21no—
171#66925—21no—
172#66925—21no—
173C42×D11—21no—
174#66923C2×C411yescharacteristic
175#66923C2×C411yescharacteristic
176#66922C2×C411yescharacteristic
177C4×Dic22C2×C411yescharacteristic
178C4×Dic22C2311yescharacteristic
179C11×C4⋊C8—21no—
180C11×C4⋊C8—21no—
181C11×C4⋊C8—21no—
182C11×C4⋊C8—21no—
183C11×C22⋊C8—21no—
184C11×C22⋊C8—21no—
185C11×C22⋊C8—21no—
186C11×C22⋊C8—21no—
187C11×#97—21no—
188C4×C8×C11—21no—
189C4×C8×C11C2311yescharacteristic
190C4×C8×C11C2311yescharacteristic
191C4×C8×C11C2311yescharacteristic
192C4×C8×C11C2311yescharacteristic
193C22⋊(C11⋊C8)—21no—
194C22⋊(C11⋊C8)—21no—
195C22⋊(C11⋊C8)—21no—
196C4⋊(C11⋊C8)—21no—
197C4⋊(C11⋊C8)—21no—
198C4⋊(C11⋊C8)—21no—
199C4⋊(C11⋊C8)C2311yescharacteristic
200C4⋊(C11⋊C8)C2311yescharacteristic
201C4⋊(C11⋊C8)C2311yescharacteristic
202C4⋊(C11⋊C8)C2311yescharacteristic
203#66867—21no—
204#66867—21no—
205C4×C11⋊C8—21no—
206#17521—111nomaximal, Sylow
207C23×D11—21no—
208C23×D11—21no—
209C11×#41—42no—
210C2×Q8×C11C22⋊C411yescharacteristic
211C2×D4×C11C22⋊C411yescharacteristic
212C2×D4×C11C22⋊C411yescharacteristic
213C2×D4×C11C22⋊C411yescharacteristic
214C22×C4×C11C22×C411yescharacteristic
215C22×C4×C11C22×C411yescharacteristic
216C22×C4×C11C22×C411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C2×C22⋊D11—21no—
226C2×C22⋊D11—21no—
227C2×C22⋊D11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230D4×D11—44no—
231#4339—22no—
232#4339—41no—
233#4339—81no—
234#4339—81no—
235C2×D44—22no—
236C2×D44—22no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44—21no—
240C2×D44—21no—
241C2×D44—41no—
242C2×D44—41no—
243C2×D44C22×C411yescharacteristic
244C2×D44C22×C411yescharacteristic
245C2×D44C22×C411yescharacteristic
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—21no—
254C2×C4×D11—21no—
255C2×C4×D11—81no—
256C2×C4×D11—81no—
257C2×C4×D11—81no—
258C2×C4×D11—81no—
259C2×Dic22—21no—
260C2×Dic22C22×C411yescharacteristic
261C11×M16—42no—
262C2×C8×C11—21no—
263C2×C8×C11—21no—
264C2×C8×C11—21no—
265C2×C8×C11—21no—
266C2×C8×C11—42no—
267C11×C4⋊C4C22⋊C411yescharacteristic
268C11×C4⋊C4C22⋊C411yescharacteristic
269C11×C4⋊C4C22⋊C411yescharacteristic
270C11×C4⋊C4C22⋊C411yescharacteristic
271C11×C4⋊C4C22⋊C411yescharacteristic
272C11×C4⋊C4C22⋊C411yescharacteristic
273C11×C22⋊C4C22⋊C411yescharacteristic
274C11×C22⋊C4C22⋊C411yescharacteristic
275C11×C22⋊C4C22⋊C411yescharacteristic
276C11×C22⋊C4C22⋊C411yescharacteristic
277C11×C22⋊C4C22⋊C411yescharacteristic
278C11×C22⋊C4C22⋊C411yescharacteristic
279C42×C11C22×C411yescharacteristic
280C42×C11C22×C411yescharacteristic
281C42×C11C22×C411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2411yescharacteristic
