Finite Group Databasebeta

← #14926344

Subgroups — #14926344

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×#10623024C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13076941C212yesmaximal, complemented
4#13076911C212yesmaximal, complemented
5#13074402C212yesmaximal, complemented
6#13074394C212yesmaximal, complemented
7#13072370C214yesmaximal, complemented
8#13072355C214yesmaximal, complemented
9#13072099C214yesmaximal, complemented
10#13072084C214yesmaximal, complemented
11#13071191C211yesmaximal, characteristic, complemented
12#13071191C211yesmaximal, characteristic, complemented
13C2×#10622571C211yesmaximal, characteristic, complemented
14C2×#10622559C211yesmaximal, characteristic, complemented
15C11×#2315C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic, complemented
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C2×#66983C2212yes—
25C2×#66983C2212yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
27C22×(C2×D11)⋊C4C2212yescomplemented
28C22×Dic11⋊C4C2211yescharacteristic, complemented
29C22×Dic11⋊C4C2212yescomplemented
30C22×C4×Dic11C2211yescharacteristic, complemented
31C2×#66947C2214yescomplemented
32#10623024—28no—
33C2×#66939C2212yes—
34C2×#66939C2212yes—
35C2×#66935C2212yes—
36C2×#66935C2212yes—
37C2×(C22⋊D11)⋊C4—28no—
38C2×(C22⋊D11)⋊C4C2214yes—
39C2×(C22⋊D11)⋊C4C2214yescomplemented
40C11×#385C2212yescomplemented
41C11×#385C2212yescomplemented
42C11×#385C2212yescomplemented
43C11×#385C2212yescomplemented
44C11×#380C2214yescomplemented
45#10622826C2212yes—
46#10622826C2212yes—
47#10622826C2214yes—
48C2×C11⋊#95C2212yescomplemented
49C2×C11⋊#95C2212yescomplemented
50#10622606C2214yescomplemented
51#10622605C2214yescomplemented
52#10622604C2214yescomplemented
53#10622603C2214yescomplemented
54#10622602C2214yescomplemented
55#10622597C2214yescomplemented
56#10622594C2214yescomplemented
57#10622571C2212yes—
58#10622571C2212yes—
59#10622571C2214yescomplemented
60#10622571C2214yescomplemented
61#10622571C2214yescomplemented
62#10622568C2212yescomplemented
63#10622568C2212yescomplemented
64#10622559C2212yescomplemented
65#10622559C2214yescomplemented
66#10622559C2212yescomplemented
67#10622556C2212yescomplemented
68#10622556C2212yescomplemented
69#10622288C2214yescomplemented
70#10622288C2214yescomplemented
71#10622285C2214yescomplemented
72#10622282C2214yescomplemented
73#10622278C2214yescomplemented
74#10622277C2214yescomplemented
75#10622273C2214yescomplemented
76#10622268C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—24no—
86C22×C22⋊D11—24no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11D418yes—
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C22×C22⋊D11C2312yes—
95C23×Dic11—24no—
96C23×Dic11—44no—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2312yes—
100C23×Dic11C2312yes—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2312yes—
104C22×D44C2312yes—
105C22×D44C2312yes—
106C22×C4×D11—24no—
107C22×C4×D11—44no—
108C22×C4×D11C2314yes—
109C2×C11×C4⋊C4C2314yes—
110C2×C11×C4⋊C4C2314yes—
111C2×C11×C22⋊C4—24no—
112C2×C11×C22⋊C4—24no—
113C2×C11×C22⋊C4—24no—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C11×C22⋊C4C2312yes—
120C2×C22⋊Dic11—24no—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2312yes—
