Finite Group Databasebeta

← #14800790

Subgroups — #14800790

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622652C211yesmaximal, characteristic, complemented
2C2×#10622830C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C22×#66896C211yesmaximal, characteristic, complemented
5#13072056C211yesmaximal, characteristic, complemented
6#13069990C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069802C211yesmaximal, characteristic, complemented
9#13069612C211yesmaximal, characteristic, complemented
10#13069491C211yesmaximal, characteristic, complemented
11#13069316C211yesmaximal, characteristic, complemented
12#13069055C211yesmaximal, characteristic, complemented
13#13069042C211yesmaximal, characteristic, complemented
14#13068808C211yesmaximal, characteristic, complemented
15C11×#2408C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66992—21no—
22C22×#4323C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66983C2211yescharacteristic
25C2×#66983C2211yescharacteristic, complemented
26C22×C4⋊Dic11C2211yescharacteristic
27C22×#4318C2211yescharacteristic, complemented
28C23×C11⋊C8C2211yescharacteristic
29C11×#394—21no—
30C11×#392—21no—
31C11×#390C2211yescharacteristic
32C11×#390C2211yescharacteristic
33C11×#380C2211yescharacteristic
34C11×#379—21no—
35#10622830—24no—
36C2×#66896—24no—
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic, complemented
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
46#10622652—24no—
47#10622624—24no—
48#10622607—21no—
49C2×#66873C2211yescharacteristic, complemented
50C2×#66873C2211yescharacteristic, complemented
51C2×#66872C2211yescharacteristic, complemented
52C2×#66872C2211yescharacteristic, complemented
53#10622574—21no—
54#10622571—21no—
55#10622552C2211yescharacteristic, complemented
56#10622541C2211yescharacteristic, complemented
57C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
58C2×#66867C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63C25×C11—21no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—21no—
67C22×D4×C11—21no—
68C22×D4×C11—22no—
69C22×D4×C11—21no—
70C22×D4×C11—22no—
71C22×D4×C11—41no—
72C22×D4×C11—41no—
73C22×D4×C11D411yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C22×D4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×C22⋊D11—21no—
80C23×Dic11—21no—
81C22×D44C2311yescharacteristic
82C11×#121—22no—
83C11×#121—22no—
84C11×#121—41no—
85C11×#121—41no—
86C11×#120—44no—
87C4×D4×C11—22no—
88C4×D4×C11—22no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2311yescharacteristic
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4—21no—
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4D411yescharacteristic
100C2×C11×C22⋊C4D411yescharacteristic
101C2×C42×C11C2311yescharacteristic
102C2×C22⋊Dic11—21no—
103#66992—44no—
104C2×#4323—22no—
105C2×#4323—22no—
106C2×#4323—22no—
107C2×#4323—22no—
108C2×#4323—41no—
109C2×#4323—41no—
110#66983—22no—
111#66983—22no—
112#66983—22no—
113#66983—41no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4—21no—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×Dic11⋊C4—21no—
125C2×#4318—22no—
126C2×#4318—22no—
127C2×#4318—41no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—22no—
130C22×C11⋊C8—41no—
131C22×C11⋊C8C2311yescharacteristic
132C22×C11⋊C8C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C11×#95—21no—
136#66896—22no—
137#66896—22no—
138#66896—22no—
139#66896—22no—
140#66896—22no—
141#66896D414yescomplemented
142C11⋊#95—21no—
143C11⋊#95—21no—
144C22⋊(C11⋊C8)—22no—
145C22⋊(C11⋊C8)D414yescomplemented
146#66873—22no—
147#66873—41no—
148#66872—22no—
149#66872—41no—
150C4⋊(C11⋊C8)—22no—
151#66867—22no—
152#25124—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—42no—
156C24×C11—42no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11—42no—
160C24×C11—81no—
161C24×C11—81no—
162C24×C11C2×D411yescharacteristic
163C24×C11C2×D411yescharacteristic
164C23×D11—21no—
165C2×D4×C11—28no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—44no—
