Finite Group Databasebeta

← #14791799

Subgroups — #14791799

Order 2816.

1480 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622652C211yesmaximal, characteristic, complemented
2C2×#10622851C211yesmaximal, characteristic, complemented
3C2×#10622840C211yesmaximal, characteristic, complemented
4C2×#10622838C211yesmaximal, characteristic, complemented
5#13072034C211yesmaximal, characteristic, complemented
6#13069852C211yesmaximal, characteristic, complemented
7#13069809C211yesmaximal, characteristic, complemented
8#13069693C211yesmaximal, characteristic, complemented
9#13069617C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic, complemented
12#13068914C211yesmaximal, characteristic, complemented
13#13068884C211yesmaximal, characteristic, complemented
14#13068556C211yesmaximal, characteristic, complemented
15C2×C11×#548C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×Q8×C11C2211yescharacteristic
18C11×#548—24no—
19C11×#548—24no—
20C2×C11×#124—21no—
21C2×C11×#124C2211yescharacteristic
22C2×C11×C22⋊Q8—21no—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121—21no—
25C2×C11×#121C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×D4×C11—21no—
28C2×C4×D4×C11C2211yescharacteristic
29C22×#4325C2211yescharacteristic
30C22×#4325C2211yescharacteristic
31C22×#4323C2211yescharacteristic
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×#4318C2211yescharacteristic
36#10622851—24no—
37#10622840—24no—
38#10622838—24no—
39C2×#66899C2211yescharacteristic
40C2×#66899C2211yescharacteristic
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45#10622836—21no—
46C2×#66896C2211yescharacteristic
47C2×#66896C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49#10622825C2211yescharacteristic
50C2×C22⋊(C11⋊C8)C2211yescharacteristic
51C2×C22⋊(C11⋊C8)C2211yescharacteristic
52C2×C22⋊(C11⋊C8)C2211yescharacteristic
53#10622652—24no—
54#10622603—21no—
55C2×#66873C2211yescharacteristic
56C2×#66872C2211yescharacteristic
57#10622572—21no—
58#10622570—21no—
59#10622552C2211yescharacteristic
60#10622541C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622162C2211yescharacteristic
64#10622162C2211yescharacteristic
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41—41no—
70C2×C11×#41—41no—
71C22×Q8×C11—21no—
72C22×Q8×C11—22no—
73C22×Q8×C11—22no—
74C22×Q8×C11—22no—
75C22×Q8×C11—41no—
76C22×Q8×C11—41no—
77C22×Q8×C11D414yescomplemented
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11—21no—
82C22×D4×C11D411yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—21no—
85C23×C4×C11—21no—
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×D44C2311yescharacteristic
91C11×#124—28no—
92C11×#124—22no—
93C11×#124—22no—
94C11×C22⋊Q8—28no—
95C11×C22⋊Q8—22no—
96C11×C22⋊Q8—22no—
97C11×#121—28no—
98C11×#121—22no—
99C11×#121D414yescomplemented
100C4×Q8×C11—22no—
101C4×Q8×C11—22no—
102C4×D4×C11—28no—
103C4×D4×C11—22no—
104C4×D4×C11—22no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4C2311yescharacteristic
109C2×C11×C22⋊C4—21no—
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4D411yescharacteristic
114C2×C11×C22⋊C4D411yescharacteristic
115C2×C42×C11—21no—
116C2×C42×C11C2311yescharacteristic
117C2×C22⋊Dic11—21no—
118C2×C22⋊Dic11—21no—
119C2×#4325—22no—
120C2×#4325—22no—
121C2×#4325—22no—
122C2×#4325—22no—
123C2×#4325—41no—
124C2×#4325—41no—
