Finite Group Databasebeta

← #14800895

Subgroups — #14800895

Order 2816.

1158 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622662C211yesmaximal, characteristic, complemented
2C2×#10622851C211yesmaximal, characteristic, complemented
3C2×#10622624C211yesmaximal, characteristic, complemented
4C2×#10622846C211yesmaximal, characteristic, complemented
5#13072034C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069809C211yesmaximal, characteristic, complemented
9#13069612C211yesmaximal, characteristic, complemented
10#13069491C211yesmaximal, characteristic, complemented
11#13069309C211yesmaximal, characteristic, complemented
12#13069055C211yesmaximal, characteristic, complemented
13#13069042C211yesmaximal, characteristic, complemented
14#13068813C211yesmaximal, characteristic, complemented
15C11×#2407C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C2×#66983C2211yescharacteristic
23C2×#66983C2211yescharacteristic
24C2×#66979C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C11×#394—21no—
28C11×#392—21no—
29C11×#391C2211yescharacteristic
30C11×#390C2211yescharacteristic
31C11×#386—21no—
32C11×#385—21no—
33C11×#380C2211yescharacteristic
34#10622851—24no—
35#10622846—24no—
36C2×#66899C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622836—21no—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43#10622825C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45C2×C22⋊(C11⋊C8)C2211yescharacteristic
46#10622662—24no—
47#10622624—24no—
48#10622603—21no—
49C2×#66873C2211yescharacteristic
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622572—21no—
54#10622570—21no—
55#10622552C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×#66867C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C2×C11×#41—22no—
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—41no—
68C2×C11×#41—41no—
69C22×Q8×C11C2311yescharacteristic
70C22×D4×C11—21no—
71C22×D4×C11—21no—
72C22×D4×C11D411yescharacteristic
73C22×D4×C11C2311yescharacteristic
74C23×C4×C11—21no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C22×C22⋊D11—21no—
78C22×C22⋊D11—21no—
79C22×D44C2311yescharacteristic
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8—41no—
82C11×#121—22no—
83C11×#121—41no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C22⋊C4—21no—
91C2×C11×C22⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C11×C22⋊C4—21no—
95C2×C11×C22⋊C4D411yescharacteristic
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C42×C11C2311yescharacteristic
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11—21no—
100C2×#4325—22no—
101C2×#4325—22no—
102C2×#4325—41no—
103C2×#4323—22no—
104C2×#4323—22no—
105C2×#4323—41no—
106#66983—22no—
107#66983—22no—
108#66983—22no—
109#66983—41no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114#66979—22no—
115#66979—41no—
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—41no—
124C22×C11⋊C8—22no—
125C22×C11⋊C8—22no—
126C22×C11⋊C8—41no—
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C22×C11⋊C8C2311yescharacteristic
130C22×C11⋊C8C2311yescharacteristic
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134#66899—22no—
135#66899—22no—
136#66899D414yescomplemented
137#66896—22no—
138#66896—22no—
139#66896—22no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C22⋊(C11⋊C8)—22no—
143C22⋊(C11⋊C8)D414yescomplemented
144#66873—22no—
145#66873—41no—
146#66872—41no—
147#66871—22no—
148C4⋊(C11⋊C8)—22no—
149#66867—22no—
150#25131—111nomaximal, Sylow
151C24×C11—21no—
152C24×C11C2×D411yescharacteristic
153C24×C11C2×D411yescharacteristic
154C23×D11—21no—
155C11×#41—28no—
156C11×#41—44no—
157C11×#41—44no—
158C11×#41—44no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C2×D412yes—
165C2×D4×C11—22no—
166C2×D4×C11—21no—
167C2×D4×C11—21no—
