Finite Group Databasebeta

← #14660278

Subgroups — #14660278

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×#66991C211yesmaximal, characteristic
2C22×#66896C211yesmaximal, characteristic, complemented
3C22×(C2×D11)⋊C8C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic, complemented
5C2×#10622189C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C22×C11×#102C211yesmaximal, characteristic, complemented
8C23×D4×C11C2211yescharacteristic
9C23×C22⋊D11—21no—
10C23×C4×D11C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C2×#66991—22no—
15C2×#66991—22no—
16C2×#66991—22no—
17C2×#66991—22no—
18C2×#66991—22no—
19C2×#66991C414yescomplemented
20C22×(C2×D11)⋊C4—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C2×C11×#102—22no—
25C2×C11×#102—22no—
26C2×C11×#102—22no—
27C2×#66896—22no—
28C2×#66896—22no—
29C2×#66896—22no—
30C2×C11⋊#95—21no—
31C2×(C2×D11)⋊C8—22no—
32C2×(C2×D11)⋊C8—22no—
33C2×(C2×D11)⋊C8—22no—
34#10622600—22no—
35#10622600—22no—
36#10622189—22no—
37#10622167—22no—
38C25×C11—21no—
39C24×D11D411yescharacteristic
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11—21no—
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11—21no—
50C22×D4×C11—21no—
51C22×D4×C11C2×C412yes—
52C22×D4×C11D412yes—
53C22×D4×C11D412yes—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11—42no—
60C22×C22⋊D11—42no—
61C22×C22⋊D11—42no—
62C22×C22⋊D11—42no—
63C23×Dic11—21no—
64C23×Dic11—21no—
65C23×Dic11D411yescharacteristic
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⋊C4D412yescomplemented
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—24no—
96#66991—28no—
97#66991—28no—
98#66991—28no—
99#66991—28no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—42no—
102C2×(C2×D11)⋊C4—42no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11—21no—
107C2×C4⋊Dic11—21no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11—21no—
111C2×C4⋊Dic11C2×C412yes—
112C2×C4⋊Dic11D412yes—
113C2×C4⋊Dic11D412yes—
114C2×C4⋊Dic11D412yescomplemented
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8—21no—
118C22×C11⋊C8—21no—
119C22×C11⋊C8—21no—
120C22×C11⋊C8—21no—
121C22×C11⋊C8D412yescomplemented
122C11×#102—28no—
123#66896—28no—
124C11⋊#95—24no—
125(C2×D11)⋊C8—28no—
126#10969—111nomaximal, Sylow
127C24×C11—22no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—41no—
131C24×C11—41no—
132C24×C11—41no—
133C24×C11—41no—
134C24×C11—41no—
135C24×C11—41no—
136C24×C11—41no—
137C24×C11—41no—
138C24×C11—41no—
139C24×C11—41no—
140C24×C11—41no—
141C24×C11—41no—
142C24×C11C2×D411yescharacteristic
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11C22⋊C412yes—
156C23×D11D812yes—
157C23×D11SD1612yes—
158C2×D4×C11—22no—
159C2×D4×C11—22no—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—22no—
166C2×D4×C11—22no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—41no—
174C2×D4×C11—41no—
175C2×D4×C11—41no—
176C2×D4×C11—41no—
177C2×D4×C11—41no—
178C2×D4×C11—41no—
179C2×D4×C11—41no—
180C2×D4×C11—41no—
181C2×D4×C11—41no—
182C2×D4×C11—41no—
183C2×D4×C11—41no—
184C2×D4×C11—41no—
185C2×D4×C11C22⋊C414yescomplemented
186C22×C4×C11—22no—
187C22×C4×C11—41no—
188C22×C4×C11—41no—
189C22×C4×C11—41no—
190C22×C4×C11—41no—
191C22×C4×C11—41no—
