Finite Group Databasebeta

← #14919942

Subgroups — #14919942

Order 2816.

1800 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11⋊#564C211yesmaximal, characteristic
2#13071801C211yesmaximal, characteristic
3#13071801C211yesmaximal, characteristic
4#13071720C212yesmaximal
5#13071718C212yesmaximal
6#13071718C212yesmaximal
7#13071715C212yesmaximal
8#13071711C212yesmaximal
9#13071707C212yesmaximal
10#13071421C212yesmaximal
11#13071419C212yesmaximal
12#13071418C212yesmaximal
13#13071356C212yesmaximal
14#13071354C212yesmaximal
15#13071352C212yesmaximal
16#125×Dic11C211yesmaximal, characteristic
17#13071171C211yesmaximal, characteristic
18#13071171C211yesmaximal, characteristic
19C11×#2382C211yesmaximal, characteristic
20C2×C11×#125C2211yescharacteristic
21C11⋊#564C4116yescomplemented
22C2×#66943C2212yes—
23C2×#66943C2212yes—
24C2×#66942C2212yes—
25C2×#66942C2212yes—
26C2×#66942C2212yes—
27C2×#66942C2212yes—
28C2×#66923C2211yescharacteristic
29C2×#66923C2211yescharacteristic
30C11×#389C2212yes—
31C11×#389C2212yes—
32C11×#387C2212yes—
33C11×#387C2212yes—
34C11×#387C2212yes—
35C11×#387C2212yes—
36C11×#382C2211yescharacteristic
37C11×#382C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622594C2212yes—
41#10622594C2212yes—
42#10622591C2212yes—
43#10622591C2212yes—
44#10622591C2212yes—
45#10622589C2212yes—
46C4⋊C4×Dic11C2212yes—
47C4⋊C4×Dic11C2212yes—
48C4⋊C4×Dic11C2211yescharacteristic
49C4⋊C4×Dic11C2211yescharacteristic
50C4⋊C4×Dic11C2211yescharacteristic
51C4⋊C4×Dic11C2211yescharacteristic
52C4⋊C4×Dic11C2211yescharacteristic
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2211yescharacteristic
55C4⋊C4×Dic11C2212yes—
56#10622586C2211yescharacteristic
57#10622586C2211yescharacteristic
58#10622586C2211yescharacteristic
59#10622586C2211yescharacteristic
60#10622586C2212yes—
61#10622585C2212yes—
62#10622585C2212yes—
63#10622585C2212yes—
64#10622585C2212yes—
65#10622585C2212yes—
66#10622549C2211yescharacteristic
67C4×C4⋊Dic11C2212yes—
68#10622546C2212yes—
69#10622545C2212yes—
70C4×Dic11⋊C4C2212yes—
71C4×Dic11⋊C4C2212yes—
72C4×Dic11⋊C4C2212yes—
73C4×Dic11⋊C4C2212yes—
74C42×Dic11C2211yescharacteristic
75#10622541C2212yes—
76#10622268C2212yes—
77#10622268C2212yes—
78#10622268C2212yes—
79#10622268C2212yes—
80#10622268C2212yes—
81#10622267C2212yes—
82#10622267C2212yes—
83#10622267C2212yes—
84#10622267C2212yes—
85#10622266C2212yes—
86#10622266C2212yes—
87#10622266C2212yes—
88#10622266C2212yes—
89#10622265C2212yes—
90#10622265C2212yes—
91#10622265C2212yes—
92#10622265C2212yes—
93#10622265C2212yes—
94#10622265C2212yes—
95#10622265C2212yes—
96#10622264C2212yes—
97#10622262C2212yes—
98#10622262C2212yes—
99#10622262C2212yes—
100#10622262C2212yes—
101#10622262C2212yes—
102#10622262C2212yes—
103#10622261C2212yes—
104#10622261C2212yes—
105#10622260C2212yes—
106#10622260C2212yes—
107#10622260C2212yes—
108C11×#125C2×C418yes—
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2312yes—
112C2×C11×C4⋊C4C2312yes—
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C42×C11C2312yes—
120C2×C42×C11C2312yes—
121C2×C42×C11C2311yescharacteristic
122C2×C4⋊Dic11C2312yes—
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2312yes—
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×Dic11⋊C4C2312yes—
133C2×Dic11⋊C4C2312yes—
134C2×Dic11⋊C4C2312yes—
135C2×Dic11⋊C4C2312yes—
136C2×Dic11⋊C4C2312yes—
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×C4×Dic11C2312yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2311yescharacteristic