168C2×D4×C11—21no—
169C2×D4×C11—21no—
170C2×D4×C11—21no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—42no—
174C2×D4×C11—42no—
175C2×D4×C11—42no—
176C2×D4×C11—42no—
177C2×D4×C11—42no—
178C2×D4×C11—81no—
179C2×D4×C11#4112yes—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
202C22×C4×C11C2411yescharacteristic
203C2×C22⋊D11—42no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—81no—
207C2×C22⋊D11—81no—
208C2×C22⋊D11—81no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—42no—
224C11×C22⋊C4—22no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4—42no—
227C11×C22⋊C4—42no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—81no—
230C11×C22⋊C4—81no—
231C42×C11—21no—
232C42×C11—21no—
233C22⋊Dic11—42no—
234C22⋊Dic11—81no—
235#4325—44no—
236#4323—44no—
237(C2×D11)⋊C4—42no—
238(C2×D11)⋊C4—42no—
239(C2×D11)⋊C4—42no—
240(C2×D11)⋊C4—81no—
241C4⋊Dic11—21no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11C2×D412yes—
247Dic11⋊C4—81no—
248C4×Dic11—42no—
249#4318—44no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—44no—
260C2×C11⋊C8C2×D412yes—
261C2×C11⋊C8C2×D412yes—
262C2×C11⋊C8C2×D412yes—
263C2×#468—111no—
264C2×#449—111no—
265C2×#435—111no—
266C2×#416—111no—
267#2414—111no—
268#2407D1111yescharacteristic, complemented
269#2067—111no—
270#2055—111no—
271#2035—111no—
272#1999—111no—
273#1972—111no—
274#1935—111no—
275#1895—111no—
276#1893—111no—
277#1854—111no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—22no—
287C23×C11—21no—
288C23×C11—21no—
289C23×C11—21no—
290C23×C11—21no—
291C23×C11—21no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11#12112yes—
299C23×C11C22×D411yescharacteristic
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—41no—
304C22×D11—41no—
305C22×D11—41no—
306C22×D11—41no—
307Q8×C11—22no—
308Q8×C11—22no—
309Q8×C11—41no—
310Q8×C11—41no—
311D4×C11—22no—
312D4×C11—22no—
313D4×C11—44no—
314D4×C11—48no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11—84no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—21no—
325C2×C4×C11—21no—
326C2×C4×C11—21no—
327C2×C4×C11—21no—
328C2×C4×C11—22no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—48no—
335C2×C4×C11—41no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11#12112yes—
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C2×#4111yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×C4×C11H(5,𝔽2)11yescharacteristic
353C2×C4×C11H(5,𝔽2)11yescharacteristic
354C22⋊D11—84no—
355C22⋊D11—84no—
356C2×Dic11—22no—
357C2×Dic11—41no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365D44—41no—
366D44—41no—
367D44—41no—
368D44—41no—
369C11⋊C8—22no—
370C11⋊C8—22no—
371C11⋊C8—22no—
372C11⋊C8—41no—
373C22×#41C2×D1111yescharacteristic
374C22×SD16—111no—
375C22×D8—111no—
376C22×M16—111no—
377C23×C8—111no—
378C2×C22⋊Q8C2×D1111yescharacteristic
379C2×#121—111no—
380C2×#121—111no—
381C2×#121C2×D1111yescharacteristic
382C2×C4×D4C2×D1111yescharacteristic
383C2×#117—111no—
384#468—224no—
385#449—224no—
386#435—224no—
387C2×#107—111no—
388C2×#106—111no—
389C2×C4⋊C8—111no—
390#416—224no—
391C2×#103—111no—
392C2×#103—111no—
393C2×#103—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102—111no—
399C2×C22⋊C8—111no—
400C2×C22⋊C8—111no—
401C2×#97—111no—
402#394—21no—
403#394—221no—
404#392—21no—
405#392—221no—
406#391C2×D1111yescharacteristic
407#390—111no—
408#390—221no—
409#390C2×D1111yescharacteristic
410#389—111no—
411#388—221no—
412#386—21no—
413#385—21no—
414#380—111no—
415#380C2×D1111yescharacteristic
416#340—111no—
417#340—111no—
418#340—111no—
419#340—111no—
420C22×C11—22no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11—42no—
428C22×C11—41no—
429C22×C11—41no—
430C22×C11—41no—
431C22×C11—41no—
432C22×C11—42no—
433C22×C11—41no—
434C22×C11—41no—
435C22×C11—41no—
