Finite Group Databasebeta

← #14660283

Subgroups — #14660283

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×#66999C211yesmaximal, characteristic
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×(C2×D11)⋊C8C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×#10622189C211yesmaximal, characteristic, complemented
6C2×#10622167C211yesmaximal, characteristic, complemented
7C22×C11×#103C211yesmaximal, characteristic, complemented
8C23×Q8×C11C2211yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C23×C8×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C2×#66999—22no—
13C2×#66999—22no—
14C2×#66999—22no—
15C2×#66999—22no—
16C2×#66999—22no—
17C2×#66999C414yescomplemented
18C22×(C2×D11)⋊C4—21no—
19C22×(C2×D11)⋊C4—21no—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4—21no—
23C23×C11⋊C8C2211yescharacteristic
24C2×C11×#103—22no—
25C2×C11×#103—22no—
26C2×C11×#103—22no—
27C2×#66899—22no—
28C2×#66899—22no—
29C2×#66899—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—
38C24×D11D411yescharacteristic
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—21no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11C2×C412yes—
51C22×Q8×C11D412yes—
52C22×Q8×C11D412yes—
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—21no—
58C23×Dic11D411yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11—21no—
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×C4×D11—21no—
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11C2×C412yes—
72C22×C4×D11D412yes—
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⋊C4D412yes—
86#66999—28no—
87#66999—28no—
88#66999—28no—
89#66999—28no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—42no—
95C2×(C2×D11)⋊C4—42no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11C2×C412yes—
105C2×C4⋊Dic11D412yes—
106C2×C4⋊Dic11D412yes—
107C2×C4⋊Dic11D412yes—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—24no—
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⋊C8D412yes—
118C11×#103—28no—
119#66899—28no—
120C11⋊#95—24no—
121(C2×D11)⋊C8—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—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
151C2×Q8×C11—22no—
152C2×Q8×C11—22no—
153C2×Q8×C11—22no—
154C2×Q8×C11—41no—
155C2×Q8×C11—41no—
156C2×Q8×C11—41no—
157C2×Q8×C11—41no—
158C2×Q8×C11—41no—
159C2×Q8×C11—41no—
160C2×Q8×C11—41no—
161C2×Q8×C11—41no—
162C2×Q8×C11—41no—
163C2×Q8×C11—41no—
164C2×Q8×C11—41no—
165C2×Q8×C11—41no—
166C2×Q8×C11C22⋊C414yescomplemented
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—41no—
172C22×C4×C11—41no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—41no—
176C22×C4×C11—41no—
177C22×C4×C11—41no—
178C22×C4×C11—41no—
179C22×C4×C11—41no—
180C22×C4×C11—41no—
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11#4111yescharacteristic
192C22×C4×C11#4111yescharacteristic
193C22×C4×C11#4111yescharacteristic
194C22×C4×C11#4111yescharacteristic
195C22×Dic11—22no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—41no—
206C22×Dic11—41no—
207C22×Dic11—41no—
208C22×Dic11—41no—
209C22×Dic11—41no—
210C22×Dic11—41no—
211C22×Dic11—41no—
212C22×Dic11—41no—
213C22×Dic11—41no—
214C22×Dic11—41no—
215C22×Dic11C22⋊C412yes—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—22no—
221C2×C4×D11—22no—
222C2×C4×D11—22no—
223C2×C4×D11—22no—
224C2×C4×D11—22no—
225C2×C4×D11—22no—
226C2×C4×D11—22no—
227C2×C4×D11—22no—
228C2×C4×D11—41no—
229C2×C4×D11—41no—
230C2×C4×D11—41no—
231C2×C4×D11—41no—
232C2×C4×D11—41no—
233C2×C4×D11—41no—
234C2×C4×D11—41no—
235C2×C4×D11—41no—
236C2×C4×D11—41no—
237C2×C4×D11—41no—
238C2×C4×D11—41no—
239C2×C4×D11—41no—
240C2×C4×D11—41no—
241C2×C4×D11—41no—
242C2×C4×D11—41no—
243C2×C4×D11—41no—
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—41no—
254C11×C4⋊C4—41no—
255(C2×D11)⋊C4—216no—
256(C2×D11)⋊C4—48no—
257C4⋊Dic11—22no—
258C4⋊Dic11—22no—
259C4⋊Dic11—22no—
260C4⋊Dic11—22no—
261C4⋊Dic11—22no—
262C4⋊Dic11—41no—
263C4⋊Dic11—41no—
264C4⋊Dic11C22⋊C414yescomplemented
265Dic11⋊C4—216no—
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×#103D1111yescharacteristic, complemented
276C22×C22⋊C8—111no—
277C2×#380—111no—
278C2×#340—111no—
279C2×#340—111no—
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
330Q8×C11—24no—
331Q8×C11—24no—
332Q8×C11—42no—
333Q8×C11—42no—
334Q8×C11—42no—
335Q8×C11—42no—
336Q8×C11—42no—
337Q8×C11—42no—
