Finite Group Databasebeta

← #14769374

Subgroups — #14769374

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623360C211yesmaximal, characteristic
2C2×#10622741C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4#13071541C211yesmaximal, characteristic, complemented
5#13069545C211yesmaximal, characteristic, complemented
6#13069424C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069046C211yesmaximal, characteristic, complemented
9#13068933C211yesmaximal, characteristic, complemented
10#13068925C211yesmaximal, characteristic, complemented
11#13068624C211yesmaximal, characteristic, complemented
12#13068556C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#102×Dic11C211yesmaximal, characteristic, complemented
15C2×C11×#417C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic, complemented
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20#10623360—24no—
21#10623360C418yescomplemented
22C2×#67000C2211yescharacteristic
23C2×#66999C2211yescharacteristic
24C2×#66992—21no—
25C2×#66990—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66982—21no—
29C2×C4×C22⋊D11C2211yescharacteristic
30C22×(C2×D11)⋊C4—21no—
31C22×#4313C2211yescharacteristic
32C2×#66945C2211yescharacteristic
33C11×#417—24no—
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×#103C2211yescharacteristic, complemented
36C2×C11×#102C2211yescharacteristic
37C2×C11×#102C2211yescharacteristic
38C2×#66899C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622826—21no—
43#10622825C2211yescharacteristic, complemented
44C4×C22⋊Dic11—21no—
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46#10622741—24no—
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×(C2×D11)⋊C8C2211yescharacteristic
50C2×Dic11⋊C8C2211yescharacteristic, complemented
51C2×C8×Dic11C2211yescharacteristic, complemented
52#10622603—21no—
53#10622600C2211yescharacteristic
54#10622591—21no—
55#10622590C2211yescharacteristic, complemented
56C4⋊C4×Dic11C2211yescharacteristic, complemented
57C2×#66873C2211yescharacteristic
58C2×#66873C2211yescharacteristic
59#10622383—24no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—41no—
69C2×C11×#41—41no—
70C2×C11×#41C2×C414yes—
71C22×Q8×C11C2311yescharacteristic
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×C22⋊D11D411yescharacteristic
80C23×Dic11—21no—
81C2×D4×D11—22no—
82C2×D4×D11—22no—
83C2×D4×D11—22no—
84C2×D4×D11—41no—
85C2×D4×D11—41no—
86C2×D4×D11C2×C414yescomplemented
87C22×D44C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16—41no—
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C22⋊Dic11—21no—
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11D411yescharacteristic
102#67000—22no—
103#67000C2×C414yescomplemented
104#66999—22no—
105#66999C2×C414yescomplemented
106#66992—28no—
107#66990—28no—
108D4×Dic11—22no—
109D4×Dic11C2×C414yescomplemented
110#66983—22no—
111#66983C2×C414yes—
112#66982—28no—
113C4×C22⋊D11C2×C414yes—
114C4×C22⋊D11D414yes—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×(C2×D11)⋊C4—21no—
119C2×(C2×D11)⋊C4—28no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122C2×(C2×D11)⋊C4D411yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4D411yescharacteristic
128C2×C4×Dic11—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11C2311yescharacteristic
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C2×#4313—22no—
134C2×#4313—22no—
135C2×#4313—41no—
136#66945—22no—
137#66945—41no—
138C11×#103—22no—
139C11×#103—22no—
140C11×#102—22no—
141C11×#102D414yescomplemented
142#66899—41no—
143#66899—41no—
144#66896—22no—
145#66896—22no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C22⋊(C11⋊C8)—22no—
152#66885—22no—
153#66885—41no—
154(C2×D11)⋊C8—22no—
155Dic11⋊C8—22no—
156C8×Dic11—22no—
157#66873—22no—
158#66873—41no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—24no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—81no—
169C23×D11—81no—
170C23×D11C2×D411yescharacteristic
171C11×#41—28no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—21no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11C22×C412yes—
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11C22×C412yes—
188C2×D4×C11C2×D412yes—
189C2×D4×C11#4112yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—24no—
197C22×C4×C11—21no—
198C22×C4×C11—42no—
199C22×C4×C11—42no—
200C22×C4×C11—42no—
201C22×C4×C11—42no—
202C22×C4×C11—81no—
203C22×C4×C11C22×C412yes—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—41no—
210C2×C22⋊D11—41no—
211C2×C22⋊D11—42no—
212C2×C22⋊D11—42no—
213C2×C22⋊D11—81no—
214C2×C22⋊D11—81no—
215C2×C22⋊D11C22⋊C414yes—
216C22×Dic11—24no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—81no—
221C22×Dic11—81no—
222C22×Dic11C2×D411yescharacteristic
223C22×Dic11C2×D411yescharacteristic
224C22×Dic11C2×D411yescharacteristic
225D4×D11—28no—
226D4×D11—44no—
227D4×D11—44no—
228D4×D11—44no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44C22×C412yes—
235C2×C4×D11—21no—
236C2×C4×D11—21no—
237C2×C4×D11—21no—
