Finite Group Databasebeta

← #14660280

Subgroups — #14660280

Order 2816.

1922 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic
2C22×#66885C211yesmaximal, characteristic, complemented
3C22×#66873C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×C11×#340C211yesmaximal, characteristic, complemented
8C23×D44—21no—
9C23×D44C2211yescharacteristic
10C23×C4×D11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4—21no—
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×#66948—22no—
19C2×#66948—22no—
20C2×#66948—22no—
21C2×#66948—22no—
22C2×#66948—22no—
23C2×#66948C414yescomplemented
24C2×C11⋊#95—21no—
25C2×#66885—22no—
26C2×#66885—22no—
27C2×#66885—22no—
28C2×(C2×D11)⋊C8—22no—
29C2×(C2×D11)⋊C8—22no—
30C2×(C2×D11)⋊C8—22no—
31#10622600—22no—
32#10622600—22no—
33C2×#66873—22no—
34C2×#66873—22no—
35C2×#66873—22no—
36C11×#340—22no—
37#10622167—22no—
38C24×D11—21no—
39C24×D11D411yescharacteristic
40C23×C4×C11—21no—
41C23×C4×C11—21no—
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C22×D44—21no—
46C22×D44—21no—
47C22×D44—21no—
48C22×D44—21no—
49C22×D44—21no—
50C22×D44—21no—
51C22×D44—21no—
52C22×D44—21no—
53C22×D44—24no—
54C22×D44—24no—
55C22×D44—24no—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44—42no—
60C22×D44—42no—
61C22×D44—42no—
62C22×D44—42no—
63C22×D44C2×C412yes—
64C22×D44D412yes—
65C22×D44D412yes—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C22×C4×D11—21no—
77C22×C4×D11—21no—
78C22×C4×D11C2×C412yes—
79C22×C4×D11D412yes—
80C22×C8×C11—21no—
81C22×C8×C11—21no—
82C22×C8×C11—21no—
83C22×C8×C11—21no—
84C22×C8×C11—21no—
85C22×C8×C11—21no—
86C22×C8×C11D412yescomplemented
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4—21no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4—21no—
95C2×C11×C4⋊C4C2×C412yes—
96C2×C11×C4⋊C4D412yes—
97C2×C11×C4⋊C4D412yes—
98C2×C11×C4⋊C4D412yescomplemented
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—42no—
104C2×(C2×D11)⋊C4—42no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11D412yescomplemented
111C22×C11⋊C8—21no—
112C22×C11⋊C8—21no—
113C22×C11⋊C8—21no—
114C22×C11⋊C8—21no—
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8D412yescomplemented
118#66948—28no—
119#66948—28no—
120#66948—28no—
121#66948—28no—
122C11⋊#95—24no—
123#66885—28no—
124(C2×D11)⋊C8—28no—
125#66873—28no—
126#10969—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C23×D11—21no—
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—22no—
141C23×D11—22no—
142C23×D11—22no—
143C23×D11—41no—
144C23×D11—41no—
145C23×D11—41no—
146C23×D11—41no—
147C23×D11—41no—
148C23×D11—41no—
149C23×D11—41no—
150C23×D11—41no—
151C23×D11—41no—
152C23×D11—41no—
153C23×D11—41no—
154C23×D11—41no—
155C23×D11C22⋊C412yes—
156C23×D11D812yes—
157C23×D11SD1612yes—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—41no—
163C22×C4×C11—41no—
164C22×C4×C11—41no—
165C22×C4×C11—41no—
166C22×C4×C11—41no—
167C22×C4×C11—41no—
168C22×C4×C11—41no—
169C22×C4×C11—41no—
170C22×C4×C11—41no—
171C22×C4×C11—41no—
172C22×C4×C11C22×C411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11#4111yescharacteristic
