Finite Group Databasebeta

← #14721552

Subgroups — #14721552

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082451C211yesmaximal, characteristic
2#13077644C211yesmaximal, characteristic, complemented
3#13071524C211yesmaximal, characteristic, complemented
4#13067186C211yesmaximal, characteristic, complemented
5#13067182C211yesmaximal, characteristic, complemented
6#13067158C211yesmaximal, characteristic, complemented
7#13067156C211yesmaximal, characteristic, complemented
8#13067152C211yesmaximal, characteristic, complemented
9#13067142C211yesmaximal, characteristic, complemented
10#13067141C211yesmaximal, characteristic, complemented
11#13067119C211yesmaximal, characteristic, complemented
12#13067117C211yesmaximal, characteristic, complemented
13D11×#328C211yesmaximal, characteristic, complemented
14D11×#327C211yesmaximal, characteristic, complemented
15C11×#1512C211yesmaximal, characteristic, complemented
16C11×#529C2211yescharacteristic
17#10623240—21no—
18#10623236—21no—
19#10623226C411yescharacteristic, complemented
20#10623225C411yescharacteristic, complemented
21#10623208C411yescharacteristic, complemented
22#10623207C411yescharacteristic, complemented
23#10623196—21no—
24#10623184—21no—
25#10623158C2211yescharacteristic
26D11×C22⋊Q8C2211yescharacteristic
27#10623137C2211yescharacteristic
28D11×#121C2211yescharacteristic
29#10623112C411yescharacteristic, complemented
30#10623107C411yescharacteristic, complemented
31#10623091—21no—
32#10623089C411yescharacteristic, complemented
33#10623085C411yescharacteristic, complemented
34#10623076—21no—
35#10623061—21no—
36#10623058—21no—
37C2×#66946—21no—
38#10623010C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C11×#432C2211yescharacteristic, complemented
41C11×#382C2211yescharacteristic, complemented
42#10622586—21no—
43C4×C4⋊Dic11C2211yescharacteristic, complemented
44#10622539C2211yescharacteristic, complemented
45#10622449—21no—
46#10622449—21no—
47#10622339C2211yescharacteristic, complemented
48#10622339C2211yescharacteristic, complemented
49D11×C22⋊C8C2211yescharacteristic
50D11×C22⋊C8C2211yescharacteristic
51#10622319—21no—
52#10622319—21no—
53#10622281—21no—
54#10622281—21no—
55#10622280C2211yescharacteristic
56#10622280C2211yescharacteristic, complemented
57D11×#95C2211yescharacteristic
58D11×#95C2211yescharacteristic, complemented
59C11×#328C2211yescharacteristic, complemented
60C11×#328C2211yescharacteristic, complemented
61C11×#327C2211yescharacteristic
62C11×#327C2211yescharacteristic
63#10622176C2211yescharacteristic, complemented
64#10622176C2211yescharacteristic, complemented
65#10622175C2211yescharacteristic
66#10622175C2211yescharacteristic
67#10622108C2211yescharacteristic
68#10622108C2211yescharacteristic
69#10622105C2211yescharacteristic, complemented
70#10622105C2211yescharacteristic, complemented
71#10622090C2211yescharacteristic, complemented
