Finite Group Databasebeta

← #14769277

Subgroups — #14769277

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623083C211yesmaximal, characteristic
2C2×#10622624C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic, complemented
4C22×#66874C211yesmaximal, characteristic, complemented
5#13069548C211yesmaximal, characteristic, complemented
6#13069430C211yesmaximal, characteristic, complemented
7#13069047C211yesmaximal, characteristic, complemented
8#13069042C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068618C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068550C211yesmaximal, characteristic, complemented
14#13068449C211yesmaximal, characteristic, complemented
15D4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C2×C4×D4×C11—21no—
19C2×C4×D4×C11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C2×#66992—21no—
23C2×#66983C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27#10623083—24no—
28#10623083C418yescomplemented
29C2×#66949—21no—
30C2×#66938—21no—
31C2×(C22⋊D11)⋊C4—21no—
32C2×#66928C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#389—21no—
35C11×#385—21no—
36C11×#385—21no—
37C11×#384C2211yescharacteristic
38C11×#380C2211yescharacteristic
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2211yescharacteristic
43#10622624—24no—
44C2×#66874—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×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C23×Dic11—21no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—22no—
75C2×#4339—41no—
76C2×#4339—41no—
77C2×#4339C2×C414yescomplemented
78C22×D44C2311yescharacteristic
79C22×C4×D11—21no—
80C22×Dic22—22no—
81C22×Dic22—22no—
82C22×Dic22—21no—
83C22×Dic22—22no—
84C22×Dic22—41no—
85C22×Dic22—41no—
86C22×Dic22C2×C414yescomplemented
87C22×Dic22C2311yescharacteristic
88C22×Dic22C2311yescharacteristic
89C4×D4×C11—44no—
90C4×D4×C11C2×C414yes—
91C4×D4×C11D414yes—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—21no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—41no—
99C2×C11×C4⋊C4—41no—
100C2×C11×C4⋊C4D411yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C11×C22⋊C4D411yescharacteristic
108C2×C11×C22⋊C4D411yescharacteristic
109C2×C42×C11—21no—
110C2×C42×C11C2311yescharacteristic
111C2×C22⋊Dic11—21no—
112#66992—28no—
113#66983—22no—
114#66983C2×C414yescomplemented
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×C4⋊Dic11C2311yescharacteristic
119#66977—22no—
120#66977C2×C414yescomplemented
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×C4×Dic11—21no—
124C2×#4318—22no—
125C2×#4318—22no—
126C2×#4318—41no—
127C22×C11⋊C8—22no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—41no—
130C22×C11⋊C8C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134#66949—28no—
135#66938—28no—
136(C22⋊D11)⋊C4—28no—
137#66928—22no—
138#66928C2×C414yescomplemented
139C4×Dic22—22no—
140C4×Dic22C2×C414yescomplemented
141C11×#95—21no—
142C11×#95—21no—
143C11×#95—21no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)—22no—
146#66874—22no—
147#66874—22no—
148#66874—22no—
149#66874—22no—
150#66874—22no—