436C22×C11—42no—
437C22×C11—81no—
438C22×C11—81no—
439C22×C11—81no—
440C22×C11—81no—
441C22×C11C2×#12111yescharacteristic
442C22×C11D4211yescharacteristic
443C22×C11#54611yescharacteristic
444C22×C11#57511yescharacteristic
445C22×C11#57511yescharacteristic
446C22×C11#57611yescharacteristic
447C22×C11#57711yescharacteristic
448C2×D11—81no—
449C2×D11—81no—
450C2×D11—81no—
451C2×D11—81no—
452C2×D11—81no—
453C2×D11—81no—
454C2×D11—81no—
455C4×C11—22no—
456C4×C11—41no—
457C4×C11—42no—
458C4×C11—41no—
459C4×C11—41no—
460C4×C11—81no—
461C4×C11—81no—
462C4×C11#52511yescharacteristic
463C4×C11#53811yescharacteristic
464C4×C11D4211yescharacteristic
465C4×C11#54611yescharacteristic
466Dic11—42no—
467Dic11—81no—
468Dic11—81no—
469C2×#41—22no—
470C2×#41—22no—
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—41no—
474C2×#41—41no—
475C22×Q8C22×D1111yescharacteristic
476C22×D4—21no—
477C22×D4—21no—
478C22×D4—111no—
479C22×D4—221no—
480C22×D4—221no—
481C22×D4C22⋊D1111yescharacteristic
482C22×D4C22×D1111yescharacteristic
483C23×C4—21no—
484C23×C4C22×D1111yescharacteristic
485C23×C4C22×D1111yescharacteristic
486C2×SD16—222no—
487C2×SD16—222no—
488C2×SD16—441no—
489C2×D8—222no—
490C2×D8—222no—
491C2×D8—441no—
492C2×M16—222no—
493C2×M16—222no—
494C2×M16—441no—
495C22×C8—111no—
496C22×C8—111no—
497C22×C8—111no—
498C22×C8—111no—
499C22×C8—222no—
500C22×C8—222no—
501C22×C8—441no—
502C22⋊Q8—22no—
503C22⋊Q8—41no—
504#121—22no—
505#121—41no—
506#121—222no—
507#121—222no—
508#121—222no—
509#121—441no—
510C4×D4—22no—
511C4×D4—22no—
512#117—222no—
513#117—441no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—111no—
516C2×C4⋊C4—111no—
517C2×C4⋊C4—111no—
518C2×C4⋊C4—221no—
519C2×C4⋊C4C22⋊D1111yescharacteristic
520C2×C4⋊C4C22×D1111yescharacteristic
521C2×C4⋊C4C22×D1111yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—221no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C22⋊C4C22⋊D1111yescharacteristic
534C2×C22⋊C4C22⋊D1111yescharacteristic
535C2×C42—221no—
536C2×C42C22×D1111yescharacteristic
537#107—222no—
538#106—441no—
539C4⋊C8—222no—
540#103—114no—
541#103—222no—
542#103—222no—
543#102—222no—
544#102—222no—
545#102—222no—
546#102—222no—
547#102—441no—
548C22⋊C8—114no—
549C22⋊C8—222no—
550#97—222no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—221no—
555#95—221no—
556C2×C11—42no—
557C2×C11—81no—
558C2×C11—82no—
559C2×C11#242411yescharacteristic
560C2×C11#305411yescharacteristic
561C2×C11#306211yescharacteristic
562C2×C11#326811yescharacteristic
563C2×C11#327111yescharacteristic
564C2×C11#330711yescharacteristic
565C2×C11#331911yescharacteristic
566D11—161no—
567C24—21no—
568C24—221no—
569C24C2×C22⋊D1111yescharacteristic
570C24C2×C22⋊D1111yescharacteristic
571#41—28no—
572#41—44no—
573#41—44no—
574#41—44no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8D4×D1112yes—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—41no—
588C2×D4—41no—
589C2×D4—42no—
590C2×D4—42no—
591C2×D4—42no—
592C2×D4—42no—
593C2×D4—42no—
594C2×D4—81no—
595C2×D4—221no—
596C2×D4—221no—
597C2×D4—221no—
598C2×D4—221no—
599C2×D4—221no—
600C2×D4—221no—
601C2×D4—442no—
602C2×D4—442no—
603C2×D4—442no—
604C2×D4—881no—
605C2×D4—881no—
606C2×D4—881no—
607C2×D4#434112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—221no—
625C22×C4—221no—
626C22×C4—221no—
627C22×C4D4×D1112yes—
628C22×C4#434112yes—
629C22×C4C2×C22⋊D1111yescharacteristic
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C2×C22⋊D1111yescharacteristic
632C22×C4C2×C22⋊D1111yescharacteristic
633C22×C4C23×D1111yescharacteristic
634SD16—444no—
635D8—444no—
636M16—444no—
637C2×C8—112no—
638C2×C8—112no—
639C2×C8—112no—
640C2×C8—221no—
641C2×C8—221no—
642C2×C8—221no—
643C2×C8—221no—
644C2×C8—221no—
645C2×C8—221no—
646C2×C8—221no—