72#10622090C2211yescharacteristic, complemented
73#10622089C2211yescharacteristic
74#10622089C2211yescharacteristic
75C2×#4343C2×C411yescharacteristic, complemented
76C2×Q8×D11C2×C411yescharacteristic, complemented
77C2×#4341C2×C411yescharacteristic, complemented
78C2×D4×D11—21no—
79C2×D4×D11C2×C411yescharacteristic, complemented
80C22×D44D411yescharacteristic
81C22×C4×D11—21no—
82C22×C4×D11—21no—
83C22×C4×D11C2311yescharacteristic
84C22×C4×D11C2311yescharacteristic
85C11×#126—21no—
86C11×#125C2×C411yescharacteristic, complemented
87C11×#124C2×C411yescharacteristic, complemented
88C11×#123—21no—
89C11×C22⋊Q8C2311yescharacteristic
90C11×#121C2311yescharacteristic
91C4×Q8×C11C2×C411yescharacteristic, complemented
92C4×D4×C11—21no—
93C4×D4×C11C2×C411yescharacteristic, complemented
94C11×#117—21no—
95C2×C11×C4⋊C4—21no—
96C2×C42×C11C2311yescharacteristic
97#66999C2×C411yescharacteristic, complemented
98#66999C2×C411yescharacteristic, complemented
99#66992—21no—
100#66991C2×C411yescharacteristic, complemented
101#66991C2×C411yescharacteristic, complemented
102#66990—21no—
103D4×Dic11—21no—
104#66983—21no—
105#66983C2311yescharacteristic
106#66982—21no—
107#66982—21no—
108C4×C22⋊D11—21no—
109C4×C22⋊D11—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4D411yescharacteristic
114C2×(C2×D11)⋊C4D411yescharacteristic
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11D411yescharacteristic
117#66977C2311yescharacteristic
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×C4×Dic11—21no—
121C2×#4313—21no—
122C2×#4313—21no—
123C2×C8×D11—21no—
124C2×C8×D11—21no—
125#66951—21no—
126#66951—21no—
127#66950—21no—
128#66950C2×C411yescharacteristic, complemented
129#66950C2×C411yescharacteristic, complemented
130#66949—21no—
131#66948—21no—
132#66948—21no—
133#66948C2×C411yescharacteristic, complemented
134#66948C2×C411yescharacteristic, complemented
135#66947—21no—
136#66947—21no—
137#66947—21no—
138#66947—21no—
139#66946—21no—
140#66946—21no—
141#66946—44no—
142#66945—21no—
143#66945C2×C411yescharacteristic, complemented
144#66945C2×C411yescharacteristic, complemented
145C4⋊C4×D11—21no—
146C4⋊C4×D11C2×C411yescharacteristic, complemented
147C4⋊C4×D11C2×C411yescharacteristic, complemented
148#66943—21no—
149#66942—21no—
150#66939—21no—
151#66938—21no—
152#66937—21no—
153#66937—21no—
154#66937—21no—
155#66937—21no—
156#66936—21no—
157#66936—21no—
158#66935—21no—
159#66935—21no—
160#66935—21no—
161(C22⋊D11)⋊C4—21no—
162(C22⋊D11)⋊C4—21no—
163(C22⋊D11)⋊C4—21no—
164C22⋊C4×D11—21no—
165C22⋊C4×D11—21no—
166C22⋊C4×D11—21no—
167#66932—21no—
168#66931—21no—
169#66931—21no—
170#66929—21no—
171#66929—21no—
172#66928—21no—
173#66928C2×C411yescharacteristic, complemented
174C4×D44—21no—
175C4×D44C2×C411yescharacteristic
176C4×D44C2×C411yescharacteristic
177C4×D44C2×C411yescharacteristic
178C4×D44C2×C411yescharacteristic
179C4×D44C2×C411yescharacteristic, complemented
