Finite Group Databasebeta

← #14926340

Subgroups — #14926340

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623335C211yesmaximal, characteristic
2#13076938C212yesmaximal, complemented
3#13076908C212yesmaximal, complemented
4#13074396C212yesmaximal, complemented
5#13074389C212yesmaximal, complemented
6#13072360C214yesmaximal, complemented
7#13072345C214yesmaximal, complemented
8#13072087C214yesmaximal, complemented
9#13072072C214yesmaximal, complemented
10#13071228C211yesmaximal, characteristic, complemented
11#13071194C211yesmaximal, characteristic, complemented
12#13071191C211yesmaximal, characteristic, complemented
13C2×#10622826C211yesmaximal, characteristic, complemented
14C2×#10622823C211yesmaximal, characteristic, complemented
15C22×C4×D4×C11C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic, complemented
19C23×C22⋊D11C2211yescharacteristic
20C2×C4×D4×C11—28no—
21C2×C4×D4×C11C2214yes—
22C2×C4×D4×C11C2214yescomplemented
23C22×C11×C4⋊C4C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic, complemented
26C22×C42×C11C2211yescharacteristic, complemented
27C2×#67006C2212yes—
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31#10623335—28no—
32C2×#66992C2212yes—
33C2×#66992C2212yes—
34C2×#66990C2212yes—
35C2×#66988C2212yes—
36C2×#66982C2212yes—
37C2×#66982C2214yescomplemented
38C22×(C2×D11)⋊C4C2212yescomplemented
39C22×Dic11⋊C4C2212yescomplemented
40#10622860C2212yescomplemented
41#10622833C2214yes—
42#10622833C2214yescomplemented
43#10622826C2212yes—
44#10622826C2212yes—
45#10622826C2212yes—
46#10622826C2212yes—
47#10622826C2214yescomplemented
48#10622826C2214yescomplemented
49#10622824C2212yescomplemented
50#10622824C2214yescomplemented
51#10622823C2212yescomplemented
52#10622823C2212yescomplemented
53#10622823C2212yescomplemented
54#10622823C2214yescomplemented
55#10622823C2214yescomplemented
56#10622823C2212yescomplemented
57C2×C11⋊#95C2212yescomplemented
58C2×C11⋊#95C2212yescomplemented
59#10622606C2214yescomplemented
60#10622605C2214yescomplemented
61#10622595C2214yescomplemented
62#10622593C2214yescomplemented
63#10622572C2214yescomplemented
64#10622572C2214yescomplemented
65#10622571C2214yescomplemented
66#10622568C2212yescomplemented
67#10622565C2214yescomplemented
68#10622565C2214yescomplemented
69#10622559C2212yescomplemented
70#10622559C2212yescomplemented
71#10622556C2212yescomplemented
72#10622555C2214yescomplemented
73#10622553C2214yescomplemented
74#10622553C2214yescomplemented
75#10622546C2214yescomplemented
76#10622546C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—24no—
82C22×D4×C11D418yes—
83C22×D4×C11C2312yes—
84C22×D4×C11C2312yes—
85C23×C4×C11—24no—
86C23×C4×C11—24no—
87C23×C4×C11—44no—
88C23×C4×C11—44no—
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2312yes—
91C23×C4×C11C2312yes—
92C23×C4×C11C2314yes—
93C23×C4×C11C2311yescharacteristic
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11C2312yes—
101C22×C22⋊D11C2312yes—
102C22×C22⋊D11C2312yes—
103C22×C22⋊D11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2312yes—
107C23×Dic11C2312yes—
108C23×Dic11C2311yescharacteristic
109C4×D4×C11—216no—
110C4×D4×C11—216no—
111C2×C11×C4⋊C4—24no—
112C2×C11×C4⋊C4C2314yes—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4—24no—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2314yes—
118C2×C42×C11—24no—
119C2×C42×C11C2314yes—
120#67006—28no—