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291C22⋊Dic11—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—21no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—21no—
305(C2×D11)⋊C4—21no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11—21no—
311C4⋊Dic11C22×C411yescharacteristic
312C4⋊Dic11C22×C411yescharacteristic
313C4⋊Dic11C22×C411yescharacteristic
314C4⋊Dic11C22×C411yescharacteristic
315Dic11⋊C4—21no—
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—21no—
319Dic11⋊C4—21no—
320Dic11⋊C4—21no—
321Dic11⋊C4—21no—
322Dic11⋊C4—21no—
323C4×Dic11—21no—
324C4×Dic11—21no—
325C4×Dic11—21no—
326#4318—81no—
327C2×C11⋊C8—21no—
328C2×C11⋊C8—21no—
329C2×C11⋊C8—21no—
330C2×C11⋊C8—21no—
331C2×C11⋊C8—81no—
332C2×C11⋊C8—81no—
333#3481—111no—
334#2990—111no—
335#2922D1111yescharacteristic, complemented
336#1496—111no—
337#1495—111no—
338#1494—111no—
339#1490—111no—
340#1488—111no—
341#1486—111no—
342#1483—111no—
343#1482—111no—
344#1480—111no—
345#1478—111no—
346#1477—111no—
347C2×D4⋊C8—111no—
348C23×C11C2×C22⋊C411yescharacteristic
349C23×C11C2×C22⋊C411yescharacteristic
350C23×C11C2×C22⋊C411yescharacteristic
351C22×D11—21no—
352C22×D11—21no—
353C22×D11—21no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11—81no—
359C22×D11—81no—
360Q8×C11—41no—
361D4×C11—22no—
362D4×C11—22no—
363D4×C11—41no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—21no—
375C2×C4×C11—21no—
376C2×C4×C11—21no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11C2×C22⋊C411yescharacteristic
380C2×C4×C11C2×C22⋊C411yescharacteristic
381C2×C4×C11C2×C22⋊C411yescharacteristic
382C2×C4×C11C2×C22⋊C411yescharacteristic
383C2×C4×C11C2×C22⋊C411yescharacteristic
384C2×C4×C11C2×C22⋊C411yescharacteristic
385C2×C4×C11C2×C22⋊C411yescharacteristic
386C2×C4×C11C2×C22⋊C411yescharacteristic
387C2×C4×C11C2×C22⋊C411yescharacteristic
388C2×C4×C11C23×C411yescharacteristic
389C2×C4×C11C22×D411yescharacteristic
390C2×C4×C11C22×D411yescharacteristic
391C22⋊D11—42no—
392C22⋊D11—42no—
393C22⋊D11—42no—
394C22⋊D11—81no—
395C22⋊D11—81no—
396C2×Dic11—21no—
397C2×Dic11—21no—
398C2×Dic11—21no—
399C2×Dic11—21no—
400C2×Dic11—21no—
401C2×Dic11—81no—
402C2×Dic11—81no—
403D44—21no—
404D44—21no—
405D44—21no—
406D44—21no—
407D44—21no—
408D44—42no—
409D44—42no—
410D44—42no—
411D44—81no—
412D44#13112yes—
413C4×D11—42no—
414C4×D11—42no—
415C4×D11—41no—
416C4×D11—41no—
417C4×D11—41no—
418C4×D11—41no—
419C4×D11—41no—
420C4×D11—41no—
421C4×D11—81no—
422C4×D11—81no—
423C4×D11—81no—
424C4×D11—81no—
425Dic22—21no—
426Dic22—21no—
427Dic22—81no—
428C8×C11—41no—
429C8×C11—41no—
430C8×C11—41no—
431C8×C11—41no—
432C11⋊C8—41no—
433C11⋊C8—41no—
434C11⋊C8—41no—
435C11⋊C8—41no—
436#559—111no—
437#554—111no—
438#554—111no—
439#553—111no—
440#553—111no—
441#553—221no—
442#551—221no—
443#551—221no—
444#546—111no—
