Finite Group Databasebeta

← #14927232

Subgroups — #14927232

Order 2816.

2778 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623158C211yesmaximal, characteristic, complemented
2C2×#10623055C211yesmaximal, characteristic, complemented
3#13076965C211yesmaximal, characteristic, complemented
4#13076962C211yesmaximal, characteristic, complemented
5#13076920C211yesmaximal, characteristic, complemented
6#13076918C211yesmaximal, characteristic, complemented
7#13074351C214yesmaximal, complemented
8#13074226C214yesmaximal, complemented
9#13074223C214yesmaximal, complemented
10#13073081C211yesmaximal, characteristic, complemented
11#13073074C211yesmaximal, characteristic, complemented
12#13073066C211yesmaximal, characteristic, complemented
13#13072245C211yesmaximal, characteristic, complemented
14#13072243C211yesmaximal, characteristic, complemented
15#13072237C211yesmaximal, characteristic, complemented
16#13072235C211yesmaximal, characteristic, complemented
17#13071315C214yesmaximal, complemented
18C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
19C11×#2499C211yesmaximal, characteristic, complemented
20C22×#4343C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#117C2211yescharacteristic
25C2×#67000C2211yescharacteristic, complemented
26C2×#66999C2211yescharacteristic
27C2×#66997C2211yescharacteristic, complemented
28C2×#66983C2211yescharacteristic
29#10623158—28no—
30#10623055—28no—
31C2×#66950C2211yescharacteristic
32C2×#66950C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66948C2211yescharacteristic
35C2×#66948C2211yescharacteristic
36C2×#66948C2214yes—
37C2×#66947C2212yes—
38C2×#66946C2212yes—
39C2×#66945C2211yescharacteristic
40C2×#66939C2212yes—
41C2×#66935C2212yes—
42C2×#66935C2212yes—
43C2×(C22⋊D11)⋊C4C2212yes—
44C2×C22⋊C4×D11C2212yes—
45C2×#66928C2211yescharacteristic, complemented
46C2×#66927C2211yescharacteristic, complemented
47C2×C4×D44C2212yes—
48C2×C4×D44C2212yes—
49C2×C42×D11C2211yescharacteristic
50C2×C42×D11C2211yescharacteristic
51C11×#397C2214yes—
52C11×#391C2211yescharacteristic, complemented
53C11×#391C2211yescharacteristic, complemented
54C11×#387C2214yescomplemented
55C11×#384C2211yescharacteristic, complemented
56C11×#382C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2211yescharacteristic
58C4×C22⋊Dic11C2211yescharacteristic
59#10622606C2214yes—
60#10622602C2214yescomplemented
61#10622601C2214yescomplemented
62#10622601C2211yescharacteristic, complemented
63#10622601C2211yescharacteristic, complemented
64#10622601C2211yescharacteristic, complemented
65#10622594C2214yescomplemented
66#10622590C2211yescharacteristic, complemented
67#10622589C2211yescharacteristic, complemented
68#10622587C2211yescharacteristic, complemented
69#10622573C2214yes—
70#10622572C2214yes—
71#10622572C2214yes—
72C22⋊C4×Dic11C2212yes—
73#10622553C2214yescomplemented
74#10622552C2211yescharacteristic, complemented
75C4×(C2×D11)⋊C4C2211yescharacteristic
76C4×(C2×D11)⋊C4C2211yescharacteristic
77#10622542C2211yescharacteristic, complemented
78#10622285C2214yes—
79#10622285C2214yes—
80#10622284C2214yes—
81#10622283C2214yescomplemented
82#10622282C2214yescomplemented
83#10622282C2214yescomplemented
84#10622281C2214yescomplemented
85#10622280C2214yes—
86#10622279C2212yes—
87#10622278C2214yes—
88#10622278C2214yes—
89#10622278C2214yescomplemented
90#10622278C2214yescomplemented
91D11×#95C2212yes—
92#10622260C2214yescomplemented