192C22×C4×C11—41no—
193C22×C4×C11C22×C411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D411yescharacteristic
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11#4111yescharacteristic
204C22×C4×C11#4111yescharacteristic
205C22×C4×C11#4111yescharacteristic
206C22×C4×C11#4111yescharacteristic
207C2×C22⋊D11—216no—
208C2×C22⋊D11—48no—
209C2×C22⋊D11—48no—
210C2×C22⋊D11—48no—
211C2×C22⋊D11—48no—
212C2×C22⋊D11—48no—
213C2×C22⋊D11—48no—
214C22×Dic11—22no—
215C22×Dic11—21no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—22no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—41no—
225C22×Dic11—41no—
226C22×Dic11—41no—
227C22×Dic11—41no—
228C22×Dic11—41no—
229C22×Dic11—41no—
230C22×Dic11—41no—
231C22×Dic11—41no—
232C22×Dic11—41no—
233C22×Dic11—41no—
234C22×Dic11C22⋊C412yes—
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—41no—
273C11×C4⋊C4—41no—
274C22⋊Dic11—216no—
275(C2×D11)⋊C4—48no—
276C4⋊Dic11—22no—
277C4⋊Dic11—22no—
278C4⋊Dic11—22no—
279C4⋊Dic11—22no—
280C4⋊Dic11—22no—
281C4⋊Dic11—41no—
282C4⋊Dic11—41no—
283C4⋊Dic11C22⋊C414yescomplemented
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×#102D1111yescharacteristic, complemented
294C22×C22⋊C8—111no—
295C2×#380—111no—
296C2×#340—111no—
297C2×#340—111no—
298C23×C11—24no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11—42no—
310C23×C11—42no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—81no—
318C23×C11—81no—
319C23×C11—81no—
320C23×C11—81no—
321C23×C11—81no—
322C23×C11—81no—
323C23×C11—81no—
324C23×C11—81no—
325C23×C11—81no—
326C23×C11—81no—
327C23×C11—81no—
328C23×C11—81no—
329C23×C11—81no—
330C23×C11—81no—
331C23×C11—81no—
332C23×C11—81no—
333C23×C11C2×C22⋊C411yescharacteristic
334C23×C11#12011yescharacteristic
335C23×C11#12011yescharacteristic
336C23×C11#12011yescharacteristic
337C23×C11#12111yescharacteristic
338C23×C11#12111yescharacteristic
339C23×C11#12311yescharacteristic
340C23×C11C2×D811yescharacteristic
341C23×C11C2×SD1611yescharacteristic
342C23×C11#13511yescharacteristic
343C23×C11#13511yescharacteristic
344C23×C11AGL(1,ℤ/8)11yescharacteristic
345C23×C11AGL(1,ℤ/8)11yescharacteristic
346C23×C11AGL(1,ℤ/8)11yescharacteristic
347C23×C11#13711yescharacteristic
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—41no—
367C22×D11—41no—
368C22×D11—41no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11—41no—
382C22×D11#10214yescomplemented
383D4×C11—24no—
384D4×C11—24no—
385D4×C11—42no—
386D4×C11—42no—
387D4×C11—42no—
388D4×C11—42no—
389D4×C11—42no—
390D4×C11—42no—
391C2×C4×C11—42no—
392C2×C4×C11—42no—
393C2×C4×C11—42no—
394C2×C4×C11—81no—
395C2×C4×C11—81no—
396C2×C4×C11—81no—
397C2×C4×C11—81no—
398C2×C4×C11C2×C22⋊C411yescharacteristic
399C2×C4×C11C2×C22⋊C411yescharacteristic
400C2×C4×C11C4×D411yescharacteristic
401C2×C4×C11C4×D411yescharacteristic
402C2×C4×C11C4×D411yescharacteristic
403C2×C4×C11C4×D411yescharacteristic
404C2×C4×C11#12011yescharacteristic
405C2×C4×C11#12011yescharacteristic
406C2×C4×C11#12011yescharacteristic
407C2×C4×C11#12011yescharacteristic
408C2×C4×C11#12011yescharacteristic
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#12111yescharacteristic
419C2×C4×C11#12311yescharacteristic
