Finite Group Databasebeta

← #14769429

Subgroups — #14769429

Order 2816.

1582 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623365C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic, complemented
4C2×#10622416C211yesmaximal, characteristic, complemented
5#13071512C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069420C211yesmaximal, characteristic, complemented
8#13069052C211yesmaximal, characteristic, complemented
9#13069051C211yesmaximal, characteristic, complemented
10#13068931C211yesmaximal, characteristic, complemented
11#13068930C211yesmaximal, characteristic, complemented
12#13068619C211yesmaximal, characteristic, complemented
13#13068555C211yesmaximal, characteristic, complemented
14#103×Dic11C211yesmaximal, characteristic, complemented
15C11×#1788C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×#4343C2211yescharacteristic
18#10623365—24no—
19#10623365C418yescomplemented
20C2×Q8×Dic11C2211yescharacteristic
21C2×#66993—21no—
22C2×#66993C2211yescharacteristic
23C2×#66991—21no—
24C2×#66991C2211yescharacteristic
25C2×#66983—21no—
26C2×#66983C2211yescharacteristic
27C2×C4×C22⋊D11—21no—
28C2×C4×C22⋊D11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—21no—
34C2×C11×#103C2211yescharacteristic
35C2×C11×#103C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×C11×C22⋊C8C2211yescharacteristic
39C11×#380C2211yescharacteristic
40#10622845—24no—
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×(C2×D11)⋊C8C2211yescharacteristic
48C2×Dic11⋊C8C2211yescharacteristic
49C2×C8×Dic11C2211yescharacteristic
50#10622600C2211yescharacteristic
51#10622589C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54C2×#66873C2211yescharacteristic
55#10622559—21no—
56#10622416—24no—
57#10622342—24no—
58#10622281—21no—
59#10622260—21no—
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C2×C11×#41C2×C414yescomplemented
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11C2311yescharacteristic
73C23×C4×C11—21no—
74C23×C4×C11C2311yescharacteristic
75C22×C22⋊D11—21no—
76C22×C22⋊D11—21no—
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×C22⋊D11D411yescharacteristic
80C23×Dic11—21no—
81C2×#4343—22no—
82C2×#4343—22no—
83C2×#4343—22no—
84C2×#4343—41no—
85C2×#4343—41no—
86C2×#4343C2×C414yescomplemented
87C22×D44—21no—
88C22×D44C2311yescharacteristic
89C22×C4×D11—21no—
90C22×C4×D11—21no—
91C22×C4×D11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11D411yescharacteristic
99Q8×Dic11—22no—
100Q8×Dic11C2×C414yescomplemented
101#66993—28no—
102#66993—22no—
103#66993C2×C414yescomplemented
104#66991—22no—
105#66991—28no—
106#66991C2×C414yescomplemented
107#66983—22no—
108#66983—28no—
109#66983C2×C414yescomplemented
110C4×C22⋊D11—28no—
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4D411yescharacteristic
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—41no—
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4D411yescharacteristic
127C2×C4×Dic11—21no—
128C2×C4×Dic11—21no—
129C2×C4×Dic11C2311yescharacteristic
130C2×#4318—22no—
131C2×#4318—22no—
132C2×#4318—41no—
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C2×#4313—22no—
136C2×#4313—22no—
137C2×#4313—41no—
138C4⋊C4×D11—22no—
139C4⋊C4×D11—41no—
140(C22⋊D11)⋊C4—44no—
141C11×#103—22no—
142C11×#103—22no—
143C11×#102—41no—
144C11×#102—41no—
145C11×C22⋊C8—22no—
146C11×#95—21no—
147#66899—22no—
148#66899D414yescomplemented
149#66896—22no—
150#66896—22no—
151C11⋊#95—21no—
152C11⋊#95—21no—
153#66885—22no—
154#66885—41no—
155(C2×D11)⋊C8—22no—
156Dic11⋊C8—22no—
157C8×Dic11—22no—
158#66873—22no—
159#66873—41no—
160#22432—111nomaximal, Sylow
161C24×C11—21no—
162C24×C11C2×D411yescharacteristic
163C23×D11—21no—
164C23×D11C2×D411yescharacteristic
165C11×#41—28no—
166C11×#41—44no—
167C11×#41—44no—
168C11×#41—44no—
169C2×Q8×C11—21no—
170C2×Q8×C11—21no—
171C2×Q8×C11—21no—
172C2×Q8×C11C22×C412yes—
173C2×Q8×C11C2×D412yes—
174C2×Q8×C11#4112yes—
175C2×D4×C11—24no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—42no—
182C2×D4×C11—42no—