123#66983—28no—
124#66983—28no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—44no—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×(C2×D11)⋊C4C2314yes—
136C2×(C2×D11)⋊C4C2314yes—
137C2×(C2×D11)⋊C4C2314yes—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2312yes—
140C2×Dic11⋊C4—24no—
141C2×Dic11⋊C4—44no—
142C2×Dic11⋊C4C2314yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×C4×Dic11—24no—
146C2×C4×Dic11C2314yes—
147#66947—48no—
148#66939—28no—
149#66939—28no—
150#66935—28no—
151#66935—28no—
152(C22⋊D11)⋊C4—216no—
153(C22⋊D11)⋊C4—216no—
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—42no—
166C24×C11—42no—
167C24×C11C2×D414yes—
168C24×C11#4114yes—
169C24×C11#4114yes—
170C24×C11C2411yescharacteristic
171C24×C11C2411yescharacteristic
172C24×C11C2411yescharacteristic
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—22no—
176C23×D11—22no—
177C23×D11—22no—
178C23×D11—42no—
179C23×D11—42no—
180C23×D11—42no—
181C23×D11—42no—
182C23×D11C2×D414yes—
183C23×D11C2412yes—
184C23×D11C2412yes—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11—24no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11—42no—
195C22×C4×C11—42no—
196C22×C4×C11C2412yes—
197C22×C4×C11C2414yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2412yes—
200C22×C4×C11C2412yes—
201C2×C22⋊D11—232no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—24no—
206C2×C22⋊D11—24no—
207C2×C22⋊D11—24no—
208C2×C22⋊D11—24no—
209C2×C22⋊D11—24no—
210C2×C22⋊D11—24no—
211C2×C22⋊D11—24no—
212C2×C22⋊D11—416no—
213C2×C22⋊D11C2×D418yes—
214C2×C22⋊D11C2×D418yes—
215C22×Dic11—24no—
216C22×Dic11—24no—
217C22×Dic11—24no—
218C22×Dic11—22no—
219C22×Dic11—24no—
220C22×Dic11—24no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—24no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—42no—
229C22×Dic11—42no—
230C22×Dic11—42no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—416no—
234C22×Dic11C2×D414yes—
235C22×Dic11C2412yes—
236C22×Dic11C2414yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C2×D44—24no—
241C2×D44—24no—
242C2×D44—44no—
243C2×D44—44no—
244C2×C4×D11—28no—
245C2×C4×D11—28no—
246C2×C4×D11—44no—
247C2×C4×D11—416no—
248C11×C4⋊C4—44no—
249C11×C4⋊C4—44no—
250C11×C22⋊C4—24no—
251C11×C22⋊C4—24no—
252C11×C22⋊C4—24no—
253C11×C22⋊C4—24no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C22⋊Dic11—24no—
257C22⋊Dic11—24no—
258(C2×D11)⋊C4—24no—
259(C2×D11)⋊C4—24no—
260(C2×D11)⋊C4—28no—
261(C2×D11)⋊C4—28no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267(C2×D11)⋊C4—44no—
268(C2×D11)⋊C4—44no—
269C4⋊Dic11—24no—
270C4⋊Dic11—24no—
271Dic11⋊C4—28no—
272Dic11⋊C4—28no—
273Dic11⋊C4—44no—
274C4×Dic11—28no—
275C2×#534—111no—
276C22×C4×D4—111no—
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#2315D1111yescharacteristic, complemented
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—44no—
297C23×C11—44no—
298C23×C11—48no—
299C23×C11—48no—
300C23×C11#123116yescomplemented
301C23×C11C22×D412yes—
302C23×C11C22×D412yes—
303C23×C11C22×D412yes—
304C23×C11C2×#4112yes—
305C23×C11C2×#4112yes—
306C23×C11C2×#4112yes—
307C23×C11C2×#4112yes—
308C23×C11C2×#4112yes—
309C23×C11C2×#4112yes—
310C23×C11C2511yescharacteristic