420C2×C4×C11#12311yescharacteristic
421C2×C4×C11#12311yescharacteristic
422C2×C4×C11#12411yescharacteristic
423C2×C4×C11#12411yescharacteristic
424C2×C4×C11#12711yescharacteristic
425C2×C4×C11#12711yescharacteristic
426C22⋊D11—432no—
427C2×Dic11—24no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—42no—
436C2×Dic11—42no—
437C2×Dic11—42no—
438C2×Dic11—42no—
439C2×Dic11—42no—
440C2×Dic11—42no—
441C2×Dic11—42no—
442C2×Dic11—42no—
443C2×Dic11—42no—
444C2×Dic11—81no—
445C2×Dic11—81no—
446C2×Dic11—81no—
447C2×Dic11—81no—
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—221no—
459C23×D4C2×D1111yescharacteristic
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⋊C4—111no—
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4—221no—
473C22×C22⋊C4—221no—
474C2×#102—22no—
475C2×#102—22no—
476C2×#102—22no—
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—222no—
487#340—222no—
488C22×C11—44no—
489C22×C11—44no—
490C22×C11—44no—
491C22×C11—82no—
492C22×C11—82no—
493C22×C11—82no—
494C22×C11—82no—
495C22×C11—82no—
496C22×C11—82no—
497C22×C11—82no—
498C22×C11—82no—
499C22×C11—82no—
500C22×C11—82no—
501C22×C11—82no—
502C22×C11—82no—
503C22×C11#37911yescharacteristic
504C22×C11#38611yescharacteristic
505C22×C11#38611yescharacteristic
506C22×C11#39211yescharacteristic
507C22×C11#39211yescharacteristic
508C22×C11#39411yescharacteristic
509C22×C11#39411yescharacteristic
510C22×C11C2×#10211yescharacteristic
511C22×C11#41611yescharacteristic
512C22×C11#41711yescharacteristic
513C22×C11#41811yescharacteristic
514C22×C11#44711yescharacteristic
515C22×C11#44711yescharacteristic
516C22×C11#44711yescharacteristic
517C22×C11#44811yescharacteristic
518C22×C11#44911yescharacteristic
519C22×C11#44911yescharacteristic
520C22×C11#44911yescharacteristic
521C22×C11#44911yescharacteristic
522C22×C11#45011yescharacteristic
523C22×C11#45011yescharacteristic
524C22×C11#45211yescharacteristic
525C22×C11#45211yescharacteristic
526C22×C11#46511yescharacteristic
527C22×C11#46511yescharacteristic
528C22×C11#46611yescharacteristic
529C22×C11#46611yescharacteristic
530C22×C11#46811yescharacteristic
531C22×C11#46811yescharacteristic
532C22×C11#46911yescharacteristic
533C22×C11#46911yescharacteristic
534C22×C11#48011yescharacteristic
535C22×C11#48111yescharacteristic
536C22×C11#48211yescharacteristic
537C22×C11#48211yescharacteristic
538C2×D11—24no—
539C2×D11—24no—
540C2×D11—24no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—42no—
544C2×D11—42no—
545C2×D11—42no—
546C2×D11—42no—
547C2×D11—42no—
548C2×D11—42no—
549C2×D11—42no—
550C2×D11—42no—
551C2×D11—42no—
552C2×D11—42no—
553C4×C11—82no—
554C4×C11#38611yescharacteristic
555C4×C11#38611yescharacteristic
556C4×C11#39011yescharacteristic
557C4×C11#39011yescharacteristic
558C4×C11#39211yescharacteristic
559C4×C11#39211yescharacteristic
560C4×C11#39411yescharacteristic
561C4×C11#39411yescharacteristic
562Dic11—42no—
563Dic11—44no—
564Dic11—82no—
565C25—21no—
566C25—111no—
567C22×D4—21no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—21no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—224no—
579C22×D4—224no—
580C22×D4—224no—
581C22×D4—442no—
582C22×D4—442no—
583C22×D4—442no—