238C2×C4×D11—21no—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C2×D412yes—
241C11×M16—44no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11C2×D412yes—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—42no—
252C11×C4⋊C4C2×D412yes—
253C22⋊Dic11—24no—
254C22⋊Dic11—42no—
255C22⋊Dic11C22⋊C414yes—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—81no—
262(C2×D11)⋊C4C22⋊C414yes—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11C22×C412yes—
269Dic11⋊C4—24no—
270Dic11⋊C4C22⋊C414yes—
271C4×Dic11—42no—
272C4×Dic11—81no—
273C4×Dic11C22×C412yes—
274C4×Dic11C2×D412yes—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8—21no—
281#4313—44no—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417D1111yescharacteristic, complemented
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—21no—
300C23×C11—22no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—22no—
319C22×D11—48no—
320C22×D11—48no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11C2×C22⋊C412yes—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—41no—
336Q8×C11—41no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—22no—
340D4×C11—48no—
341D4×C11C4×D414yes—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—48no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—84no—
359C2×C4×C11C2×C22⋊C412yes—
360C2×C4×C11C23×C411yescharacteristic
361C2×C4×C11C22×D411yescharacteristic
362C2×C4×C11C22×D411yescharacteristic
363C2×C4×C11C2×#4111yescharacteristic
364C2×C4×C11H(5,𝔽2)11yescharacteristic
365C2×C4×C11H(5,𝔽2)11yescharacteristic
366C22⋊D11—44no—
367C22⋊D11—48no—
368C22⋊D11—84no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
373C2×Dic11—21no—
374C2×Dic11—21no—
375C2×Dic11—22no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—84no—
385C2×Dic11C2×C22⋊C412yes—
386C2×Dic11C2×C22⋊C412yes—
387C2×Dic11C2×C22⋊C412yes—
388D44—22no—
389D44—22no—
390D44—41no—
391D44—41no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—22no—
396C8×C11—22no—
397C8×C11—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41C2×D1111yescharacteristic
401C23×D4—111no—
402C22×M16—111no—
403C22×M16C2×D1111yescharacteristic, complemented
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×#117—111no—
415C22×C4⋊C4C2×D1111yescharacteristic, complemented
416C22×C22⋊C4—221no—
417#436—224no—
418C2×C4⋊C8—111no—
419#418—224no—
420#417—24no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103C2×D1111yescharacteristic, complemented
424C2×#103C2×D1111yescharacteristic, complemented
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8—111no—
436#388—221no—
437#387—221no—
438#386—221no—
439#382—111no—
440#380—111no—
441#380—111no—
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—24no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—42no—
453C22×C11—42no—
454C22×C11—41no—
455C22×C11—42no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—41no—
460C22×C11—42no—
461C22×C11—41no—
462C22×C11C22×C22⋊C411yescharacteristic
463C22×C11D4211yescharacteristic
464C22×C11#54611yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57511yescharacteristic
467C22×C11#57611yescharacteristic
468C22×C11#57711yescharacteristic
469C2×D11—22no—
470C2×D11—22no—
471C2×D11—22no—
472C2×D11—41no—
473C2×D11—41no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C4×C11—22no—
485C4×C11—42no—
486C4×C11—42no—
487C4×C11—81no—
488C4×C11C2×C4×D411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11D4211yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—22no—
493Dic11—22no—
494Dic11—22no—
495Dic11—42no—
496Dic11—81no—
497Dic11—81no—
498C25—221no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41C4×D1114yes—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—21no—
507C22×D4—111no—
508C22×D4—114no—
509C22×D4—111no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—222no—
514C22×D4—221no—
515C22×D4—441no—
516C22×D4—441no—
517C22×D4C22×D1111yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—111no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—222no—
527C2×M16—222no—
528C2×M16—441no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—114no—
537C22⋊Q8—222no—
538#121—114no—
539#121—228no—
540#121—222no—
541#120—228no—
542C4×D4—114no—
543C4×D4—114no—
544C4×D4—114no—
545C4×D4—222no—
546#117—222no—
547#117—441no—
548C2×C4⋊C4—22no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—111no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—228no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C42—111no—
570C2×C42—221no—
571C2×C42—221no—
572C4⋊C8—222no—
573#103—22no—
574#103—22no—
575#103—441no—
576#103—441no—
577#102—22no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—441no—
583#102—441no—
584#102C22⋊D1114yescomplemented
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—221no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—44no—
594C2×C11—42no—
595C2×C11D4×C22⋊C411yescharacteristic
596C2×C11#289611yescharacteristic
597C2×C11#289711yescharacteristic
598C2×C11#327311yescharacteristic
599C2×C11#327511yescharacteristic
600C2×C11#332211yescharacteristic