121C2×C22⋊Dic11—24no—
122C2×C22⋊Dic11—24no—
123C2×C22⋊Dic11—24no—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127C2×C22⋊Dic11C2312yes—
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2312yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2314yes—
133C2×C22⋊Dic11C2314yes—
134#66992—28no—
135#66992—28no—
136#66990—28no—
137#66988—28no—
138#66982—28no—
139#66982—48no—
140C2×(C2×D11)⋊C4—44no—
141C2×(C2×D11)⋊C4C2314yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2314yes—
145C2×(C2×D11)⋊C4C2314yes—
146C2×(C2×D11)⋊C4C2314yes—
147C2×Dic11⋊C4—44no—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2314yes—
152C2×Dic11⋊C4C2314yes—
153C2×Dic11⋊C4C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163C11⋊#95C2314yes—
164#34983—111nomaximal, Sylow
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11C2×D414yes—
172C24×C11C2×D414yes—
173C24×C11#4114yes—
174C24×C11#4114yes—
175C24×C11C2412yes—
176C24×C11C2411yescharacteristic
177C24×C11C2411yescharacteristic
178C24×C11C2411yescharacteristic
179C23×D11—22no—
180C23×D11—22no—
181C23×D11—22no—
182C23×D11—42no—
183C23×D11—42no—
184C23×D11C2412yes—
185C2×D4×C11—232no—
186C2×D4×C11—24no—
187C2×D4×C11—24no—
188C2×D4×C11—24no—
189C2×D4×C11—24no—
190C2×D4×C11C2×D418yes—
191C2×D4×C11C2×D418yes—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—24no—
196C22×C4×C11—22no—
197C22×C4×C11—22no—
198C22×C4×C11—22no—
199C22×C4×C11—28no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—24no—
204C22×C4×C11—28no—
205C22×C4×C11—42no—
206C22×C4×C11—44no—
207C22×C4×C11—42no—
208C22×C4×C11—42no—
209C22×C4×C11—42no—
210C22×C4×C11—42no—
211C22×C4×C11—416no—
212C22×C4×C11—416no—
213C22×C4×C11C2×D414yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—24no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—416no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—24no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—24no—
237C22×Dic11—42no—
238C22×Dic11—42no—
239C22×Dic11—42no—
240C22×Dic11—42no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2414yes—
246C22×Dic11C2414yes—
247C22×Dic11C2412yes—
248C11×C4⋊C4—28no—
249C11×C22⋊C4—28no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C42×C11—28no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—24no—
260C22⋊Dic11—24no—
261C22⋊Dic11—44no—
262C22⋊Dic11—44no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269Dic11⋊C4—24no—
270Dic11⋊C4—24no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C2×#534—111no—
276C22×C4×D4D1111yescharacteristic, complemented
277#2853—112no—
278#2849—112no—
279#2623—112no—
280#2622—112no—
281#2444—114no—
282#2443—114no—
283#2419—114no—
284#2418—114no—
285#2315—111no—
286#2308—111no—
287#2308—111no—
288C2×#386—111no—
289C2×#385—111no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—28no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—44no—
302C23×C11—44no—
303C23×C11—44no—
304C23×C11—44no—
305C23×C11—48no—
306C23×C11—48no—
307C23×C11—48no—
308C23×C11—48no—
309C23×C11#123116yescomplemented
310C23×C11C22×D414yes—
311C23×C11C22×D412yes—
312C23×C11C22×D412yes—
313C23×C11C22×D412yes—
314C23×C11C2×#4112yes—
315C23×C11C2×#4112yes—
316C23×C11C2×#4112yes—
317C23×C11C2×#4112yes—
318C23×C11C2×#4112yes—
319C23×C11C2×#4112yes—
320C23×C11C2511yescharacteristic
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—24no—
325C22×D11—24no—
326C22×D11—48no—
327C22×D11—44no—