445#546—111no—
446#546—221no—
447D42—111no—
448#532—111no—
449#529—111no—
450#529—111no—
451#529—221no—
452#525—221no—
453#525—221no—
454C4×#41—111no—
455C4×#41C2×D1111yescharacteristic
456C2×C4×D4—111no—
457C2×C4×D4—111no—
458C2×C4×D4—221no—
459#446—221no—
460#435—221no—
461#435—221no—
462C8×D4—221no—
463#433—21no—
464#433—21no—
465#432—111no—
466#432—111no—
467#431—111no—
468#431C2×D1111yescharacteristic, complemented
469#431C2×D1111yescharacteristic, complemented
470#431C2×D1111yescharacteristic, complemented
471#431C2×D1111yescharacteristic, complemented
472#424—21no—
473#423—111no—
474C2×C4⋊C8—111no—
475C2×C4⋊C8—111no—
476#408—21no—
477C4×M16C2×D1111yescharacteristic, complemented
478C2×C4×C8C2×D1111yescharacteristic, complemented
479Q8⋊C8—111no—
480Q8⋊C8—111no—
481Q8⋊C8—111no—
482Q8⋊C8—111no—
483D4⋊C8—111no—
484D4⋊C8—111no—
485D4⋊C8—111no—
486D4⋊C8—111no—
487D4⋊C8—111no—
488D4⋊C8—111no—
489D4⋊C8—111no—
490D4⋊C8—111no—
491D4⋊C8—111no—
492D4⋊C8—111no—
493D4⋊C8—111no—
494D4⋊C8—111no—
495C22×C11—21no—
496C22×C11—21no—
497C22×C11—21no—
498C22×C11—21no—
499C22×C11—21no—
500C22×C11—21no—
501C22×C11—21no—
502C22×C11—21no—
503C22×C11#42112yes—
504C22×C11C22×C22⋊C411yescharacteristic
505C2×D11—22no—
506C2×D11—41no—
507C2×D11—41no—
508C2×D11—41no—
509C2×D11—41no—
510C2×D11—41no—
511C2×D11—41no—
512C2×D11—41no—
513C2×D11—41no—
514C2×D11—84no—
515C2×D11—84no—
516C4×C11—21no—
517C4×C11—21no—
518C4×C11—21no—
519C4×C11—21no—
520C4×C11—21no—
521C4×C11—21no—
522C4×C11—21no—
523C4×C11—21no—
524C4×C11—21no—
525C4×C11—21no—
526C4×C11C2×#13111yescharacteristic
527C4×C11#56811yescharacteristic
528C4×C11#57611yescharacteristic
529C4×C11#57711yescharacteristic
530Dic11—41no—
531Dic11—41no—
532Dic11—41no—
533Dic11—41no—
534Dic11—41no—
535C2×#41—111no—
536C2×#41—221no—
537C2×#41C22⋊D1111yescharacteristic
538C22×D4—111no—
539C22×D4—111no—
540C22×D4—221no—
541C23×C4—221no—
542C23×C4—221no—
543C2×M16—21no—
544C2×M16—221no—
545C22×C8—21no—
546C22×C8—221no—
547C22×C8—221no—
548C4⋊Q8—111no—
549#127—111no—
550#126—221no—
551#126—221no—
552#126—221no—
553#126—221no—
554#125—111no—
555#125—111no—
556#125—221no—
557#124—111no—
558#124—111no—
559#124—221no—
560#124—221no—
561#123—221no—
562#123—221no—
563#123—221no—
564#123—221no—
565#123—221no—
566#123—221no—
567#123—221no—
568#123—221no—
569C22⋊Q8—111no—
570C22⋊Q8—111no—
571C22⋊Q8—221no—
572C22⋊Q8—221no—
573C22⋊Q8—221no—
574C22⋊Q8—221no—
575C22⋊Q8—221no—
576#121—111no—
577#121—111no—
578#121—111no—
579#121—111no—
580#121—221no—
581#121—221no—
582#121—221no—
583#121—221no—
584#121—221no—
585#121—221no—
586#120—221no—
587#120—221no—
588#120—221no—
589#120—221no—
590C4×Q8—111no—
591C4×Q8—111no—
592C4×Q8C4×D1111yescharacteristic
593C4×Q8D4411yescharacteristic