183C2×D4×C11C22×C412yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—24no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2411yescharacteristic
198C2×C22⋊D11—24no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—22no—
201C2×C22⋊D11—22no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11—81no—
209C2×C22⋊D11—81no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11C22⋊C414yes—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—42no—
217C22×Dic11—42no—
218C22×Dic11—81no—
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221C22×Dic11C2×D411yescharacteristic
222#4343—28no—
223#4343—44no—
224#4343—44no—
225#4343—44no—
226C2×D44—24no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—42no—
233C2×D44—42no—
234C2×D44C22×C412yes—
235C2×C4×D11—24no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11—21no—
240C2×C4×D11—42no—
241C2×C4×D11—42no—
242C2×C4×D11—42no—
243C2×C4×D11—42no—
244C2×C4×D11—81no—
245C2×C4×D11C22×C412yes—
246C2×C4×D11C2×D412yes—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4—21no—
255C11×C4⋊C4—21no—
256C11×C4⋊C4—21no—
257C11×C22⋊C4—42no—
258C22⋊Dic11—24no—
259C22⋊Dic11C22⋊C414yes—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4C22⋊C414yes—
263C4⋊Dic11—24no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—42no—
269C4⋊Dic11C22×C412yes—
270C4⋊Dic11C2×D412yes—
271Dic11⋊C4—42no—
272Dic11⋊C4—42no—
273Dic11⋊C4—81no—
274Dic11⋊C4C22⋊C414yes—
275C4×Dic11—24no—
276C4×Dic11—42no—
277C4×Dic11C22×C412yes—
278C4×Dic11C2×D412yes—
279#4318—44no—
280C2×C11⋊C8—21no—
281C2×C11⋊C8—21no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8C2×D412yes—
286#4313—44no—
287C2×#550—111no—
288C2×#436—111no—
289C2×#417—111no—
290C2×#417—111no—
291D4×C4⋊C4—111no—
292#1982—111no—
293#1957—111no—
294#1895—111no—
295#1895—111no—
296#1874—111no—
297#1874—111no—
298#1803—111no—
299#1788—111no—
300#1788D1111yescharacteristic, complemented
301C4×#103—111no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11C2×C22⋊C412yes—
316C23×C11C22×D411yescharacteristic
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—21no—
321C22×D11—21no—
322C22×D11—21no—
323C22×D11—22no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11C2×C22⋊C412yes—
331Q8×C11—22no—
332Q8×C11—22no—
333Q8×C11—22no—
334Q8×C11C4×D414yescomplemented
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—41no—
339D4×C11—41no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—21no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—48no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11C2×C22⋊C412yes—
357C2×C4×C11C23×C411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C22×D411yescharacteristic
360C2×C4×C11C2×#4111yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C2×C4×C11H(5,𝔽2)11yescharacteristic
363C22⋊D11—28no—
364C22⋊D11—48no—
365C22⋊D11—84no—
366C22⋊D11—84no—
367C22⋊D11—84no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—84no—
382C2×Dic11C2×C22⋊C412yes—
383C2×Dic11C2×C22⋊C412yes—
384C2×Dic11C2×C22⋊C412yes—
385C2×Dic11AGL(1,ℤ/8)12yes—
386C2×Dic11#13712yes—
387D44—22no—
388D44—22no—
389D44—48no—
390D44—41no—
391D44—41no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—22no—
396C4×D11—48no—
397C4×D11—84no—
398C8×C11—41no—
399C8×C11—41no—
400C11⋊C8—22no—
401C11⋊C8—41no—
402C22×#41—111no—
403C22×#41C2×D1111yescharacteristic
404C22×M16—111no—
405C22×M16—111no—
406#550—118no—
407#550—224no—
408C2×#127—111no—
409C2×#127—221no—
410C2×#121—111no—
411C2×#121—111no—
412C2×#121—221no—
413C2×#121—221no—
414C2×C4×Q8—111no—
415C2×C4×D4—111no—
416C2×C4×D4—221no—
417C2×C4×D4—221no—
418C22×C4⋊C4—111no—
419C22×C4⋊C4—111no—
420#436—224no—
421C2×C4⋊C8—111no—
422#417—224no—
423#417—224no—
424C2×#103—111no—
425C2×#103—111no—
426C2×#103C2×D1111yescharacteristic
427C2×#103C2×D1111yescharacteristic
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×#102—111no—
434C2×#102C2×D1111yescharacteristic
435C2×#102C2×D1111yescharacteristic
436C2×C22⋊C8—111no—
437C2×C22⋊C8C2×D1111yescharacteristic
438C2×C4×C8—111no—
439#389—221no—
440#385—221no—
441#385—221no—
442#384—111no—
443#380—111no—
444#380C2×D1111yescharacteristic