180C2×D4×C11—44no—
181C2×D4×C11—42no—
182C2×D4×C11—42no—
183C2×D4×C11—44no—
184C2×D4×C11—42no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11—81no—
190C2×D4×C11—81no—
191C2×D4×C11C2×D412yes—
192C2×D4×C11#4112yes—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D412yes—
210C22×C4×C11#4112yes—
211C22×C4×C11C2411yescharacteristic
212C2×C22⋊D11—42no—
213C2×C22⋊D11—42no—
214C2×C22⋊D11—42no—
215C2×C22⋊D11—42no—
216C2×C22⋊D11—42no—
217C2×C22⋊D11—81no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—42no—
222C22×Dic11—42no—
223C22×Dic11—81no—
224C2×D44—21no—
225C2×D44—21no—
226C2×D44—21no—
227C2×D44—21no—
228C2×D44—21no—
229C2×D44—21no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—21no—
234C11×C4⋊C4—21no—
235C11×C22⋊C4—22no—
236C11×C22⋊C4—22no—
237C11×C22⋊C4—42no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—42no—
241C11×C22⋊C4—42no—
242C11×C22⋊C4—81no—
243C11×C22⋊C4—81no—
244C42×C11—21no—
245C42×C11—21no—
246C22⋊Dic11—42no—
247#4323—44no—
248#4323—44no—
249(C2×D11)⋊C4—42no—
250(C2×D11)⋊C4—42no—
251(C2×D11)⋊C4—42no—
252(C2×D11)⋊C4—81no—
253C4⋊Dic11—21no—
254C4⋊Dic11—21no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—42no—
259C4⋊Dic11C2×D412yes—
260Dic11⋊C4—42no—
261#4318—44no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×C11⋊C8—21no—
265C2×C11⋊C8—21no—
266C2×C11⋊C8—21no—
267C2×C11⋊C8—21no—
268C2×C11⋊C8—21no—
269C2×C11⋊C8—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—44no—
272C2×C11⋊C8C2×D412yes—
273C2×C11⋊C8C2×D412yes—
274C2×C11⋊C8C2×D412yes—
275C2×#469—111no—
276C2×#447—111no—
277C2×#435—111no—
278C22×#102—111no—
279#2416—111no—
280#2408D1111yescharacteristic, complemented
281#2065—111no—
282#2054—111no—
283#2034—111no—
284#1999—111no—
285#1972—111no—
286#1936—111no—
287#1895—111no—
288#1893—111no—
289#1853—111no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—21no—
293C23×C11—21no—
294C23×C11—21no—
295C23×C11—22no—
296C23×C11—21no—
297C23×C11—22no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—48no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—84no—
317C23×C11—84no—
318C23×C11—84no—
319C23×C11—84no—
320C23×C11—84no—
321C23×C11—84no—
322C23×C11#12112yes—
323C23×C11AGL(1,ℤ/8)12yes—
324C23×C11AGL(1,ℤ/8)12yes—
325C23×C11C22×D411yescharacteristic
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333D4×C11—22no—
334D4×C11—22no—
335D4×C11—22no—
336D4×C11—22no—
337D4×C11—48no—
338D4×C11—44no—
339D4×C11—41no—
340D4×C11—41no—
341D4×C11—41no—
342D4×C11—41no—
343D4×C11—84no—
344D4×C11—84no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—21no—
352C2×C4×C11—21no—
353C2×C4×C11—21no—
354C2×C4×C11—21no—
355C2×C4×C11—21no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—21no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11#12112yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D411yescharacteristic
373C2×C4×C11C2×#4111yescharacteristic
374C2×C4×C11C2×#4111yescharacteristic
375C2×C4×C11H(5,𝔽2)11yescharacteristic
376C2×C4×C11H(5,𝔽2)11yescharacteristic
377C22⋊D11—84no—
378C22⋊D11—84no—
379C2×Dic11—22no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—41no—
383C2×Dic11—41no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—84no—
389D44—41no—
390D44—41no—
391D44—41no—
392D44—41no—
393C11⋊C8—22no—
394C11⋊C8—22no—
395C11⋊C8—22no—
396C11⋊C8—41no—
397C23×D4C2×D1111yescharacteristic
398C22×D8—111no—
399C22×D8—111no—
400C22×M16—111no—
401C23×C8—111no—
402C2×#121—111no—
403C2×#121—111no—
404C2×#121—221no—
405C2×#121C2×D1111yescharacteristic
406C2×#121C2×D1111yescharacteristic
407C2×#120—21no—
408C2×C4×D4C2×D1111yescharacteristic
409C22×C4⋊C4—111no—
410#469—224no—
411#447—224no—
412#435—224no—
413C2×#106—111no—
414C2×#106—111no—
415C2×C4⋊C8—111no—
416C2×#102—111no—
417C2×#102—111no—
418C2×#102—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—224no—
425C2×C22⋊C8—111no—
426C2×C22⋊C8—111no—
427C2×#97—111no—
428#396—221no—
429#394—21no—
430#394—221no—
431#392—21no—
