Finite Group Databasebeta

← #14769372

Subgroups — #14769372

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×#10623207C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic, complemented
3C2×#10622416C211yesmaximal, characteristic, complemented
4C2×#10622383C211yesmaximal, characteristic, complemented
5#13071542C211yesmaximal, characteristic, complemented
6#13069549C211yesmaximal, characteristic, complemented
7#13069051C211yesmaximal, characteristic, complemented
8#13069046C211yesmaximal, characteristic, complemented
9#13068930C211yesmaximal, characteristic, complemented
10#13068925C211yesmaximal, characteristic, complemented
11#13068623C211yesmaximal, characteristic, complemented
12#13068555C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1958C211yesmaximal, characteristic, complemented
16C22×#4343C2211yescharacteristic
17C22×D4×D11C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×#66999C2211yescharacteristic
20C2×#66991C2211yescharacteristic
21C22×#4313C2211yescharacteristic
22C22×#4313C2211yescharacteristic, complemented
23#10623207—24no—
24#10623207C418yescomplemented
25C2×#66945C2211yescharacteristic
26C2×C4⋊C4×D11C2211yescharacteristic, complemented
27C2×#66937—21no—
28C2×#66936—21no—
29C2×#66935—21no—
30C2×C22⋊C4×D11—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic, complemented
34C2×C11×#103C2211yescharacteristic, complemented
35C2×C11×#102C2211yescharacteristic
36C2×C11×#102C2211yescharacteristic
37C2×C4×C8×C11C2211yescharacteristic, complemented
38C11×#382C2211yescharacteristic, complemented
39C2×#66899C2211yescharacteristic, complemented
40C2×#66899C2211yescharacteristic, complemented
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×(C2×D11)⋊C8C2211yescharacteristic
46C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
47#10622600C2211yescharacteristic
48#10622600C2211yescharacteristic, complemented
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic, complemented
52C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
53#10622416—24no—
54#10622383—24no—
55#10622301—24no—
56#10622282—21no—
57#10622279—21no—
58#10622278—21no—
59#10622267—21no—
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×Q8×C11C2311yescharacteristic
66C22×D4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C22×C22⋊D11—21no—
69C2×#4343—22no—
70C2×#4343—22no—
71C2×#4343—22no—
72C2×#4343—41no—
73C2×#4343—41no—
74C2×#4343C2×C414yes—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—41no—
79C2×D4×D11—41no—
80C2×D4×D11C2×C414yescomplemented
81C22×D44—21no—
82C22×D44D411yescharacteristic
83C22×D44C2311yescharacteristic
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11C2311yescharacteristic
88C22×C4×D11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C11×#124—22no—
92C11×#124C2×C414yescomplemented
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99#66999—22no—
100#66999C2×C414yescomplemented
101#66991—22no—
102#66991C2×C414yes—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4D411yescharacteristic
109C2×(C2×D11)⋊C4D411yescharacteristic
110C2×C4⋊Dic11D411yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C2×#4313—22no—
121C2×#4313—22no—
122C2×#4313—22no—
123C2×#4313—22no—
124C2×#4313—41no—
125C2×#4313—41no—
126#66945—22no—
127#66945—41no—
128C4⋊C4×D11—22no—
129C4⋊C4×D11—41no—
130#66937—28no—
131#66936—28no—
132#66935—28no—
133C22⋊C4×D11—28no—
134C4×D44—22no—
135C4×D44C2×C414yes—
136C4×D44C2×C414yescomplemented
137C4×D44D414yes—
138C11×#103—22no—
139C11×#103—41no—
140C11×#102—22no—
141C11×#102—41no—
142C4×C8×C11—22no—
143C11×#95—21no—
144C11×#95—21no—
145#66899—22no—
146#66899—41no—
147#66896—22no—
148#66896—41no—
149C11⋊#95—21no—
150C11⋊#95—21no—
151C11⋊#95—21no—
152#66885—22no—
153#66885D414yescomplemented
154(C2×D11)⋊C8—22no—