183C22×C4×C11#4111yescharacteristic
184C22×C4×C11#4111yescharacteristic
185C22×C4×C11#4111yescharacteristic
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—41no—
194C22×Dic11—41no—
195C22×Dic11—41no—
196C22×Dic11—41no—
197C22×Dic11—41no—
198C22×Dic11—41no—
199C22×Dic11C22⋊C412yes—
200C2×D44—216no—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—22no—
209C2×D44—22no—
210C2×D44—22no—
211C2×D44—22no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44—22no—
215C2×D44—22no—
216C2×D44—48no—
217C2×D44—48no—
218C2×D44—48no—
219C2×D44—48no—
220C2×D44—48no—
221C2×D44—48no—
222C2×D44—41no—
223C2×D44—41no—
224C2×D44—41no—
225C2×D44—41no—
226C2×D44—41no—
227C2×D44—41no—
228C2×D44—41no—
229C2×D44—41no—
230C2×D44—41no—
231C2×D44—41no—
232C2×D44—41no—
233C2×D44—41no—
234C2×D44C22⋊C414yescomplemented
235C2×C4×D11—22no—
236C2×C4×D11—22no—
237C2×C4×D11—22no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—22no—
244C2×C4×D11—22no—
245C2×C4×D11—22no—
246C2×C4×D11—22no—
247C2×C4×D11—41no—
248C2×C4×D11—41no—
249C2×C4×D11—41no—
250C2×C4×D11—41no—
251C2×C4×D11—41no—
252C2×C4×D11—41no—
253C2×C4×D11—41no—
254C2×C4×D11—41no—
255C2×C4×D11—41no—
256C2×C4×D11—41no—
257C2×C4×D11—41no—
258C2×C4×D11—41no—
259C2×C4×D11—41no—
260C2×C4×D11—41no—
261C2×C4×D11—41no—
262C2×C4×D11—41no—
263C2×C8×C11—22no—
264C2×C8×C11—22no—
265C2×C8×C11—22no—
266C2×C8×C11—41no—
267C2×C8×C11—41no—
268C2×C8×C11—41no—
269C2×C8×C11—41no—
270C11×C4⋊C4—22no—
271C11×C4⋊C4—22no—
272C11×C4⋊C4—22no—
273C11×C4⋊C4—22no—
274C11×C4⋊C4—22no—
275C11×C4⋊C4—41no—
276C11×C4⋊C4—41no—
277C11×C4⋊C4C22⋊C414yescomplemented
278(C2×D11)⋊C4—216no—
279(C2×D11)⋊C4—48no—
280C4⋊Dic11—22no—
281C4⋊Dic11—22no—
282C4⋊Dic11—41no—
283C4⋊Dic11—41no—
284C2×C11⋊C8—22no—
285C2×C11⋊C8—22no—
286C2×C11⋊C8—22no—
287C2×C11⋊C8—41no—
288C2×C11⋊C8—41no—
289C2×C11⋊C8—41no—
290C2×C11⋊C8—41no—
291C22×#121—111no—
292C22×#102—111no—
293C22×#102—111no—
294C22×C22⋊C8—111no—
295C2×#380—111no—
296C2×#340—111no—
297C2×#340D1111yescharacteristic, complemented
298C23×C11C2×C22⋊C411yescharacteristic
299C23×C11#12011yescharacteristic
300C23×C11#12011yescharacteristic
301C23×C11#12011yescharacteristic
302C23×C11#12111yescharacteristic
303C23×C11#12111yescharacteristic
304C23×C11#12311yescharacteristic
305C23×C11C2×D811yescharacteristic
306C23×C11C2×SD1611yescharacteristic
307C23×C11#13511yescharacteristic
308C23×C11#13511yescharacteristic
309C23×C11AGL(1,ℤ/8)11yescharacteristic
310C23×C11AGL(1,ℤ/8)11yescharacteristic
311C23×C11AGL(1,ℤ/8)11yescharacteristic
312C23×C11#13711yescharacteristic
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—24no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—81no—
367C22×D11—81no—
368C22×D11—81no—
369C22×D11—81no—
370C22×D11—81no—
371C22×D11—81no—
372C22×D11—81no—
373C22×D11—81no—
374C22×D11—81no—
375C22×D11—81no—
376C22×D11—81no—
377C22×D11—81no—
378C22×D11—81no—
379C22×D11—81no—
380C22×D11—81no—
381C22×D11—81no—
382C22×D11#10214yescomplemented
383C2×C4×C11—24no—
384C2×C4×C11—42no—
385C2×C4×C11—42no—
386C2×C4×C11—42no—
387C2×C4×C11—42no—
388C2×C4×C11—42no—
389C2×C4×C11—42no—