151#66874—41no—
152#66874—41no—
153#66874D414yescomplemented
154#66873—22no—
155#66873—22no—
156#66873—41no—
157#66873—41no—
158C4⋊(C11⋊C8)—22no—
159#66867—22no—
160#22421—111nomaximal, Sylow
161C24×C11C2×D411yescharacteristic
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11C22⋊C414yes—
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—21no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—81no—
184C22×C4×C11—81no—
185C22×C4×C11C22×C412yes—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2411yescharacteristic
194C2×C22⋊D11—24no—
195C2×C22⋊D11—24no—
196C2×C22⋊D11—42no—
197C2×C22⋊D11—42no—
198C2×C22⋊D11—42no—
199C2×C22⋊D11—42no—
200C22×Dic11—24no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—42no—
205C22×Dic11—42no—
206#4339—28no—
207#4339—44no—
208#4339—44no—
209#4339—44no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44C22×C412yes—
216C2×C4×D11—24no—
217C2×C4×D11—42no—
218C2×C4×D11—42no—
219C2×Dic22—28no—
220C2×Dic22—24no—
221C2×Dic22—21no—
222C2×Dic22—21no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22—21no—
229C2×Dic22—44no—
230C2×Dic22—44no—
231C2×Dic22—44no—
232C2×Dic22—42no—
233C2×Dic22—42no—
234C2×Dic22C22×C412yes—
235C2×Dic22C22×C412yes—
236C2×Dic22C2×D412yes—
237C2×Dic22#4112yes—
238C11×C4⋊C4—21no—
239C11×C4⋊C4—21no—
240C11×C4⋊C4—21no—
241C11×C4⋊C4—21no—
242C11×C4⋊C4—21no—
243C11×C4⋊C4—21no—
244C11×C4⋊C4—21no—
245C11×C4⋊C4—42no—
246C11×C4⋊C4—42no—
247C11×C4⋊C4—42no—
248C11×C4⋊C4—81no—
249C11×C4⋊C4C22⋊C414yes—
250C11×C4⋊C4C2×D412yes—
251C11×C22⋊C4—42no—
252C11×C22⋊C4—42no—
253C11×C22⋊C4C22⋊C414yes—
254C11×C22⋊C4C22⋊C414yes—
255C42×C11—42no—
256C42×C11C22×C412yes—
257C42×C11C2×D412yes—
258C22⋊Dic11—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262C4⋊Dic11—21no—
263C4⋊Dic11C22×C412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266C4×Dic11—24no—
267#4318—44no—
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—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—44no—
280C2×C11⋊C8C2×D412yes—
281C2×#548—111no—
282C2×#435—111no—
283C2×#417—111no—
284C22×#103—111no—
285D4×C4⋊C4D1111yescharacteristic, complemented
286#1983—111no—
287#1959—111no—
288#1894—111no—
289#1893—111no—
290#1874—111no—
291#1872—111no—
292#1803—111no—
293#1788—111no—
294#1787—111no—
295#1763—111no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11C2×C22⋊C412yes—
307C23×C11C2×C22⋊C412yes—
308C23×C11AGL(1,ℤ/8)12yes—
309C23×C11#13712yes—
310C23×C11C22×D411yescharacteristic
311C22×D11—22no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318D4×C11—28no—
319C2×C4×C11—21no—
320C2×C4×C11—21no—
321C2×C4×C11—21no—
322C2×C4×C11—21no—
323C2×C4×C11—21no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
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—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—84no—
348C2×C4×C11—84no—
349C2×C4×C11C2×C22⋊C412yes—
350C2×C4×C11C2×C22⋊C412yes—
351C2×C4×C11C2×C22⋊C412yes—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C23×C411yescharacteristic
354C2×C4×C11C22×D411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C2×#4111yescharacteristic