338C2×C4×C11—24no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—42no—
347C2×C4×C11—42no—
348C2×C4×C11—81no—
349C2×C4×C11—81no—
350C2×C4×C11—81no—
351C2×C4×C11—81no—
352C2×C4×C11C2×C22⋊C411yescharacteristic
353C2×C4×C11C2×C22⋊C411yescharacteristic
354C2×C4×C11C4×D411yescharacteristic
355C2×C4×C11C4×D411yescharacteristic
356C2×C4×C11C4×D411yescharacteristic
357C2×C4×C11C4×D411yescharacteristic
358C2×C4×C11#12011yescharacteristic
359C2×C4×C11#12011yescharacteristic
360C2×C4×C11#12011yescharacteristic
361C2×C4×C11#12011yescharacteristic
362C2×C4×C11#12011yescharacteristic
363C2×C4×C11#12111yescharacteristic
364C2×C4×C11#12111yescharacteristic
365C2×C4×C11#12111yescharacteristic
366C2×C4×C11#12111yescharacteristic
367C2×C4×C11#12111yescharacteristic
368C2×C4×C11#12111yescharacteristic
369C2×C4×C11#12111yescharacteristic
370C2×C4×C11#12111yescharacteristic
371C2×C4×C11#12111yescharacteristic
372C2×C4×C11#12111yescharacteristic
373C2×C4×C11#12311yescharacteristic
374C2×C4×C11#12311yescharacteristic
375C2×C4×C11#12311yescharacteristic
376C2×C4×C11#12411yescharacteristic
377C2×C4×C11#12411yescharacteristic
378C2×C4×C11#12711yescharacteristic
379C2×C4×C11#12711yescharacteristic
380C2×Dic11—22no—
381C2×Dic11—24no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—41no—
385C2×Dic11—41no—
386C2×Dic11—41no—
387C2×Dic11—41no—
388C2×Dic11—42no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11—42no—
392C2×Dic11—42no—
393C2×Dic11—42no—
394C2×Dic11—42no—
395C2×Dic11—42no—
396C2×Dic11—42no—
397C2×Dic11—81no—
398C2×Dic11—81no—
399C2×Dic11—81no—
400C2×Dic11—81no—
401C4×D11—42no—
402C4×D11—42no—
403C4×D11—42no—
404C4×D11—42no—
405C4×D11—42no—
406C4×D11—42no—
407C4×D11—42no—
408C4×D11—42no—
409C8×C11—42no—
410C11⋊C8—42no—
411C23×Q8C2×D1111yescharacteristic
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—111no—
423C22×C4⋊C4—221no—
424C22×C4⋊C4C2×D1111yescharacteristic
425C22×C22⋊C4—221no—
426C22×C22⋊C4—221no—
427C2×#103—22no—
428C2×#103—22no—
429C2×#103—22no—
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—222no—
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—42no—
502Dic11—44no—
503Dic11—82no—
504C25—111no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8—21no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8—21no—
512C22×Q8—21no—
513C22×Q8—21no—
514C22×Q8—21no—
515C22×Q8—21no—
516C22×Q8C4×D1112yes—
517C22×Q8D4412yes—
518C22×Q8C22⋊D1112yes—
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×C8C22⋊D1112yes—
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—112no—
563C2×C4⋊C4—112no—
564C2×C4⋊C4—112no—
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⋊C4—221no—
575C2×C4⋊C4—221no—
576C2×C4⋊C4—221no—
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—28no—
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—22no—
621C2×Q8—22no—
622C2×Q8—22no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—22no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—22no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—41no—
636C2×Q8—41no—
637C2×Q8—41no—
638C2×Q8—41no—
639C2×Q8—41no—
640C2×Q8—41no—
641C2×Q8—41no—
642C2×Q8—41no—
643C2×Q8—41no—
644C2×Q8—41no—
645C2×Q8—41no—
646C2×Q8—41no—
647C2×Q8(C2×D11)⋊C414yescomplemented
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—222no—
665C22×C4—221no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—222no—
670C22×C4—221no—
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×C4#433911yescharacteristic
714C22×C4#433911yescharacteristic
715C22×C4D4×D1111yescharacteristic
716C22×C4D4×D1111yescharacteristic
717C22×C4D4×D1111yescharacteristic
718C22×C4D4×D1111yescharacteristic
719C22×C4D4×D1111yescharacteristic
720C22×C4#434111yescharacteristic
721C22×C4#434111yescharacteristic
722C22×C4C2×C22⋊D1111yescharacteristic
723C22×C4C2×C22⋊D1111yescharacteristic
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—41no—
742C4⋊C4—41no—
743C4⋊C4—114no—
744C4⋊C4—2216no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4—222no—
749C4⋊C4—222no—
750C4⋊C4—441no—
751C4⋊C4—441no—
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#6693611yescharacteristic
793C23#6693711yescharacteristic
794C23SD16×D1111yescharacteristic
795C23#6696711yescharacteristic
796C23#6696811yescharacteristic
797C23#6696911yescharacteristic
798C23Q16×D1111yescharacteristic
799C23#6697111yescharacteristic
