Finite Group Databasebeta

← #14660285

Subgroups — #14660285

Order 2816.

1578 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic
2C22×#66880C211yesmaximal, characteristic, complemented
3C22×#66874C211yesmaximal, characteristic, complemented
4C22×(C2×D11)⋊C8C211yesmaximal, characteristic
5C2×#10622600C211yesmaximal, characteristic
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×C11×#340C211yesmaximal, characteristic, complemented
8C23×C4×D11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×(C2×D11)⋊C4—21no—
14C22×(C2×D11)⋊C4—21no—
15C22×C4⋊Dic11—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C2×#66950—22no—
19C2×#66950—22no—
20C2×#66950—22no—
21C2×#66950—22no—
22C2×#66950—22no—
23C2×#66950C414yescomplemented
24C2×C11⋊#95—21no—
25C2×(C2×D11)⋊C8—22no—
26C2×(C2×D11)⋊C8—22no—
27C2×(C2×D11)⋊C8—22no—
28C2×#66880—22no—
29C2×#66880—22no—
30C2×#66880—22no—
31#10622600—22no—
32#10622600—22no—
33C2×#66874—22no—
34C2×#66874—22no—
35C2×#66874—22no—
36C11×#340—22no—
37#10622167—22no—
38C24×D11D411yescharacteristic
39C23×C4×C11—21no—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11—21no—
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C22×C4×D11—21no—
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11—21no—
49C22×C4×D11—21no—
50C22×C4×D11—21no—
51C22×C4×D11—21no—
52C22×C4×D11—21no—
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11—21no—
56C22×C4×D11—21no—
57C22×C4×D11C2×C412yes—
58C22×C4×D11D412yes—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×Dic22—21no—
65C22×Dic22—21no—
66C22×Dic22—21no—
67C22×Dic22—21no—
68C22×Dic22—21no—
69C22×Dic22—21no—
70C22×Dic22C2×C412yes—
71C22×Dic22D412yes—
72C22×Dic22D412yes—
73C22×C8×C11—21no—
74C22×C8×C11—21no—
75C22×C8×C11—21no—
76C22×C8×C11—21no—
77C22×C8×C11—21no—
78C22×C8×C11—21no—
79C22×C8×C11D412yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4C2×C412yes—
89C2×C11×C4⋊C4D412yes—
90C2×C11×C4⋊C4D412yes—
91C2×C11×C4⋊C4D412yes—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—42no—
97C2×(C2×D11)⋊C4—42no—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11D412yes—
107C22×C11⋊C8—21no—
108C22×C11⋊C8—21no—
109C22×C11⋊C8—21no—
110C22×C11⋊C8—21no—
111C22×C11⋊C8—21no—
112C22×C11⋊C8—21no—
113C22×C11⋊C8D412yes—
114#66950—28no—
115#66950—28no—
116#66950—28no—
117#66950—28no—
118C11⋊#95—24no—
119(C2×D11)⋊C8—28no—
120#66880—28no—
121#66874—28no—
122#10970—111nomaximal, Sylow
123C24×C11C2×D411yescharacteristic
124C23×D11—21no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11—21no—
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×D11C22⋊C412yes—
137C23×D11SD1612yes—
138C23×D11Q1612yes—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—41no—
144C22×C4×C11—41no—
145C22×C4×C11—41no—
146C22×C4×C11—41no—
147C22×C4×C11—41no—
148C22×C4×C11—41no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—41no—
152C22×C4×C11—41no—
153C22×C4×C11C22×C411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11#4111yescharacteristic
166C22×C4×C11#4111yescharacteristic
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—41no—
178C22×Dic11—41no—
179C22×Dic11—41no—
180C22×Dic11—41no—
181C22×Dic11—41no—
182C22×Dic11—41no—
183C22×Dic11—41no—
184C22×Dic11—41no—
185C22×Dic11—41no—
186C22×Dic11—41no—
187C22×Dic11C22⋊C412yes—
188C2×C4×D11—22no—
189C2×C4×D11—22no—
190C2×C4×D11—22no—
191C2×C4×D11—22no—