357C2×C4×C11H(5,𝔽2)11yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C22⋊D11—48no—
360C22⋊D11—48no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—48no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371D44—22no—
372D44—22no—
373D44—41no—
374D44—41no—
375C4×D11—48no—
376Dic22—22no—
377Dic22—22no—
378Dic22—22no—
379Dic22—22no—
380Dic22—22no—
381Dic22—48no—
382Dic22—41no—
383Dic22—41no—
384Dic22C4×D414yescomplemented
385C11⋊C8—22no—
386C11⋊C8—41no—
387C11⋊C8—41no—
388C11⋊C8—41no—
389C22×#41—111no—
390C23×Q8—111no—
391C22×M16—111no—
392C23×C8—111no—
393#548—118no—
394#548—224no—
395C2×#124—111no—
396C2×#124—221no—
397C2×C22⋊Q8—111no—
398C2×C22⋊Q8—221no—
399C2×#121—111no—
400C2×#121—221no—
401C2×C4×Q8—111no—
402C2×C4×D4—21no—
403C2×C4×D4—221no—
404C2×C4×D4C2×D1111yescharacteristic
405C22×C4⋊C4C2×D1111yescharacteristic
406C22×C4⋊C4C2×D1111yescharacteristic
407#435—224no—
408C2×C4⋊C8—111no—
409#417—224no—
410C2×#103—111no—
411C2×#103—111no—
412C2×#103—111no—
413C2×#103—111no—
414C2×#103—111no—
415C2×#103—111no—
416C2×#103—111no—
417C2×#103—111no—
418C2×#103—224no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×C22⋊C8—111no—
424C2×C22⋊C8—111no—
425C2×#97—111no—
426#389—21no—
427#385—21no—
428#385—21no—
429#384C2×D1111yescharacteristic
430#380C2×D1111yescharacteristic
431#380C2×D1111yescharacteristic
432C4×C4⋊C4C2×D1111yescharacteristic
433#340—111no—
434#340—111no—
435#340—111no—
436#340—111no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—41no—
447C22×C11—41no—
448C22×C11—41no—
449C22×C11—41no—
450C22×C11#41714yescomplemented
451C22×C11C22×C22⋊C411yescharacteristic
452C22×C11D4211yescharacteristic
453C22×C11#54611yescharacteristic
454C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
455C22×C11C2×#13711yescharacteristic
456C22×C11#57711yescharacteristic
457C22×C11#57811yescharacteristic
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—42no—
461C2×D11—81no—
462C2×D11—81no—
463C2×D11—81no—
464C2×D11—81no—
465C4×C11—22no—
466C4×C11—22no—
467C4×C11—22no—
468C4×C11—22no—
469C4×C11—42no—
470C4×C11—81no—
471C4×C11—81no—
472C4×C11—81no—
473C4×C11C2×C4×D411yescharacteristic
474C4×C11#51811yescharacteristic
475C4×C11D4211yescharacteristic
476C4×C11#54611yescharacteristic
477Dic11—24no—
478Dic11—42no—
479Dic11—42no—
480C2×#41—114no—
481C2×#41—222no—
482C2×#41—222no—
483C2×#41—222no—
484C2×#41—441no—
485C2×#41—441no—
486C22×Q8—114no—
487C22×Q8—111no—
488C22×Q8—111no—
489C22×Q8—222no—
490C22×Q8—222no—
491C22×Q8—222no—
492C22×Q8—221no—
493C22×Q8—441no—
494C22×Q8—441no—
495C22×D4—111no—
496C22×D4—221no—
497C22×D4—221no—
498C22×D4C22⋊D1111yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—221no—
502C23×C4—221no—
503C23×C4C22×D1111yescharacteristic
504C23×C4C22×D1111yescharacteristic
505C2×M16—222no—
506C2×M16—222no—
507C2×M16—441no—
508C22×C8—111no—
509C22×C8—111no—
510C22×C8—111no—
511C22×C8—111no—
512C22×C8—222no—
513C22×C8—222no—
514C22×C8—441no—
515#124—114no—
516#124—228no—
517#124—222no—
518C22⋊Q8—114no—
519C22⋊Q8—222no—
520C22⋊Q8—228no—
521#121—114no—