445C4×C4⋊C4—111no—
446#340—111no—
447#340—111no—
448#340—111no—
449#340—111no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—81no—
461C22×C11—81no—
462C22×C11—81no—
463C22×C11—81no—
464C22×C11C22×C22⋊C411yescharacteristic
465C22×C11D4211yescharacteristic
466C22×C11#54611yescharacteristic
467C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C11C2×#13711yescharacteristic
469C22×C11#57611yescharacteristic
470C22×C11#57711yescharacteristic
471C2×D11—22no—
472C2×D11—22no—
473C2×D11—22no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—41no—
477C2×D11—41no—
478C2×D11—42no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C2×D11—81no—
485C4×C11—22no—
486C4×C11—24no—
487C4×C11—81no—
488C4×C11—81no—
489C4×C11C2×C4×D411yescharacteristic
490C4×C11#51811yescharacteristic
491C4×C11D4211yescharacteristic
492C4×C11#54611yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—42no—
497Dic11—81no—
498Dic11#41714yescomplemented
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—114no—
505C2×#41—222no—
506C2×#41—222no—
507C2×#41—222no—
508C2×#41—441no—
509C2×#41—441no—
510C2×#41C4×D1114yescomplemented
511C22×Q8C22×D1111yescharacteristic
512C22×D4—21no—
513C22×D4—111no—
514C22×D4—111no—
515C22×D4—221no—
516C22×D4—221no—
517C22×D4—221no—
518C22×D4—221no—
519C22×D4—221no—
520C22×D4C22×D1111yescharacteristic
521C23×C4—21no—
522C23×C4—111no—
523C23×C4—221no—
524C23×C4—221no—
525C23×C4—221no—
526C23×C4C22×D1111yescharacteristic
527C2×M16—222no—
528C2×M16—222no—
529C2×M16—222no—
530C2×M16—222no—
531C2×M16—441no—
532C2×M16—441no—
533C22×C8—111no—
534C22×C8—111no—
535C22×C8C22×D1111yescharacteristic
536C22×C8C22×D1111yescharacteristic
537#127—114no—
538#127—222no—
539#127—228no—
540#121—114no—
541#121—114no—
542#121—228no—
543#121—228no—
544#121—222no—
545#121—222no—
546C4×Q8—114no—
547C4×Q8—222no—
548C4×D4—114no—
549C4×D4—114no—
550C4×D4—228no—
551C4×D4—444no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—111no—
556C2×C4⋊C4—222no—
557C2×C4⋊C4—222no—
558C2×C4⋊C4—221no—
559C2×C4⋊C4—221no—
560C2×C4⋊C4—221no—
561C2×C4⋊C4—221no—
562C2×C4⋊C4—221no—
563C2×C4⋊C4—441no—
564C2×C4⋊C4—441no—
565C2×C4⋊C4C22×D1111yescharacteristic
566C2×C4⋊C4C22×D1111yescharacteristic
567C2×C22⋊C4—21no—
568C2×C22⋊C4—111no—
569C2×C22⋊C4—111no—
570C2×C22⋊C4—221no—
571C2×C22⋊C4—221no—
572C2×C22⋊C4—221no—
573C2×C42—111no—
574C2×C42—221no—
575C2×C42—221no—
576C4⋊C8—222no—
577#103—22no—
578#103—22no—
579#103—114no—
580#103—222no—
581#102—41no—
582#102—41no—
583#102—222no—
584#102—222no—
585#102—222no—
586#102—222no—
587#102—441no—
588#102—441no—
589C22⋊C8—22no—
590C22⋊C8—222no—
591C4×C8—222no—
592#95—21no—
593#95—221no—
594#95—221no—
595C2×C11—42no—
596C2×C11—82no—
597C2×C11D4×C22⋊C411yescharacteristic
598C2×C11C2×#41711yescharacteristic
599C2×C11#289711yescharacteristic
600C2×C11#327411yescharacteristic
601C2×C11#327811yescharacteristic
602C2×C11#333211yescharacteristic
603C2×C11#333311yescharacteristic
604D11—42no—
605D11—82no—
606C24—21no—
607C24—111no—
608C24—221no—
609C24D4×D1111yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614#41—228no—
615#41—444no—
616#41—444no—
617#41—444no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C2×C4×D1112yes—
622C2×Q8D4×D1112yes—
623C2×Q8#434112yes—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—114no—
633C2×D4—112no—
634C2×D4—224no—
635C2×D4—222no—
636C2×D4—222no—
637C2×D4—224no—
638C2×D4—224no—
639C2×D4—224no—
640C2×D4—224no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—221no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4—881no—
653C2×D4—881no—
654C2×D4—881no—
655C2×D4—881no—
656C2×D4C2×C4×D1112yes—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—24no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—111no—
670C22×C4—112no—
671C22×C4—112no—
672C22×C4—224no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—442no—
681C22×C4—442no—
682C22×C4—442no—
683C22×C4—442no—
684C22×C4—442no—
685C22×C4—442no—
686C22×C4—881no—
687C22×C4—881no—
688C22×C4C2×C4×D1112yes—
689C22×C4D4×D1111yescharacteristic
690C22×C4D4×D1112yes—