180C4×D44D411yescharacteristic
181C4×D44D411yescharacteristic
182C4×D44D411yescharacteristic
183C4×D44D411yescharacteristic
184#66925—21no—
185#66925—21no—
186#66923C2×C411yescharacteristic, complemented
187C4×Dic22C2×C411yescharacteristic, complemented
188C11×C4⋊C8—21no—
189C11×C22⋊C8C2311yescharacteristic
190C11×C22⋊C8C2311yescharacteristic
191C11×#97—21no—
192C11×#95—21no—
193C11×#95C2311yescharacteristic
194C11×#95C2311yescharacteristic
195C11⋊#95—21no—
196C11⋊#95—21no—
197C11⋊#95C2311yescharacteristic
198C11⋊#95C2311yescharacteristic
199C22⋊(C11⋊C8)C2311yescharacteristic
200C22⋊(C11⋊C8)C2311yescharacteristic
201(C2×D11)⋊C8—21no—
202(C2×D11)⋊C8—21no—
203(C2×D11)⋊C8—21no—
204(C2×D11)⋊C8—21no—
205C4⋊(C11⋊C8)—21no—
206#66867—21no—
207#17622—111nomaximal, Sylow
208C23×D11—21no—
209C23×D11C2×D411yescharacteristic
210C23×D11C2×D411yescharacteristic
211C2×Q8×C11C22×C411yescharacteristic
212C2×D4×C11—21no—
213C2×D4×C11C22×C411yescharacteristic
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—21no—
221C2×C22⋊D11—21no—
222C2×C22⋊D11—21no—
223C2×C22⋊D11—21no—
224C2×C22⋊D11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11C2×D411yescharacteristic
229C22×Dic11C2×D411yescharacteristic
230#4343—81no—
231Q8×D11—81no—
232#4341—81no—
233D4×D11—42no—
234D4×D11—42no—
235D4×D11—81no—
236C2×D44—21no—
237C2×D44—21no—
238C2×D44—21no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44C22⋊C411yescharacteristic
242C2×D44C22⋊C411yescharacteristic
243C2×D44C22⋊C411yescharacteristic
244C2×D44C22⋊C411yescharacteristic
245C2×D44C22×C411yescharacteristic
246C2×C4×D11—21no—
247C2×C4×D11—21no—
248C2×C4×D11—21no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—42no—
252C2×C4×D11—42no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11—81no—
256C2×C4×D11—81no—
257C2×C4×D11—81no—
258C2×C4×D11—81no—
259C2×C4×D11C22×C411yescharacteristic
260C2×C4×D11C22×C411yescharacteristic
261C2×C4×D11C22×C411yescharacteristic
262C2×C4×D11C22×C411yescharacteristic
263C2×C4×D11C2×D411yescharacteristic
264C2×C4×D11C2×D411yescharacteristic
265C2×C4×D11C2×D411yescharacteristic
266C2×C4×D11C2×D411yescharacteristic
267C2×Dic22—21no—
268C2×Dic22C22×C411yescharacteristic
269C2×C8×C11—21no—
270C2×C8×C11—21no—
271C11×C4⋊C4—21no—
272C11×C4⋊C4—21no—
273C11×C4⋊C4—21no—
274C11×C4⋊C4—21no—
275C11×C4⋊C4—42no—
276C11×C4⋊C4C22×C411yescharacteristic
277C11×C4⋊C4C22×C411yescharacteristic
278C11×C22⋊C4—21no—
279C11×C22⋊C4—21no—
280C11×C22⋊C4—21no—
281C11×C22⋊C4—21no—
282C11×C22⋊C4—21no—
283C42×C11—21no—
284C42×C11C22×C411yescharacteristic
285C42×C11C22×C411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C22⋊Dic11—21no—
289C22⋊Dic11—21no—
290C22⋊Dic11—21no—
291(C2×D11)⋊C4—21no—
292(C2×D11)⋊C4—21no—
293(C2×D11)⋊C4—21no—
294(C2×D11)⋊C4—21no—
295(C2×D11)⋊C4—21no—
296(C2×D11)⋊C4—21no—
297(C2×D11)⋊C4—21no—
298(C2×D11)⋊C4—21no—
299(C2×D11)⋊C4—21no—
300(C2×D11)⋊C4—21no—