192C2×C4×D11—22no—
193C2×C4×D11—22no—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—22no—
197C2×C4×D11—22no—
198C2×C4×D11—22no—
199C2×C4×D11—22no—
200C2×C4×D11—41no—
201C2×C4×D11—41no—
202C2×C4×D11—41no—
203C2×C4×D11—41no—
204C2×C4×D11—41no—
205C2×C4×D11—41no—
206C2×C4×D11—41no—
207C2×C4×D11—41no—
208C2×C4×D11—41no—
209C2×C4×D11—41no—
210C2×C4×D11—41no—
211C2×C4×D11—41no—
212C2×C4×D11—41no—
213C2×C4×D11—41no—
214C2×C4×D11—41no—
215C2×C4×D11—41no—
216C2×Dic22—22no—
217C2×Dic22—22no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22—22no—
221C2×Dic22—22no—
222C2×Dic22—22no—
223C2×Dic22—22no—
224C2×Dic22—22no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—22no—
228C2×Dic22—22no—
229C2×Dic22—22no—
230C2×Dic22—22no—
231C2×Dic22—41no—
232C2×Dic22—41no—
233C2×Dic22—41no—
234C2×Dic22—41no—
235C2×Dic22—41no—
236C2×Dic22—41no—
237C2×Dic22—41no—
238C2×Dic22—41no—
239C2×Dic22—41no—
240C2×Dic22—41no—
241C2×Dic22—41no—
242C2×Dic22—41no—
243C2×Dic22C22⋊C414yescomplemented
244C2×C8×C11—22no—
245C2×C8×C11—22no—
246C2×C8×C11—22no—
247C2×C8×C11—41no—
248C2×C8×C11—41no—
249C2×C8×C11—41no—
250C2×C8×C11—41no—
251C11×C4⋊C4—22no—
252C11×C4⋊C4—22no—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—22no—
256C11×C4⋊C4—41no—
257C11×C4⋊C4—41no—
258C11×C4⋊C4C22⋊C414yescomplemented
259(C2×D11)⋊C4—216no—
260(C2×D11)⋊C4—48no—
261C4⋊Dic11—216no—
262C4⋊Dic11—22no—
263C4⋊Dic11—22no—
264C4⋊Dic11—41no—
265C4⋊Dic11—41no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8—22no—
268C2×C11⋊C8—22no—
269C2×C11⋊C8—41no—
270C2×C11⋊C8—41no—
271C2×C11⋊C8—41no—
272C2×C11⋊C8—41no—
273C22×C22⋊Q8—111no—
274C22×#103—111no—
275C22×#103—111no—
276C22×C22⋊C8—111no—
277C2×#380—111no—
278C2×#340—111no—
279C2×#340D1111yescharacteristic, complemented
280C23×C11C2×C22⋊C411yescharacteristic
281C23×C11#12011yescharacteristic
282C23×C11#12011yescharacteristic
283C23×C11#12011yescharacteristic
284C23×C11#12111yescharacteristic
285C23×C11#12111yescharacteristic
286C23×C11#12311yescharacteristic
287C23×C11C2×SD1611yescharacteristic
288C23×C11C2×Q1611yescharacteristic
289C23×C11#13511yescharacteristic
290C23×C11#13511yescharacteristic
291C23×C11AGL(1,ℤ/8)11yescharacteristic
292C23×C11#13711yescharacteristic
293C23×C11#13711yescharacteristic
294C23×C11#13711yescharacteristic
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11#10314yescomplemented
330C2×C4×C11—24no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11—42no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—81no—
341C2×C4×C11—81no—
342C2×C4×C11—81no—
343C2×C4×C11—81no—
344C2×C4×C11C2×C22⋊C411yescharacteristic
345C2×C4×C11C2×C22⋊C411yescharacteristic
346C2×C4×C11C4×D411yescharacteristic
347C2×C4×C11C4×D411yescharacteristic
348C2×C4×C11C4×D411yescharacteristic
349C2×C4×C11C4×D411yescharacteristic
350C2×C4×C11#12011yescharacteristic
351C2×C4×C11#12011yescharacteristic
352C2×C4×C11#12011yescharacteristic
353C2×C4×C11#12011yescharacteristic
354C2×C4×C11#12011yescharacteristic
355C2×C4×C11#12111yescharacteristic
356C2×C4×C11#12111yescharacteristic
357C2×C4×C11#12111yescharacteristic
358C2×C4×C11#12111yescharacteristic
359C2×C4×C11#12111yescharacteristic
360C2×C4×C11#12111yescharacteristic
361C2×C4×C11#12111yescharacteristic
362C2×C4×C11#12111yescharacteristic
363C2×C4×C11#12111yescharacteristic
364C2×C4×C11#12111yescharacteristic