584C22×D4—442no—
585C22×D4C4×D1112yes—
586C22×D4D4412yes—
587C22×D4C22⋊D1112yes—
588C23×C4—21no—
589C23×C4—111no—
590C23×C4—112no—
591C23×C4—112no—
592C23×C4—221no—
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×C8C22⋊D1112yescomplemented
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—112no—
631C2×C4⋊C4—112no—
632C2×C4⋊C4—112no—
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⋊C4—221no—
640C2×C4⋊C4—221no—
641C2×C4⋊C4—221no—
642C2×C4⋊C4C22⋊D1112yescomplemented
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—28no—
650#102—228no—
651C22⋊C8—228no—
652#95—224no—
653C2×C11—84no—
654C2×C11#143811yescharacteristic
655C2×C11#178611yescharacteristic
656C2×C11#178811yescharacteristic
657C2×C11#187411yescharacteristic
658C2×C11#187511yescharacteristic
659C2×C11#189311yescharacteristic
660C2×C11#189511yescharacteristic
661C2×C11#199911yescharacteristic
662C2×C11#199911yescharacteristic
663C2×C11#200011yescharacteristic
664C2×C11#200011yescharacteristic
665C2×C11#203311yescharacteristic
666C2×C11#203311yescharacteristic
667C2×C11#203411yescharacteristic
668C2×C11#203411yescharacteristic
669D11—44no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—41no—
674C24—41no—
675C24—41no—
676C24—41no—
677C24—41no—
678C24—41no—
679C24—41no—
680C24—41no—
681C24—41no—
682C24—41no—
683C24—41no—
684C24—41no—
685C24—112no—
686C24—112no—
687C24—112no—
688C24—221no—
689C24—221no—
690C24—221no—
691C24—221no—
692C24—221no—
693C24—221no—
694C24—221no—
695C24—221no—
696C24—221no—
697C24—221no—
698C24—221no—
699C24—221no—
700C24D4×D1111yescharacteristic
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—22no—
705C2×D4—22no—
706C2×D4—22no—
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—22no—
710C2×D4—22no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—22no—
716C2×D4—41no—
717C2×D4—41no—
718C2×D4—41no—
719C2×D4—41no—
720C2×D4—41no—
721C2×D4—41no—
722C2×D4—41no—
723C2×D4—41no—
724C2×D4—41no—
725C2×D4—41no—
726C2×D4—41no—
727C2×D4—41no—
728C2×D4—2216no—
729C2×D4—448no—
730C2×D4—448no—
731C2×D4—448no—
732C2×D4—448no—
733C2×D4—448no—
734C2×D4—448no—
735C2×D4(C2×D11)⋊C414yescomplemented
736C22×C4—22no—
737C22×C4—41no—
738C22×C4—41no—
739C22×C4—41no—
740C22×C4—41no—
741C22×C4—41no—
742C22×C4—41no—
743C22×C4—112no—
744C22×C4—222no—
745C22×C4—221no—
746C22×C4—222no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—222no—
752C22×C4—221no—
753C22×C4—222no—
754C22×C4—222no—
755C22×C4—222no—
756C22×C4—222no—
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—441no—
767C22×C4—441no—
768C22×C4—441no—
769C22×C4—441no—
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×C4#433911yescharacteristic
795C22×C4#433911yescharacteristic
796C22×C4D4×D1111yescharacteristic
797C22×C4D4×D1111yescharacteristic
798C22×C4D4×D1111yescharacteristic
799C22×C4D4×D1111yescharacteristic
800C22×C4D4×D1111yescharacteristic
801C22×C4#434111yescharacteristic
802C22×C4#434111yescharacteristic
803C22×C4C2×C22⋊D1111yescharacteristic
804C22×C4C2×C22⋊D1111yescharacteristic
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—41no—
823C4⋊C4—41no—
824C4⋊C4—114no—
825C4⋊C4—222no—
826C4⋊C4—222no—
827C4⋊C4—222no—
828C4⋊C4—222no—
829C4⋊C4—222no—
830C4⋊C4—441no—