647C2×C8—221no—
648C2×C8—221no—
649C2×C8—444no—
650C4⋊C4—22no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—42no—
656C4⋊C4—112no—
657C4⋊C4—221no—
658C4⋊C4—221no—
659C4⋊C4—221no—
660C4⋊C4—221no—
661C4⋊C4—221no—
662C4⋊C4—881no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—42no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—81no—
669C22⋊C4—81no—
670C22⋊C4—442no—
671C22⋊C4—442no—
672C22⋊C4—442no—
673C22⋊C4—442no—
674C22⋊C4—881no—
675C22⋊C4—881no—
676C42—21no—
677C42—21no—
678C42—442no—
679C11#2513111yescharacteristic, complemented, Sylow
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—22no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23—41no—
700C23—441no—
701C23—441no—
702C23—441no—
703C23—441no—
704C23—441no—
705C23—441no—
706C23—441no—
707C23#6699212yes—
708C23C22×C22⋊D1111yescharacteristic
709Q8—22no—
710Q8—22no—
711Q8—41no—
712Q8—41no—
713D4—22no—
714D4—22no—
715D4—44no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4—84no—
720D4—441no—
721D4—441no—
722D4—441no—
723D4—441no—
724D4—884no—
725D4—884no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—48no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—222no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—441no—
760C2×C4—441no—
761C2×C4—441no—
762C2×C4—441no—
763C2×C4—441no—
764C2×C4#6699212yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4C2×D4×D1111yescharacteristic
767C2×C4C2×#434111yescharacteristic
768C2×C4C2×#434111yescharacteristic
769C2×C4#6703711yescharacteristic
770C2×C4#6703711yescharacteristic
771C8—222no—
772C8—222no—
773C8—222no—
774C8—441no—
775C22—22no—
776C22—22no—
777C22—22no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—42no—
784C22—41no—
785C22—42no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—42no—
791C22—41no—
792C22—81no—
793C22—81no—
794C22—81no—
795C22—81no—
796C22—881no—
797C22—881no—
798C22—881no—
799C22—881no—
800C22—881no—
801C22—881no—
802C22—881no—
803C22D4×C22⋊D1111yescharacteristic
804C22C2×#6699211yescharacteristic
805C22#1062333711yescharacteristic
806C22#1062335311yescharacteristic
807C22#1062335311yescharacteristic
808C22#1062336611yescharacteristic
809C22#1062336811yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—42no—
814C4—41no—
815C4—81no—
816C4—81no—
817C4—442no—
818C4—881no—
819C4—881no—
820C4#1062311711yescharacteristic
821C4#1062312111yescharacteristic
822C4#1062312211yescharacteristic
823C4#1062312411yescharacteristic
824C2—42no—
825C2—81no—
826C2—82no—
827C2—1761no—
828C2#1307215611yescharacteristic
829C2#1307822211yescharacteristic
830C2#1307829811yescharacteristic
831C2#1308015711yescharacteristic
832C2#1308020211yescharacteristic
833C2#1308059211yescharacteristic
834C2#1308077211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2407C2
socleC23×C11C22×D4
hypercenter#2407D11
hypocenterC11#25131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2407

Complements

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

NH ≅ G/Ntype
1. C2×#10622662C2semidirect
2. C2×#10622851C2semidirect
3. C2×#10622624C2semidirect
4. C2×#10622846C2semidirect
5. #13072034C2semidirect
6. #13070004C2semidirect
7. #13069931C2semidirect
8. #13069809C2semidirect
9. #13069612C2semidirect
10. #13069491C2semidirect
11. #13069309C2semidirect
12. #13069055C2semidirect
13. #13069042C2semidirect
14. #13068813C2semidirect
15. C11×#2407C2semidirect
136. #66899D4semidirect
143. C22⋊(C11⋊C8)D4semidirect
268. #2407D11semidirect
679. C11#25131semidirect

Maximal subgroups

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

subgroupindex
C2×#106226622
C2×#106228512
C2×#106226242
C2×#106228462
#130720342
#130700042
#130699312
#130698092
#130696122
#130694912
#130693092
#130690552
#130690422
#130688132
C11×#24072
#2513111