Finite Group Databasebeta

← #14769262

Subgroups — #14769262

Order 2816.

1478 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C2×#10622615C211yesmaximal, characteristic, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069435C211yesmaximal, characteristic, complemented
7#13069047C211yesmaximal, characteristic, complemented
8#13069037C211yesmaximal, characteristic, complemented
9#13068928C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068554C211yesmaximal, characteristic, complemented
14#13068444C211yesmaximal, characteristic, complemented
15C11×#2352C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C22×#4339C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C2×#66991—21no—
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C23×C11⋊C8C2211yescharacteristic
26#10623082—24no—
27#10623082C418yescomplemented
28C2×C4⋊C4×D11—21no—
29C2×#66936—21no—
30C2×#66936—21no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C11×#388—21no—
34C11×#387—21no—
35C11×#386—21no—
36C11×#382C2211yescharacteristic
37C11×#380C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C4×C11×C4⋊C4C2211yescharacteristic
40C4×C11×C22⋊C4—21no—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622624—24no—
44#10622615—24no—
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53#10622579—24no—
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic
57C2×#66873C2211yescharacteristic
58C2×C4⋊(C11⋊C8)C2211yescharacteristic
59C2×#66867C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—22no—
76C2×#4339—41no—
77C2×#4339—41no—
78C2×#4339—41no—
79C2×#4339—41no—
80C2×#4339C2×C414yes—
81C2×#4339C2×C414yescomplemented
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×Dic22C2311yescharacteristic
87C22×Dic22C2311yescharacteristic
88C4×D4×C11C2×C414yes—
89C4×D4×C11D414yes—
90C11×#117—22no—
91C11×#117—41no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C4⋊C4D411yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C11×C22⋊C4—21no—
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C11×C22⋊C4D411yescharacteristic
105C2×C42×C11—21no—
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108C2×C22⋊Dic11—21no—
109C2×C22⋊Dic11—21no—
110#66991—28no—
111C2×(C2×D11)⋊C4—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11C2311yescharacteristic
115#66977—22no—
116#66977—22no—
117#66977C2×C414yes—
118#66977C2×C414yescomplemented
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C4⋊C4×D11—28no—
132#66936—28no—
133#66936—28no—
134C4×D44—22no—
135C4×D44C2×C414yescomplemented
136#66922—22no—
137#66922C2×C414yescomplemented
138C11×#95—21no—
139C11×#95—21no—
140C11×#95—21no—
141C11×#95—21no—
142C11×#95—21no—
143C22⋊(C11⋊C8)—22no—
144C22⋊(C11⋊C8)—22no—
145#66874—22no—
146#66874—22no—
147#66874—22no—
148#66874—22no—
149#66874—41no—
150#66874—41no—
151#66874—41no—
152#66874—41no—
153#66873—22no—
154#66873—22no—
155#66873—22no—
156#66873D414yescomplemented
157C4⋊(C11⋊C8)—22no—
158#66867—22no—
159#22420—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C2×D4×C11—41no—
164C2×D4×C11—41no—
165C2×D4×C11C22⋊C414yes—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—81no—
181C22×C4×C11C22×C412yes—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2411yescharacteristic
190C2×C22⋊D11—24no—
191C2×C22⋊D11—24no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—42no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199#4339—28no—
200#4339—28no—
201#4339—44no—
202#4339—44no—
203#4339—44no—
204#4339—44no—
205#4339—44no—
206#4339—44no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44C22×C412yes—
211C2×D44C2×D412yes—