151C2×C4×Dic11C2311yescharacteristic
152C2×C4×Dic11C2311yescharacteristic
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2312yes—
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166#66943C2×C4116yes—
167#66943C2×C4116yes—
168#66942C2×C4116yes—
169#66942C2×C4116yes—
170#66942C2×C4116yes—
171#66942C2×C4116yes—
172#66923C2×C418yes—
173#66923C2×C418yes—
174C11×#95C2312yes—
175C11×#95C2312yes—
176C11×#95C2312yes—
177C11×#95C2312yes—
178C11×#95C2312yes—
179C11×#95C2312yes—
180C11×#95C2312yes—
181C11×#95C2312yes—
182C11⋊#95C2312yes—
183C11⋊#95C2312yes—
184C11⋊#95C2312yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204#34530—111nomaximal, Sylow
205C22×C4×C11C2412yes—
206C22×C4×C11C2412yes—
207C22×C4×C11C2412yes—
208C22×C4×C11C2412yes—
209C22×C4×C11C2411yescharacteristic
210C22×C4×C11C2411yescharacteristic
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2411yescharacteristic
217C22×Dic11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2411yescharacteristic
222C22×Dic11C2411yescharacteristic
223C22×Dic11C2411yescharacteristic
224C11×C4⋊C4—42no—
225C11×C4⋊C4—41no—
226C11×C4⋊C4—41no—
227C11×C4⋊C4—41no—
228C11×C4⋊C4—41no—
229C11×C4⋊C4—42no—
230C11×C4⋊C4C22×C414yes—
231C11×C4⋊C4C22×C414yes—
232C11×C4⋊C4C22×C418yes—
233C11×C4⋊C4C22×C418yes—
234C42×C11—42no—
235C42×C11—42no—
236C42×C11C22×C414yes—
237C4⋊Dic11—24no—
238C4⋊Dic11—41no—
239C4⋊Dic11—41no—
240C4⋊Dic11—42no—
241C4⋊Dic11C22×C414yes—
242C4⋊Dic11C22×C414yes—
243C4⋊Dic11C22×C414yes—
244C4⋊Dic11C22×C414yes—
245C4⋊Dic11C22×C418yes—
246C4⋊Dic11C22×C418yes—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—42no—
250Dic11⋊C4—42no—
251Dic11⋊C4—42no—
252Dic11⋊C4—42no—
253Dic11⋊C4—42no—
254Dic11⋊C4—42no—
255Dic11⋊C4C22×C418yes—
256Dic11⋊C4C22×C418yes—
257Dic11⋊C4C22×C418yes—
258Dic11⋊C4C22×C418yes—
259Dic11⋊C4C22×C418yes—
260Dic11⋊C4C22×C418yes—
261Dic11⋊C4C22×C418yes—
262Dic11⋊C4C22×C418yes—
263C4×Dic11—22no—
264C4×Dic11—22no—
265C4×Dic11—22no—
266C4×Dic11—24no—
267C4×Dic11—24no—
268C4×Dic11—24no—
269C4×Dic11—41no—
270C4×Dic11—42no—
271C4×Dic11—41no—
272C4×Dic11—41no—
273C4×Dic11—42no—
274C4×Dic11—42no—
275C4×Dic11—42no—
276C4×Dic11—42no—
277C4×Dic11—42no—
278C4×Dic11—42no—
279C4×Dic11C22×C418yes—
280C4×Dic11C22×C418yes—
281C2×#564—111no—
282#2382—111no—
283#2382—111no—
284#2382D1111yescharacteristic
285#2371—112no—
286#2371—112no—
287#2371—112no—
288#2370—112no—
289#2370—112no—
290#2370—112no—
291#2336—112no—
292#2336—112no—
293#2336—112no—
294#2330—112no—
295#2330—112no—
296#2330—112no—
297C4×#125—111no—
298C4×#125—111no—
299C4×#125—111no—
300C23×C11C2511yescharacteristic
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—22no—
304C2×C4×C11—21no—
305C2×C4×C11—22no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11C23×C414yes—
324C2×C4×C11C23×C414yes—
325C2×C4×C11C23×C412yes—
326C2×C4×C11C23×C412yes—
327C2×C4×C11C23×C412yes—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—21no—
347C2×Dic11—21no—
348C2×Dic11—22no—
349C2×Dic11—21no—
350C2×Dic11—22no—
351C2×Dic11C23×C414yes—
352C2×Dic11C23×C414yes—
353C2×Dic11C23×C414yes—
354C2×Dic11C23×C414yes—
355C2×Dic112−1+412yes—
356C2×Dic112−1+412yes—
357C2×Dic112−1+412yes—
358#564—1116no—
359C2×#125—112no—
360C2×#125—112no—
361C2×#125—112no—
362C2×#125—112no—
363C2×#125—112no—
364C2×#125—112no—
365C2×#125—111no—
366C2×#125—111no—
367C2×#125C2×D1111yescharacteristic
368#389—111no—
369#389—111no—
370#389—111no—
371#389—111no—
372#389—111no—
373#389—111no—
374#389—112no—
375#389—112no—