390C2×C4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11—42no—
393C2×C4×C11—81no—
394C2×C4×C11—81no—
395C2×C4×C11—81no—
396C2×C4×C11—81no—
397C2×C4×C11C2×C22⋊C411yescharacteristic
398C2×C4×C11C2×C22⋊C411yescharacteristic
399C2×C4×C11C4×D411yescharacteristic
400C2×C4×C11C4×D411yescharacteristic
401C2×C4×C11C4×D411yescharacteristic
402C2×C4×C11C4×D411yescharacteristic
403C2×C4×C11#12011yescharacteristic
404C2×C4×C11#12011yescharacteristic
405C2×C4×C11#12011yescharacteristic
406C2×C4×C11#12011yescharacteristic
407C2×C4×C11#12011yescharacteristic
408C2×C4×C11#12111yescharacteristic
409C2×C4×C11#12111yescharacteristic
410C2×C4×C11#12111yescharacteristic
411C2×C4×C11#12111yescharacteristic
412C2×C4×C11#12111yescharacteristic
413C2×C4×C11#12111yescharacteristic
414C2×C4×C11#12111yescharacteristic
415C2×C4×C11#12111yescharacteristic
416C2×C4×C11#12111yescharacteristic
417C2×C4×C11#12111yescharacteristic
418C2×C4×C11#12311yescharacteristic
419C2×C4×C11#12311yescharacteristic
420C2×C4×C11#12311yescharacteristic
421C2×C4×C11#12411yescharacteristic
422C2×C4×C11#12411yescharacteristic
423C2×C4×C11#12711yescharacteristic
424C2×C4×C11#12711yescharacteristic
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—42no—
433C2×Dic11—42no—
434C2×Dic11—42no—
435C2×Dic11—81no—
436C2×Dic11—81no—
437C2×Dic11—81no—
438C2×Dic11—81no—
439D44—24no—
440D44—24no—
441D44—432no—
442D44—42no—
443D44—42no—
444D44—42no—
445D44—42no—
446D44—42no—
447D44—42no—
448C4×D11—42no—
449C4×D11—42no—
450C4×D11—42no—
451C4×D11—42no—
452C4×D11—42no—
453C4×D11—42no—
454C4×D11—42no—
455C4×D11—42no—
456C8×C11—42no—
457C11⋊C8—42no—
458C23×D4—111no—
459C23×D4—221no—
460C24×C4—111no—
461C23×C8—111no—
462C23×C8C2×D1111yescharacteristic
463C2×#121—114no—
464C2×#121—222no—
465C2×#121—222no—
466C2×#121—222no—
467C2×#121—222no—
468C2×#121—222no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4C2×D1111yescharacteristic
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4—221no—
473C22×C22⋊C4—221no—
474C2×#102—222no—
475C2×#102—222no—
476C2×#102—222no—
477C2×#102—222no—
478C2×#102—222no—
479C2×#102—222no—
480C2×C22⋊C8—222no—
481C2×C22⋊C8—222no—
482C2×C22⋊C8—222no—
483#380—222no—
484#380—222no—
485C2×#95—221no—
486#340—22no—
487#340—222no—
488C22×C11#37911yescharacteristic
489C22×C11#38611yescharacteristic
490C22×C11#38611yescharacteristic
491C22×C11#39211yescharacteristic
492C22×C11#39211yescharacteristic
493C22×C11#39411yescharacteristic
494C22×C11#39411yescharacteristic
495C22×C11C2×#10211yescharacteristic
496C22×C11#41611yescharacteristic
497C22×C11#41711yescharacteristic
498C22×C11#41811yescharacteristic
499C22×C11#44711yescharacteristic
500C22×C11#44711yescharacteristic
501C22×C11#44711yescharacteristic
502C22×C11#44811yescharacteristic
503C22×C11#44911yescharacteristic
504C22×C11#44911yescharacteristic
505C22×C11#44911yescharacteristic
506C22×C11#44911yescharacteristic
507C22×C11#45011yescharacteristic
508C22×C11#45011yescharacteristic
509C22×C11#45211yescharacteristic
510C22×C11#45211yescharacteristic
511C22×C11#46511yescharacteristic