328C22×D11—82no—
329C22×D11—82no—
330C22×D11—84no—
331D4×C11—216no—
332D4×C11—216no—
333C2×C4×C11—28no—
334C2×C4×C11—28no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—24no—
344C2×C4×C11—22no—
345C2×C4×C11—24no—
346C2×C4×C11—48no—
347C2×C4×C11—48no—
348C2×C4×C11—416no—
349C2×C4×C11—44no—
350C2×C4×C11—44no—
351C2×C4×C11—44no—
352C2×C4×C11C22×D414yes—
353C2×C4×C11H(5,𝔽2)14yes—
354C22⋊D11—48no—
355C22⋊D11—48no—
356C22⋊D11—84no—
357C22⋊D11—84no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—24no—
368C2×Dic11—24no—
369C2×Dic11—24no—
370C2×Dic11—24no—
371C2×Dic11—48no—
372C2×Dic11—44no—
373C2×Dic11—82no—
374C2×Dic11—82no—
375C2×Dic11—84no—
376C23×D4—111no—
377C23×D4C2×D1111yescharacteristic
378C24×C4C2×D1111yescharacteristic
379C24×C4C2×D1111yescharacteristic, complemented
380#534—228no—
381C2×#123—112no—
382C2×#123—112no—
383C2×#123—114no—
384C2×#121—112no—
385C2×#121—112no—
386C2×#120—112no—
387C2×#120—112no—
388C2×C4×D4—28no—
389C2×C4×D4C2×D1114yes—
390C2×C4×D4C2×D1114yescomplemented
391C22×C4⋊C4—112no—
392C22×C4⋊C4C2×D1111yescharacteristic, complemented
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—112no—
397C22×C22⋊C4C2×D1111yescharacteristic
398C22×C22⋊C4C2×D1111yescharacteristic, complemented
399C22×C42C2×D1111yescharacteristic, complemented
400#400—114no—
401#399—114no—
402#398—114no—
403#397—114no—
404#397—114no—
405#397—114no—
406#394—114no—
407#394—114no—
408#388—114no—
409#388—114no—
410#387—114no—
411#387—114no—
412#386—114no—
413#386—114no—
414#386—112no—
415#386—112no—
416#386—112no—
417#386—114no—
418#386—112no—
419#386—114no—
420#386—114no—
421#385—112no—
422#385—112no—
423#385—112no—
424#385—114no—
425#385—112no—
426#385—114no—
427#385—112no—
428#385—112no—
429#381—112no—
430#381—114no—
431#381—112no—
432#380—114no—
433#379—112no—
434#379—112no—
435C2×#95—112no—
436C2×#95—112no—
437C22×C11—24no—
438C22×C11—24no—
439C22×C11—24no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—22no—
445C22×C11—22no—
446C22×C11—24no—
447C22×C11—24no—
448C22×C11—24no—
449C22×C11—24no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—416no—
453C22×C11—416no—
454C22×C11—44no—
455C22×C11—44no—
456C22×C11C2×#12314yes—
457C22×C11C2×#12314yes—
458C22×C11C2×#12314yes—
459C22×C11C23×D411yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C22×#4111yescharacteristic
462C22×C11C2×H(5,𝔽2)12yes—
463C22×C11#58512yes—
464C2×D11—42no—
465C2×D11—44no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—44no—
469C2×D11—88no—
470C4×C11—24no—
471C4×C11—24no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—42no—
475Dic11—42no—
476Dic11—44no—
477Dic11—42no—
478Dic11—42no—
479Dic11—44no—
480C25—111no—
481C25C22×D1111yescharacteristic
482C25C22×D1111yescharacteristic
483C22×D4—24no—
484C22×D4—24no—
485C22×D4—112no—
486C22×D4—112no—
487C22×D4—112no—
488C22×D4—112no—
489C22×D4—224no—
490C22×D4—224no—
491C22×D4—224no—
492C22×D4C22⋊D1118yes—
493C22×D4C22×D1112yes—
494C22×D4C22×D1112yes—
495C23×C4—24no—
496C23×C4—24no—
497C23×C4—44no—
498C23×C4—44no—
499C23×C4—111no—
500C23×C4—112no—
501C23×C4—111no—
502C23×C4—112no—
503C23×C4—111no—
504C23×C4C22×D1111yescharacteristic
505C23×C4C22×D1112yes—
506C23×C4C22×D1112yes—
507C23×C4C22×D1114yes—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1111yescharacteristic
512#123—228no—
513#123—228no—
514#123—448no—
515#121—228no—
516#121—228no—
517#120—228no—