93C24×D11C2311yescharacteristic
94C22×Q8×C11C2311yescharacteristic
95C23×C4×C11C2311yescharacteristic
96C22×C22⋊D11C2312yes—
97C22×C22⋊D11C2312yes—
98C23×Dic11C2311yescharacteristic
99C2×#4343—24no—
100C2×#4343—42no—
101C2×#4343—42no—
102C2×#4339—24no—
103C2×#4339—42no—
104C2×#4339—42no—
105C22×D44C2312yes—
106C22×D44C2311yescharacteristic
107C22×D44C2311yescharacteristic
108C22×D44C2312yes—
109C22×D44C2312yes—
110C22×D44C2314yes—
111C22×D44C2312yes—
112C22×C4×D11—42no—
113C22×C4×D11—42no—
114C22×C4×D11D418yescomplemented
115C22×C4×D11C2311yescharacteristic
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2312yes—
118C22×C4×D11C2312yes—
119C22×C4×D11C2312yes—
120C22×C4×D11C2311yescharacteristic
121C22×C4×D11C2311yescharacteristic
122C22×C4×D11C2312yes—
123C22×Dic22C2311yescharacteristic
124C11×C22⋊Q8—24no—
125C11×#117—24no—
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2312yes—
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2314yes—
131C2×C11×C22⋊C4C2312yes—
132C2×C11×C22⋊C4C2312yes—
133C2×C11×C22⋊C4C2312yes—
134C2×C42×C11C2311yescharacteristic
135C2×C42×C11C2311yescharacteristic
136C2×C42×C11C2312yes—
137C2×C22⋊Dic11C2312yes—
138#67000—42no—
139#66999—24no—
140#66997—42no—
141#66983—24no—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2312yes—
146C2×(C2×D11)⋊C4C2312yes—
147C2×(C2×D11)⋊C4C2312yes—
148C2×(C2×D11)⋊C4C2312yes—
149C2×(C2×D11)⋊C4C2312yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2314yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2314yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2311yescharacteristic
161C2×Dic11⋊C4C2312yes—
162C2×Dic11⋊C4C2314yes—
163C2×Dic11⋊C4C2314yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169#66950—24no—
170#66950—24no—
171#66948—24no—
172#66948—24no—
173#66948—24no—
174#66948—216no—
175#66947—28no—
176#66946—28no—
177#66945—24no—
178#66939—28no—
179#66935—28no—
180#66935—28no—
181(C22⋊D11)⋊C4—28no—
182C22⋊C4×D11—28no—
183#66928—42no—
184#66927—42no—
185C4×D44—28no—
186C4×D44—28no—
187C42×D11—42no—
188C42×D11—42no—
189C11×#95C2314yes—
190C11×#95C2312yes—
191C11×#95C2314yes—
192C11×#95C2314yes—
193C11⋊#95C2314yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2314yes—
198C11⋊#95C2314yes—
199#35032—111nomaximal, Sylow
200C24×C11C2411yescharacteristic
201C23×D11—24no—
202C23×D11—41no—
203C23×D11—41no—
204C23×D11—42no—
205C23×D11C2×D414yes—
206C23×D11C2412yes—
207C23×D11C2412yes—
208C23×D11C2411yescharacteristic
209C23×D11C2411yescharacteristic
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11C2×D414yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—42no—
227C2×C22⋊D11—42no—
228C2×C22⋊D11—44no—
229C22×Dic11—41no—
230C22×Dic11—41no—
231C22×Dic11C2×D414yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2411yescharacteristic
236C22×Dic11C2411yescharacteristic
237C22×Dic11C2412yes—
238#4343—416no—
239#4339—416no—
240C2×D44—24no—
241C2×D44—24no—
242C2×D44—24no—
243C2×D44—24no—
244C2×D44—28no—
245C2×D44—28no—
246C2×D44—22no—
247C2×D44—22no—
248C2×D44—28no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—44no—
254C2×D44—42no—
255C2×D44—42no—
256C2×D44—44no—
257C2×D44—44no—
258C2×C4×D11—24no—
259C2×C4×D11—24no—
260C2×C4×D11—24no—
261C2×C4×D11—22no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—42no—
266C2×C4×D11—42no—
267C2×C4×D11—41no—
268C2×C4×D11—41no—
269C2×C4×D11—41no—
270C2×C4×D11—41no—
271C2×C4×D11—42no—
272C2×C4×D11—42no—
273C2×C4×D11—42no—
274C2×C4×D11—42no—