512C22×C11#46511yescharacteristic
513C22×C11#46611yescharacteristic
514C22×C11#46611yescharacteristic
515C22×C11#46811yescharacteristic
516C22×C11#46811yescharacteristic
517C22×C11#46911yescharacteristic
518C22×C11#46911yescharacteristic
519C22×C11#48011yescharacteristic
520C22×C11#48111yescharacteristic
521C22×C11#48211yescharacteristic
522C22×C11#48211yescharacteristic
523C2×D11—24no—
524C2×D11—24no—
525C2×D11—24no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—44no—
539C2×D11—44no—
540C2×D11—44no—
541C2×D11—82no—
542C2×D11—82no—
543C2×D11—82no—
544C2×D11—82no—
545C2×D11—82no—
546C2×D11—82no—
547C2×D11—82no—
548C2×D11—82no—
549C2×D11—82no—
550C2×D11—82no—
551C2×D11—82no—
552C2×D11—82no—
553C4×C11—44no—
554C4×C11—82no—
555C4×C11#38611yescharacteristic
556C4×C11#38611yescharacteristic
557C4×C11#39011yescharacteristic
558C4×C11#39011yescharacteristic
559C4×C11#39211yescharacteristic
560C4×C11#39211yescharacteristic
561C4×C11#39411yescharacteristic
562C4×C11#39411yescharacteristic
563Dic11—42no—
564Dic11—82no—
565C25—111no—
566C25—221no—
567C22×D4—112no—
568C22×D4—112no—
569C22×D4—112no—
570C22×D4—224no—
571C22×D4—224no—
572C22×D4—224no—
573C22×D4—221no—
574C22×D4—221no—
575C22×D4—221no—
576C22×D4—221no—
577C22×D4—221no—
578C22×D4—221no—
579C22×D4—221no—
580C22×D4—221no—
581C22×D4—221no—
582C22×D4—221no—
583C22×D4—221no—
584C22×D4—442no—
585C22×D4—442no—
586C22×D4—442no—
587C22×D4—442no—
588C23×C4—21no—
589C23×C4—21no—
590C23×C4—111no—
591C23×C4—112no—
592C23×C4—112no—
593C23×C4—221no—
594C23×C4—221no—
595C23×C4—221no—
596C23×C4—221no—
597C23×C4—221no—
598C23×C4—221no—
599C23×C4—221no—
600C23×C4—221no—
601C23×C4—221no—
602C23×C4—221no—
603C23×C4—221no—
604C23×C4—221no—
605C23×C4—221no—
606C23×C4C22×D1111yescharacteristic
607C22×C8—21no—
608C22×C8—21no—
609C22×C8—21no—
610C22×C8—21no—
611C22×C8—21no—
612C22×C8—21no—
613C22×C8—112no—
614C22×C8—221no—
615C22×C8—221no—
616C22×C8—221no—
617C22×C8—221no—
618C22×C8—221no—
619C22×C8—221no—
620C22×C8D4412yescomplemented
621#121—228no—
622#121—228no—
623#121—228no—
624#121—228no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—112no—
634C2×C4⋊C4—221no—
635C2×C4⋊C4—221no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4—221no—
638C2×C4⋊C4—221no—
639C2×C4⋊C4C4×D1112yes—
640C2×C4⋊C4D4412yes—
641C2×C4⋊C4D4412yescomplemented
642C2×C4⋊C4C22⋊D1112yes—
643C2×C22⋊C4—224no—
644C2×C22⋊C4—224no—
645C2×C22⋊C4—224no—
646C2×C22⋊C4—224no—
647C2×C22⋊C4—442no—
648C2×C22⋊C4—442no—
649#102—228no—
650#102—228no—
651C22⋊C8—228no—
652#95—224no—
653C2×C11#143811yescharacteristic
654C2×C11#178611yescharacteristic
655C2×C11#178811yescharacteristic
656C2×C11#187411yescharacteristic
657C2×C11#187511yescharacteristic
658C2×C11#189311yescharacteristic
659C2×C11#189511yescharacteristic
660C2×C11#199911yescharacteristic
661C2×C11#199911yescharacteristic
662C2×C11#200011yescharacteristic
663C2×C11#200011yescharacteristic
664C2×C11#203311yescharacteristic
665C2×C11#203311yescharacteristic
666C2×C11#203411yescharacteristic
667C2×C11#203411yescharacteristic
668D11—44no—
669D11—84no—
670C24—112no—
671C24—112no—