432#390—111no—
433#390C2×D1111yescharacteristic
434#390C2×D1111yescharacteristic
435#389—111no—
436#386—221no—
437#380—111no—
438#380C2×D1111yescharacteristic
439#379—21no—
440#340—111no—
441#340—111no—
442#340—111no—
443#340—111no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—41no—
451C22×C11—42no—
452C22×C11—42no—
453C22×C11—41no—
454C22×C11—42no—
455C22×C11—41no—
456C22×C11—42no—
457C22×C11—41no—
458C22×C11—42no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11—42no—
463C22×C11—816no—
464C22×C11—81no—
465C22×C11—81no—
466C22×C11—81no—
467C22×C11—81no—
468C22×C11—81no—
469C22×C11—81no—
470C22×C11—81no—
471C22×C11—81no—
472C22×C11#46914yescomplemented
473C22×C11C2×#12111yescharacteristic
474C22×C11D4211yescharacteristic
475C22×C11#54611yescharacteristic
476C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
477C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
478C22×C11#57611yescharacteristic
479C22×C11#57711yescharacteristic
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C2×D11—81no—
485C2×D11—81no—
486C2×D11—81no—
487C4×C11—22no—
488C4×C11—41no—
489C4×C11—41no—
490C4×C11—41no—
491C4×C11—81no—
492C4×C11—81no—
493C4×C11#52511yescharacteristic
494C4×C11#53811yescharacteristic
495C4×C11D4211yescharacteristic
496C4×C11#54611yescharacteristic
497Dic11—42no—
498Dic11—81no—
499Dic11—81no—
500C25—21no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—21no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—111no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4C22⋊D1111yescharacteristic
514C22×D4C22×D1111yescharacteristic
515C22×D4C22×D1111yescharacteristic
516C23×C4—221no—
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519C2×D8—222no—
520C2×D8—222no—
521C2×D8—222no—
522C2×D8—222no—
523C2×D8—441no—
524C2×D8—441no—
525C2×M16—222no—
526C2×M16—222no—
527C2×M16—441no—
528C22×C8—111no—
529C22×C8—111no—
530C22×C8—111no—
531C22×C8—111no—
532C22×C8—222no—
533C22×C8—222no—
534C22×C8—441no—
535#121—22no—
536#121—22no—
537#121—41no—
538#121—41no—
539#121—222no—
540#121—222no—
541#121—222no—
542#121—441no—
543#121—444no—
544#120—44no—
545C4×D4—22no—
546C4×D4—22no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—222no—
551C2×C4⋊C4—221no—
552C2×C4⋊C4—221no—
553C2×C4⋊C4—441no—
554C2×C4⋊C4C22⋊D1111yescharacteristic
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4—221no—
568C2×C22⋊C4—221no—
569C2×C22⋊C4C22⋊D1111yescharacteristic
570C2×C22⋊C4C22⋊D1111yescharacteristic
571C2×C42C22×D1111yescharacteristic
572#106—222no—
573#106—441no—
574C4⋊C8—222no—
575#102—114no—
576#102—222no—
577#102—222no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—441no—
583C22⋊C8—114no—
584C22⋊C8—222no—
585#97—222no—
586#95—21no—
587#95—221no—
588#95—221no—
589C2×C11—24no—
590C2×C11—81no—
591C2×C11—82no—
592C2×C11—82no—
593C2×C11#242411yescharacteristic
594C2×C11C2×#46911yescharacteristic
595C2×C11#306211yescharacteristic
596C2×C11#326411yescharacteristic
597C2×C11#326511yescharacteristic
598C2×C11#330611yescharacteristic
599C2×C11#331811yescharacteristic
600D11—161no—
601C24—21no—
602C24—21no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—81no—
609C24—81no—
610C24—221no—
611C24C2×C22⋊D1111yescharacteristic
612C24C2×C22⋊D1111yescharacteristic
613C2×D4—28no—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4—44no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—81no—
638C2×D4—81no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—221no—
644C2×D4—221no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4D4×D1112yes—
652C2×D4#434112yes—
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—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—881no—
671C22×C4D4×D1112yes—
672C22×C4#434112yes—
673C22×C4C2×C22⋊D1111yescharacteristic
674C22×C4C2×C22⋊D1111yescharacteristic
675C22×C4C2×C22⋊D1111yescharacteristic
676C22×C4C2×C22⋊D1111yescharacteristic
677C22×C4C23×D1111yescharacteristic
678D8—444no—
679D8—444no—
680M16—444no—
681C2×C8—112no—
