Finite Group Databasebeta

← #14769188

Subgroups — #14769188

Order 2816.

1638 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×#10623161C211yesmaximal, characteristic
2C2×(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
3C2×#10622417C211yesmaximal, characteristic, complemented
4C22×#66873C211yesmaximal, characteristic, complemented
5#13071541C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069424C211yesmaximal, characteristic, complemented
8#13069043C211yesmaximal, characteristic, complemented
9#13069040C211yesmaximal, characteristic, complemented
10#13068937C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1872C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C22×C8×D11C2211yescharacteristic, complemented
24#10623161—24no—
25#10623161C418yescomplemented
26C2×#66948—21no—
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic, complemented
31C2×#66935—21no—
32C2×C22⋊C4×D11—21no—
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×#66899C2211yescharacteristic, complemented
37C2×#66899C2211yescharacteristic, complemented
38#10622826—21no—
39#10622825C2211yescharacteristic
40C4×C22⋊Dic11—21no—
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×Dic11⋊C8C2211yescharacteristic, complemented
47C2×C8×Dic11C2211yescharacteristic, complemented
48#10622603—21no—
49#10622600C2211yescharacteristic, complemented
50#10622591—21no—
51#10622590C2211yescharacteristic, complemented
52C4⋊C4×Dic11C2211yescharacteristic, complemented
53C2×#66873—24no—
54C2×#66873C2211yescharacteristic
55C2×#66873C2211yescharacteristic
56C2×#66873C2211yescharacteristic
57C2×#66873C2211yescharacteristic
58#10622417—24no—
59(C22⋊D11)⋊C8—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11—21no—
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11D411yescharacteristic
69C2×#4343—22no—
70C2×#4343—22no—
71C2×#4343—22no—
72C2×#4343—41no—
73C2×#4343—41no—
74C2×#4343C2×C414yescomplemented
75C22×D44—22no—
76C22×D44—22no—
77C22×D44—21no—
78C22×D44—21no—
79C22×D44—22no—
80C22×D44—21no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44C2×C414yes—
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8C2×C414yes—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C22⋊C4—21no—
101C2×C22⋊Dic11—21no—
102C2×C22⋊Dic11D411yescharacteristic
103#67000—22no—
104#67000C2×C414yescomplemented
105C4×C22⋊D11C2×C414yes—
106C4×C22⋊D11D414yes—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×Dic11⋊C4D411yescharacteristic
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11C2311yescharacteristic
120C22×C11⋊C8—22no—
121C22×C11⋊C8—22no—
122C22×C11⋊C8—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C2×C8×D11—22no—
126C2×C8×D11—22no—
127C2×C8×D11—41no—
128#66948—22no—
129#66948—28no—
130#66948C2×C414yescomplemented
131#66947—28no—
132#66946—22no—
133#66946C2×C414yescomplemented
134#66945—22no—
135#66945—41no—
136#66935—28no—
137C22⋊C4×D11—28no—
138C11×#103—22no—
139C11×#103—41no—
140C11×C22⋊C8—22no—
141#66899—22no—
142#66899—41no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148#66885—22no—
149#66885—22no—
150#66885—41no—
151#66885—41no—
152(C2×D11)⋊C8—22no—
153Dic11⋊C8—22no—
154C8×Dic11—22no—
155#66873—22no—
156#66873—22no—
157#66873—22no—
158#66873D414yescomplemented
159#22414—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C23×D11—21no—
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
171C2×Q8×C11—21no—
172C2×Q8×C11—21no—
173C2×Q8×C11—21no—
174C2×Q8×C11—21no—
175C2×Q8×C11—21no—
176C2×Q8×C11C22×C412yes—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11—81no—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11C22⋊C414yes—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200#4343—28no—
201#4343—44no—
202#4343—44no—
203#4343—44no—
204C2×D44—24no—
205C2×D44—24no—
206C2×D44—28no—
207C2×D44—24no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—42no—
217C2×D44—42no—
218C2×D44—44no—
219C2×D44—44no—
220C2×D44—44no—
221C2×D44—42no—
222C2×D44—42no—
223C2×D44—81no—
224C2×D44—81no—
225C2×D44C22×C412yes—
226C2×D44C22×C412yes—
227C2×D44C2×D412yes—
228C2×D44#4112yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—21no—
232C2×C4×D11—21no—
233C2×C4×D11—21no—
234C2×C4×D11—21no—
235C2×C4×D11—42no—
236C2×C4×D11—42no—
237C2×C4×D11—81no—
238C2×C4×D11—81no—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C2×D412yes—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C11×C4⋊C4—24no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—42no—
253C11×C4⋊C4C22×C412yes—
254C11×C4⋊C4C2×D412yes—
255C11×C22⋊C4—24no—
256C22⋊Dic11—42no—
257C22⋊Dic11C22⋊C414yes—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4—81no—
264(C2×D11)⋊C4C22⋊C414yes—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269Dic11⋊C4C22⋊C414yes—
270C4×Dic11—42no—
271C4×Dic11—81no—
272C4×Dic11C22×C412yes—
273C4×Dic11C2×D412yes—