311C22×D11—28no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—24no—
320C22×D11—24no—
321C22×D11—44no—
322C22×D11—44no—
323C22×D11—48no—
324C22×D11—48no—
325C22×D11—48no—
326C22×D11—44no—
327C22×D11—82no—
328C22×D11—82no—
329C22×D11—84no—
330C22×D11C22×D414yes—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—24no—
337C2×C4×C11—24no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—44no—
343C2×C4×C11—44no—
344C2×C4×C11—82no—
345C2×C4×C11—82no—
346C2×C4×C11—84no—
347C22⋊D11—216no—
348C22⋊D11—216no—
349C22⋊D11—48no—
350C22⋊D11—48no—
351C2×Dic11—28no—
352C2×Dic11—28no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—24no—
366C2×Dic11—48no—
367C2×Dic11—48no—
368C2×Dic11—48no—
369C2×Dic11—44no—
370C2×Dic11—44no—
371C2×Dic11C22×D414yes—
372C2×Dic11H(5,𝔽2)14yes—
373D44—84no—
374D44—84no—
375C4×D11—416no—
376C23×D4—111no—
377C23×D4—111no—
378C24×C4—111no—
379C24×C4—111no—
380#534—228no—
381C2×#123—114no—
382C2×#123—112no—
383C2×#123—112no—
384C2×#121—112no—
385C2×#121—112no—
386C2×#120—112no—
387C2×#120—112no—
388C2×C4×D4—114no—
389C2×C4×D4—114no—
390C2×C4×D4—228no—
391C22×C4⋊C4—111no—
392C22×C4⋊C4—112no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—112no—
396C22×C22⋊C4C2×D1111yescharacteristic
397C22×C22⋊C4C2×D1111yescharacteristic
398C22×C22⋊C4C2×D1111yescharacteristic
399C22×C42—111no—
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—112no—
413#386—112no—
414#386—114no—
415#386—114no—
416#386—114no—
417#386—112no—
418#386—112no—
419#386—114no—
420#386—114no—
421#385—114no—
422#385—112no—
423#385—112no—
424#385—114no—
425#385C2×D1112yescomplemented
426#385C2×D1112yescomplemented
427#385C2×D1112yescomplemented
428#385C2×D1112yescomplemented
429#381—112no—
430#381—112no—
431#381—114no—
432#380C2×D1114yescomplemented
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—416no—
450C22×C11C2×#12314yes—
451C22×C11C2×#12314yes—
452C22×C11C2×#12314yes—
453C22×C11C23×D411yescharacteristic
454C22×C11C22×#4111yescharacteristic
455C22×C11C22×#4111yescharacteristic
456C22×C11C2×H(5,𝔽2)12yes—
457C22×C11#58512yes—
458C2×D11—24no—
459C2×D11—24no—
460C2×D11—24no—
461C2×D11—416no—
462C2×D11—44no—
463C2×D11—44no—
464C2×D11—42no—
465C2×D11—44no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—44no—
469C2×D11—88no—
470C4×C11—42no—
471C4×C11—42no—
472C4×C11—42no—
473C4×C11—42no—
474C4×C11—44no—
475Dic11—24no—
476Dic11—24no—
477Dic11—42no—
478Dic11—44no—
479Dic11—42no—
480C25—111no—
481C25—111no—
482C25C22×D1111yescharacteristic
483C22×D4—118no—
484C22×D4—112no—
485C22×D4—112no—
486C22×D4—112no—
487C22×D4—112no—
488C22×D4—112no—
489C22×D4—112no—
490C22×D4—224no—
491C22×D4—224no—
492C22×D4—224no—
493C22×D4—224no—
494C22×D4—224no—
495C23×C4—111no—
496C23×C4—111no—
497C23×C4—111no—
498C23×C4—112no—
499C23×C4—112no—
500C23×C4—111no—
501C23×C4—112no—
502C23×C4—114no—
503C23×C4—224no—
504C23×C4—224no—
505C23×C4—444no—
506C23×C4—444no—
507C23×C4C22×D1112yes—
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—2216no—
520C4×D4—2216no—
521C2×C4⋊C4—114no—
522C2×C4⋊C4—114no—
523C2×C4⋊C4—112no—
524C2×C4⋊C4—112no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—224no—
527C2×C4⋊C4—444no—
528C2×C4⋊C4C22×D1114yes—