376#389—112no—
377#389—112no—
378#389—112no—
379#389—112no—
380#389—112no—
381#389—112no—
382#389—112no—
383#389—112no—
384#389C2×D1112yes—
385#389C2×D1112yes—
386#387—112no—
387#387—112no—
388#387—112no—
389#387—112no—
390#387—112no—
391#387—112no—
392#387—112no—
393#387—112no—
394#387—112no—
395#387—112no—
396#387—112no—
397#387—112no—
398#387—112no—
399#387—112no—
400#387—112no—
401#387—112no—
402#387—112no—
403#387—112no—
404#387—112no—
405#387—112no—
406#387—112no—
407#387—112no—
408#387—112no—
409#387—112no—
410#387—112no—
411#387—112no—
412#387C2×D1112yes—
413#387C2×D1112yes—
414#387C2×D1112yes—
415#387C2×D1112yes—
416#384—112no—
417#383—112no—
418#382—111no—
419#382C2×D1111yescharacteristic
420#382C2×D1111yescharacteristic
421C4×C4⋊C4—112no—
422C4×C4⋊C4—111no—
423C4×C4⋊C4—111no—
424C4×C4⋊C4—111no—
425C4×C4⋊C4—112no—
426C4×C4⋊C4—111no—
427C4×C4⋊C4—111no—
428C4×C4⋊C4—111no—
429C4×C4⋊C4—112no—
430C4×C4⋊C4—112no—
431C4×C4⋊C4—112no—
432C4×C4⋊C4—112no—
433C4×C4⋊C4—112no—
434C4×C4⋊C4—112no—
435C4×C4⋊C4—112no—
436C4×C4⋊C4—112no—
437C4×C4⋊C4—112no—
438C4×C4⋊C4—112no—
439C4×C4⋊C4—112no—
440C4×C4⋊C4—112no—
441C4×C4⋊C4—112no—
442#376—112no—
443#376—112no—
444#376—112no—
445C43—111no—
446C22×C11C24×C411yescharacteristic
447C22×C11C2×2−1+411yescharacteristic
448C22×C11C2×2−1+411yescharacteristic
449C22×C11C2×2−1+411yescharacteristic
450C22×C11#58511yescharacteristic
451C22×C11#58511yescharacteristic
452C22×C11#58511yescharacteristic
453C4×C11—22no—
454C4×C11—22no—
455C4×C11—22no—
456C4×C11—24no—
457C4×C11—24no—
458C4×C11—42no—
459C4×C11—42no—
460C4×C11—42no—
461C4×C11—42no—
462Dic11—24no—
463Dic11—24no—
464Dic11—24no—
465Dic11—24no—
466Dic11—22no—
467Dic11—22no—
468Dic11—22no—
469Dic11—42no—
470Dic11—42no—
471Dic11—41no—
472#125—1116no—
473#125—1116no—
474#125—1116no—
475#125—1116no—
476#125—1116no—
477#125—1116no—
478#125—118no—
479#125—118no—
480#125C4×D1118yes—
481C2×C4⋊C4—112no—
482C2×C4⋊C4—112no—
483C2×C4⋊C4—112no—
484C2×C4⋊C4—112no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—112no—
487C2×C4⋊C4—112no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—112no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—111no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—112no—
504C2×C4⋊C4—112no—
505C2×C4⋊C4—112no—
506C2×C4⋊C4—112no—
507C2×C4⋊C4C22×D1111yescharacteristic
508C2×C4⋊C4C22×D1111yescharacteristic
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1111yescharacteristic
511C2×C4⋊C4C22×D1112yes—
512C2×C4⋊C4C22×D1112yes—
513C2×C4⋊C4C22×D1112yes—
514C2×C4⋊C4C22×D1112yes—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C4⋊C4C22×D1111yescharacteristic
517C2×C42—112no—
518C2×C42—112no—
519C2×C42—111no—
520C2×C42—111no—
521C2×C42—111no—
522C2×C42—112no—
523C2×C42—112no—
524C2×C42—112no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—111no—
528C2×C42—112no—
529C2×C42—112no—
530C2×C42—112no—
531C2×C42—112no—
532C2×C42—112no—
533C2×C42—112no—
534C2×C42—112no—
535C2×C42C22×D1112yes—
536C2×C42C22×D1112yes—
537C2×C42C22×D1111yescharacteristic
538#95—112no—
539#95—112no—
540#95—112no—
541#95—112no—
542#95—112no—
543#95—112no—
544#95—112no—
545#95—112no—
546#95—112no—
547#95—112no—
548#95—112no—
549#95—112no—
550#95—112no—
551#95—112no—
552#95—112no—
553#95—112no—
554#95—112no—
555#95—112no—
556#95—112no—
557#95—112no—
558#95—112no—
559#95—112no—
560#95C22×D1112yes—
561#95C22×D1112yes—
562#95C22×D1112yes—
563#95C22×D1112yes—
564#95C22×D1112yes—
565#95C22×D1112yes—
566#95C22×D1112yes—