212C2×D44#4112yes—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—42no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—21no—
230C2×Dic22—21no—
231C2×Dic22—21no—
232C2×Dic22C22×C412yes—
233C2×Dic22C22×C412yes—
234C11×C4⋊C4—21no—
235C11×C4⋊C4—21no—
236C11×C4⋊C4—21no—
237C11×C4⋊C4—21no—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—42no—
242C11×C4⋊C4C22⋊C414yes—
243C11×C4⋊C4C2×D412yes—
244C11×C22⋊C4—42no—
245C11×C22⋊C4—42no—
246C11×C22⋊C4—81no—
247C11×C22⋊C4C22⋊C414yes—
248C11×C22⋊C4C22⋊C414yes—
249C42×C11—42no—
250C42×C11—81no—
251C42×C11C22×C412yes—
252C42×C11C2×D412yes—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255(C2×D11)⋊C4—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—24no—
258C4⋊Dic11—21no—
259C4⋊Dic11C22×C412yes—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262#4318—44no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—44no—
275C2×C11⋊C8C2×D412yes—
276C2×#547—111no—
277C2×#435—111no—
278C2×#417—111no—
279C2×#416—111no—
280#2352D1111yescharacteristic, complemented
281#1981—111no—
282#1960—111no—
283#1894—111no—
284#1892—111no—
285#1873—111no—
286#1872—111no—
287#1804—111no—
288#1788—111no—
289#1788—111no—
290#1762—111no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11C2×C22⋊C412yes—
304C23×C11C2×C22⋊C412yes—
305C23×C11C22×D411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313D4×C11—44no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—41no—
334C2×C4×C11—41no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—84no—
343C2×C4×C11C2×C22⋊C412yes—
344C2×C4×C11C2×C22⋊C412yes—
345C2×C4×C11C2×C22⋊C412yes—
346C2×C4×C11C2×C22⋊C412yes—
347C2×C4×C11C23×C411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4111yescharacteristic
351C2×C4×C11H(5,𝔽2)11yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C22⋊D11—48no—
354C22⋊D11—48no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364D44—22no—
365D44—22no—
366D44—22no—
367D44C4×D414yes—
368C4×D11—48no—
369C4×D11—48no—
370C4×D11—48no—
371Dic22—22no—
372Dic22—22no—
373Dic22—22no—
374Dic22—22no—
375Dic22—41no—
376Dic22—41no—
377Dic22—41no—
378Dic22—41no—
379C11⋊C8—22no—
380C11⋊C8—41no—
381C11⋊C8—41no—
382C11⋊C8—41no—
383C22×#41—111no—
384C22×#41—111no—
385C22×M16—111no—
386C23×C8—111no—
387#547—118no—
388#547—224no—
389C2×C4⋊Q8—111no—
390C2×#123—221no—
391C2×#123—221no—
392C2×C22⋊Q8—111no—
393C2×C22⋊Q8—111no—
394C2×#121—221no—
395C2×C4×D4—111no—
396C2×C4×D4C2×D1111yescharacteristic
397C2×#117C2×D1111yescharacteristic
398C22×C4⋊C4—221no—
399C22×C4⋊C4C2×D1111yescharacteristic
400#435—224no—
401C2×C4⋊C8—111no—
402#417—224no—
403#416—224no—
404C2×#103—111no—
405C2×#103—111no—
406C2×#103—111no—
407C2×#103—111no—
408C2×#103—111no—
409C2×#103—111no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#102—111no—
413C2×#102—111no—
414C2×#102—111no—
415C2×#102—111no—
416C2×C22⋊C8—111no—
417C2×C22⋊C8—111no—
418C2×#97—111no—
419#388—21no—
420#387—21no—
421#386—21no—
422#382C2×D1111yescharacteristic
423#380C2×D1111yescharacteristic
424#380C2×D1111yescharacteristic
425C4×C4⋊C4C2×D1111yescharacteristic
426C4×C22⋊C4—21no—
427#340—111no—
428#340—111no—
429#340—111no—
430#340—111no—
431C22×C11—22no—
432C22×C11—22no—
433C22×C11—22no—
434C22×C11—22no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—41no—
438C22×C11—41no—
439C22×C11—41no—
440C22×C11—41no—
441C22×C11—41no—
442C22×C11—41no—
443C22×C11—41no—
444C22×C11—41no—
445C22×C11C22×C22⋊C411yescharacteristic
446C22×C11D4211yescharacteristic
447C22×C11#54611yescharacteristic
448C22×C11#57511yescharacteristic
449C22×C11#57511yescharacteristic
450C22×C11#57711yescharacteristic
451C22×C11#57811yescharacteristic
452C2×D11—24no—
453C2×D11—42no—