125C2×#4323—22no—
126C2×#4323—22no—
127C2×#4323—41no—
128#66983—22no—
129#66983—22no—
130#66983—22no—
131#66983—41no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136#66979—22no—
137#66979—41no—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141C2×Dic11⋊C4—21no—
142C2×C4×Dic11—21no—
143C2×#4318—22no—
144C2×#4318—22no—
145C2×#4318—41no—
146C22×C11⋊C8C2311yescharacteristic
147C22×C11⋊C8C2311yescharacteristic
148C22×C11⋊C8C2311yescharacteristic
149C22×C11⋊C8C2311yescharacteristic
150#66899—22no—
151#66899—22no—
152#66899—22no—
153#66899—22no—
154#66899—22no—
155#66899D414yescomplemented
156#66896—22no—
157#66896—22no—
158#66896—41no—
159C11⋊#95—21no—
160C11⋊#95—21no—
161C22⋊(C11⋊C8)—22no—
162C22⋊(C11⋊C8)—22no—
163C22⋊(C11⋊C8)—41no—
164#66873—22no—
165#66872—22no—
166#24455—111nomaximal, Sylow
167C24×C11—21no—
168C24×C11C2×D411yescharacteristic
169C24×C11C2×D411yescharacteristic
170C23×D11—21no—
171C11×#41—44no—
172C11×#41—44no—
173C11×#41—44no—
174C11×#41—44no—
175C2×Q8×C11—24no—
176C2×Q8×C11—21no—
177C2×Q8×C11—21no—
178C2×Q8×C11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—28no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—21no—
184C2×Q8×C11—21no—
185C2×Q8×C11—42no—
186C2×Q8×C11—42no—
187C2×Q8×C11—44no—
188C2×Q8×C11—44no—
189C2×Q8×C11—44no—
190C2×Q8×C11C2×D412yes—
191C2×Q8×C11C2×D412yes—
192C2×Q8×C11C2×D412yes—
193C2×Q8×C11#4112yes—
194C2×D4×C11—24no—
195C2×D4×C11—22no—
196C2×D4×C11—24no—
197C2×D4×C11—21no—
198C2×D4×C11—21no—
199C2×D4×C11—21no—
200C2×D4×C11—21no—
201C2×D4×C11—21no—
202C2×D4×C11—41no—
203C2×D4×C11—41no—
204C2×D4×C11—42no—
205C2×D4×C11—42no—
206C2×D4×C11—42no—
207C2×D4×C11—42no—
208C2×D4×C11C2×D412yes—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—24no—
215C22×C4×C11—24no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2×D412yes—
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—42no—
236C2×C22⋊D11—42no—
237C2×C22⋊D11—42no—
238C2×C22⋊D11—81no—
239C2×C22⋊D11—81no—
240C2×C22⋊D11—81no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C2×D44—21no—
245C2×D44—21no—
246C2×D44—21no—
247C2×D44—21no—
248C2×D44—21no—
249C2×D44—21no—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—21no—
254C11×C4⋊C4C2×D412yes—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—22no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—22no—
261C42×C11—24no—
262C42×C11—21no—
263C42×C11—21no—
264C22⋊Dic11—42no—
265C22⋊Dic11—81no—
266#4325—44no—
267#4325—44no—
268#4323—44no—
269(C2×D11)⋊C4—42no—
270(C2×D11)⋊C4—42no—
271(C2×D11)⋊C4—42no—
272(C2×D11)⋊C4—81no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11—21no—
277C4⋊Dic11—21no—
278C4⋊Dic11C2×D412yes—
279Dic11⋊C4—81no—
280C4×Dic11—42no—
281#4318—44no—
282C2×C11⋊C8—21no—
283C2×C11⋊C8—21no—
284C2×C11⋊C8—21no—
285C2×C11⋊C8—21no—
286C2×C11⋊C8—21no—
287C2×C11⋊C8—21no—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8C2×D412yes—
294C2×#548D1111yescharacteristic, complemented
295C2×#469—111no—
296C2×#449—111no—
297C2×#448—111no—
298C2×#419—111no—
299#2414—111no—
300#2042—111no—
301#2035—111no—
302#2012—111no—
303#2000—111no—
304#1880—111no—
305#1875—111no—
306#1870—111no—
307#1865—111no—
308#1788—111no—
309C23×C11—21no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—21no—
315C23×C11—21no—
316C23×C11—22no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11—21no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11—41no—