518#120—228no—
519C4×D4—216no—
520C4×D4—216no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—112no—
524C2×C4⋊C4—112no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4—444no—
529C2×C4⋊C4C22×D1114yes—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—112no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—224no—
549C2×C22⋊C4—224no—
550C2×C22⋊C4—224no—
551C2×C22⋊C4—444no—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1112yes—
554C2×C22⋊C4C22×D1114yes—
555C2×C42—24no—
556C2×C42C22×D1114yes—
557#95—114no—
558#95—114no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565#95—114no—
566#95—114no—
567C2×C11—24no—
568C2×C11—24no—
569C2×C11—24no—
570C2×C11—44no—
571C2×C11C22×#12311yescharacteristic
572C2×C11#345912yes—
573C2×C11#348411yescharacteristic
574C2×C11#348511yescharacteristic
575C2×C11#350512yes—
576D11—82no—
577C24—22no—
578C24—22no—
579C24—42no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—112no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—442no—
588C24—442no—
589C24#433914yes—
590C24#433914yes—
591C24C2×C22⋊D1114yes—
592C24C2×C22⋊D1114yes—
593C24C23×D1112yes—
594C24C23×D1111yescharacteristic
595C24C23×D1111yescharacteristic
596C24C23×D1111yescharacteristic
597C2×D4—232no—
598C2×D4—24no—
599C2×D4—24no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—224no—
603C2×D4—224no—
604C2×D4—224no—
605C2×D4—224no—
606C2×D4—224no—
607C2×D4—224no—
608C2×D4—224no—
609C2×D4—224no—
610C2×D4—444no—
611C2×D4—444no—
612C2×D4—4416no—
613C2×D4C2×C22⋊D1118yes—
614C2×D4C2×C22⋊D1118yes—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—24no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—28no—
623C22×C4—24no—
624C22×C4—24no—
625C22×C4—24no—
626C22×C4—24no—
627C22×C4—28no—
628C22×C4—42no—
629C22×C4—44no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4—416no—
635C22×C4—416no—
636C22×C4—112no—
637C22×C4—114no—
638C22×C4—114no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—224no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—222no—
645C22×C4—224no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—442no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4C2×C22⋊D1114yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—28no—
661C4⋊C4—228no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—444no—
665C4⋊C4—444no—
666C4⋊C4—444no—
667C22⋊C4—28no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—224no—
671C22⋊C4—224no—
672C22⋊C4—224no—
673C22⋊C4—224no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C22⋊C4—224no—
678C22⋊C4—228no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C42—28no—
687C11#3498311yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—28no—
695C23—22no—
696C23—22no—
697C23—24no—
698C23—24no—
699C23—44no—
700C23—44no—
701C23—48no—
702C23—48no—
703C23—44no—
704C23—44no—
705C23—48no—
706C23—48no—
707C23—222no—
708C23—222no—
709C23—224no—
710C23—224no—
711C23—222no—
712C23—448no—
713C23—444no—
714C23—884no—
715C23—882no—
716C23—882no—
717C23#66982116yescomplemented
718C23C2×#433912yes—
719C23C2×#433912yes—
720C23C2×#433912yes—
721C23C2×#433912yes—
722C23C2×#433912yes—
723C23C2×#433912yes—
724C23C22×C22⋊D1114yes—
725C23C22×C22⋊D1112yes—
726C23C22×C22⋊D1112yes—
727C23C22×C22⋊D1112yes—
728C23C24×D1111yescharacteristic
729D4—216no—
730D4—216no—
731D4—448no—
732D4—448no—
733D4—884no—
734D4—884no—
735C2×C4—28no—