454C2×D11—42no—
455C2×D11—42no—
456C2×D11—42no—
457C2×D11—42no—
458C2×D11—42no—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11—22no—
462C4×C11—22no—
463C4×C11—42no—
464C4×C11—81no—
465C4×C11—81no—
466C4×C11—81no—
467C4×C11C2×C4×D411yescharacteristic
468C4×C11#51811yescharacteristic
469C4×C11D4211yescharacteristic
470C4×C11#54611yescharacteristic
471Dic11—42no—
472Dic11—42no—
473Dic11—42no—
474C2×#41—114no—
475C2×#41—114no—
476C2×#41—222no—
477C2×#41—222no—
478C2×#41—222no—
479C2×#41—222no—
480C2×#41—222no—
481C2×#41—222no—
482C2×#41—441no—
483C2×#41—441no—
484C2×#41—441no—
485C2×#41—441no—
486C22×Q8—111no—
487C22×Q8—111no—
488C22×D4—111no—
489C22×D4—221no—
490C22×D4—221no—
491C22×D4C22⋊D1111yescharacteristic
492C23×C4—21no—
493C23×C4—221no—
494C23×C4—221no—
495C23×C4—221no—
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C2×M16—222no—
499C2×M16—222no—
500C2×M16—441no—
501C22×C8—111no—
502C22×C8—111no—
503C22×C8—111no—
504C22×C8—111no—
505C22×C8—222no—
506C22×C8—222no—
507C22×C8—441no—
508C4⋊Q8—114no—
509C4⋊Q8—222no—
510#123—228no—
511#123—228no—
512C22⋊Q8—114no—
513C22⋊Q8—114no—
514C22⋊Q8—222no—
515C22⋊Q8—222no—
516#121—228no—
517C4×D4—114no—
518C4×D4—222no—
519C4×D4C4×D1114yes—
520C4×D4D4414yes—
521#117—22no—
522#117—41no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—41no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—221no—
528C2×C4⋊C4—221no—
529C2×C4⋊C4—221no—
530C2×C4⋊C4—221no—
531C2×C4⋊C4—228no—
532C2×C4⋊C4C22⋊D1111yescharacteristic
533C2×C4⋊C4C22×D1111yescharacteristic
534C2×C4⋊C4C22×D1111yescharacteristic
535C2×C4⋊C4C22×D1111yescharacteristic
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—221no—
541C2×C22⋊C4—221no—
542C2×C22⋊C4—221no—
543C2×C22⋊C4C22⋊D1111yescharacteristic
544C2×C22⋊C4C22⋊D1111yescharacteristic
545C2×C42—21no—
546C2×C42—21no—
547C2×C42C22×D1111yescharacteristic
548C4⋊C8—222no—
549#103—222no—
550#103—222no—
551#103—222no—
552#103—222no—
553#103—441no—
554#103—441no—
555#103—441no—
556#103—441no—
557#102—114no—
558#102—222no—
559#102—222no—
560#102—222no—
561C22⋊C8—222no—
562C22⋊C8—222no—
563#97—222no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569C2×C11—42no—
570C2×C11—42no—
571C2×C11D4×C22⋊C411yescharacteristic
572C2×C11#289611yescharacteristic
573C2×C11#289811yescharacteristic
574C2×C11#326711yescharacteristic
575C2×C11#326911yescharacteristic
576C2×C11#330711yescharacteristic
577C2×C11#331511yescharacteristic
578D11—44no—
579C24—221no—
580C24C2×C22⋊D1111yescharacteristic
581C24C2×C22⋊D1111yescharacteristic
582#41—228no—
583#41—228no—
584#41—444no—
585#41—444no—
586#41—444no—
587#41—444no—
588#41—444no—
589#41—444no—
590C2×Q8—112no—
591C2×Q8—112no—
592C2×Q8—221no—
593C2×Q8—221no—
594C2×Q8—221no—
595C2×Q8—221no—
596C2×Q8—221no—
597C2×Q8—221no—
598C2×Q8—221no—
599C2×Q8—221no—
600C2×Q8—221no—
601C2×Q8—221no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—112no—
605C2×D4—112no—
606C2×D4—112no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—221no—
610C2×D4—221no—
611C2×D4—221no—
612C2×D4—442no—
613C2×D4—442no—
614C2×D4—442no—
615C2×D4—442no—
616C2×D4(C2×D11)⋊C414yes—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—81no—
632C22×C4—221no—
633C22×C4—221no—
634C22×C4—221no—
635C22×C4—224no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4—442no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—442no—
644C22×C4C2×C4×D1112yes—
645C22×C4C2×C4×D1112yes—
646C22×C4C2×D4412yes—
647C22×C4C2×D4412yes—
648C22×C4C2×C22⋊D1111yescharacteristic
649C22×C4C2×C22⋊D1111yescharacteristic
650C22×C4C2×C22⋊D1111yescharacteristic
651C22×C4C2×C22⋊D1111yescharacteristic
652C22×C4C23×D1111yescharacteristic