326C23×C11—41no—
327C23×C11—41no—
328C23×C11—41no—
329C23×C11#12012yes—
330C23×C11C22×D411yescharacteristic
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338Q8×C11—22no—
339Q8×C11—22no—
340Q8×C11—22no—
341Q8×C11—22no—
342Q8×C11—22no—
343Q8×C11—48no—
344Q8×C11—41no—
345Q8×C11—41no—
346Q8×C11#12114yes—
347D4×C11—22no—
348D4×C11—22no—
349D4×C11—48no—
350D4×C11—44no—
351D4×C11—48no—
352D4×C11—41no—
353D4×C11—41no—
354C2×C4×C11—22no—
355C2×C4×C11—21no—
356C2×C4×C11—22no—
357C2×C4×C11—21no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—21no—
364C2×C4×C11—21no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—48no—
375C2×C4×C11—48no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11#12012yes—
385C2×C4×C11C22×D411yescharacteristic
386C2×C4×C11C22×D411yescharacteristic
387C2×C4×C11C22×D411yescharacteristic
388C2×C4×C11C2×#4111yescharacteristic
389C2×C4×C11H(5,𝔽2)11yescharacteristic
390C2×C4×C11H(5,𝔽2)11yescharacteristic
391C22⋊D11—84no—
392C22⋊D11—84no—
393C2×Dic11—22no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402D44—41no—
403D44—41no—
404D44—41no—
405D44—41no—
406C11⋊C8—22no—
407C11⋊C8—41no—
408C11⋊C8—41no—
409C11⋊C8—41no—
410C22×#41C2×D1111yescharacteristic
411C23×Q8C2×D1111yescharacteristic
412C22×SD16—111no—
413C22×SD16—111no—
414C22×D8—111no—
415C22×M16—111no—
416#548—24no—
417#548—24no—
418C2×#124—21no—
419C2×#124C2×D1111yescharacteristic
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8C2×D1111yescharacteristic
422C2×#121—21no—
423C2×#121—111no—
424C2×#121—111no—
425C2×#121C2×D1111yescharacteristic
426C2×C4×Q8C2×D1111yescharacteristic
427C2×C4×D4—21no—
428C2×C4×D4C2×D1111yescharacteristic
429C2×#117—111no—
430#469—224no—
431#449—224no—
432#448—224no—
433C2×#106—111no—
434#419—224no—
435C2×#103—111no—
436C2×#103—111no—
437C2×#103—111no—
438C2×#103—111no—
439C2×#103—111no—
440C2×#103—111no—
441C2×#102—111no—
442C2×#102—111no—
443C2×#102—111no—
444C2×#102—111no—
445C2×C22⋊C8—111no—
446C2×C22⋊C8—111no—
447C2×C22⋊C8—111no—
448#394—221no—
449#392—221no—
450#390—111no—
451#390—221no—
452#389—111no—
453#388—221no—
454#380—111no—
455#340—111no—
456#340—111no—
457#336—111no—
458#336—111no—
459C22×C11—22no—
460C22×C11—22no—
461C22×C11—22no—
462C22×C11—41no—
463C22×C11—41no—
464C22×C11—41no—
465C22×C11—41no—
466C22×C11—42no—
467C22×C11—41no—
468C22×C11—41no—
469C22×C11—42no—
470C22×C11—41no—
471C22×C11—42no—
472C22×C11—41no—
473C22×C11—41no—
474C22×C11—41no—
475C22×C11—41no—
476C22×C11—81no—
477C22×C11—81no—
478C22×C11—81no—
479C22×C11—81no—
480C22×C11C2×#12011yescharacteristic
481C22×C11D4211yescharacteristic
482C22×C11#54611yescharacteristic
483C22×C11#57511yescharacteristic
484C22×C11#57511yescharacteristic
485C22×C11#57711yescharacteristic
486C22×C11#57711yescharacteristic
487C2×D11—81no—
488C2×D11—81no—
489C2×D11—81no—
490C2×D11—81no—
491C2×D11—81no—
492C2×D11—81no—
493C2×D11—81no—
494C4×C11—22no—
495C4×C11—24no—
496C4×C11—41no—
497C4×C11—42no—
498C4×C11—41no—
499C4×C11—42no—
500C4×C11—41no—
501C4×C11C2×#12111yescharacteristic
502C4×C11#53411yescharacteristic
503C4×C11D4211yescharacteristic
504C4×C11#54611yescharacteristic
505Dic11—42no—
506Dic11—81no—
507Dic11—81no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C22×Q8—21no—
515C22×Q8—22no—
516C22×Q8—22no—