567#95C22×D1112yes—
568C2×C11C4×2−1+411yescharacteristic
569C2×C11C4×2−1+411yescharacteristic
570C2×C11C4×2−1+411yescharacteristic
571C2×C11#356311yescharacteristic
572C2×C11#356311yescharacteristic
573C2×C11#356311yescharacteristic
574C2×C11#356711yescharacteristic
575C22×C4—111no—
576C22×C4—111no—
577C22×C4—111no—
578C22×C4—112no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—111no—
585C22×C4C23×D1112yes—
586C22×C4C23×D1112yes—
587C22×C4C23×D1112yes—
588C22×C4C23×D1112yes—
589C22×C4C23×D1112yes—
590C22×C4C23×D1112yes—
591C22×C4C23×D1111yescharacteristic
592C22×C4C23×D1111yescharacteristic
593C22×C4C23×D1111yescharacteristic
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—41no—
597C4⋊C4—41no—
598C4⋊C4—41no—
599C4⋊C4—41no—
600C4⋊C4—118no—
601C4⋊C4—118no—
602C4⋊C4—118no—
603C4⋊C4—118no—
604C4⋊C4—118no—
605C4⋊C4—118no—
606C4⋊C4—118no—
607C4⋊C4—118no—
608C4⋊C4—118no—
609C4⋊C4—118no—
610C4⋊C4—114no—
611C4⋊C4—114no—
612C4⋊C4—114no—
613C4⋊C4—114no—
614C4⋊C4—224no—
615C4⋊C4—224no—
616C4⋊C4—224no—
617C4⋊C4—442no—
618C4⋊C4—442no—
619C4⋊C4—442no—
620C4⋊C4—442no—
621C4⋊C4—442no—
622C4⋊C4—442no—
623C4⋊C4—442no—
624C4⋊C4—441no—
625C4⋊C4—441no—
626C4⋊C4C2×C4×D1118yes—
627C4⋊C4C2×C4×D1118yes—
628C4⋊C4C2×C4×D1114yes—
629C4⋊C4C2×C4×D1114yes—
630C42—42no—
631C42—42no—
632C42—118no—
633C42—118no—
634C42—222no—
635C42—222no—
636C42—222no—
637C42—224no—
638C42—224no—
639C42—224no—
640C42—442no—
641C42—441no—
642C42—441no—
643C42—441no—
644C42—442no—
645C42—442no—
646C42—442no—
647C42—442no—
648C42—442no—
649C42—442no—
650C42C2×C4×D1114yes—
651C11#3453011yescharacteristic, complemented, Sylow
652C23C24×D1111yescharacteristic
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—114no—
676C2×C4—114no—
677C2×C4—114no—
678C2×C4—114no—
679C2×C4—112no—
680C2×C4—112no—
681C2×C4—112no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—222no—
690C2×C4—222no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—221no—
694C2×C4—222no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—221no—
698C2×C4—222no—
699C2×C4—221no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—221no—
704C2×C4—222no—
705C2×C4C22×C4×D1114yes—
706C2×C4C22×C4×D1114yes—
707C2×C4C22×C4×D1112yes—
708C2×C4C22×C4×D1112yes—
709C2×C4C22×C4×D1112yes—
710C22C23×C4×D1111yescharacteristic
711C22#1062345511yescharacteristic
712C22#1062345511yescharacteristic
713C22D11×2−1+411yescharacteristic
714C22D11×2−1+411yescharacteristic
715C22D11×2−1+411yescharacteristic
716C22#1062345711yescharacteristic
717C4—22no—
718C4—24no—
719C4—24no—
720C4—22no—
721C4—22no—
722C4—42no—
723C4—42no—
724C4—42no—
725C4—42no—
726C4—222no—
727C4—222no—
728C4—222no—
729C4—224no—
730C4—224no—
731C4—224no—
732C4—224no—
733C4—442no—
734C4—442no—
735C4—441no—
736C2#1308182511yescharacteristic
737C2#1308182711yescharacteristic
738C2#1308182711yescharacteristic
739C2#1308321611yescharacteristic
740C2#1308321611yescharacteristic
741C2#1308322511yescharacteristic
742C2#1308330311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2382C2
socle, prime radical, cosocleC23×C11C25
hypercenter#2382D11
hypocenterC11#34530
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
21. C11⋊#564C4semidirect
651. C11#34530semidirect

Maximal subgroups

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

subgroupindex
C2×C11⋊#5642
#130718012
#130717202
#130717182
#130717152
#130717112
#130717072
#130714212
#130714192
#130714182
#130713562
#130713542
#130713522
#125×Dic112
#130711712
C11×#23822
#3453011