365C2×C4×C11#12311yescharacteristic
366C2×C4×C11#12311yescharacteristic
367C2×C4×C11#12311yescharacteristic
368C2×C4×C11#12411yescharacteristic
369C2×C4×C11#12411yescharacteristic
370C2×C4×C11#12711yescharacteristic
371C2×C4×C11#12711yescharacteristic
372C2×Dic11—22no—
373C2×Dic11—24no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—42no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—41no—
381C2×Dic11—41no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11—81no—
390C2×Dic11—81no—
391C2×Dic11—81no—
392C2×Dic11—81no—
393C4×D11—42no—
394C4×D11—42no—
395C4×D11—42no—
396C4×D11—42no—
397C4×D11—42no—
398C4×D11—42no—
399C4×D11—42no—
400C4×D11—42no—
401Dic22—24no—
402Dic22—24no—
403Dic22—42no—
404Dic22—42no—
405Dic22—42no—
406Dic22—42no—
407Dic22—42no—
408Dic22—42no—
409C8×C11—42no—
410C11⋊C8—42no—
411C23×Q8—111no—
412C24×C4—111no—
413C23×C8—111no—
414C23×C8C2×D1111yescharacteristic
415C2×C22⋊Q8—114no—
416C2×C22⋊Q8—222no—
417C2×C22⋊Q8—222no—
418C2×C22⋊Q8—222no—
419C2×C22⋊Q8—222no—
420C2×C22⋊Q8—222no—
421C22×C4⋊C4—111no—
422C22×C4⋊C4—221no—
423C22×C4⋊C4C2×D1111yescharacteristic
424C22×C4⋊C4C2×D1111yescharacteristic
425C22×C22⋊C4—221no—
426C22×C22⋊C4—221no—
427C2×#103—222no—
428C2×#103—222no—
429C2×#103—222no—
430C2×#103—222no—
431C2×#103—222no—
432C2×#103—222no—
433C2×C22⋊C8—222no—
434C2×C22⋊C8—222no—
435C2×C22⋊C8—222no—
436#380—222no—
437#380—222no—
438C2×#95—221no—
439#340—22no—
440#340—222no—
441C22×C11#37911yescharacteristic
442C22×C11#38611yescharacteristic
443C22×C11#38611yescharacteristic
444C22×C11#39211yescharacteristic
445C22×C11#39211yescharacteristic
446C22×C11#39411yescharacteristic
447C22×C11#39411yescharacteristic
448C22×C11C2×#10311yescharacteristic
449C22×C11#41611yescharacteristic
450C22×C11#41711yescharacteristic
451C22×C11#41911yescharacteristic
452C22×C11#44811yescharacteristic
453C22×C11#44811yescharacteristic
454C22×C11#44911yescharacteristic
455C22×C11#44911yescharacteristic
456C22×C11#45011yescharacteristic
457C22×C11#45111yescharacteristic
458C22×C11#45111yescharacteristic
459C22×C11#45111yescharacteristic
460C22×C11#45211yescharacteristic
461C22×C11#45211yescharacteristic
462C22×C11#45211yescharacteristic
463C22×C11#45211yescharacteristic
464C22×C11#46511yescharacteristic
465C22×C11#46511yescharacteristic
466C22×C11#46711yescharacteristic
467C22×C11#46711yescharacteristic
468C22×C11#46811yescharacteristic
469C22×C11#46811yescharacteristic
470C22×C11#47011yescharacteristic
471C22×C11#47011yescharacteristic
472C22×C11#48311yescharacteristic
473C22×C11#48411yescharacteristic
474C22×C11#48511yescharacteristic
475C22×C11#48511yescharacteristic
476C2×D11—24no—
477C2×D11—24no—
478C2×D11—24no—
479C2×D11—42no—
480C2×D11—42no—
481C2×D11—42no—
482C2×D11—42no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C2×D11—42no—
491C4×C11—44no—
492C4×C11—82no—
493C4×C11#38611yescharacteristic
494C4×C11#38611yescharacteristic
495C4×C11#39011yescharacteristic
496C4×C11#39011yescharacteristic
497C4×C11#39211yescharacteristic
498C4×C11#39211yescharacteristic
499C4×C11#39411yescharacteristic
500C4×C11#39411yescharacteristic
501Dic11—44no—
502Dic11—42no—
503Dic11—82no—
504C25—111no—
505C22×Q8—112no—
506C22×Q8—112no—
507C22×Q8—112no—
508C22×Q8—221no—
509C22×Q8—221no—
510C22×Q8—221no—
511C22×Q8—221no—
512C22×Q8—221no—
513C22×Q8—221no—
514C22×Q8—221no—
