Finite Group Databasebeta

← #14769371

Subgroups — #14769371

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×#10623161C211yesmaximal, characteristic
2C2×#10622342C211yesmaximal, characteristic, complemented
3C2×#10622416C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5#13071546C211yesmaximal, characteristic, complemented
6#13069545C211yesmaximal, characteristic, complemented
7#13069424C211yesmaximal, characteristic, complemented
8#13069053C211yesmaximal, characteristic, complemented
9#13069050C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1873C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×C11×#117C2211yescharacteristic
20C2×#67000C2211yescharacteristic
21C2×C4×C22⋊D11C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4313C2211yescharacteristic, complemented
24#10623161—24no—
25#10623161C418yescomplemented
26C2×#66948—21no—
27C2×#66948C2211yescharacteristic
28C2×#66947—21no—
29C2×#66946C2211yescharacteristic
30C2×C4⋊C4×D11C2211yescharacteristic, 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#10622825C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic
43C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
44C2×Dic11⋊C8C2211yescharacteristic, complemented
45C2×C8×Dic11C2211yescharacteristic, complemented
46#10622614—24no—
47#10622600C2211yescharacteristic, complemented
48#10622590C2211yescharacteristic, complemented
49C4⋊C4×Dic11C2211yescharacteristic, complemented
50C2×#66873C2211yescharacteristic
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic
54#10622569—21no—
55#10622558—21no—
56C4×(C2×D11)⋊C4—21no—
57#10622546—21no—
58#10622416—24no—
59#10622342—24no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11D411yescharacteristic
68C2×#4343—22no—
69C2×#4343—22no—
70C2×#4343—22no—
71C2×#4343—41no—
72C2×#4343—41no—
73C2×#4343C2×C414yes—
74C22×D44—22no—
75C22×D44—22no—
76C22×D44—21no—
77C22×D44—21no—
78C22×D44—22no—
79C22×D44—21no—
80C22×D44—41no—
81C22×D44—41no—
82C22×D44C2×C414yescomplemented
83C22×D44C2311yescharacteristic
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×C4×D11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×C22⋊Q8—22no—
92C11×C22⋊Q8C2×C414yescomplemented
93C11×#117—22no—
94C11×#117—41no—
95C2×C11×C4⋊C4—21no—
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C22⋊Dic11—21no—
103C2×C22⋊Dic11D411yescharacteristic
104#67000—22no—
105#67000C2×C414yescomplemented
106C4×C22⋊D11C2×C414yes—
107C4×C22⋊D11D414yes—
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⋊C4—21no—
117C2×Dic11⋊C4D411yescharacteristic
118C2×C4×Dic11—21no—
119C2×C4×Dic11C2311yescharacteristic
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—41no—
123C22×C11⋊C8C2311yescharacteristic
124C22×C11⋊C8C2311yescharacteristic
125C2×#4313—22no—
126C2×#4313—22no—
127C2×#4313—41no—
128#66948—22no—
129#66948—28no—
130#66948C2×C414yes—
131#66947—28no—
132#66946—22no—
133#66946C2×C414yescomplemented
134C4⋊C4×D11—22no—
135C4⋊C4×D11—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#22427—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×C11C22×C412yes—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—41no—
190C2×C22⋊D11—41no—
191C2×C22⋊D11C22⋊C414yes—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11C2×D411yescharacteristic
195C22×Dic11C2×D411yescharacteristic
196C22×Dic11C2×D411yescharacteristic
197#4343—28no—
198#4343—44no—
199#4343—44no—
200#4343—44no—
201C2×D44—24no—
202C2×D44—24no—
203C2×D44—28no—
204C2×D44—24no—
205C2×D44—21no—
206C2×D44—21no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—21no—
213C2×D44—42no—
214C2×D44—42no—
215C2×D44—44no—
216C2×D44—44no—
217C2×D44—44no—
218C2×D44—42no—
219C2×D44—42no—
220C2×D44—81no—
221C2×D44—81no—
222C2×D44C22×C412yes—
223C2×D44C22×C412yes—
224C2×D44C2×D412yes—
225C2×D44#4112yes—
226C2×C4×D11—24no—
227C2×C4×D11—24no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—21no—
231C2×C4×D11—21no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—81no—
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⋊C4C22×C412yes—
253C11×C4⋊C4C2×D412yes—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—42no—
256C42×C11—42no—
257C22⋊Dic11—81no—
258C22⋊Dic11C22⋊C414yes—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—24no—
261(C2×D11)⋊C4—24no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—42no—
264(C2×D11)⋊C4C22⋊C414yes—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11—21no—
268C4⋊Dic11—21no—
269Dic11⋊C4—42no—
270Dic11⋊C4C22⋊C414yes—
271C4×Dic11—81no—
272C4×Dic11C22×C412yes—
273C4×Dic11C2×D412yes—
274#4318—44no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280C2×C11⋊C8C2×D412yes—
281#4313—44no—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417—111no—
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873D1111yescharacteristic, 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×C11—21no—
302C23×C11—21no—
303C23×C11C2×C22⋊C412yes—
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—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—
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×C11C2×C22⋊C412yes—
356C2×C4×C11C23×C411yescharacteristic
357C2×C4×C11C22×D411yescharacteristic
358C2×C4×C11C22×D411yescharacteristic
359C2×C4×C11C2×#4111yescharacteristic
360C2×C4×C11H(5,𝔽2)11yescharacteristic
361C2×C4×C11H(5,𝔽2)11yescharacteristic
362C22⋊D11—44no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11C2×C22⋊C412yes—
376C2×Dic11C2×C22⋊C412yes—
377C2×Dic11C2×C22⋊C412yes—
378D44—22no—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—22no—
383D44—48no—
384D44—48no—
385D44—41no—
386D44—41no—
387D44—84no—
388D44C4×D414yes—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—48no—
394C4×D11—84no—
395C4×D11—84no—
396C8×C11—41no—
397C8×C11—41no—
398C11⋊C8—22no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4—111no—
402C22×M16—111no—
403C22×M16—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×#117C2×D1111yescharacteristic
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417#436—224no—
418C2×C4⋊C8—111no—
419#418—224no—
420#417—224no—
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×#102—111no—
432C2×#102—111no—
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—41no—
452C22×C11—41no—
453C22×C11—41no—
454C22×C11—41no—
455C22×C11C22×C22⋊C411yescharacteristic
456C22×C11D4211yescharacteristic
457C22×C11#54611yescharacteristic
458C22×C11#57511yescharacteristic
459C22×C11#57511yescharacteristic
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—111no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4C22×D1111yescharacteristic
523C2×M16—222no—
524C2×M16—222no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
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—22no—
537C22⋊Q8C4×D1114yescomplemented
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—22no—
547#117—41no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—441no—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—111no—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—228no—
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—21no—
570C2×C42—111no—
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—42no—
594C2×C11D4×C22⋊C411yescharacteristic
595C2×C11#289611yescharacteristic
596C2×C11#289711yescharacteristic
597C2×C11#327311yescharacteristic
598C2×C11#327511yescharacteristic
599C2×C11#332211yescharacteristic
600C2×C11#332311yescharacteristic
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—224no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—441no—
650C2×D4—441no—
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—111no—
662C22×C4—111no—
663C22×C4—111no—
664C22×C4—112no—
665C22×C4—112no—
666C22×C4—224no—
667C22×C4—224no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—221no—
674C22×C4—442no—
675C22×C4—442no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4—881no—
679C22×C4—881no—
680C22×C4—881no—
681C22×C4C2×C4×D1112yes—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—444no—
686M16—444no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—112no—
694C2×C8—221no—
695C2×C8—221no—
696C2×C8—221no—
697C2×C8—221no—
698C2×C8—221no—
699C4⋊C4—24no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—114no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—442no—
710C4⋊C4C2×C4×D1112yes—
711C4⋊C4D4×D1112yes—
712C22⋊C4—24no—
713C22⋊C4—42no—
714C22⋊C4—114no—
715C22⋊C4—114no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—224no—
720C22⋊C4—442no—
721C22⋊C4—881no—
722C42—42no—
723C42—112no—
724C42—112no—
725C42—881no—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—112no—
734C23—222no—
735C23—221no—
736C23—221no—
737C23—221no—
738C23—221no—
739C23—221no—
740C23—222no—
741C23—221no—
742C23—222no—
743C23—222no—
744C23—448no—
745C23—448no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
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—114no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—448no—
775D4—444no—
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—112no—
798C2×C4—112no—
799C2×C4—112no—
800C2×C4—221no—
801C2×C4—221no—
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—448no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—884no—
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—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—222no—
838C22—224no—
839C22—222no—
840C22—222no—
841C22—442no—
842C22—442no—
843C22—441no—
844C22—442no—
845C22—441no—
846C22—442no—
847C22—441no—
848C22—442no—
849C22—441no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062312111yescharacteristic
861C22#1062318511yescharacteristic
862C22#1062330011yescharacteristic
863C22#1062330111yescharacteristic
864C22#1062330811yescharacteristic
865C22#1062330811yescharacteristic
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—42no—
881C2—442no—
882C2—444no—
883C2—882no—
884C2#1307143411yescharacteristic
885C2#1307713411yescharacteristic
886C2#1307713811yescharacteristic
887C2#1308022011yescharacteristic
888C2#1308024011yescharacteristic
889C2#1308081511yescharacteristic
890C2#1308083011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1873C2
socleC23×C11C22×D4
prime radicalC2×#10623161C2
cosocleC22×C4×C11C24
hypercenter#1873D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1873