672C24—112no—
673C24—221no—
674C24—221no—
675C24—221no—
676C24—221no—
677C24—221no—
678C24—221no—
679C24—221no—
680C24—221no—
681C24—221no—
682C24—221no—
683C24—221no—
684C24—221no—
685C24—222no—
686C24—222no—
687C24—222no—
688C24—441no—
689C24—441no—
690C24—441no—
691C24—441no—
692C24—441no—
693C24—441no—
694C24—441no—
695C24—441no—
696C24—441no—
697C24—441no—
698C24—441no—
699C24—441no—
700C24D4×D1111yescharacteristic
701C2×D4—114no—
702C2×D4—2216no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—222no—
706C2×D4—222no—
707C2×D4—222no—
708C2×D4—222no—
709C2×D4—222no—
710C2×D4—222no—
711C2×D4—222no—
712C2×D4—222no—
713C2×D4—222no—
714C2×D4—222no—
715C2×D4—222no—
716C2×D4—222no—
717C2×D4—222no—
718C2×D4—448no—
719C2×D4—448no—
720C2×D4—448no—
721C2×D4—448no—
722C2×D4—448no—
723C2×D4—448no—
724C2×D4—441no—
725C2×D4—441no—
726C2×D4—441no—
727C2×D4—441no—
728C2×D4—441no—
729C2×D4—441no—
730C2×D4—441no—
731C2×D4—441no—
732C2×D4—441no—
733C2×D4—441no—
734C2×D4—441no—
735C2×D4—441no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—41no—
744C22×C4—41no—
745C22×C4—41no—
746C22×C4—41no—
747C22×C4—41no—
748C22×C4—41no—
749C22×C4—41no—
750C22×C4—112no—
751C22×C4—221no—
752C22×C4—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—221no—
756C22×C4—221no—
757C22×C4—222no—
758C22×C4—222no—
759C22×C4—222no—
760C22×C4—222no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—222no—
766C22×C4—222no—
767C22×C4—222no—
768C22×C4—222no—
769C22×C4—222no—
770C22×C4—441no—
771C22×C4—441no—
772C22×C4—441no—
773C22×C4—441no—
774C22×C4—441no—
775C22×C4—441no—
776C22×C4—441no—
777C22×C4—441no—
778C22×C4—441no—
779C22×C4—441no—
780C22×C4—441no—
781C22×C4—441no—
782C22×C4—441no—
783C22×C4—441no—
784C22×C4—441no—
785C22×C4—441no—
786C22×C4—441no—
787C22×C4—441no—
788C22×C4—441no—
789C22×C4—441no—
790C22×C4—441no—
791C22×C4—441no—
792C22×C4C2×C4×D1111yescharacteristic
793C22×C4C2×D4411yescharacteristic
794C22×C4C2×D4411yescharacteristic
795C22×C4C2×D4411yescharacteristic
796C22×C4#433911yescharacteristic
797C22×C4#433911yescharacteristic
798C22×C4D4×D1111yescharacteristic
799C22×C4D4×D1111yescharacteristic
800C22×C4D4×D1111yescharacteristic
801C22×C4D4×D1111yescharacteristic
802C22×C4D4×D1111yescharacteristic
803C22×C4#434311yescharacteristic
804C22×C4#434311yescharacteristic
805C22×C4C2×C22⋊D1111yescharacteristic
806C2×C8—22no—
807C2×C8—22no—
808C2×C8—22no—
809C2×C8—41no—
810C2×C8—41no—
811C2×C8—41no—
812C2×C8—41no—
813C2×C8—222no—
814C2×C8—222no—
815C2×C8—222no—
816C2×C8—441no—
817C2×C8—441no—
818C2×C8—441no—
819C2×C8—441no—
820C4⋊C4—22no—
821C4⋊C4—22no—
822C4⋊C4—22no—
823C4⋊C4—22no—
824C4⋊C4—22no—
825C4⋊C4—41no—
826C4⋊C4—41no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—441no—
830C4⋊C4—441no—
831C4⋊C4(C2×D11)⋊C414yescomplemented
832C22⋊C4—2216no—
833C22⋊C4—448no—
834C11#1096911yescharacteristic, complemented, Sylow
835C23—114no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—224no—
855C23—441no—
856C23—441no—
857C23—441no—
858C23—441no—
859C23—441no—
860C23—441no—
861C23—441no—
862C23—441no—
863C23—441no—
864C23—441no—