682C2×C8—112no—
683C2×C8—112no—
684C2×C8—221no—
685C2×C8—221no—
686C2×C8—221no—
687C2×C8—221no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—444no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—112no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—442no—
706C4⋊C4—442no—
707C22⋊C4—22no—
708C22⋊C4—22no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—81no—
715C22⋊C4—81no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C22⋊C4—442no—
720C22⋊C4—881no—
721C42—21no—
722C42—21no—
723C11#2512411yescharacteristic, complemented, Sylow
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—441no—
757C23—441no—
758C23—441no—
759C23—441no—
760C23—441no—
761C23—441no—
762C23—441no—
763C23#6698512yes—
764C23#6699212yes—
765C23#6700212yes—
766C23C22×C22⋊D1111yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—44no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4—84no—
779D4—441no—
780D4—441no—
781D4—441no—
782D4—441no—
783D4—884no—
784D4—884no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—222no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—441no—
815C2×C4—441no—
816C2×C4—441no—
817C2×C4—441no—
818C2×C4—441no—
819C2×C4—884no—
820C2×C4#6699212yes—
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×D4×D1111yescharacteristic
823C2×C4C2×#434111yescharacteristic
824C2×C4C2×#434111yescharacteristic
825C2×C4#6703711yescharacteristic
826C2×C4#6703711yescharacteristic
827C8—222no—
828C8—222no—
829C8—222no—
830C8—441no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—42no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—41no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—881no—
860C22—881no—
861C22—881no—
862C22—881no—
863C22—881no—
864C22—881no—
865C22—881no—
866C22#1062265214yescomplemented
867C22C2×#6698511yescharacteristic
868C22D4×C22⋊D1111yescharacteristic
869C22C2×#6699211yescharacteristic
870C22#1062333711yescharacteristic
871C22C2×#6700211yescharacteristic
872C22#1062336611yescharacteristic
873C22#1062336711yescharacteristic
874C4—22no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—81no—
879C4—81no—
880C4—442no—
881C4—881no—
882C4—881no—
883C4#1062311711yescharacteristic
884C4#1062312111yescharacteristic
885C4#1062312211yescharacteristic
886C4#1062312411yescharacteristic
887C2—24no—
888C2—81no—
889C2—82no—
890C2—82no—
891C2—1761no—
892C2#1307215611yescharacteristic
893C2C2×#1062265211yescharacteristic
894C2#1307829211yescharacteristic
895C2#1308009711yescharacteristic
896C2#1308010711yescharacteristic
897C2#1308057711yescharacteristic
898C2#1308075711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2408C2
socleC23×C11C22×D4
hypercenter#2408D11
hypocenterC11#25124
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#10622652C2semidirect
2. C2×#10622830C2semidirect
3. C2×#10622624C2semidirect
4. C22×#66896C2semidirect
5. #13072056C2semidirect
6. #13069990C2semidirect
7. #13069926C2semidirect
8. #13069802C2semidirect
9. #13069612C2semidirect
10. #13069491C2semidirect
11. #13069316C2semidirect
12. #13069055C2semidirect
13. #13069042C2semidirect
14. #13068808C2semidirect
15. C11×#2408C2semidirect
25. C2×#66983C22semidirect
27. C22×#4318C22semidirect
43. #10622825C22semidirect
45. C2×C22⋊(C11⋊C8)C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
51. C2×#66872C22semidirect
52. C2×#66872C22semidirect
55. #10622552C22semidirect
56. #10622541C22semidirect
57. C2×C4⋊(C11⋊C8)C22semidirect
58. C2×#66867C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
62. #10622167C22semidirect
141. #66896D4semidirect
145. C22⋊(C11⋊C8)D4semidirect
280. #2408D11semidirect
472. C22×C11#469semidirect
723. C11#25124semidirect
866. C22#10622652semidirect

Maximal subgroups

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

subgroupindex
C2×#106226522
C2×#106228302
C2×#106226242
C22×#668962
#130720562
#130699902
#130699262
#130698022
#130696122
#130694912
#130693162
#130690552
#130690422
#130688082
C11×#24082
#2512411