800C23#6697111yescharacteristic
801C23#6697211yescharacteristic
802C23#6699011yescharacteristic
803C23#6699011yescharacteristic
804C23#6699111yescharacteristic
805Q8—24no—
806Q8—24no—
807Q8—42no—
808Q8—42no—
809Q8—42no—
810Q8—42no—
811Q8—42no—
812Q8—42no—
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—224no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—442no—
832C2×C4—442no—
833C2×C4—441no—
834C2×C4—441no—
835C2×C4—441no—
836C2×C4—441no—
837C2×C4—442no—
838C2×C4—442no—
839C2×C4—442no—
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×C4C22⋊C4×D1111yescharacteristic
857C2×C4(C22⋊D11)⋊C411yescharacteristic
858C2×C4(C22⋊D11)⋊C411yescharacteristic
859C2×C4#6693511yescharacteristic
860C2×C4#6693511yescharacteristic
861C2×C4#6693611yescharacteristic
862C2×C4#6693711yescharacteristic
863C2×C4#6693711yescharacteristic
864C2×C4#6693711yescharacteristic
865C2×C4#6693811yescharacteristic
866C2×C4#6693811yescharacteristic
867C2×C4#6693911yescharacteristic
868C2×C4C2×(C2×D11)⋊C411yescharacteristic
869C2×C4C4×C22⋊D1111yescharacteristic
870C2×C4C4×C22⋊D1111yescharacteristic
871C2×C4#6698211yescharacteristic
872C2×C4#6698311yescharacteristic
873C2×C4#6698311yescharacteristic
874C2×C4#6699011yescharacteristic
875C2×C4#6699011yescharacteristic
876C2×C4#6699111yescharacteristic
877C2×C4#6699211yescharacteristic
878C2×C4#6699211yescharacteristic
879C2×C4#6699211yescharacteristic
880C2×C4#6699211yescharacteristic
881C2×C4#6699311yescharacteristic
882C2×C4#6699311yescharacteristic
883C2×C4#6700611yescharacteristic
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—
901C22D11×#10311yescharacteristic
902C22#1062241511yescharacteristic
903C22#1062241611yescharacteristic
904C22#1062241711yescharacteristic
905C22#1062241811yescharacteristic
906C22#1062241911yescharacteristic
907C22#1062242011yescharacteristic
908C22#1062242111yescharacteristic
909C22#1062242211yescharacteristic
910C22#1062242311yescharacteristic
911C22#1062242411yescharacteristic
912C22#1062242511yescharacteristic
913C22#1062242611yescharacteristic
914C22#1062242711yescharacteristic
915C22#1062242811yescharacteristic
916C22#1062242911yescharacteristic
917C22#1062256811yescharacteristic
918C22#1062256911yescharacteristic
919C22#1062256911yescharacteristic
920C22#1062257211yescharacteristic
921C22#1062257311yescharacteristic
922C22#1062257411yescharacteristic
923C22#1062278211yescharacteristic
924C22#1062278311yescharacteristic
925C22#1062278411yescharacteristic
926C22#1062278511yescharacteristic
927C22#1062278611yescharacteristic
928C22#1062278711yescharacteristic
929C22#1062279911yescharacteristic
930C22#1062279911yescharacteristic
931C22#1062280011yescharacteristic
932C22#1062280011yescharacteristic
933C22#1062280111yescharacteristic
934C22#1062280211yescharacteristic
935C22#1062283611yescharacteristic
936C4—44no—
937C4—82no—
938C4—444no—
939C4—442no—
940C4—882no—
941C4#1062257011yescharacteristic
942C4#1062257011yescharacteristic
943C4#1062257111yescharacteristic
944C4#1062257211yescharacteristic
945C4#1062257311yescharacteristic
946C4#1062257411yescharacteristic
947C4#1062282611yescharacteristic
948C4#1062283611yescharacteristic
949C2—444no—
950C2#1306685511yescharacteristic
951C2#1306854911yescharacteristic
952C2#1306855511yescharacteristic
953C2#1306892011yescharacteristic
954C2#1306892511yescharacteristic
955C2#1306903611yescharacteristic
956C2#1306904611yescharacteristic
957C2#1306961611yescharacteristic
958C2#1306961811yescharacteristic
959C2#1306962311yescharacteristic
960C2#1306962511yescharacteristic
961C2#1306981011yescharacteristic
962C2#1306981111yescharacteristic
963C2#1306981711yescharacteristic
964C2#1306981811yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC22×C11×#103C2
socleC24×C11C2×D4
prime radicalC24×D11D4
cosocleC23×C4×C11C23
hypercenterC22×#103D11
hypocenterC11#10970
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#66899C2semidirect
5. C2×#10622189C2semidirect
6. C2×#10622167C2semidirect
7. C22×C11×#103C2semidirect
17. C2×#66999C4semidirect
166. C2×Q8×C11C22⋊C4semidirect
264. C4⋊Dic11C22⋊C4semidirect
275. C22×#103D11semidirect
329. C22×D11#103semidirect
647. C2×Q8(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×#669992
C22×#668992
C22×(C2×D11)⋊C82
C2×#106226002
C2×#106221892
C2×#106221672
C22×C11×#1032
#1097011