831C4⋊C4—441no—
832C22⋊C4—2216no—
833C22⋊C4—448no—
834C11#1096911yescharacteristic, complemented, Sylow
835C23—24no—
836C23—42no—
837C23—42no—
838C23—42no—
839C23—42no—
840C23—42no—
841C23—42no—
842C23—42no—
843C23—42no—
844C23—42no—
845C23—42no—
846C23—42no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—42no—
854C23—81no—
855C23—81no—
856C23—81no—
857C23—81no—
858C23—81no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23—81no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23—81no—
870C23—114no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—222no—
877C23—222no—
878C23—222no—
879C23—222no—
880C23—222no—
881C23—222no—
882C23—222no—
883C23—222no—
884C23—222no—
885C23—222no—
886C23—222no—
887C23—222no—
888C23—222no—
889C23—441no—
890C23—441no—
891C23—441no—
892C23—441no—
893C23—441no—
894C23—441no—
895C23—441no—
896C23—441no—
897C23—441no—
898C23—441no—
899C23—441no—
900C23—441no—
901C23—441no—
902C23—441no—
903C23—441no—
904C23—441no—
905C23C22⋊C4×D1111yescharacteristic
906C23#6693511yescharacteristic
907C23#6693611yescharacteristic
908C23#6693711yescharacteristic
909C23D8×D1111yescharacteristic
910C23#6696411yescharacteristic
911C23#6696411yescharacteristic
912C23#6696511yescharacteristic
913C23SD16×D1111yescharacteristic
914C23#6696711yescharacteristic
915C23#6696811yescharacteristic
916C23#6696911yescharacteristic
917C23#6699011yescharacteristic
918C23#6699011yescharacteristic
919C23#6699111yescharacteristic
920D4—24no—
921D4—24no—
922D4—42no—
923D4—42no—
924D4—42no—
925D4—42no—
926D4—42no—
927D4—42no—
928D4—4432no—
929C2×C4—42no—
930C2×C4—42no—
931C2×C4—42no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—222no—
937C2×C4—224no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—442no—
941C2×C4—442no—
942C2×C4—441no—
943C2×C4—441no—
944C2×C4—441no—
945C2×C4—441no—
946C2×C4—442no—
947C2×C4—442no—
948C2×C4—442no—
949C2×C4—442no—
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×C4C22⋊C4×D1111yescharacteristic
966C2×C4(C22⋊D11)⋊C411yescharacteristic
967C2×C4(C22⋊D11)⋊C411yescharacteristic
968C2×C4#6693511yescharacteristic
969C2×C4#6693511yescharacteristic
970C2×C4#6693611yescharacteristic
971C2×C4#6693711yescharacteristic
972C2×C4#6693711yescharacteristic
973C2×C4#6693711yescharacteristic
974C2×C4#6693811yescharacteristic
975C2×C4#6693811yescharacteristic
976C2×C4#6693911yescharacteristic
977C2×C4C2×(C2×D11)⋊C411yescharacteristic
978C2×C4C4×C22⋊D1111yescharacteristic
979C2×C4C4×C22⋊D1111yescharacteristic
980C2×C4#6698211yescharacteristic
981C2×C4#6698311yescharacteristic
982C2×C4#6698311yescharacteristic
983C2×C4#6699011yescharacteristic
984C2×C4#6699011yescharacteristic
985C2×C4#6699111yescharacteristic
986C2×C4#6699211yescharacteristic
987C2×C4#6699211yescharacteristic
988C2×C4#6699211yescharacteristic
989C2×C4#6699211yescharacteristic
990C2×C4#6699311yescharacteristic
991C2×C4#6699311yescharacteristic
992C2×C4#6700611yescharacteristic
993C8—42no—
994C8—442no—
995C22—44no—
996C22—44no—
997C22—44no—
998C22—82no—
999C22—82no—
1000C22—82no—
1001C22—82no—
1002C22—82no—
1003C22—82no—
1004C22—82no—
1005C22—82no—
1006C22—82no—
1007C22—82no—
1008C22—82no—
1009C22—82no—
1010C22—224no—