529C2×C4⋊C4C22×D1114yes—
530C2×C22⋊C4—24no—
531C2×C22⋊C4—24no—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—114no—
536C2×C22⋊C4—114no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—224no—
547C2×C22⋊C4—224no—
548C2×C22⋊C4—444no—
549C2×C22⋊C4C22×D1112yes—
550C2×C22⋊C4C22×D1112yes—
551C2×C22⋊C4C22×D1112yes—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1112yes—
554C2×C22⋊C4C22×D1112yes—
555C2×C42—114no—
556C2×C42—224no—
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#95C22×D1114yes—
566#95C22×D1114yes—
567C2×C11—24no—
568C2×C11—24no—
569C2×C11—24no—
570C2×C11C22×#12311yescharacteristic
571C2×C11#345912yes—
572C2×C11#348411yescharacteristic
573C2×C11#348511yescharacteristic
574C2×C11#350512yes—
575D11—44no—
576D11—82no—
577C24—42no—
578C24—42no—
579C24—112no—
580C24—114no—
581C24—112no—
582C24—222no—
583C24—222no—
584C24—222no—
585C24—222no—
586C24—222no—
587C24—442no—
588C24—442no—
589C24—442no—
590C24—442no—
591C24#433914yes—
592C24D4×D1114yes—
593C24#434314yes—
594C24C23×D1111yescharacteristic
595C24C23×D1111yescharacteristic
596C24C23×D1111yescharacteristic
597C2×D4—118no—
598C2×D4—118no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—2232no—
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—224no—
611C2×D4—224no—
612C2×D4—444no—
613C2×D4—444no—
614C2×D4—4416no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—42no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—114no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—114no—
631C22×C4—112no—
632C22×C4—228no—
633C22×C4—228no—
634C22×C4—224no—
635C22×C4—224no—
636C22×C4—224no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—222no—
645C22×C4—224no—
646C22×C4—222no—
647C22×C4—444no—
648C22×C4—4416no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4—442no—
652C22×C4—442no—
653C22×C4—442no—
654C22×C4—4416no—
655C22×C4C23×D1114yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C4⋊C4—44no—
661C4⋊C4—44no—
662C4⋊C4—228no—
663C4⋊C4—228no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—444no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—228no—
674C22⋊C4—224no—
675C22⋊C4—224no—
676C22⋊C4—228no—
677C22⋊C4—224no—
678C22⋊C4—224no—
679C22⋊C4—224no—
680C22⋊C4—224no—
681C22⋊C4—444no—
682C22⋊C4—444no—
683C22⋊C4—444no—
684C22⋊C4—444no—
685C22⋊C4—444no—
686C42—228no—
687C11#3498311yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—22no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—44no—
695C23—48no—
696C23—44no—
697C23—48no—
698C23—114no—
699C23—228no—
700C23—222no—
701C23—222no—
702C23—224no—
703C23—224no—
704C23—222no—
705C23—222no—
706C23—222no—
707C23—224no—
708C23—224no—
709C23—444no—
710C23—444no—
711C23—448no—
712C23—448no—
713C23—448no—
714C23—444no—
715C23—884no—
716C23—882no—
717C23—882no—
718C23#66947116yescomplemented
719C23C2×#433912yes—
720C23C2×#433912yes—
721C23C2×#433912yes—
722C23C2×D4×D1112yes—
723C23C2×D4×D1112yes—
724C23C2×D4×D1112yes—
725C23C2×#434312yes—
726C23C2×#434312yes—
727C23C2×#434312yes—
728C23C24×D1111yescharacteristic
729D4—2216no—
730D4—2216no—
731D4—448no—
732D4—448no—
733D4—884no—
734D4—884no—
735C2×C4—24no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—24no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—84no—