301(C2×D11)⋊C4—21no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—42no—
304(C2×D11)⋊C4—42no—
305(C2×D11)⋊C4C22⋊C411yescharacteristic
306(C2×D11)⋊C4C22⋊C411yescharacteristic
307(C2×D11)⋊C4C22⋊C411yescharacteristic
308(C2×D11)⋊C4C22⋊C411yescharacteristic
309(C2×D11)⋊C4C22⋊C411yescharacteristic
310(C2×D11)⋊C4C22⋊C411yescharacteristic
311(C2×D11)⋊C4C22⋊C411yescharacteristic
312(C2×D11)⋊C4C22⋊C411yescharacteristic
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11—42no—
316C4⋊Dic11C22⋊C411yescharacteristic
317C4⋊Dic11C22⋊C411yescharacteristic
318C4⋊Dic11C22⋊C411yescharacteristic
319C4⋊Dic11C22⋊C411yescharacteristic
320C4⋊Dic11C22×C411yescharacteristic
321C4⋊Dic11C22×C411yescharacteristic
322Dic11⋊C4—21no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325Dic11⋊C4—21no—
326Dic11⋊C4—21no—
327Dic11⋊C4—21no—
328Dic11⋊C4—21no—
329Dic11⋊C4—21no—
330Dic11⋊C4—81no—
331Dic11⋊C4—81no—
332C4×Dic11—21no—
333C4×Dic11—21no—
334C4×Dic11—21no—
335C4×Dic11—42no—
336C2×C11⋊C8—21no—
337C2×C11⋊C8—21no—
338#4313—81no—
339#4313—81no—
340C8×D11—81no—
341C8×D11—81no—
342#3505—111no—
343#2973—111no—
344#2349—111no—
345#1520—111no—
346#1519—111no—
347#1513—111no—
348#1513—111no—
349#1512—111no—
350#1512D1111yescharacteristic, complemented
351#1509—111no—
352#1509—111no—
353#1504—111no—
354#1504—111no—
355C2×#328—111no—
356C2×#327—111no—
357C23×C11—21no—
358C23×C11C22×D411yescharacteristic
359C22×D11—21no—
360C22×D11—21no—
361C22×D11—21no—
362C22×D11—41no—
363C22×D11—41no—
364C22×D11—41no—
365C22×D11—41no—
366C22×D11—42no—
367C22×D11—81no—
368C22×D11—81no—
369C22×D11C2×C22⋊C411yescharacteristic
370C22×D11C2×C22⋊C411yescharacteristic
371C22×D11C2×C22⋊C411yescharacteristic
372C22×D11C2×C22⋊C411yescharacteristic
373C22×D11AGL(1,ℤ/8)12yes—
374C22×D11#13712yes—
375Q8×C11—41no—
376D4×C11—41no—
377D4×C11—41no—
378D4×C11—41no—
379C2×C4×C11—21no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—81no—
393C2×C4×C11C2×C22⋊C411yescharacteristic
394C2×C4×C11C2×C22⋊C411yescharacteristic
395C2×C4×C11C2×C22⋊C411yescharacteristic
396C2×C4×C11C2×C22⋊C411yescharacteristic
397C2×C4×C11C23×C411yescharacteristic
398C2×C4×C11C22×D411yescharacteristic
399C22⋊D11—41no—
400C22⋊D11—41no—
401C22⋊D11—42no—
402C22⋊D11—81no—
403C22⋊D11—81no—
404C22⋊D11—81no—
405C2×Dic11—22no—
406C2×Dic11—21no—
407C2×Dic11—21no—
408C2×Dic11—21no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—81no—
417C2×Dic11C2×C22⋊C411yescharacteristic
418C2×Dic11C2×C22⋊C411yescharacteristic
419C2×Dic11C2×C22⋊C411yescharacteristic
420C2×Dic11C2×C22⋊C411yescharacteristic
421D44—22no—
422D44—22no—
423D44—22no—
424D44—22no—
425D44—41no—
426D44—42no—
427D44—81no—
428D44—81no—
429C4×D11—41no—
430C4×D11—41no—
431C4×D11—41no—
432C4×D11—41no—
433C4×D11—41no—
434C4×D11—41no—
435C4×D11—41no—
436C4×D11—41no—
437C4×D11—42no—
438C4×D11—81no—
439C4×D11—81no—
440C4×D11—81no—
441C4×D11—81no—
442C4×D11—84no—