594C4×D4—111no—
595C4×D4—111no—
596C4×D4—111no—
597C4×D4—111no—
598C4×D4—111no—
599C4×D4—111no—
600C4×D4—111no—
601C4×D4—111no—
602C4×D4—221no—
603C4×D4—221no—
604C4×D4—221no—
605C4×D4—221no—
606C4×D4—221no—
607C4×D4—221no—
608C4×D4—221no—
609C4×D4—221no—
610C4×D4—221no—
611C4×D4—221no—
612C4×D4—221no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4C4×D1111yescharacteristic
616C4×D4C4×D1111yescharacteristic
617C4×D4C4×D1111yescharacteristic
618C4×D4D4411yescharacteristic
619C4×D4D4411yescharacteristic
620C4×D4D4411yescharacteristic
621#117—111no—
622#117—221no—
623#117—221no—
624#117—221no—
625#117C22⋊D1111yescharacteristic
626#117C22⋊D1111yescharacteristic
627#117C22⋊D1111yescharacteristic
628C2×C4⋊C4—111no—
629C2×C4⋊C4—111no—
630C2×C4⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C22⋊C4—221no—
635C2×C42—221no—
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C4⋊C8—21no—
640C4⋊C8—21no—
641C4⋊C8—21no—
642C4⋊C8—21no—
643C4⋊C8—111no—
644C4⋊C8—111no—
645C4⋊C8—111no—
646C4⋊C8—111no—
647C4⋊C8—221no—
648C4⋊C8—221no—
649C4⋊C8—221no—
650C22⋊C8—21no—
651C22⋊C8—21no—
652C22⋊C8—21no—
653C22⋊C8—21no—
654C22⋊C8—221no—
655C22⋊C8—221no—
656C22⋊C8—221no—
657#97—21no—
658#97—221no—
659#97—221no—
660C4×C8—21no—
661C4×C8—221no—
662C4×C8C22×D1111yescharacteristic
663C4×C8C22×D1111yescharacteristic
664C4×C8C22×D1111yescharacteristic
665C4×C8C22×D1111yescharacteristic
666C2×C11—22no—
667C2×C11—41no—
668C2×C11—41no—
669C2×C11#288011yescharacteristic
670C2×C11#289711yescharacteristic
671C2×C11C2×#42111yescharacteristic
672D11—42no—
673D11—81no—
674D11—81no—
675C24—221no—
676C24—221no—
677#41—42no—
678#41—222no—
679#41—441no—
680#41—881no—
681#41—881no—
682C2×Q8—111no—
683C2×Q8—221no—
684C2×Q8(C2×D11)⋊C411yescharacteristic
685C2×D4—111no—
686C2×D4—111no—
687C2×D4—111no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—221no—
691C2×D4—221no—
692C2×D4—221no—
693C2×D4—221no—
694C2×D4—221no—
695C2×D4—221no—
696C2×D4—221no—
697C2×D4—221no—
698C2×D4—221no—
699C2×D4—441no—
700C2×D4—441no—
701C2×D4—444no—
702C2×D4(C2×D11)⋊C411yescharacteristic
703C2×D4(C2×D11)⋊C411yescharacteristic
704C2×D4(C2×D11)⋊C411yescharacteristic
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—881no—
717C22×C4—881no—
718C22×C4—881no—
719C22×C4—881no—
720C22×C4C2×C4×D1111yescharacteristic
721C22×C4C2×C4×D1111yescharacteristic
722C22×C4C2×C4×D1111yescharacteristic
723C22×C4C2×D4411yescharacteristic
724C22×C4C2×D4411yescharacteristic
725C22×C4C2×D4411yescharacteristic
726C22×C4C2×C22⋊D1111yescharacteristic
727C22×C4C2×C22⋊D1111yescharacteristic
728C22×C4C2×C22⋊D1111yescharacteristic
729M16—42no—
730M16—881no—
731C2×C8—21no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—42no—
736C2×C8—221no—