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—
281C8×D11—44no—
282C2×#546—111no—
283C2×C8×D4—111no—
284C2×#416—111no—
285C22×#102—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1893—111no—
290#1892—111no—
291#1875—111no—
292#1872D1111yescharacteristic, complemented
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11C2×C22⋊C412yes—
302C23×C11#13512yes—
303C23×C11#13512yes—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—21no—
307C22×D11—22no—
308C22×D11—21no—
309C22×D11—22no—
310C22×D11—21no—
311C22×D11—21no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—22no—
315C22×D11—48no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—48no—
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—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—84no—
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—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—21no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11C2×C22⋊C412yes—
377C2×Dic11C2×C22⋊C412yes—
378C2×Dic11C2×C22⋊C412yes—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—48no—
385D44—48no—
386D44—41no—
387D44—41no—
388D44—84no—
389D44C4×D414yes—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—22no—
394C4×D11—48no—
395C4×D11—84no—
396C8×C11—41no—
397C8×C11—41no—
398C11⋊C8—22no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4—111no—
402C23×C8—111no—
403C23×C8—111no—
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8C2×D1111yescharacteristic
409C2×#121—111no—
410C2×#121—221no—
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4—111no—
414C2×#117—111no—
415C22×C4⋊C4C2×D1111yescharacteristic
416C22×C22⋊C4—221no—
417C8×D4—224no—
418C2×C4⋊C8—111no—
419#416—224no—
420C2×#103—111no—
421C2×#103—111no—
422C2×#103C2×D1111yescharacteristic, complemented
423C2×#103C2×D1111yescharacteristic, complemented
424C2×#102—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—224no—
433C2×C22⋊C8—111no—
434C2×C22⋊C8C2×D1111yescharacteristic
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#340C2×D1111yescharacteristic, complemented
447#340C2×D1111yescharacteristic, complemented
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11#41614yescomplemented
455C22×C11C22×C22⋊C411yescharacteristic
456C22×C11D4211yescharacteristic
457C22×C11#54611yescharacteristic
458C22×C11C2×#13511yescharacteristic
459C22×C11C2×#13511yescharacteristic
460C22×C11#57611yescharacteristic
461C22×C11#57711yescharacteristic
462C2×D11—24no—
463C2×D11—22no—
464C2×D11—22no—
465C2×D11—22no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—41no—
469C2×D11—42no—
470C2×D11—41no—
471C2×D11—42no—
472C2×D11—41no—
473C2×D11—42no—
474C2×D11—41no—
475C2×D11—42no—
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—42no—
488C4×C11—81no—
489C4×C11C2×C4×D411yescharacteristic
490C4×C11#51811yescharacteristic
491C4×C11D4211yescharacteristic
492C4×C11#54611yescharacteristic
493Dic11—22no—
494Dic11—22no—
495Dic11—22no—
496Dic11—81no—
497Dic11—81no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8C22×D1111yescharacteristic
506C22×D4—111no—
507C22×D4—114no—
508C22×D4—111no—
509C22×D4—111no—
510C22×D4—222no—
511C22×D4—222no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—221no—
515C22×D4—222no—
516C22×D4—441no—
517C22×D4—441no—
518C23×C4—21no—
519C23×C4—111no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C22×C8—111no—
524C22×C8—111no—
525C22×C8—222no—
526C22×C8—222no—
527C22×C8—222no—
528C22×C8—222no—
529C22×C8—441no—
530C22×C8—441no—
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—22no—
537C22⋊Q8C4×D1114yes—
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—21no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—111no—
554C2×C4⋊C4—111no—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—111no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—228no—
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—41no—
575#103—222no—
576#103—441no—
577#102—114no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584#102—441no—
585C22⋊C8—22no—
586C22⋊C8—222no—
587C4×C8—222no—
588#95—221no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—24no—
594C2×C11D4×C22⋊C411yescharacteristic
595C2×C11C2×#41611yescharacteristic
596C2×C11#289711yescharacteristic
597C2×C11#328011yescharacteristic
598C2×C11#328211yescharacteristic
599C2×C11#329611yescharacteristic
600C2×C11#329711yescharacteristic
601D11—42no—
602D11—44no—
603D11—82no—
604C24—111no—
605C24—221no—
606C24—221no—
607C24—224no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—881no—
613C24—881no—
614C24D4×D1111yescharacteristic
615#41—228no—
616#41—444no—
617#41—444no—
618#41—444no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×C4×D1112yes—
625C2×D4—114no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—228no—
631C2×D4—224no—
632C2×D4—224no—
633C2×D4—222no—
634C2×D4—222no—