749C2×C4—82no—
750C2×C4—82no—
751C2×C4—114no—
752C2×C4—114no—
753C2×C4—228no—
754C2×C4—228no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—224no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—224no—
768C2×C4—4416no—
769C2×C4—448no—
770C2×C4—448no—
771C2×C4—444no—
772C2×C4—448no—
773C2×C4—444no—
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—416no—
787C22—224no—
788C22—224no—
789C22—224no—
790C22—4416no—
791C22—444no—
792C22—444no—
793C22—444no—
794C22—442no—
795C22—442no—
796C22—444no—
797C22—442no—
798C22—888no—
799C22C2×#6694714yes—
800C22C2×#6694714yes—
801C22C2×#6694714yes—
802C22C22×#433911yescharacteristic
803C22C22×D4×D1111yescharacteristic
804C22C22×#434311yescharacteristic
805C22D11×H(5,𝔽2)12yes—
806C22#1062345512yes—
807C4—44no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—224no—
813C4—224no—
814C4—442no—
815C4—444no—
816C4—442no—
817C2—24no—
818C2—24no—
819C2—24no—
820C2—444no—
821C2—882no—
822C2C22×#6694711yescharacteristic
823C2#1308202812yes—
824C2#1308224811yescharacteristic
825C2#1308225711yescharacteristic
826C2#1308244612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2315C2
prime radicalC2×#10623024C2
hypercenter#2315D11
hypocenterC11#34983
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13076941C2semidirect
4. #13076911C2semidirect
5. #13074402C2semidirect
6. #13074394C2semidirect
7. #13072370C2semidirect
8. #13072355C2semidirect
9. #13072099C2semidirect
10. #13072084C2semidirect
11. #13071191C2semidirect
12. #13071191C2semidirect
13. C2×#10622571C2semidirect
14. C2×#10622559C2semidirect
15. C11×#2315C2semidirect
19. C23×C4×D11C22semidirect
26. C22×(C2×D11)⋊C4C22semidirect
27. C22×(C2×D11)⋊C4C22semidirect
28. C22×Dic11⋊C4C22semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×C4×Dic11C22semidirect
31. C2×#66947C22semidirect
39. C2×(C22⋊D11)⋊C4C22semidirect
40. C11×#385C22semidirect
41. C11×#385C22semidirect
42. C11×#385C22semidirect
43. C11×#385C22semidirect
44. C11×#380C22semidirect
48. C2×C11⋊#95C22semidirect
49. C2×C11⋊#95C22semidirect
50. #10622606C22semidirect
51. #10622605C22semidirect
52. #10622604C22semidirect
53. #10622603C22semidirect
54. #10622602C22semidirect
55. #10622597C22semidirect
56. #10622594C22semidirect
59. #10622571C22semidirect
60. #10622571C22semidirect
61. #10622571C22semidirect
62. #10622568C22semidirect
63. #10622568C22semidirect
64. #10622559C22semidirect
65. #10622559C22semidirect
66. #10622559C22semidirect
67. #10622556C22semidirect
68. #10622556C22semidirect
69. #10622288C22semidirect
70. #10622288C22semidirect
71. #10622285C22semidirect
72. #10622282C22semidirect
73. #10622278C22semidirect
74. #10622277C22semidirect
75. #10622273C22semidirect
76. #10622268C22semidirect
285. #2315D11semidirect
300. C23×C11#123semidirect
425. #385C2×D11semidirect
426. #385C2×D11semidirect
427. #385C2×D11semidirect
428. #385C2×D11semidirect
432. #380C2×D11semidirect
687. C11#34983semidirect
718. C23#66947semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C22×(C22⋊D11)⋊C42
#130769412
#130769112
#130744022
#130743942
#130723702
#130723552
#130720992
#130720842
#130711912
C2×#106225712
C2×#106225592
C11×#23152
#3498311