515C22×Q8—221no—
516C22×Q8—221no—
517C22×Q8—221no—
518C22×Q8—221no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—111no—
522C23×C4—112no—
523C23×C4—112no—
524C23×C4—221no—
525C23×C4—221no—
526C23×C4—221no—
527C23×C4—221no—
528C23×C4—221no—
529C23×C4—221no—
530C23×C4—221no—
531C23×C4—221no—
532C23×C4—221no—
533C23×C4—221no—
534C23×C4—221no—
535C23×C4—221no—
536C23×C4—221no—
537C23×C4—221no—
538C23×C4C22×D1111yescharacteristic
539C22×C8—21no—
540C22×C8—21no—
541C22×C8—21no—
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8—112no—
546C22×C8—221no—
547C22×C8—221no—
548C22×C8—221no—
549C22×C8—221no—
550C22×C8—221no—
551C22×C8—221no—
552C22×C8D4412yes—
553C22⋊Q8—228no—
554C22⋊Q8—228no—
555C22⋊Q8—228no—
556C22⋊Q8—228no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—112no—
566C2×C4⋊C4—224no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—224no—
569C2×C4⋊C4—221no—
570C2×C4⋊C4—221no—
571C2×C4⋊C4—221no—
572C2×C4⋊C4—221no—
573C2×C4⋊C4—221no—
574C2×C4⋊C4C4×D1112yes—
575C2×C4⋊C4D4412yes—
576C2×C4⋊C4D4412yes—
577C2×C4⋊C4C22⋊D1112yes—
578C2×C22⋊C4—224no—
579C2×C22⋊C4—224no—
580C2×C22⋊C4—224no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—442no—
583C2×C22⋊C4—442no—
584#103—228no—
585#103—228no—
586C22⋊C8—228no—
587#95—224no—
588C2×C11#143811yescharacteristic
589C2×C11#178711yescharacteristic
590C2×C11#178811yescharacteristic
591C2×C11#187211yescharacteristic
592C2×C11#187311yescharacteristic
593C2×C11#189211yescharacteristic
594C2×C11#189411yescharacteristic
595C2×C11#200011yescharacteristic
596C2×C11#200011yescharacteristic
597C2×C11#200111yescharacteristic
598C2×C11#200111yescharacteristic
599C2×C11#203511yescharacteristic
600C2×C11#203511yescharacteristic
601C2×C11#203611yescharacteristic
602C2×C11#203611yescharacteristic
603D11—44no—
604C24—112no—
605C24—112no—
606C24—112no—
607C24—221no—
608C24—221no—
609C24—221no—
610C24—221no—
611C24—221no—
612C24—221no—
613C24—221no—
614C24—221no—
615C24—221no—
616C24—221no—
617C24—221no—
618C24—221no—
619C24D4×D1111yescharacteristic
620C2×Q8—114no—
621C2×Q8—222no—
622C2×Q8—222no—
623C2×Q8—222no—
624C2×Q8—222no—
625C2×Q8—222no—
626C2×Q8—222no—
627C2×Q8—222no—
628C2×Q8—222no—
629C2×Q8—222no—
630C2×Q8—222no—
631C2×Q8—222no—
632C2×Q8—222no—
633C2×Q8—222no—
634C2×Q8—222no—
635C2×Q8—222no—
636C2×Q8—441no—
637C2×Q8—441no—
638C2×Q8—441no—
639C2×Q8—441no—
640C2×Q8—441no—
641C2×Q8—441no—
642C2×Q8—441no—
643C2×Q8—441no—
644C2×Q8—441no—
645C2×Q8—441no—
646C2×Q8—441no—
647C2×Q8—441no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4—41no—
660C22×C4—41no—
661C22×C4—41no—
662C22×C4—112no—
663C22×C4—222no—
664C22×C4—221no—
665C22×C4—222no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—221no—
670C22×C4—222no—
671C22×C4—221no—
672C22×C4—222no—
673C22×C4—222no—
674C22×C4—222no—
675C22×C4—222no—
676C22×C4—222no—
677C22×C4—222no—
678C22×C4—222no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4—222no—
682C22×C4—222no—
683C22×C4—222no—
684C22×C4—222no—
685C22×C4—441no—
686C22×C4—441no—
687C22×C4—441no—
688C22×C4—441no—
689C22×C4—441no—
690C22×C4—441no—
691C22×C4—441no—
692C22×C4—441no—
693C22×C4—441no—
694C22×C4—441no—
695C22×C4—441no—
696C22×C4—441no—
697C22×C4—441no—
698C22×C4—441no—
699C22×C4—441no—
700C22×C4—441no—
701C22×C4—441no—
702C22×C4—441no—
703C22×C4—441no—
704C22×C4—441no—
705C22×C4—441no—