1011C22—224no—
1012C22—224no—
1013C22—442no—
1014C22—442no—
1015C22—442no—
1016C22—442no—
1017C22—442no—
1018C22—442no—
1019C22—442no—
1020C22—442no—
1021C22—442no—
1022C22—442no—
1023C22—442no—
1024C22—442no—
1025C22D11×#10211yescharacteristic
1026C22#1062238311yescharacteristic
1027C22#1062238411yescharacteristic
1028C22#1062238511yescharacteristic
1029C22#1062238611yescharacteristic
1030C22#1062238711yescharacteristic
1031C22#1062238811yescharacteristic
1032C22#1062238911yescharacteristic
1033C22#1062239011yescharacteristic
1034C22#1062239111yescharacteristic
1035C22#1062239211yescharacteristic
1036C22#1062239311yescharacteristic
1037C22#1062239411yescharacteristic
1038C22#1062239511yescharacteristic
1039C22#1062239611yescharacteristic
1040C22#1062239711yescharacteristic
1041C22#1062256811yescharacteristic
1042C22#1062256911yescharacteristic
1043C22#1062256911yescharacteristic
1044C22#1062257211yescharacteristic
1045C22#1062257311yescharacteristic
1046C22#1062257411yescharacteristic
1047C22#1062276911yescharacteristic
1048C22#1062276911yescharacteristic
1049C22#1062277011yescharacteristic
1050C22#1062277111yescharacteristic
1051C22#1062277111yescharacteristic
1052C22#1062277211yescharacteristic
1053C22#1062278211yescharacteristic
1054C22#1062278311yescharacteristic
1055C22#1062278411yescharacteristic
1056C22#1062278511yescharacteristic
1057C22#1062278611yescharacteristic
1058C22#1062278711yescharacteristic
1059C22#1062283611yescharacteristic
1060C4—82no—
1061C4—444no—
1062C4—442no—
1063C4—882no—
1064C4#1062257011yescharacteristic
1065C4#1062257011yescharacteristic
1066C4#1062257111yescharacteristic
1067C4#1062257211yescharacteristic
1068C4#1062257311yescharacteristic
1069C4#1062257411yescharacteristic
1070C4#1062282611yescharacteristic
1071C4#1062283611yescharacteristic
1072C2—84no—
1073C2—444no—
1074C2#1306685511yescharacteristic
1075C2#1306854511yescharacteristic
1076C2#1306855311yescharacteristic
1077C2#1306893011yescharacteristic
1078C2#1306893511yescharacteristic
1079C2#1306904111yescharacteristic
1080C2#1306905111yescharacteristic
1081C2#1306961111yescharacteristic
1082C2#1306961311yescharacteristic
1083C2#1306961611yescharacteristic
1084C2#1306962011yescharacteristic
1085C2#1306979611yescharacteristic
1086C2#1306979711yescharacteristic
1087C2#1306980311yescharacteristic
1088C2#1306980411yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC22×#66991C2
cosocleC23×C4×C11C23
hypercenterC22×#102D11
hypocenterC11#10969
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#66896C2semidirect
3. C22×(C2×D11)⋊C8C2semidirect
4. C2×#10622600C2semidirect
5. C2×#10622189C2semidirect
6. C2×#10622167C2semidirect
7. C22×C11×#102C2semidirect
19. C2×#66991C4semidirect
86. C22×C8×C11D4semidirect
92. C2×C11×C4⋊C4D4semidirect
114. C2×C4⋊Dic11D4semidirect
121. C22×C11⋊C8D4semidirect
185. C2×D4×C11C22⋊C4semidirect
283. C4⋊Dic11C22⋊C4semidirect
293. C22×#102D11semidirect
382. C22×D11#102semidirect
620. C22×C8C22⋊D11semidirect
642. C2×C4⋊C4C22⋊D11semidirect
735. C2×D4(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×#669912
C22×#668962
C22×(C2×D11)⋊C82
C2×#106226002
C2×#106221892
C2×#106221672
C22×C11×#1022
#1096911