522#121—228no—
523#121—222no—
524C4×Q8—114no—
525C4×Q8—222no—
526C4×D4—44no—
527C4×D4—228no—
528C4×D4C4×D1114yes—
529C4×D4D4414yes—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—111no—
539C2×C4⋊C4—221no—
540C2×C4⋊C4—221no—
541C2×C4⋊C4C22⋊D1111yescharacteristic
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1111yescharacteristic
545C2×C4⋊C4C22×D1111yescharacteristic
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—221no—
549C2×C22⋊C4—221no—
550C2×C22⋊C4—221no—
551C2×C22⋊C4—221no—
552C2×C22⋊C4C22⋊D1111yescharacteristic
553C2×C22⋊C4C22⋊D1111yescharacteristic
554C2×C42—21no—
555C2×C42—221no—
556C2×C42C22×D1111yescharacteristic
557C4⋊C8—222no—
558#103—114no—
559#103—222no—
560#103—222no—
561#103—222no—
562#103—222no—
563#103—222no—
564#103—441no—
565#103—441no—
566#102—222no—
567#102—222no—
568#102—441no—
569#102—441no—
570C22⋊C8—222no—
571C22⋊C8—222no—
572#97—222no—
573#95—21no—
574#95—21no—
575#95—21no—
576C2×C11—24no—
577C2×C11—42no—
578C2×C11D4×C22⋊C411yescharacteristic
579C2×C11C2×#41711yescharacteristic
580C2×C11#289811yescharacteristic
581C2×C11#326511yescharacteristic
582C2×C11#327011yescharacteristic
583C2×C11#330811yescharacteristic
584C2×C11#331611yescharacteristic
585D11—82no—
586C24—221no—
587C24C2×C22⋊D1111yescharacteristic
588C24C2×C22⋊D1111yescharacteristic
589#41—228no—
590#41—444no—
591#41—444no—
592#41—444no—
593C2×Q8—112no—
594C2×Q8—112no—
595C2×Q8—112no—
596C2×Q8—112no—
597C2×Q8—228no—
598C2×Q8—224no—
599C2×Q8—221no—
600C2×Q8—221no—
601C2×Q8—221no—
602C2×Q8—221no—
603C2×Q8—221no—
604C2×Q8—221no—
605C2×Q8—221no—
606C2×Q8—221no—
607C2×Q8—442no—
608C2×Q8—442no—
609C2×Q8—444no—
610C2×Q8—444no—
611C2×Q8—444no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—112no—
615C2×D4—224no—
616C2×D4—224no—
617C2×D4—221no—
618C2×D4—221no—
619C2×D4—221no—
620C2×D4—221no—
621C2×D4—221no—
622C2×D4—442no—
623C2×D4—442no—
624C2×D4—442no—
625C2×D4—442no—
626C2×D4(C2×D11)⋊C414yes—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4—221no—
646C22×C4—224no—
647C22×C4—221no—
648C22×C4—221no—
649C22×C4—224no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4C2×C4×D1112yes—
655C22×C4C2×C4×D1112yes—
656C22×C4C2×D4412yes—
657C22×C4C2×D4412yes—
658C22×C4C2×C22⋊D1111yescharacteristic
659C22×C4C2×C22⋊D1111yescharacteristic
660C22×C4C2×C22⋊D1111yescharacteristic
661C22×C4C2×C22⋊D1111yescharacteristic
662C22×C4C23×D1111yescharacteristic
663M16—444no—
664C2×C8—112no—
665C2×C8—221no—
666C2×C8—221no—
667C2×C8—221no—
668C2×C8—221no—
669C2×C8—221no—
670C2×C8—221no—
671C2×C8—221no—
672C2×C8—221no—
673C2×C8—221no—
674C2×C8—221no—
675C2×C8—221no—
676C2×C8—444no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—81no—
688C4⋊C4—112no—
689C4⋊C4—224no—
690C4⋊C4—224no—
691C4⋊C4—221no—
692C4⋊C4(C2×D11)⋊C414yes—
693C4⋊C4D4×D1112yes—
694C22⋊C4—42no—
695C22⋊C4—42no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4(C2×D11)⋊C414yes—
701C22⋊C4(C2×D11)⋊C414yes—
702C42—42no—
703C42—224no—
704C42C2×C4×D1112yes—
705C42C2×D4412yes—
706C11#2242111yescharacteristic, complemented, Sylow