635C2×D4—224no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—444no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—442no—
651C2×D4—881no—
652C2×D4—881no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—81no—
664C22×C4—111no—
665C22×C4—111no—
666C22×C4—111no—
667C22×C4—112no—
668C22×C4—112no—
669C22×C4—224no—
670C22×C4—224no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—221no—
675C22×C4—221no—
676C22×C4—221no—
677C22×C4—442no—
678C22×C4—442no—
679C22×C4—881no—
680C22×C4—881no—
681C22×C4C2×C4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1112yes—
684C22×C4C23×D1111yescharacteristic
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—112no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—444no—
698C2×C8—444no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—42no—
705C4⋊C4—114no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4C2×C4×D1112yes—
711C4⋊C4D4×D1112yes—
712C22⋊C4—24no—
713C22⋊C4—114no—
714C22⋊C4—114no—
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#2241411yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—112no—
732C23—222no—
733C23—221no—
734C23—221no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—222no—
739C23—221no—
740C23—222no—
741C23—222no—
742C23—448no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—448no—
753C23—441no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23C22⋊C4×D1112yes—
760C23#6696912yes—
761C23#6697212yes—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—114no—
768D4—228no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4—441no—
777D4—441no—
778D4—884no—
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—22no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4—112no—
799C2×C4—112no—
800C2×C4—112no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—221no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—448no—
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×D4×D1111yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4#6703711yescharacteristic
824C2×C4#41×D1111yescharacteristic
825C2×C4#6704211yescharacteristic
826C8—41no—
827C8—41no—
828C8—222no—
829C8—441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—222no—
837C22—224no—
838C22—222no—
839C22—222no—
840C22—442no—
841C22—441no—
842C22—442no—
843C22—441no—
844C22—442no—
845C22—442no—
846C22—441no—
847C22—442no—
848C22—441no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—8816no—
854C22—881no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22#1062241714yescomplemented
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062312111yescharacteristic
861C22#1062318511yescharacteristic
862C22C2×#6696911yescharacteristic
863C22C2×#6697211yescharacteristic
864C22#1062330511yescharacteristic
865C22#1062330911yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—222no—
872C4—222no—
873C4—222no—
874C4—881no—
875C4—881no—
876C4C4×D4×D1111yescharacteristic
877C4#1062307611yescharacteristic
878C4#1062314011yescharacteristic
879C4#1062314111yescharacteristic
880C2—24no—
881C2—442no—
882C2—444no—
883C2—882no—
884C2#1307143411yescharacteristic
885C2C2×#1062241711yescharacteristic
886C2#1307714011yescharacteristic
887C2#1308029411yescharacteristic
888C2#1308031611yescharacteristic
889C2#1308044911yescharacteristic
890C2#1308046411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1872C2
socleC23×C11C22×D4
prime radicalC2×#10623161C2
cosocleC22×C4×C11C24
hypercenter#1872D11
hypocenterC11#22414
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D11)⋊C8C2semidirect
3. C2×#10622417C2semidirect
4. C22×#66873C2semidirect
5. #13071541C2semidirect
6. #13069545C2semidirect
7. #13069424C2semidirect
8. #13069043C2semidirect
9. #13069040C2semidirect
10. #13068937C2semidirect
11. #13068625C2semidirect
12. #13068555C2semidirect
13. #13068548C2semidirect
14. #13068430C2semidirect
15. C11×#1872C2semidirect
23. C22×C8×D11C22semidirect
25. #10623161C4semidirect
30. C2×#66945C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#103C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×Dic11⋊C8C22semidirect
47. C2×C8×Dic11C22semidirect
49. #10622600C22semidirect
51. #10622590C22semidirect
52. C4⋊C4×Dic11C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
74. C2×#4343C2×C4semidirect
104. #67000C2×C4semidirect
130. #66948C2×C4semidirect
133. #66946C2×C4semidirect
158. #66873D4semidirect
292. #1872D11semidirect
422. C2×#103C2×D11semidirect
423. C2×#103C2×D11semidirect
446. #340C2×D11semidirect
447. #340C2×D11semidirect
454. C22×C11#416semidirect
726. C11#22414semidirect
858. C22#10622417semidirect

Maximal subgroups

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

subgroupindex
C2×#106231612
C2×(C22⋊D11)⋊C82
C2×#106224172
C22×#668732
#130715412
#130695452
#130694242
#130690432
#130690402
#130689372
#130686252
#130685552
#130685482
#130684302
C11×#18722
#2241411