443C4×D11—84no—
444Dic22—41no—
445Dic22—81no—
446C8×C11—41no—
447C8×C11—41no—
448C11⋊C8—41no—
449C11⋊C8—41no—
450#553—111no—
451#553—111no—
452#553—221no—
453#553—221no—
454#552—111no—
455#552—111no—
456#551—221no—
457#551—221no—
458#548—111no—
459#548—111no—
460#546—111no—
461#546—111no—
462#539—221no—
463#538—221no—
464#534—221no—
465#529—111no—
466#529C2×D1111yescharacteristic
467#525—111no—
468#525—111no—
469C2×C22⋊Q8—111no—
470C2×#121—111no—
471#518—221no—
472C2×C4×D4—111no—
473C2×C4×D4—221no—
474#435—221no—
475#435—221no—
476#435—221no—
477#435—221no—
478#432—111no—
479#432C2×D1111yescharacteristic, complemented
480#407—111no—
481#407—111no—
482C2×C22⋊C8—111no—
483C2×C22⋊C8—111no—
484#389—221no—
485#385—221no—
486#385—221no—
487#382C2×D1111yescharacteristic, complemented
488#380—111no—
489#380—111no—
490C4×C4⋊C4—111no—
491C2×#95—111no—
492C2×#95—111no—
493#328—111no—
494#328—111no—
495#328—111no—
496#328—111no—
497#328—111no—
498#328—111no—
499#328C2×D1111yescharacteristic, complemented
500#328C2×D1111yescharacteristic, complemented
501#327—111no—
502#327—111no—
503#327—111no—
504#327—111no—
505#327—111no—
506#327—111no—
507#327C2×D1111yescharacteristic
508#327C2×D1111yescharacteristic
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—41no—
512C22×C11—41no—
513C22×C11—41no—
514C22×C11C22×C22⋊C411yescharacteristic
515C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
516C22×C11C2×#13711yescharacteristic
517C2×D11—21no—
518C2×D11—21no—
519C2×D11—21no—
520C2×D11—21no—
521C2×D11—21no—
522C2×D11—21no—
523C2×D11—21no—
524C2×D11—21no—
525C2×D11—21no—
526C2×D11—21no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—41no—
532C2×D11—41no—
533C2×D11—41no—
534C2×D11—162no—
535C2×D11#41712yes—
536C2×D11#41712yes—
537C4×C11—21no—
538C4×C11—21no—
539C4×C11—21no—
540C4×C11—21no—
541C4×C11—21no—
542C4×C11—21no—
543C4×C11—41no—
544C4×C11—41no—
545C4×C11—41no—
546C4×C11—81no—
547C4×C11—81no—
548Dic11—21no—
549Dic11—21no—
550Dic11—21no—
551Dic11—21no—
552Dic11—42no—
553Dic11—41no—
554Dic11—41no—
555Dic11—41no—
556Dic11—81no—
557C2×#41—111no—
558C2×#41—111no—
559C22×Q8—111no—
560C22×D4—111no—
561C22×D4—111no—
562C22×D4—221no—
563C23×C4—111no—
564C23×C4—111no—
565C23×C4—221no—
566C23×C4—221no—
567C2×M16—221no—
568C2×M16—221no—
569C22×C8—221no—
570C22×C8—221no—
571#126—21no—
572#126—221no—
573#126—221no—
574#126—221no—
575#126—221no—
576#126—221no—
577#125—111no—
578#125—221no—
579#125—221no—
580#125C4×D1111yescharacteristic, complemented
581#124—111no—
582#124—221no—
583#124—221no—
584#124C4×D1111yescharacteristic, complemented
585#123—21no—
586#123—221no—
587#123—221no—
588#123—221no—
589#123—221no—
590#123—221no—
591#123—221no—
592#123—221no—
593#123—221no—
594#123—221no—
595C22⋊Q8—111no—
596C22⋊Q8—111no—
597C22⋊Q8—111no—
598C22⋊Q8—111no—
599C22⋊Q8—111no—
600C22⋊Q8—221no—
601C22⋊Q8—221no—
602C22⋊Q8—221no—
603C22⋊Q8—221no—