736C2×C4—28no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—48no—
749C2×C4—48no—
750C2×C4—416no—
751C2×C4—44no—
752C2×C4—44no—
753C2×C4—44no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—448no—
768C2×C4—444no—
769C2×C4—884no—
770C2×C4—882no—
771C2×C4—882no—
772C2×C4#6703714yes—
773C2×C4C22×C22⋊D1114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—22no—
778C22—22no—
779C22—22no—
780C22—22no—
781C22—22no—
782C22—22no—
783C22—24no—
784C22—24no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—416no—
790C22—416no—
791C22—44no—
792C22—44no—
793C22—444no—
794C22—442no—
795C22—442no—
796C22—444no—
797C22—442no—
798C22—888no—
799C22C2×#6698214yes—
800C22C2×#6698214yes—
801C22C2×#6698214yes—
802C22C22×#433911yescharacteristic
803C22C22×#433911yescharacteristic
804C22C2×#6703712yes—
805C22#1062345312yes—
806C22C23×C22⋊D1111yescharacteristic
807C4—24no—
808C4—24no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—444no—
813C4—442no—
814C4—442no—
815C4—444no—
816C4—442no—
817C2—24no—
818C2—24no—
819C2—24no—
820C2—44no—
821C2—882no—
822C2C22×#6698211yescharacteristic
823C2#1308202512yes—
824C2#1308225111yescharacteristic
825C2#1308226011yescharacteristic
826C2#1308245512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C4×D4×C11C2
prime radicalC2×#10623335C2
hypercenterC22×C4×D4D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. #13076938C2semidirect
3. #13076908C2semidirect
4. #13074396C2semidirect
5. #13074389C2semidirect
6. #13072360C2semidirect
7. #13072345C2semidirect
8. #13072087C2semidirect
9. #13072072C2semidirect
10. #13071228C2semidirect
11. #13071194C2semidirect
12. #13071191C2semidirect
13. C2×#10622826C2semidirect
14. C2×#10622823C2semidirect
15. C22×C4×D4×C11C2semidirect
18. C24×C4×C11C22semidirect
22. C2×C4×D4×C11C22semidirect
23. C22×C11×C4⋊C4C22semidirect
25. C22×C11×C22⋊C4C22semidirect
26. C22×C42×C11C22semidirect
37. C2×#66982C22semidirect
38. C22×(C2×D11)⋊C4C22semidirect
39. C22×Dic11⋊C4C22semidirect
40. #10622860C22semidirect
42. #10622833C22semidirect
47. #10622826C22semidirect
48. #10622826C22semidirect
49. #10622824C22semidirect
50. #10622824C22semidirect
51. #10622823C22semidirect
52. #10622823C22semidirect
53. #10622823C22semidirect
54. #10622823C22semidirect
55. #10622823C22semidirect
56. #10622823C22semidirect
57. C2×C11⋊#95C22semidirect
58. C2×C11⋊#95C22semidirect
59. #10622606C22semidirect
60. #10622605C22semidirect
61. #10622595C22semidirect
62. #10622593C22semidirect
63. #10622572C22semidirect
64. #10622572C22semidirect
65. #10622571C22semidirect
66. #10622568C22semidirect
67. #10622565C22semidirect
68. #10622565C22semidirect
69. #10622559C22semidirect
70. #10622559C22semidirect
71. #10622556C22semidirect
72. #10622555C22semidirect
73. #10622553C22semidirect
74. #10622553C22semidirect
75. #10622546C22semidirect
76. #10622546C22semidirect
276. C22×C4×D4D11semidirect
309. C23×C11#123semidirect
379. C24×C4C2×D11semidirect
390. C2×C4×D4C2×D11semidirect
392. C22×C4⋊C4C2×D11semidirect
398. C22×C22⋊C4C2×D11semidirect
399. C22×C42C2×D11semidirect
687. C11#34983semidirect
717. C23#66982semidirect

Maximal subgroups

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

subgroupindex
C2×#106233352
#130769382
#130769082
#130743962
#130743892
#130723602
#130723452
#130720872
#130720722
#130712282
#130711942
#130711912
C2×#106228262
C2×#106228232
C22×C4×D4×C112
#3498311