155(C2×D11)⋊C8—22no—
156#66873—22no—
157#66873—22no—
158C4⋊(C11⋊C8)—22no—
159#22427—111nomaximal, Sylow
160C24×C11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C23×D11C2×D411yescharacteristic
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—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—21no—
180C2×D4×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11C22×C412yes—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2411yescharacteristic
189C2×C22⋊D11—24no—
190C2×C22⋊D11—24no—
191C2×C22⋊D11—42no—
192C2×C22⋊D11—42no—
193C2×C22⋊D11—81no—
194C2×C22⋊D11—81no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11C2×D411yescharacteristic
199C22×Dic11C2×D411yescharacteristic
200#4343—28no—
201#4343—44no—
202#4343—44no—
203#4343—44no—
204D4×D11—28no—
205D4×D11—44no—
206D4×D11—44no—
207D4×D11—44no—
208C2×D44—24no—
209C2×D44—21no—
210C2×D44—21no—
211C2×D44—21no—
212C2×D44—41no—
213C2×D44—41no—
214C2×D44—42no—
215C2×D44—42no—
216C2×D44C22⋊C414yes—
217C2×D44C22×C412yes—
218C2×D44C2×D412yes—
219C2×D44#4112yes—
220C2×C4×D11—24no—
221C2×C4×D11—24no—
222C2×C4×D11—21no—
223C2×C4×D11—21no—
224C2×C4×D11—21no—
225C2×C4×D11—21no—
226C2×C4×D11—21no—
227C2×C4×D11—21no—
228C2×C4×D11—21no—
229C2×C4×D11—21no—
230C2×C4×D11—42no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—81no—
235C2×C4×D11—81no—
236C2×C4×D11—81no—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C22×C412yes—
239C2×C4×D11C2×D412yes—
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×C11C2×D412yes—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C42×C11C22×C412yes—
254C42×C11C2×D412yes—
255C22⋊Dic11—24no—
256(C2×D11)⋊C4—24no—
257(C2×D11)⋊C4—24no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—81no—
261(C2×D11)⋊C4C22⋊C414yes—
262(C2×D11)⋊C4C22⋊C414yes—
263C4⋊Dic11—21no—
264C4⋊Dic11—21no—
265C4⋊Dic11—21no—
266C4⋊Dic11—21no—
267C4⋊Dic11C22⋊C414yes—
268C4⋊Dic11C22×C412yes—
269C4⋊Dic11C2×D412yes—
270Dic11⋊C4—24no—
271Dic11⋊C4—42no—
272C4×Dic11—42no—
273C4×Dic11—81no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—21no—
276C2×C11⋊C8—21no—
277C2×C11⋊C8—21no—
278C2×C11⋊C8—21no—
279C2×C11⋊C8—21no—
280#4313—44no—
281#4313—44no—
282C2×#546—111no—
283C2×#436—111no—
284C2×#417—111no—
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958D1111yescharacteristic, complemented
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—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11C22×D411yescharacteristic
305C22×D11—22no—
306C22×D11—21no—
307C22×D11—21no—
308C22×D11—22no—
309C22×D11—21no—
310C22×D11—21no—
311C22×D11—22no—
312C22×D11—21no—
313C22×D11—21no—
314C22×D11—21no—
315C22×D11—21no—
316C22×D11—21no—
317C22×D11—21no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—48no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11C2×C22⋊C412yes—
332C22×D11C2×C22⋊C412yes—
333Q8×C11—22no—
334Q8×C11—22no—
335Q8×C11—41no—
336Q8×C11—41no—
337D4×C11—22no—
338D4×C11—22no—
339D4×C11—41no—
340D4×C11—41no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
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×C11C2×C22⋊C412yes—
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—48no—
363C22⋊D11—84no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11C2×C22⋊C412yes—
378C2×Dic11C2×C22⋊C412yes—
379D44—22no—
380D44—22no—
381D44—22no—
382D44—44no—
383D44—48no—
384D44C4×D414yes—
385C4×D11—22no—
386C4×D11—22no—
387C4×D11—22no—
388C4×D11—22no—
389C4×D11—22no—
390C4×D11—22no—
391C4×D11—22no—
392C4×D11—22no—
393C4×D11—48no—
394C4×D11—84no—
395C4×D11—84no—
396C8×C11—22no—
397C8×C11—41no—
398C11⋊C8—41no—
399C11⋊C8—41no—
400C22×#41—111no—
401C23×D4—111no—
402C22×M16—111no—
403C22×M16—111no—
404#546—118no—
405#546—224no—
406C2×#124C2×D1111yescharacteristic