517C22×Q8—22no—
518C22×Q8—41no—
519C22×Q8—41no—
520C22×Q8C22⋊D1114yescomplemented
521C22×Q8C22×D1111yescharacteristic
522C22×Q8C22×D1111yescharacteristic
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—111no—
526C22×D4—221no—
527C22×D4—221no—
528C22×D4C22⋊D1111yescharacteristic
529C22×D4C22×D1111yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C2×SD16—222no—
535C2×SD16—222no—
536C2×SD16—222no—
537C2×SD16—222no—
538C2×SD16—441no—
539C2×SD16—441no—
540C2×D8—222no—
541C2×D8—222no—
542C2×D8—441no—
543C2×M16—222no—
544C2×M16—222no—
545C2×M16—441no—
546C22×C8—111no—
547C22×C8—111no—
548C22×C8—111no—
549C22×C8—111no—
550#124—28no—
551#124—22no—
552#124—22no—
553C22⋊Q8—28no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556#121—28no—
557#121—22no—
558#121—222no—
559#121—222no—
560#121—222no—
561#121—441no—
562#121C22⋊D1114yescomplemented
563C4×Q8—22no—
564C4×Q8—22no—
565C4×D4—28no—
566C4×D4—22no—
567C4×D4—22no—
568#117—222no—
569#117—441no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—111no—
573C2×C4⋊C4—111no—
574C2×C4⋊C4—111no—
575C2×C4⋊C4—221no—
576C2×C4⋊C4C22⋊D1111yescharacteristic
577C2×C4⋊C4C22×D1111yescharacteristic
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—221no—
583C2×C22⋊C4—221no—
584C2×C22⋊C4—221no—
585C2×C22⋊C4—221no—
586C2×C22⋊C4—221no—
587C2×C22⋊C4—221no—
588C2×C22⋊C4C22⋊D1111yescharacteristic
589C2×C22⋊C4C22⋊D1111yescharacteristic
590C2×C42—21no—
591C2×C42—221no—
592C2×C42C22×D1111yescharacteristic
593#106—222no—
594#103—114no—
595#103—222no—
596#103—222no—
597#103—222no—
598#103—222no—
599#103—222no—
600#102—222no—
601#102—222no—
602#102—222no—
603#102—441no—
604C22⋊C8—222no—
605C22⋊C8—222no—
606C22⋊C8—441no—
607#95—221no—
608#95—221no—
609C2×C11—42no—
610C2×C11—81no—
611C2×C11—82no—
612C2×C11#241011yescharacteristic
613C2×C11#300511yescharacteristic
614C2×C11#301011yescharacteristic
615C2×C11#327111yescharacteristic
616C2×C11#327511yescharacteristic
617C2×C11#332111yescharacteristic
618C2×C11#332611yescharacteristic
619D11—161no—
620C24—21no—
621C24—221no—
622C24C2×C22⋊D1111yescharacteristic
623C24C2×C22⋊D1111yescharacteristic
624#41—44no—
625#41—44no—
626#41—44no—
627#41—44no—
628C2×Q8—24no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—28no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8D4×D1112yes—
644C2×Q8#434112yes—
645C2×Q8C2×C22⋊D1112yes—
646C2×Q8C2×C22⋊D1112yes—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—41no—
656C2×D4—41no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—221no—
662C2×D4—221no—
663C2×D4—221no—
664C2×D4—221no—
665C2×D4—221no—
666C2×D4—221no—
667C2×D4—442no—
668C2×D4—442no—
669C2×D4—442no—
670C2×D4—881no—
671C2×D4—881no—
672C2×D4—881no—
673C2×D4C2×C22⋊D1112yes—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4C2×C22⋊D1111yescharacteristic
697C22×C4C2×C22⋊D1111yescharacteristic
698C22×C4C2×C22⋊D1111yescharacteristic
699C22×C4C2×C22⋊D1111yescharacteristic
700C22×C4C2×C22⋊D1112yes—
701C22×C4C2×C22⋊D1112yes—
702C22×C4C23×D1111yescharacteristic
703SD16—444no—
704SD16—444no—
705D8—444no—
706M16—444no—
707C2×C8—112no—
708C2×C8—221no—
709C2×C8—221no—
710C2×C8—221no—
711C2×C8—221no—
712C2×C8—221no—
713C2×C8—221no—
714C2×C8—221no—
715C2×C8—221no—
716C2×C8—221no—
717C2×C8—221no—
718C2×C8—221no—
719C4⋊C4—24no—
720C4⋊C4—24no—
721C4⋊C4—22no—
722C4⋊C4—21no—