275C2×C4×D11—42no—
276C2×C4×D11—42no—
277C2×C4×D11—416no—
278C2×C4×D11C2×D414yes—
279C2×C4×D11C2×D414yes—
280C2×C4×D11C2×D414yes—
281C2×C4×D11C2×D414yes—
282C2×C4×D11#4118yescomplemented
283C2×Dic22—22no—
284C2×Dic22—22no—
285C2×Dic22—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—24no—
288C11×C4⋊C4—22no—
289C11×C4⋊C4—22no—
290C11×C4⋊C4—28no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C42×C11—24no—
295C42×C11—22no—
296C42×C11—22no—
297C22⋊Dic11—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—28no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313(C2×D11)⋊C4—44no—
314C4⋊Dic11—24no—
315C4⋊Dic11—24no—
316C4⋊Dic11—22no—
317Dic11⋊C4—24no—
318Dic11⋊C4—44no—
319Dic11⋊C4—44no—
320C4×Dic11—24no—
321C4×Dic11—22no—
322C4×Dic11—22no—
323C4×Dic11—42no—
324C4×Dic11—42no—
325C2×#525—111no—
326C2×#525—111no—
327#2857—111no—
328#2856—111no—
329#2850—111no—
330#2850—111no—
331#2617—114no—
332#2602—114no—
333#2602—114no—
334#2500—111no—
335#2500—111no—
336#2499—111no—
337#2499D1111yescharacteristic, complemented
338#2432—111no—
339#2432—111no—
340#2431—111no—
341#2431—111no—
342#2325—114no—
343C2×C4×C22⋊C4—111no—
344C23×C11—22no—
345C23×C11—21no—
346C23×C11—21no—
347C23×C11—22no—
348C23×C11C22×D412yes—
349C23×C11C2511yescharacteristic
350C22×D11—21no—
351C22×D11—21no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—21no—
355C22×D11—21no—
356C22×D11—22no—
357C22×D11—28no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—24no—
361C22×D11—24no—
362C22×D11—22no—
363C22×D11—22no—
364C22×D11—22no—
365C22×D11—22no—
366C22×D11—24no—
367C22×D11—24no—
368C22×D11—44no—
369C22×D11—44no—
370C22×D11—48no—
371C22×D11—48no—
372C22×D11C22×D412yes—
373C22×D11C22×D412yes—
374C22×D11C2×#4114yes—
375Q8×C11—44no—
376C2×C4×C11—22no—
377C2×C4×C11—21no—
378C2×C4×C11—21no—
379C2×C4×C11—22no—
380C2×C4×C11—28no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—24no—
387C2×C4×C11—24no—
388C2×C4×C11—22no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—24no—
392C2×C4×C11—22no—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C2×#4114yes—
396C2×C4×C11H(5,𝔽2)12yes—
397C2×C4×C11H(5,𝔽2)12yes—
398C22⋊D11—48no—
399C22⋊D11—48no—
400C2×Dic11—22no—
401C2×Dic11—21no—
402C2×Dic11—21no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—22no—
409C2×Dic11—22no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—24no—
413C2×Dic11—22no—
414C2×Dic11—44no—
415C2×Dic11C22×D412yes—
416C2×Dic11C22×D412yes—
417C2×Dic11C2×#4114yes—
418D44—48no—
419D44—48no—
420D44—48no—
421D44—48no—
422D44—44no—
423D44—44no—
424D44—88no—
425C4×D11—28no—
426C4×D11—28no—
427C4×D11—44no—
428C4×D11—44no—
429C4×D11—48no—
430C4×D11—48no—
431C4×D11—48no—
432C4×D11—48no—
433Dic22—44no—
434C22×#41—111no—
435C22×#41—111no—
436C24×C4—111no—
437C2×C4⋊Q8—111no—
438C2×#127—111no—
439C2×#124—111no—
440C2×#124—111no—
441#525—228no—
442#525—228no—
443C2×#123—112no—
444C2×#123—112no—
445C2×C22⋊Q8—111no—
446C2×C22⋊Q8—111no—
447C2×C22⋊Q8—111no—
448C2×C22⋊Q8C2×D1111yescharacteristic
449C2×#121—111no—
450C2×#121—114no—
451C2×#121—111no—
452C2×#121—111no—
453C2×#121—111no—
454C2×#120—112no—
455C2×#120—112no—
456C2×C4×D4—112no—
457C2×C4×D4—112no—
458C2×C4×D4—112no—
459C2×C4×D4—112no—
460C2×#117—111no—
461C2×#117C2×D1111yescharacteristic
462C22×C22⋊C4—112no—
463C22×C42—111no—
464C22×C42—111no—
465#397—114no—
466#397C2×D1114yes—
467#394—114no—
468#394—114no—
469#394—114no—
470#394—114no—
471#392—114no—
472#392—114no—
473#391—111no—