865C23—441no—
866C23—441no—
867C23—441no—
868C23—441no—
869C23—441no—
870C23—441no—
871C23—442no—
872C23—442no—
873C23—442no—
874C23—442no—
875C23—442no—
876C23—442no—
877C23—442no—
878C23—442no—
879C23—442no—
880C23—442no—
881C23—442no—
882C23—442no—
883C23—442no—
884C23—442no—
885C23—442no—
886C23—442no—
887C23—442no—
888C23—442no—
889C23—881no—
890C23—881no—
891C23—881no—
892C23—881no—
893C23—881no—
894C23—881no—
895C23—881no—
896C23—881no—
897C23—881no—
898C23—881no—
899C23—881no—
900C23—881no—
901C23—881no—
902C23—881no—
903C23—881no—
904C23—881no—
905C23C22⋊C4×D1111yescharacteristic
906C23#6693511yescharacteristic
907C23#6693511yescharacteristic
908C23#6693711yescharacteristic
909C23#6694711yescharacteristic
910C23#6694811yescharacteristic
911C23D8×D1111yescharacteristic
912C23#6696411yescharacteristic
913C23SD16×D1111yescharacteristic
914C23#6696711yescharacteristic
915C23#6696711yescharacteristic
916C23#6696911yescharacteristic
917C23#6697111yescharacteristic
918C23#6697211yescharacteristic
919C23#6699011yescharacteristic
920D4—224no—
921D4—224no—
922D4—4432no—
923D4—442no—
924D4—442no—
925D4—442no—
926D4—442no—
927D4—442no—
928D4—442no—
929C2×C4—24no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—42no—
933C2×C4—42no—
934C2×C4—42no—
935C2×C4—42no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—42no—
939C2×C4—81no—
940C2×C4—81no—
941C2×C4—81no—
942C2×C4—81no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—441no—
947C2×C4—441no—
948C2×C4—441no—
949C2×C4—441no—
950C2×C4—442no—
951C2×C4—442no—
952C2×C4—442no—
953C2×C4—442no—
954C2×C4—442no—
955C2×C4—442no—
956C2×C4—442no—
957C2×C4—442no—
958C2×C4—442no—
959C2×C4—442no—
960C2×C4—442no—
961C2×C4—881no—
962C2×C4—881no—
963C2×C4—881no—
964C2×C4—881no—
965C2×C4C4×D4411yescharacteristic
966C2×C4C4×D4411yescharacteristic
967C2×C4#6692711yescharacteristic
968C2×C4#6692811yescharacteristic
969C2×C4C22⋊C4×D1111yescharacteristic
970C2×C4#6693511yescharacteristic
971C2×C4#6693511yescharacteristic
972C2×C4#6693511yescharacteristic
973C2×C4#6693511yescharacteristic
974C2×C4#6693711yescharacteristic
975C2×C4#6693711yescharacteristic
976C2×C4#6693711yescharacteristic
977C2×C4#6694611yescharacteristic
978C2×C4#6694611yescharacteristic
979C2×C4#6694711yescharacteristic
980C2×C4#6694711yescharacteristic
981C2×C4#6694711yescharacteristic
982C2×C4#6694811yescharacteristic
983C2×C4#6694811yescharacteristic
984C2×C4#6694811yescharacteristic
985C2×C4#6694811yescharacteristic
986C2×C4#6694811yescharacteristic
987C2×C4C2×(C2×D11)⋊C411yescharacteristic
988C2×C4#6698311yescharacteristic
989C2×C4#6698311yescharacteristic
990C2×C4#6699011yescharacteristic
991C2×C4#6699311yescharacteristic
992C2×C4#6700011yescharacteristic
993C8—42no—
994C8—442no—
995C22—224no—
996C22—224no—
997C22—224no—
998C22—442no—
999C22—442no—
1000C22—442no—
1001C22—442no—
1002C22—442no—
1003C22—442no—
1004C22—442no—
1005C22—442no—
1006C22—442no—
1007C22—442no—
1008C22—442no—
1009C22—442no—
1010C22—444no—
1011C22—444no—
1012C22—444no—
1013C22—882no—
1014C22—882no—
1015C22—882no—
1016C22—882no—
1017C22—882no—