604C22⋊Q8C22×D1111yescharacteristic
605#121—111no—
606#121—111no—
607#121—111no—
608#121—111no—
609#121—111no—
610#121—221no—
611#121—221no—
612#121—221no—
613#121—221no—
614#121—221no—
615#121—221no—
616#121—221no—
617#121—221no—
618#121C22×D1111yescharacteristic
619#120—221no—
620#120—221no—
621#120—221no—
622#120—221no—
623C4×Q8—111no—
624C4×Q8C4×D1111yescharacteristic, complemented
625C4×D4—21no—
626C4×D4—111no—
627C4×D4—111no—
628C4×D4—111no—
629C4×D4—111no—
630C4×D4—111no—
631C4×D4—111no—
632C4×D4—111no—
633C4×D4—111no—
634C4×D4—111no—
635C4×D4—221no—
636C4×D4—221no—
637C4×D4—221no—
638C4×D4—221no—
639C4×D4—221no—
640C4×D4—221no—
641C4×D4—221no—
642C4×D4—221no—
643C4×D4—221no—
644C4×D4—444no—
645C4×D4C4×D1111yescharacteristic, complemented
646#117—21no—
647#117—111no—
648#117—111no—
649#117—221no—
650#117—221no—
651#117—221no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—111no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—111no—
656C2×C4⋊C4—221no—
657C2×C4⋊C4—221no—
658C2×C4⋊C4—221no—
659C2×C4⋊C4—221no—
660C2×C22⋊C4—111no—
661C2×C22⋊C4—111no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C22⋊C4—221no—
666C2×C22⋊C4—221no—
667C2×C22⋊C4—221no—
668C2×C42—221no—
669C2×C42C22×D1111yescharacteristic
670C4⋊C8—21no—
671C4⋊C8—221no—
672C22⋊C8—111no—
673C22⋊C8—111no—
674C22⋊C8—221no—
675C22⋊C8—221no—
676C22⋊C8—221no—
677C22⋊C8—221no—
678C22⋊C8C22×D1111yescharacteristic
679C22⋊C8C22×D1111yescharacteristic
680#97—21no—
681#97—221no—
682#95—21no—
683#95—111no—
684#95—111no—
685#95—221no—
686#95—221no—
687#95C22×D1111yescharacteristic
688#95C22×D1111yescharacteristic
689C2×C11—21no—
690C2×C11—21no—
691C2×C11—81no—
692C2×C11#288311yescharacteristic
693C2×C11C2×#41711yescharacteristic
694C2×C11#290111yescharacteristic
695D11—22no—
696D11—22no—
697D11—41no—
698D11—41no—
699D11—81no—
700C24—111no—
701C24—111no—
702C24—221no—
703#41—881no—
704#41—881no—
705C2×Q8—111no—
706C2×Q8—221no—
707C2×Q8—881no—
708C2×Q8C2×C4×D1111yescharacteristic
709C2×D4—21no—
710C2×D4—111no—
711C2×D4—111no—
712C2×D4—111no—
713C2×D4—111no—
714C2×D4—111no—
715C2×D4—222no—
716C2×D4—222no—
717C2×D4—221no—
718C2×D4—221no—
719C2×D4—221no—
720C2×D4—221no—
721C2×D4—221no—
722C2×D4—221no—
723C2×D4—221no—
724C2×D4—221no—
725C2×D4—442no—
726C2×D4—442no—
727C2×D4—881no—
728C2×D4C2×C4×D1111yescharacteristic
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—111no—
733C22×C4—111no—
734C22×C4—111no—
735C22×C4—111no—
736C22×C4—111no—
737C22×C4—111no—
738C22×C4—111no—
739C22×C4—111no—
740C22×C4—111no—
741C22×C4—111no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—442no—
751C22×C4—442no—
752C22×C4—442no—
753C22×C4—442no—
754C22×C4—881no—
755C22×C4—881no—
756C22×C4—881no—
757C22×C4—881no—
758C22×C4D4×D1111yescharacteristic
759C22×C4D4×D1111yescharacteristic
760C22×C4C23×D1111yescharacteristic
761M16—881no—
762M16—881no—
763C2×C8—21no—
764C2×C8—21no—