Complements

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

NH ≅ G/Ntype
2. C2×#10622342C2semidirect
3. C2×#10622416C2semidirect
4. C2×#10622614C2semidirect
5. #13071546C2semidirect
6. #13069545C2semidirect
7. #13069424C2semidirect
8. #13069053C2semidirect
9. #13069050C2semidirect
10. #13068932C2semidirect
11. #13068625C2semidirect
12. #13068555C2semidirect
13. #13068548C2semidirect
14. #13068430C2semidirect
15. C11×#1873C2semidirect
23. C22×#4313C22semidirect
25. #10623161C4semidirect
30. C2×C4⋊C4×D11C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#103C22semidirect
36. C2×#66899C22semidirect
37. C2×#66899C22semidirect
43. C2×(C2×D11)⋊C8C22semidirect
44. C2×Dic11⋊C8C22semidirect
45. C2×C8×Dic11C22semidirect
47. #10622600C22semidirect
48. #10622590C22semidirect
49. C4⋊C4×Dic11C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
82. C22×D44C2×C4semidirect
92. C11×C22⋊Q8C2×C4semidirect
105. #67000C2×C4semidirect
133. #66946C2×C4semidirect
158. #66873D4semidirect
292. #1873D11semidirect
423. C2×#103C2×D11semidirect
424. C2×#103C2×D11semidirect
446. #340C2×D11semidirect
447. #340C2×D11semidirect
537. C22⋊Q8C4×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×#106231612
C2×#106223422
C2×#106224162
C2×#106226142
#130715462
#130695452
#130694242
#130690532
#130690502
#130689322
#130686252
#130685552
#130685482
#130684302
C11×#18732
#2242711