691C22×C4C23×D1111yescharacteristic
692M16—444no—
693M16—444no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—112no—
701C2×C8—221no—
702C2×C8—221no—
703C2×C8—221no—
704C2×C8—221no—
705C2×C8—221no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—114no—
711C4⋊C4—112no—
712C4⋊C4—112no—
713C4⋊C4—224no—
714C4⋊C4—221no—
715C4⋊C4—221no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—442no—
719C4⋊C4—442no—
720C4⋊C4—442no—
721C4⋊C4—881no—
722C22⋊C4—42no—
723C22⋊C4—114no—
724C22⋊C4—114no—
725C22⋊C4—224no—
726C22⋊C4—224no—
727C22⋊C4—442no—
728C42—112no—
729C42—112no—
730C42—224no—
731C42—442no—
732C11#2243211yescharacteristic, complemented, Sylow
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—22no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—112no—
747C23—221no—
748C23—221no—
749C23—221no—
750C23—221no—
751C23—221no—
752C23—221no—
753C23—222no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23C22⋊C4×D1112yes—
761C23C2×D4×D1111yescharacteristic
762Q8—22no—
763Q8—22no—
764Q8—22no—
765Q8(C22⋊D11)⋊C414yescomplemented
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—228no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4—441no—
777D4—441no—
778D4—884no—
779D4—884no—
780D4—884no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—48no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—112no—
798C2×C4—112no—
799C2×C4—112no—
800C2×C4—112no—
801C2×C4—112no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—448no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—441no—
820C2×C4—884no—
821C2×C4—884no—
822C2×C4C22⋊C4×D1112yes—
823C2×C4C22×C4×D1111yescharacteristic
824C2×C4C2×D4×D1111yescharacteristic
825C2×C4C2×D4×D1111yescharacteristic
826C2×C4C2×#434111yescharacteristic
827C2×C4#6703711yescharacteristic
828C2×C4#6703711yescharacteristic
829C8—41no—
830C8—41no—
831C8—222no—
832C8—441no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—222no—
848C22—222no—
849C22—222no—
850C22—441no—
851C22—441no—
852C22—441no—
853C22—441no—
854C22—442no—
855C22—442no—
856C22—442no—
857C22—881no—
858C22—881no—
859C22—881no—
860C22—881no—
861C22C2×C22⋊C4×D1111yescharacteristic
862C22#1062312111yescharacteristic
863C22#1062312211yescharacteristic
864C22#1062330011yescharacteristic
865C22#1062330111yescharacteristic
866C22D11×AGL(1,ℤ/8)11yescharacteristic
867C22D11×#13711yescharacteristic
868C4—22no—
869C4—24no—
870C4—81no—
871C4—81no—
872C4—114no—
873C4—222no—
874C4—222no—
875C4—442no—
876C4—442no—
877C4—881no—
878C4C2×(C22⋊D11)⋊C411yescharacteristic
879C4#1062301711yescharacteristic
880C4#1062312111yescharacteristic
881C4#1062312211yescharacteristic
882C2—42no—
883C2—82no—
884C2—442no—
885C2—882no—
886C2#1307143211yescharacteristic
887C2D11×#41711yescharacteristic
888C2#1307713811yescharacteristic
889C2#1308022911yescharacteristic
890C2#1308027511yescharacteristic
891C2#1308093611yescharacteristic
892C2#1308094711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1788C2
socleC23×C11C22×D4
prime radicalC2×#10623365C2
cosocleC22×C4×C11C24
hypercenter#1788D11
hypocenterC11#22432
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. C2×#10622845C2semidirect
4. C2×#10622416C2semidirect
5. #13071512C2semidirect
6. #13069541C2semidirect
7. #13069420C2semidirect
8. #13069052C2semidirect
9. #13069051C2semidirect
10. #13068931C2semidirect
11. #13068930C2semidirect
12. #13068619C2semidirect
13. #13068555C2semidirect
14. #103×Dic11C2semidirect
15. C11×#1788C2semidirect
19. #10623365C4semidirect
69. C2×C11×#41C2×C4semidirect
86. C2×#4343C2×C4semidirect
100. Q8×Dic11C2×C4semidirect
103. #66993C2×C4semidirect
106. #66991C2×C4semidirect
109. #66983C2×C4semidirect
148. #66899D4semidirect
300. #1788D11semidirect
334. Q8×C11C4×D4semidirect
498. Dic11#417semidirect
510. C2×#41C4×D11semidirect
732. C11#22432semidirect
765. Q8(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#106233652
C2×#106223422
C2×#106228452
C2×#106224162
#130715122
#130695412
#130694202
#130690522
#130690512
#130689312
#130689302
#130686192
#130685552
#103×Dic112
C11×#17882
#2243211