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⋊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×#102C2×D1111yescharacteristic
432C2×#102C2×D1111yescharacteristic
433C2×C22⋊C8—111no—
434C2×C22⋊C8—111no—
435C2×C4×C8C2×D1111yescharacteristic, complemented
436#388—221no—
437#387—221no—
438#386—221no—
439#382C2×D1111yescharacteristic, complemented
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—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—81no—
452C22×C11—81no—
453C22×C11—81no—
454C22×C11—81no—
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—22no—
467C2×D11—22no—
468C2×D11—22no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—41no—
472C2×D11—41no—
473C2×D11—42no—
474C2×D11—41no—
475C2×D11—41no—
476C2×D11—42no—
477C2×D11—41no—
478C2×D11—41no—
479C2×D11—42no—
480C2×D11—41no—
481C2×D11—41no—
482C2×D11—42no—
483C2×D11—816no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—42no—
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—
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—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—221no—
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—111no—
519C23×C4—111no—
520C23×C4—221no—
521C23×C4—221no—
522C23×C4—221no—
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—22no—
534#124C4×D1114yescomplemented
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—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—222no—
553C2×C4⋊C4—221no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—441no—
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—221no—
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572C4⋊C8—222no—
573#103—22no—
574#103—41no—
575#103—222no—
576#103—441no—
577#102—22no—
578#102—41no—
579#102—114no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—222no—
584#102—441no—
585C22⋊C8—222no—
586C22⋊C8—222no—
587C4×C8—22no—
588#95—21no—
589#95—21no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—82no—
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—42no—
603D11—44no—
604C24—21no—
605C24—111no—
606C24—111no—
607C24—224no—
608C24—221no—
609C24—442no—
610C24—442no—
611C24—442no—
612C24—442no—
613C24—881no—
614C24—881no—
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—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—114no—
631C2×D4—112no—
632C2×D4—112no—
633C2×D4—112no—
634C2×D4—224no—
635C2×D4—224no—
636C2×D4—228no—
637C2×D4—224no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—441no—
642C2×D4—441no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—444no—
646C2×D4—444no—
647C2×D4—444no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4C2×C4×D1112yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—111no—
657C22×C4—111no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—224no—
663C22×C4—221no—
664C22×C4—221no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—221no—
671C22×C4—221no—
672C22×C4—221no—
673C22×C4—224no—
674C22×C4—221no—
675C22×C4—442no—
676C22×C4—442no—
677C22×C4—442no—
678C22×C4—442no—
679C22×C4—881no—
680C22×C4—881no—
681C22×C4—881no—
682C22×C4D4×D1111yescharacteristic
683C22×C4D4×D1111yescharacteristic
684C22×C4C23×D1111yescharacteristic
685M16—444no—
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×C8D4×D1112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—114no—
704C4⋊C4—112no—
705C4⋊C4—112no—
706C4⋊C4—224no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—221no—
711C4⋊C4—442no—
712C22⋊C4—24no—
713C22⋊C4—24no—
714C22⋊C4—114no—
715C22⋊C4—114no—
716C22⋊C4—224no—
717C22⋊C4—224no—
718C22⋊C4—224no—
719C22⋊C4—442no—
720C22⋊C4—442no—
721C22⋊C4—881no—
722C42—442no—
723C42—881no—
724C42C2×C4×D1112yes—
725C42D4×D1112yes—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—112no—
735C23—112no—
736C23—221no—
737C23—221no—
738C23—222no—
739C23—222no—