737C2×C8—221no—
738C2×C8—221no—
739C2×C8—221no—
740C2×C8—881no—
741C2×C8—881no—
742C4⋊C4—111no—
743C4⋊C4—111no—
744C4⋊C4—111no—
745C4⋊C4—111no—
746C4⋊C4—221no—
747C4⋊C4—221no—
748C4⋊C4—221no—
749C4⋊C4—221no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4—221no—
753C4⋊C4—221no—
754C4⋊C4—221no—
755C4⋊C4—221no—
756C4⋊C4—221no—
757C4⋊C4(C2×D11)⋊C411yescharacteristic
758C4⋊C4(C2×D11)⋊C411yescharacteristic
759C4⋊C4(C2×D11)⋊C411yescharacteristic
760C4⋊C4(C2×D11)⋊C411yescharacteristic
761C4⋊C4(C2×D11)⋊C411yescharacteristic
762C4⋊C4(C2×D11)⋊C411yescharacteristic
763C22⋊C4—221no—
764C22⋊C4—221no—
765C22⋊C4—221no—
766C22⋊C4—221no—
767C22⋊C4—221no—
768C22⋊C4—221no—
769C22⋊C4—221no—
770C22⋊C4—221no—
771C22⋊C4—221no—
772C22⋊C4—221no—
773C22⋊C4—221no—
774C22⋊C4—221no—
775C22⋊C4—221no—
776C22⋊C4—221no—
777C22⋊C4—221no—
778C22⋊C4—221no—
779C22⋊C4—221no—
780C22⋊C4—221no—
781C22⋊C4—221no—
782C22⋊C4(C2×D11)⋊C411yescharacteristic
783C22⋊C4(C2×D11)⋊C411yescharacteristic
784C22⋊C4(C2×D11)⋊C411yescharacteristic
785C22⋊C4(C2×D11)⋊C411yescharacteristic
786C22⋊C4(C2×D11)⋊C411yescharacteristic
787C22⋊C4(C2×D11)⋊C411yescharacteristic
788C42—221no—
789C42—221no—
790C42—221no—
791C42C2×C4×D1111yescharacteristic
792C42C2×C4×D1111yescharacteristic
793C42C2×C4×D1111yescharacteristic
794C42C2×D4411yescharacteristic
795C42C2×D4411yescharacteristic
796C42C2×D4411yescharacteristic
797C42C2×C22⋊D1111yescharacteristic
798C42C2×C22⋊D1111yescharacteristic
799C42C2×C22⋊D1111yescharacteristic
800C42C23×D1111yescharacteristic
801C11#1752111yescharacteristic, complemented, Sylow
802C23—221no—
803C23—221no—
804C23—221no—
805C23—442no—
806C23—442no—
807C23—442no—
808C23—442no—
809C23—881no—
810C23—881no—
811C23C2×(C2×D11)⋊C411yescharacteristic
812C23C2×(C2×D11)⋊C411yescharacteristic
813C23C2×(C2×D11)⋊C411yescharacteristic
814Q8—41no—
815Q8—221no—
816Q8—221no—
817Q8—881no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—112no—
822D4—221no—
823D4—221no—
824D4—221no—
825D4—221no—
826D4—221no—
827D4—442no—
828D4—442no—
829D4—442no—
830D4—442no—
831D4—442no—
832D4—442no—
833D4—881no—
834D4—881no—
835D4—881no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—221no—
852C2×C4—221no—
853C2×C4—221no—
854C2×C4—221no—
855C2×C4—221no—
856C2×C4—442no—
857C2×C4—442no—
858C2×C4—441no—
859C2×C4—441no—
860C2×C4—441no—
861C2×C4—441no—
862C2×C4—441no—
863C2×C4—441no—
864C2×C4—881no—
865C2×C4—881no—
866C2×C4—881no—
867C2×C4—881no—
868C2×C4—881no—
869C2×C4—881no—
870C2×C4C2×(C2×D11)⋊C411yescharacteristic
871C2×C4C2×(C2×D11)⋊C411yescharacteristic
872C2×C4C2×(C2×D11)⋊C411yescharacteristic
873C2×C4C2×(C2×D11)⋊C411yescharacteristic
874C2×C4C2×(C2×D11)⋊C411yescharacteristic
875C2×C4C2×(C2×D11)⋊C411yescharacteristic