706C22×C4—441no—
707C22×C4—441no—
708C22×C4—441no—
709C22×C4—441no—
710C22×C4—441no—
711C22×C4C2×C4×D1111yescharacteristic
712C22×C4C2×D4411yescharacteristic
713C22×C4C2×D4411yescharacteristic
714C22×C4C2×D4411yescharacteristic
715C22×C4#433911yescharacteristic
716C22×C4#433911yescharacteristic
717C22×C4D4×D1111yescharacteristic
718C22×C4D4×D1111yescharacteristic
719C22×C4D4×D1111yescharacteristic
720C22×C4D4×D1111yescharacteristic
721C22×C4D4×D1111yescharacteristic
722C22×C4#434311yescharacteristic
723C22×C4#434311yescharacteristic
724C22×C4C2×C22⋊D1111yescharacteristic
725C2×C8—22no—
726C2×C8—22no—
727C2×C8—22no—
728C2×C8—41no—
729C2×C8—41no—
730C2×C8—41no—
731C2×C8—41no—
732C2×C8—222no—
733C2×C8—222no—
734C2×C8—222no—
735C2×C8—441no—
736C2×C8—441no—
737C2×C8—441no—
738C2×C8—441no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—22no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—41no—
745C4⋊C4—41no—
746C4⋊C4—2216no—
747C4⋊C4—222no—
748C4⋊C4—222no—
749C4⋊C4—441no—
750C4⋊C4—441no—
751C4⋊C4(C2×D11)⋊C414yescomplemented
752C22⋊C4—2216no—
753C22⋊C4—448no—
754C11#1097011yescharacteristic, complemented, Sylow
755C23—114no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—222no—
768C23—222no—
769C23—222no—
770C23—222no—
771C23—222no—
772C23—222no—
773C23—222no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23—441no—
784C23—441no—
785C23—441no—
786C23—441no—
787C23—441no—
788C23—441no—
789C23—441no—
790C23C22⋊C4×D1111yescharacteristic
791C23#6693511yescharacteristic
792C23#6693511yescharacteristic
793C23#6693711yescharacteristic
794C23#6694711yescharacteristic
795C23#6694811yescharacteristic
796C23#6696411yescharacteristic
797C23#6696511yescharacteristic
798C23SD16×D1111yescharacteristic
799C23#6696811yescharacteristic
800C23#6696811yescharacteristic
801C23#6696911yescharacteristic
802C23Q16×D1111yescharacteristic
803C23#6697111yescharacteristic
804C23#6699011yescharacteristic
805Q8—224no—
806Q8—224no—
807Q8—442no—
808Q8—442no—
809Q8—442no—
810Q8—442no—
811Q8—442no—
812Q8—442no—
813C2×C4—24no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—42no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—42no—
820C2×C4—42no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—81no—
826C2×C4—81no—
827C2×C4—222no—
828C2×C4—222no—
829C2×C4—224no—
830C2×C4—222no—
831C2×C4—442no—
832C2×C4—442no—
833C2×C4—441no—
834C2×C4—442no—
835C2×C4—441no—
836C2×C4—442no—
837C2×C4—441no—
838C2×C4—442no—
839C2×C4—441no—
840C2×C4—442no—
841C2×C4—442no—
842C2×C4—442no—
843C2×C4—442no—
844C2×C4—442no—
845C2×C4—442no—
846C2×C4—442no—
847C2×C4—442no—
848C2×C4—442no—
849C2×C4—442no—
850C2×C4—442no—
851C2×C4—442no—
852C2×C4—881no—
853C2×C4—881no—
854C2×C4—881no—
855C2×C4—881no—
856C2×C4C4×D4411yescharacteristic
857C2×C4C4×D4411yescharacteristic
858C2×C4#6692711yescharacteristic
859C2×C4#6692811yescharacteristic
860C2×C4C22⋊C4×D1111yescharacteristic
861C2×C4#6693511yescharacteristic
862C2×C4#6693511yescharacteristic
863C2×C4#6693511yescharacteristic
864C2×C4#6693511yescharacteristic
865C2×C4#6693711yescharacteristic
866C2×C4#6693711yescharacteristic
867C2×C4#6693711yescharacteristic
868C2×C4#6694611yescharacteristic
869C2×C4#6694611yescharacteristic
870C2×C4#6694711yescharacteristic
871C2×C4#6694711yescharacteristic
872C2×C4#6694711yescharacteristic
873C2×C4#6694811yescharacteristic