601C2×C11#332311yescharacteristic
602D11—42no—
603D11—82no—
604C24—21no—
605C24—111no—
606C24—224no—
607C24—221no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—881no—
613C24—881no—
614C24D4×D1111yescharacteristic
615#41—28no—
616#41—44no—
617#41—44no—
618#41—44no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D1112yes—
625C2×D4—24no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—114no—
632C2×D4—112no—
633C2×D4—224no—
634C2×D4—228no—
635C2×D4—224no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—444no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—441no—
645C2×D4—441no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—881no—
649C2×D4—881no—
650C2×D4C2×C4×D1112yes—
651C2×D4#433912yes—
652C2×D4C2×C22⋊D1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—24no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—81no—
666C22×C4—111no—
667C22×C4—111no—
668C22×C4—111no—
669C22×C4—112no—
670C22×C4—112no—
671C22×C4—224no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—221no—
678C22×C4—221no—
679C22×C4—881no—
680C22×C4—881no—
681C22×C4C2×C4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—44no—
686M16—444no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8C2×C22⋊D1112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—42no—
703C4⋊C4—114no—
704C4⋊C4—112no—
705C4⋊C4—224no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4C2×C22⋊D1112yes—
712C22⋊C4—114no—
713C22⋊C4—114no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—442no—
720C22⋊C4—442no—
721C22⋊C4—881no—
722C42—112no—
723C42—112no—
724C42—442no—
725C42—881no—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—22no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—112no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—222no—
748C23—448no—
749C23—448no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23C22⋊C4×D1112yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—48no—
771D4—222no—
772D4—222no—
773D4—444no—
774D4—448no—
775D4—441no—
776D4—441no—
777D4—884no—
778D4C4×C22⋊D1114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—84no—
796C2×C4—112no—
797C2×C4—112no—
798C2×C4—112no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—884no—
819C2×C4C22⋊C4×D1112yes—
820C2×C4C22×C4×D1111yescharacteristic
821C2×C4C2×#433911yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#6703711yescharacteristic
825C2×C4C22×C22⋊D1111yescharacteristic
826C8—22no—
827C8—41no—
828C8—441no—
829C8—441no—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—22no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—42no—
844C22—222no—
845C22—222no—
846C22—222no—
847C22—441no—
848C22—441no—
849C22—441no—
850C22—441no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062302111yescharacteristic
861C22#1062330411yescharacteristic
862C22#1062330511yescharacteristic
863C22#1062330811yescharacteristic
864C22#1062330911yescharacteristic
865C22D4×C22⋊D1111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—81no—
870C4—222no—
871C4—222no—
872C4—222no—
873C4—442no—
874C4—881no—
875C4—881no—
876C4#1062301711yescharacteristic
877C4#1062302111yescharacteristic
878C4C2×C4×C22⋊D1111yescharacteristic
879C4D4×C22⋊D1111yescharacteristic
880C2—42no—
881C2—44no—
882C2—442no—
883C2—882no—
884C2C22⋊C4×C22⋊D1111yescharacteristic
885C2#1307713211yescharacteristic
886C2#1307714011yescharacteristic
887C2#1308022111yescharacteristic
888C2#1308024111yescharacteristic
889C2#1308081811yescharacteristic
890C2#1308083311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#417C2
socleC23×C11C22×D4
prime radicalC2×#10623360C2
cosocleC22×C4×C11C24
hypercenterC2×#417D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#10622741C2semidirect
3. C2×#10622383C2semidirect
4. #13071541C2semidirect
5. #13069545C2semidirect
6. #13069424C2semidirect
7. #13069054C2semidirect
8. #13069046C2semidirect
9. #13068933C2semidirect
10. #13068925C2semidirect
11. #13068624C2semidirect
12. #13068556C2semidirect
13. #13068545C2semidirect
14. #102×Dic11C2semidirect
15. C2×C11×#417C2semidirect
18. C22×C11×M16C22semidirect
19. C22×C11×C4⋊C4C22semidirect
21. #10623360C4semidirect
34. C2×C11×#103C22semidirect
35. C2×C11×#103C22semidirect
38. C2×#66899C22semidirect
39. C2×#66899C22semidirect
43. #10622825C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
50. C2×Dic11⋊C8C22semidirect
51. C2×C8×Dic11C22semidirect
55. #10622590C22semidirect
56. C4⋊C4×Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
86. C2×D4×D11C2×C4semidirect
103. #67000C2×C4semidirect
105. #66999C2×C4semidirect
109. D4×Dic11C2×C4semidirect
141. C11×#102D4semidirect
284. C2×#417D11semidirect
403. C22×M16C2×D11semidirect
415. C22×C4⋊C4C2×D11semidirect
423. C2×#103C2×D11semidirect
424. C2×#103C2×D11semidirect
584. #102C22⋊D11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106233602
C2×#106227412
C2×#106223832
#130715412
#130695452
#130694242
#130690542
#130690462
#130689332
#130689252
#130686242
#130685562
#130685452
#102×Dic112
C2×C11×#4172
#2242711