723C4⋊C4—112no—
724C4⋊C4—221no—
725C4⋊C4—221no—
726C4⋊C4—221no—
727C4⋊C4—221no—
728C4⋊C4—221no—
729C4⋊C4—881no—
730C4⋊C4C2×C22⋊D1112yes—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—22no—
735C22⋊C4—24no—
736C22⋊C4—22no—
737C22⋊C4—442no—
738C22⋊C4—442no—
739C22⋊C4—442no—
740C22⋊C4—442no—
741C22⋊C4—881no—
742C22⋊C4—881no—
743C42—24no—
744C42—21no—
745C42—21no—
746C42—442no—
747C11#2445511yescharacteristic, complemented, Sylow
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—22no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—441no—
769C23—441no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23#6700612yes—
776C23C22×C22⋊D1111yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8#6699214yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—441no—
794D4—441no—
795D4—441no—
796D4—441no—
797D4—884no—
798D4—884no—
799C2×C4—21no—
800C2×C4—22no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—222no—
830C2×C4—441no—
831C2×C4—441no—
832C2×C4—441no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—441no—
837C2×C4—441no—
838C2×C4#6700612yes—
839C2×C4C2×D4×D1111yescharacteristic
840C2×C4C2×#434111yescharacteristic
841C2×C4#6703711yescharacteristic
842C2×C4#6703711yescharacteristic
843C2×C4C22×C22⋊D1111yescharacteristic
844C2×C4C22×C22⋊D1111yescharacteristic
845C8—222no—
846C8—441no—
847C8—441no—
848C8—441no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—41no—
865C22—41no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—881no—
871C22—881no—
872C22—881no—
873C22—881no—
874C22—881no—
875C22—881no—
876C22—881no—
877C22D4×C22⋊D1111yescharacteristic
878C22#1062333711yescharacteristic
879C22#1062335311yescharacteristic
880C22#1062335311yescharacteristic
881C22#1062336811yescharacteristic
882C22#1062336811yescharacteristic
883C22C2×#6700611yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—442no—
892C4—881no—
893C4—881no—
894C4D4×C22⋊D1111yescharacteristic
895C4C2×#6699211yescharacteristic
896C4#1062333511yescharacteristic
897C4#1062333711yescharacteristic
898C2—42no—
899C2—81no—
900C2—82no—
901C2—1761no—
902C2#1307199011yescharacteristic
903C2#1307785811yescharacteristic
904C2#1307790211yescharacteristic
905C2#1308020211yescharacteristic
906C2#1308024811yescharacteristic
907C2#1308080211yescharacteristic
908C2#1308086911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#548C2
socleC23×C11C22×D4
hypercenterC2×#548D11
hypocenterC11#24455
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#10622652C2semidirect
2. C2×#10622851C2semidirect
3. C2×#10622840C2semidirect
4. C2×#10622838C2semidirect
5. #13072034C2semidirect
6. #13069852C2semidirect
7. #13069809C2semidirect
8. #13069693C2semidirect
9. #13069617C2semidirect
10. #13068971C2semidirect
11. #13068939C2semidirect
12. #13068914C2semidirect
13. #13068884C2semidirect
14. #13068556C2semidirect
15. C2×C11×#548C2semidirect
77. C22×Q8×C11D4semidirect
99. C11×#121D4semidirect
155. #66899D4semidirect
294. C2×#548D11semidirect
520. C22×Q8C22⋊D11semidirect
562. #121C22⋊D11semidirect
747. C11#24455semidirect

Maximal subgroups

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

subgroupindex
C2×#106226522
C2×#106228512
C2×#106228402
C2×#106228382
#130720342
#130698522
#130698092
#130696932
#130696172
#130689712
#130689392
#130689142
#130688842
#130685562
C2×C11×#5482
#2445511