874C2×C4#6694811yescharacteristic
875C2×C4#6694811yescharacteristic
876C2×C4#6694811yescharacteristic
877C2×C4#6694811yescharacteristic
878C2×C4C2×(C2×D11)⋊C411yescharacteristic
879C2×C4#6698311yescharacteristic
880C2×C4#6698311yescharacteristic
881C2×C4#6699011yescharacteristic
882C2×C4#6699311yescharacteristic
883C2×C4#6700011yescharacteristic
884C8—42no—
885C8—442no—
886C22—224no—
887C22—224no—
888C22—224no—
889C22—442no—
890C22—442no—
891C22—442no—
892C22—442no—
893C22—442no—
894C22—442no—
895C22—442no—
896C22—442no—
897C22—442no—
898C22—442no—
899C22—442no—
900C22—442no—
901C22#1062227811yescharacteristic
902C22#1062227811yescharacteristic
903C22#1062228411yescharacteristic
904C22#1062228511yescharacteristic
905C22#1062238411yescharacteristic
906C22#1062238511yescharacteristic
907C22#1062238911yescharacteristic
908C22#1062239111yescharacteristic
909C22#1062239311yescharacteristic
910C22#1062239411yescharacteristic
911C22#1062239611yescharacteristic
912C22#1062239611yescharacteristic
913C22D11×#10311yescharacteristic
914C22#1062241511yescharacteristic
915C22#1062241911yescharacteristic
916C22#1062242111yescharacteristic
917C22#1062242111yescharacteristic
918C22#1062242311yescharacteristic
919C22#1062242611yescharacteristic
920C22#1062242911yescharacteristic
921C22#1062247511yescharacteristic
922C22#1062247711yescharacteristic
923C22#1062248011yescharacteristic
924C22#1062248111yescharacteristic
925C22#1062249711yescharacteristic
926C22#1062249911yescharacteristic
927C22#1062250011yescharacteristic
928C22#1062250111yescharacteristic
929C22#1062256811yescharacteristic
930C22#1062257311yescharacteristic
931C22#1062260411yescharacteristic
932C22#1062277111yescharacteristic
933C22#1062278311yescharacteristic
934C22#1062278611yescharacteristic
935C22#1062279911yescharacteristic
936C4—44no—
937C4—82no—
938C4—442no—
939C4—444no—
940C4—882no—
941C4#1062227811yescharacteristic
942C4#1062227811yescharacteristic
943C4#1062228411yescharacteristic
944C4#1062228511yescharacteristic
945C4#1062255211yescharacteristic
946C4#1062257311yescharacteristic
947C4#1062260111yescharacteristic
948C4#1062260411yescharacteristic
949C2—444no—
950C2#1306685611yescharacteristic
951C2#1306854911yescharacteristic
952C2#1306855311yescharacteristic
953C2#1306892211yescharacteristic
954C2#1306892711yescharacteristic
955C2#1306903811yescharacteristic
956C2#1306904811yescharacteristic
957C2#1306962011yescharacteristic
958C2#1306962211yescharacteristic
959C2#1306962511yescharacteristic
960C2#1306962711yescharacteristic
961C2#1306981411yescharacteristic
962C2#1306981511yescharacteristic
963C2#1306982111yescharacteristic
964C2#1306982211yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#340C2
socleC24×C11C2×D4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC2×#340D11
hypocenterC11#10970
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×#66880C2semidirect
3. C22×#66874C2semidirect
6. C2×#10622167C2semidirect
7. C2×C11×#340C2semidirect
23. C2×#66950C4semidirect
243. C2×Dic22C22⋊C4semidirect
258. C11×C4⋊C4C22⋊C4semidirect
279. C2×#340D11semidirect
329. C22×D11#103semidirect
751. C4⋊C4(C2×D11)⋊C4semidirect
754. C11#10970semidirect

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#668802
C22×#668742
C22×(C2×D11)⋊C82
C2×#106226002
C2×#106221672
C2×C11×#3402
#1097011