653M16—444no—
654C2×C8—112no—
655C2×C8—221no—
656C2×C8—221no—
657C2×C8—221no—
658C2×C8—221no—
659C2×C8—221no—
660C2×C8—221no—
661C2×C8—221no—
662C2×C8—221no—
663C2×C8—221no—
664C2×C8—221no—
665C2×C8—221no—
666C2×C8—444no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—112no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—224no—
680C4⋊C4—221no—
681C4⋊C4(C2×D11)⋊C414yes—
682C4⋊C4D4×D1112yes—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—81no—
686C22⋊C4—224no—
687C22⋊C4—224no—
688C22⋊C4—224no—
689C22⋊C4(C2×D11)⋊C414yes—
690C22⋊C4(C2×D11)⋊C414yes—
691C42—42no—
692C42—81no—
693C42C2×C4×D1112yes—
694C42C2×D4412yes—
695C11#2242011yescharacteristic, complemented, Sylow
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—441no—
712C23—441no—
713C23—441no—
714C23—441no—
715C23C2×(C2×D11)⋊C412yes—
716C23C2×(C2×D11)⋊C412yes—
717C23C22×C22⋊D1111yescharacteristic
718Q8—222no—
719Q8—222no—
720Q8—222no—
721Q8—222no—
722Q8—441no—
723Q8—441no—
724Q8—441no—
725Q8—441no—
726D4—44no—
727D4—114no—
728D4—222no—
729D4—222no—
730D4—222no—
731D4—448no—
732D4—448no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—84no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—448no—
766C2×C4—448no—
767C2×C4—448no—
768C2×C4—441no—
769C2×C4—441no—
770C2×C4—441no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4C2×(C2×D11)⋊C412yes—
775C2×C4C2×(C2×D11)⋊C412yes—
776C2×C4C2×(C2×D11)⋊C412yes—
777C2×C4C2×(C2×D11)⋊C412yes—
778C2×C4C22×C4×D1111yescharacteristic
779C2×C4C22×D4411yescharacteristic
780C2×C4C2×D4×D1111yescharacteristic
781C2×C4#6703711yescharacteristic
782C2×C4#41×D1111yescharacteristic
783C2×C4#6704211yescharacteristic
784C8—222no—
785C8—441no—
786C8—441no—
787C8—441no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—224no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22C22×(C2×D11)⋊C411yescharacteristic
810C22D4×C22⋊D1111yescharacteristic
811C22#1062335311yescharacteristic
812C22#1062335311yescharacteristic
813C22#1062336011yescharacteristic
814C22#1062336711yescharacteristic
815C22#1062336911yescharacteristic
816C4—22no—
817C4—22no—
818C4—22no—
819C4—22no—
820C4—42no—
821C4—81no—
822C4—81no—
823C4—81no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4C4×D4×D1111yescharacteristic
828C4#1062307611yescharacteristic
829C4D4×D4411yescharacteristic
830C4#1062308511yescharacteristic
831C2—42no—
832C2—42no—
833C2—444no—
834C2D4×(C2×D11)⋊C411yescharacteristic
835C2#1307713311yescharacteristic
836C2#1307714611yescharacteristic
837C2#1308013711yescharacteristic
838C2#1308017211yescharacteristic
839C2#1308058611yescharacteristic
840C2#1308070611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2352C2
socleC23×C11C22×D4
prime radicalC2×#10623082C2
cosocleC22×C4×C11C24
hypercenter#2352D11
hypocenterC11#22420
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#10622624C2semidirect
3. C2×#10622579C2semidirect
4. C2×#10622615C2semidirect
5. #13069539C2semidirect
6. #13069435C2semidirect
7. #13069047C2semidirect
8. #13069037C2semidirect
9. #13068928C2semidirect
10. #13068923C2semidirect
11. #13068623C2semidirect
12. #13068554C2semidirect
13. #13068554C2semidirect
14. #13068444C2semidirect
15. C11×#2352C2semidirect
27. #10623082C4semidirect
81. C2×#4339C2×C4semidirect
118. #66977C2×C4semidirect
135. C4×D44C2×C4semidirect
137. #66922C2×C4semidirect
156. #66873D4semidirect
280. #2352D11semidirect
695. C11#22420semidirect

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106226242
C2×#106225792
C2×#106226152
#130695392
#130694352
#130690472
#130690372
#130689282
#130689232
#130686232
#130685542
#130684442
C11×#23522
#2242011