740C23—221no—
741C23—221no—
742C23—221no—
743C23—221no—
744C23—221no—
745C23—221no—
746C23—221no—
747C23—221no—
748C23—221no—
749C23—221no—
750C23—222no—
751C23—448no—
752C23—448no—
753C23—441no—
754C23—441no—
755C23—441no—
756C23—441no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23—884no—
761C23—884no—
762C23C2×D4×D1111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—41no—
770D4—41no—
771D4—114no—
772D4—222no—
773D4—222no—
774D4—222no—
775D4—444no—
776D4—448no—
777D4—448no—
778D4—884no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—112no—
793C2×C4—112no—
794C2×C4—221no—
795C2×C4—221no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—222no—
801C2×C4—222no—
802C2×C4—222no—
803C2×C4—222no—
804C2×C4—222no—
805C2×C4—222no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—448no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—884no—
817C2×C4—884no—
818C2×C4C22⋊C4×D1112yes—
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—22no—
827C8—41no—
828C8—441no—
829C8—441no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—81no—
837C22—222no—
838C22—222no—
839C22—224no—
840C22—222no—
841C22—222no—
842C22—222no—
843C22—222no—
844C22—442no—
845C22—442no—
846C22—441no—
847C22—441no—
848C22—442no—
849C22—441no—
850C22—441no—
851C22—442no—
852C22—441no—
853C22—441no—
854C22—442no—
855C22—441no—
856C22—441no—
857C22—442no—
858C22—8816no—
859C22C2×C22⋊C4×D1111yescharacteristic
860C22#1062320711yescharacteristic
861C22#1062324811yescharacteristic
862C22#1062329911yescharacteristic
863C22#1062329911yescharacteristic
864C22#1062330011yescharacteristic
865C22#1062330111yescharacteristic
866C4—22no—
867C4—22no—
868C4—42no—
869C4—81no—
870C4—81no—
871C4—222no—
872C4—222no—
873C4—442no—
874C4—442no—
875C4—881no—
876C4C4×D4×D1111yescharacteristic
877C4#1062307611yescharacteristic
878C4#1062314011yescharacteristic
879C4#1062314311yescharacteristic
880C2—82no—
881C2—442no—
882C2—442no—
883C2—444no—
884C2#1307143711yescharacteristic
885C2#1307713111yescharacteristic
886C2#1307713811yescharacteristic
887C2#1308022511yescharacteristic
888C2#1308024611yescharacteristic
889C2#1308081611yescharacteristic
890C2#1308083111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1958C2
socleC23×C11C22×D4
prime radicalC2×#10623207C2
cosocleC22×C4×C11C24
hypercenter#1958D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1958

Complements

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

NH ≅ G/Ntype
2. C2×#10622301C2semidirect
3. C2×#10622416C2semidirect
4. C2×#10622383C2semidirect
5. #13071542C2semidirect
6. #13069549C2semidirect
7. #13069051C2semidirect
8. #13069046C2semidirect
9. #13068930C2semidirect
10. #13068925C2semidirect
11. #13068623C2semidirect
12. #13068555C2semidirect
13. #13068545C2semidirect
14. C4×#66885C2semidirect
15. C11×#1958C2semidirect
22. C22×#4313C22semidirect
24. #10623207C4semidirect
26. C2×C4⋊C4×D11C22semidirect
33. C2×C11×#103C22semidirect
34. C2×C11×#103C22semidirect
37. C2×C4×C8×C11C22semidirect
38. C11×#382C22semidirect
39. C2×#66899C22semidirect
40. C2×#66899C22semidirect
46. C2×(C2×D11)⋊C8C22semidirect
48. #10622600C22semidirect
51. C4×C4⋊Dic11C22semidirect
52. C2×C4⋊(C11⋊C8)C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
80. C2×D4×D11C2×C4semidirect
92. C11×#124C2×C4semidirect
100. #66999C2×C4semidirect
136. C4×D44C2×C4semidirect
153. #66885D4semidirect
288. #1958D11semidirect
423. C2×#103C2×D11semidirect
424. C2×#103C2×D11semidirect
435. C2×C4×C8C2×D11semidirect
439. #382C2×D11semidirect
534. #124C4×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×#106232072
C2×#106223012
C2×#106224162
C2×#106223832
#130715422
#130695492
#130690512
#130690462
#130689302
#130689252
#130686232
#130685552
#130685452
C4×#668852
C11×#19582
#2242711