1018C22—882no—
1019C22—882no—
1020C22—882no—
1021C22—882no—
1022C22—882no—
1023C22—882no—
1024C22—882no—
1025C22#1062227811yescharacteristic
1026C22#1062227811yescharacteristic
1027C22#1062228411yescharacteristic
1028C22#1062228511yescharacteristic
1029C22D11×#10211yescharacteristic
1030C22#1062238311yescharacteristic
1031C22#1062238611yescharacteristic
1032C22#1062238611yescharacteristic
1033C22#1062238811yescharacteristic
1034C22#1062238911yescharacteristic
1035C22#1062239411yescharacteristic
1036C22#1062239511yescharacteristic
1037C22#1062241611yescharacteristic
1038C22#1062241711yescharacteristic
1039C22#1062241911yescharacteristic
1040C22#1062242011yescharacteristic
1041C22#1062242311yescharacteristic
1042C22#1062242411yescharacteristic
1043C22#1062242411yescharacteristic
1044C22#1062242511yescharacteristic
1045C22#1062247611yescharacteristic
1046C22#1062247711yescharacteristic
1047C22#1062247811yescharacteristic
1048C22#1062247911yescharacteristic
1049C22#1062249511yescharacteristic
1050C22#1062249611yescharacteristic
1051C22#1062249811yescharacteristic
1052C22#1062249911yescharacteristic
1053C22#1062256811yescharacteristic
1054C22#1062257311yescharacteristic
1055C22#1062260411yescharacteristic
1056C22#1062276911yescharacteristic
1057C22#1062278211yescharacteristic
1058C22#1062278511yescharacteristic
1059C22#1062280011yescharacteristic
1060C4—44no—
1061C4—82no—
1062C4—442no—
1063C4—882no—
1064C4#1062227811yescharacteristic
1065C4#1062227811yescharacteristic
1066C4#1062228411yescharacteristic
1067C4#1062228511yescharacteristic
1068C4#1062255211yescharacteristic
1069C4#1062257311yescharacteristic
1070C4#1062260111yescharacteristic
1071C4#1062260411yescharacteristic
1072C2—444no—
1073C2—884no—
1074C2#1306685611yescharacteristic
1075C2#1306854511yescharacteristic
1076C2#1306855511yescharacteristic
1077C2#1306893211yescharacteristic
1078C2#1306893711yescharacteristic
1079C2#1306904311yescharacteristic
1080C2#1306905311yescharacteristic
1081C2#1306961311yescharacteristic
1082C2#1306961511yescharacteristic
1083C2#1306961811yescharacteristic
1084C2#1306962211yescharacteristic
1085C2#1306980011yescharacteristic
1086C2#1306980111yescharacteristic
1087C2#1306980711yescharacteristic
1088C2#1306980811yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC22×#66948C2
cosocleC23×C4×C11C23
hypercenterC2×#340D11
hypocenterC11#10969
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#66885C2semidirect
3. C22×#66873C2semidirect
4. C22×(C2×D11)⋊C8C2semidirect
5. C2×#10622600C2semidirect
6. C2×#10622167C2semidirect
7. C2×C11×#340C2semidirect
23. C2×#66948C4semidirect
86. C22×C8×C11D4semidirect
98. C2×C11×C4⋊C4D4semidirect
110. C2×C4⋊Dic11D4semidirect
117. C22×C11⋊C8D4semidirect
234. C2×D44C22⋊C4semidirect
277. C11×C4⋊C4C22⋊C4semidirect
297. C2×#340D11semidirect
382. C22×D11#102semidirect
620. C22×C8D44semidirect
641. C2×C4⋊C4D44semidirect
831. C4⋊C4(C2×D11)⋊C4semidirect
834. C11#10969semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#668852
C22×#668732
C22×(C2×D11)⋊C82
C2×#106226002
C2×#106221672
C2×C11×#3402
#1096911