765C2×C8—221no—
766C2×C8—221no—
767C2×C8—881no—
768C2×C8—881no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—42no—
774C4⋊C4—111no—
775C4⋊C4—111no—
776C4⋊C4—111no—
777C4⋊C4—111no—
778C4⋊C4—111no—
779C4⋊C4—111no—
780C4⋊C4—221no—
781C4⋊C4—221no—
782C4⋊C4—221no—
783C4⋊C4—221no—
784C4⋊C4—221no—
785C4⋊C4—221no—
786C4⋊C4—221no—
787C4⋊C4—221no—
788C4⋊C4—221no—
789C4⋊C4—221no—
790C4⋊C4—442no—
791C4⋊C4—881no—
792C4⋊C4—881no—
793C4⋊C4C2×C4×D1111yescharacteristic
794C4⋊C4C2×C4×D1111yescharacteristic
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—111no—
801C22⋊C4—111no—
802C22⋊C4—111no—
803C22⋊C4—111no—
804C22⋊C4—111no—
805C22⋊C4—111no—
806C22⋊C4—111no—
807C22⋊C4—111no—
808C22⋊C4—221no—
809C22⋊C4—221no—
810C22⋊C4—221no—
811C22⋊C4—221no—
812C22⋊C4—221no—
813C22⋊C4—221no—
814C22⋊C4—221no—
815C22⋊C4—221no—
816C22⋊C4—221no—
817C22⋊C4—221no—
818C22⋊C4—221no—
819C22⋊C4—221no—
820C22⋊C4—221no—
821C22⋊C4—221no—
822C22⋊C4—221no—
823C22⋊C4—442no—
824C22⋊C4—442no—
825C42—21no—
826C42—221no—
827C42—221no—
828C42—221no—
829C42—442no—
830C42C2×C4×D1111yescharacteristic
831C42C2×C4×D1111yescharacteristic
832C42D4×D1111yescharacteristic
833C42D4×D1111yescharacteristic
834C11#1762211yescharacteristic, complemented, Sylow
835C23—21no—
836C23—111no—
837C23—111no—
838C23—112no—
839C23—112no—
840C23—111no—
841C23—111no—
842C23—221no—
843C23—221no—
844C23—221no—
845C23—441no—
846C23—441no—
847C23—441no—
848C23—441no—
849C23—442no—
850C23—881no—
851C23—881no—
852C23C2×D4×D1111yescharacteristic
853Q8—41no—
854Q8—441no—
855Q8—881no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—222no—
860D4—222no—
861D4—222no—
862D4—222no—
863D4—441no—
864D4—442no—
865D4—442no—
866D4—441no—
867D4—441no—
868D4—881no—
869D4—881no—
870D4—881no—
871D4—881no—
872D4—881no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—81no—
887C2×C4—111no—
888C2×C4—111no—
889C2×C4—111no—
890C2×C4—111no—
891C2×C4—222no—
892C2×C4—221no—
893C2×C4—221no—
894C2×C4—221no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—442no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—881no—
912C2×C4—881no—
913C2×C4—881no—
914C2×C4—881no—
915C2×C4—884no—
916C2×C4—884no—
917C2×C4—881no—
918C2×C4C22⋊C4×D1111yescharacteristic
919C2×C4C22⋊C4×D1111yescharacteristic
920C2×C4C22⋊C4×D1111yescharacteristic
921C2×C4C22⋊C4×D1111yescharacteristic
922C2×C4C22×C4×D1111yescharacteristic
923C2×C4C2×D4×D1111yescharacteristic
924C8—41no—
925C8—41no—
926C8—441no—
927C8—441no—
928C22—21no—
929C22—21no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—112no—
934C22—112no—
935C22—221no—
936C22—221no—
937C22—221no—
938C22—221no—
939C22—221no—
940C22—221no—
941C22—221no—
942C22—221no—
943C22—221no—
944C22—221no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—441no—
950C22—441no—
951C22—441no—
952C22—1762no—
953C22C2×C22⋊C4×D1111yescharacteristic
954C22D11×AGL(1,ℤ/8)11yescharacteristic