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—222no—
718C23—441no—
719C23—441no—
720C23—441no—
721C23—441no—
722C23—441no—
723C23—441no—
724C23C2×(C2×D11)⋊C412yes—
725C23C2×(C2×D11)⋊C412yes—
726C23#6698512yes—
727C23#6699512yes—
728C23C22×C22⋊D1111yescharacteristic
729Q8—114no—
730Q8—222no—
731Q8—222no—
732Q8—222no—
733Q8—222no—
734Q8—222no—
735Q8—448no—
736Q8—441no—
737Q8—441no—
738D4—28no—
739D4—222no—
740D4—222no—
741D4—448no—
742D4—448no—
743D4—441no—
744D4—441no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—448no—
781C2×C4—448no—
782C2×C4—441no—
783C2×C4—441no—
784C2×C4—441no—
785C2×C4—441no—
786C2×C4C2×(C2×D11)⋊C412yes—
787C2×C4C2×(C2×D11)⋊C412yes—
788C2×C4C2×(C2×D11)⋊C412yes—
789C2×C4C2×(C2×D11)⋊C412yes—
790C2×C4C22×C4×D1111yescharacteristic
791C2×C4C22×D4411yescharacteristic
792C2×C4C2×D4×D1111yescharacteristic
793C2×C4#6703711yescharacteristic
794C2×C4#41×D1111yescharacteristic
795C2×C4#6704211yescharacteristic
796C8—222no—
797C8—441no—
798C8—441no—
799C8—441no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—442no—
814C22—442no—
815C22—442no—
816C22—881no—
817C22—881no—
818C22—881no—
819C22—881no—
820C22#1062257914yescomplemented
821C22C22×(C2×D11)⋊C411yescharacteristic
822C22C2×#6698511yescharacteristic
823C22D4×C22⋊D1111yescharacteristic
824C22C2×#6699511yescharacteristic
825C22#1062336011yescharacteristic
826C22#1062336711yescharacteristic
827C22#1062336911yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—224no—
837C4—442no—
838C4—442no—
839C4C4×D4×D1111yescharacteristic
840C4#1062307611yescharacteristic
841C4D4×D4411yescharacteristic
842C4#1062308511yescharacteristic
843C2—24no—
844C2—42no—
845C2—882no—
846C2D4×(C2×D11)⋊C411yescharacteristic
847C2C2×#1062257911yescharacteristic
848C2#1307714611yescharacteristic
849C2#1308010711yescharacteristic
850C2#1308018711yescharacteristic
851C2#1308060111yescharacteristic
852C2#1308072111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC2×#10623083C2
cosocleC22×C4×C11C24
hypercenterD4×C4⋊C4D11
hypocenterC11#22421
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622624C2semidirect
3. C2×#10622579C2semidirect
4. C22×#66874C2semidirect
5. #13069548C2semidirect
6. #13069430C2semidirect
7. #13069047C2semidirect
8. #13069042C2semidirect
9. #13068933C2semidirect
10. #13068923C2semidirect
11. #13068618C2semidirect
12. #13068554C2semidirect
13. #13068550C2semidirect
14. #13068449C2semidirect
15. D4×C11×C4⋊C4C2semidirect
28. #10623083C4semidirect
77. C2×#4339C2×C4semidirect
86. C22×Dic22C2×C4semidirect
114. #66983C2×C4semidirect
120. #66977C2×C4semidirect
138. #66928C2×C4semidirect
140. C4×Dic22C2×C4semidirect
153. #66874D4semidirect
285. D4×C4⋊C4D11semidirect
384. Dic22C4×D4semidirect
450. C22×C11#417semidirect
706. C11#22421semidirect
820. C22#10622579semidirect

Maximal subgroups

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

subgroupindex
C2×#106230832
C2×#106226242
C2×#106225792
C22×#668742
#130695482
#130694302
#130690472
#130690422
#130689332
#130689232
#130686182
#130685542
#130685502
#130684492
D4×C11×C4⋊C42
#2242111