876C2×C4C2×(C2×D11)⋊C411yescharacteristic
877C2×C4C2×(C2×D11)⋊C411yescharacteristic
878C2×C4C2×(C2×D11)⋊C411yescharacteristic
879C2×C4C22×C4×D1111yescharacteristic
880C2×C4C22×D4411yescharacteristic
881C2×C4C22×C22⋊D1111yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—441no—
887C8—441no—
888C8—441no—
889C8—441no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—222no—
899C22—441no—
900C22—441no—
901C22—441no—
902C22—441no—
903C22—441no—
904C22—441no—
905C22—441no—
906C22—441no—
907C22—884no—
908C22—884no—
909C22#1062261812yes—
910C22C22×(C2×D11)⋊C411yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—441no—
922C4—441no—
923C4—441no—
924C4—441no—
925C4—441no—
926C4D11×#13111yescharacteristic
927C4#1062328111yescharacteristic
928C4#1062328211yescharacteristic
929C4#1062328311yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—442no—
934C2—881no—
935C2—881no—
936C2#1307706311yescharacteristic
937C2#1307714311yescharacteristic
938C2C2×#1062261811yescharacteristic
subgroupG/H
centerC2×C4C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2922C2
socleC22×C11C22×C22⋊C4
prime radical#13082226C2
cosocleC42×C11C24
hypercenter#2922D11
hypocenterC11#17521
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13077741C2semidirect
3. #13067086C2semidirect
4. #13067082C2semidirect
5. #13067077C2semidirect
6. #13067060C2semidirect
7. #13067051C2semidirect
8. #13067042C2semidirect
9. #13067030C2semidirect
10. #13067025C2semidirect
11. #13067016C2semidirect
12. #13067008C2semidirect
13. #13067004C2semidirect
14. C2×#10622097C2semidirect
15. C11×#2922C2semidirect
41. C11×#431C22semidirect
42. C11×#431C22semidirect
43. C11×#431C22semidirect
44. C11×#431C22semidirect
47. C4×C11×M16C22semidirect
48. C2×C4×C8×C11C22semidirect
53. #10622539C22semidirect
54. #10622539C22semidirect
55. #10622538C22semidirect
56. #10622537C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×C4⋊(C11⋊C8)C22semidirect
63. #10622097C22semidirect
64. #10622097C22semidirect
65. #10622097C22semidirect
66. #10622097C22semidirect
67. #10622097C22semidirect
68. #10622097C22semidirect
69. #10622097C22semidirect
70. #10622097C22semidirect
71. #10622094C22semidirect
72. #10622094C22semidirect
73. #10622094C22semidirect
74. #10622094C22semidirect
335. #2922D11semidirect
468. #431C2×D11semidirect
469. #431C2×D11semidirect
470. #431C2×D11semidirect
471. #431C2×D11semidirect
477. C4×M16C2×D11semidirect
478. C2×C4×C8C2×D11semidirect
801. C11#17521semidirect

Maximal subgroups

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

subgroupindex
#130822262
#130777412
#130670862
#130670822
#130670772
#130670602
#130670512
#130670422
#130670302
#130670252
#130670162
#130670082
#130670042
C2×#106220972
C11×#29222
#1752111