955C22D11×#13711yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—41no—
963C4—41no—
964C4—41no—
965C4—81no—
966C4—81no—
967C4—221no—
968C4—221no—
969C4—221no—
970C4—221no—
971C4—442no—
972C4—441no—
973C4—441no—
974C4—441no—
975C4—881no—
976C2—21no—
977C2—21no—
978C2—81no—
979C2—222no—
980C2—222no—
981C2—441no—
982C2—441no—
983C2—881no—
984C2#1307707511yescharacteristic
985C2D11×#41711yescharacteristic
986C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1512C2
socleC22×C11C22×C22⋊C4
prime radical#13082451C2
cosocleC22×C4×C11C24
hypercenter#1512D11
hypocenterC11#17622
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1512

Complements

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

NH ≅ G/Ntype
2. #13077644C2semidirect
3. #13071524C2semidirect
4. #13067186C2semidirect
5. #13067182C2semidirect
6. #13067158C2semidirect
7. #13067156C2semidirect
8. #13067152C2semidirect
9. #13067142C2semidirect
10. #13067141C2semidirect
11. #13067119C2semidirect
12. #13067117C2semidirect
13. D11×#328C2semidirect
14. D11×#327C2semidirect
15. C11×#1512C2semidirect
19. #10623226C4semidirect
20. #10623225C4semidirect
21. #10623208C4semidirect
22. #10623207C4semidirect
29. #10623112C4semidirect
30. #10623107C4semidirect
32. #10623089C4semidirect
33. #10623085C4semidirect
40. C11×#432C22semidirect
41. C11×#382C22semidirect
43. C4×C4⋊Dic11C22semidirect
44. #10622539C22semidirect
47. #10622339C22semidirect
48. #10622339C22semidirect
56. #10622280C22semidirect
58. D11×#95C22semidirect
59. C11×#328C22semidirect
60. C11×#328C22semidirect
63. #10622176C22semidirect
64. #10622176C22semidirect
69. #10622105C22semidirect
70. #10622105C22semidirect
71. #10622090C22semidirect
72. #10622090C22semidirect
75. C2×#4343C2×C4semidirect
76. C2×Q8×D11C2×C4semidirect
77. C2×#4341C2×C4semidirect
79. C2×D4×D11C2×C4semidirect
86. C11×#125C2×C4semidirect
87. C11×#124C2×C4semidirect
91. C4×Q8×C11C2×C4semidirect
93. C4×D4×C11C2×C4semidirect
97. #66999C2×C4semidirect
98. #66999C2×C4semidirect
100. #66991C2×C4semidirect
101. #66991C2×C4semidirect
128. #66950C2×C4semidirect
129. #66950C2×C4semidirect
133. #66948C2×C4semidirect
134. #66948C2×C4semidirect
143. #66945C2×C4semidirect
144. #66945C2×C4semidirect
146. C4⋊C4×D11C2×C4semidirect
147. C4⋊C4×D11C2×C4semidirect
173. #66928C2×C4semidirect
179. C4×D44C2×C4semidirect
186. #66923C2×C4semidirect
187. C4×Dic22C2×C4semidirect
350. #1512D11semidirect
479. #432C2×D11semidirect
487. #382C2×D11semidirect
499. #328C2×D11semidirect
500. #328C2×D11semidirect
580. #125C4×D11semidirect
584. #124C4×D11semidirect
624. C4×Q8C4×D11semidirect
645. C4×D4C4×D11semidirect
834. C11#17622semidirect

Maximal subgroups

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

subgroupindex
#130824512
#130776442
#130715242
#130671862
#130671822
#130671582
#130671562
#130671522
#130671422
#130671412
#130671192
#130671172
D11×#3282
D11×#3272
C11×#15122
#1762211