474#391—111no—
475#391C2×D1111yescharacteristic, complemented
476#391C2×D1111yescharacteristic, complemented
477#390—111no—
478#390—114no—
479#390—111no—
480#390—111no—
481#390—111no—
482#389—114no—
483#388—114no—
484#388—114no—
485#388—114no—
486#388—114no—
487#387—114no—
488#387C2×D1114yescomplemented
489#386—114no—
490#386—114no—
491#386—114no—
492#386—114no—
493#385—114no—
494#385—114no—
495#384—111no—
496#384C2×D1111yescharacteristic, complemented
497#382—111no—
498#382C2×D1111yescharacteristic, complemented
499#380—114no—
500C4×C22⋊C4—111no—
501C4×C22⋊C4—112no—
502C4×C22⋊C4—111no—
503C4×C22⋊C4—111no—
504C4×C22⋊C4—112no—
505C4×C22⋊C4C2×D1111yescharacteristic
506C2×#95—112no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—22no—
510C22×C11—42no—
511C22×C11—42no—
512C22×C11C23×D411yescharacteristic
513C22×C11C22×#4112yes—
514C22×C11C2×H(5,𝔽2)11yescharacteristic
515C22×C11C2×H(5,𝔽2)11yescharacteristic
516C22×C11#58512yes—
517C2×D11—22no—
518C2×D11—22no—
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—22no—
522C2×D11—22no—
523C2×D11—22no—
524C2×D11—416no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C2×D11—42no—
531C2×D11—42no—
532C2×D11—42no—
533C2×D11—44no—
534C2×D11—44no—
535C2×D11—44no—
536C2×D11—44no—
537C2×D11#53214yes—
538C4×C11—22no—
539C4×C11—24no—
540C4×C11—42no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11—42no—
545C4×C11#53414yes—
546Dic11—22no—
547Dic11—22no—
548Dic11—24no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552C25—111no—
553C2×#41—224no—
554C2×#41—224no—
555C2×#41—442no—
556C2×#41—442no—
557C2×#41—442no—
558C2×#41—442no—
559C22×Q8—111no—
560C22×Q8C22×D1111yescharacteristic
561C22×D4—112no—
562C22×D4—112no—
563C22×D4—112no—
564C22×D4—112no—
565C22×D4—111no—
566C22×D4—111no—
567C22×D4—112no—
568C22×D4—112no—
569C22×D4—114no—
570C23×C4—111no—
571C23×C4—111no—
572C23×C4—111no—
573C23×C4—118no—
574C23×C4—112no—
575C23×C4—111no—
576C23×C4—111no—
577C23×C4—112no—
578C23×C4—112no—
579C23×C4—112no—
580C23×C4—442no—
581C23×C4—442no—
582C23×C4C22×D1111yescharacteristic
583C4⋊Q8—442no—
584#127—442no—
585#124—442no—
586#124—442no—
587#123—228no—
588#123—228no—
589C22⋊Q8—24no—
590C22⋊Q8—224no—
591C22⋊Q8—224no—
592C22⋊Q8—224no—
593#121—224no—
594#121—224no—
595#121—224no—
596#121—2216no—
597#121—224no—
598#120—228no—
599#120—228no—
600C4×D4—228no—
601C4×D4—228no—
602C4×D4—228no—
603C4×D4—228no—
604#117—24no—
605#117—224no—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—112no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4C22×D1111yescharacteristic
613C2×C4⋊C4C22×D1111yescharacteristic
614C2×C4⋊C4C22×D1111yescharacteristic
615C2×C4⋊C4C22×D1112yes—
616C2×C4⋊C4C22×D1114yes—
617C2×C22⋊C4—112no—
618C2×C22⋊C4—112no—
619C2×C22⋊C4—112no—
620C2×C22⋊C4—112no—
621C2×C22⋊C4—112no—
622C2×C22⋊C4—112no—
623C2×C22⋊C4—112no—
624C2×C22⋊C4—112no—
625C2×C22⋊C4—112no—
626C2×C22⋊C4—112no—
627C2×C22⋊C4—112no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—228no—
635C2×C22⋊C4C22×D1112yes—
636C2×C22⋊C4C22×D1112yes—
637C2×C22⋊C4C22×D1112yes—
638C2×C42—112no—
639C2×C42—111no—
640C2×C42—111no—
641C2×C42—112no—
642C2×C42—112no—
643C2×C42—442no—
644C2×C42—442no—
645C2×C42C22×D1112yes—
646C2×C42C22×D1111yescharacteristic
647C2×C42C22×D1111yescharacteristic
648#95—112no—
649#95—112no—
650#95—112no—
651#95—114no—
652#95—114no—
653#95—114no—
654#95C22×D1112yes—
655#95C22×D1114yes—
656#95C22×D1114yes—
657#95C22×D1114yes—
658C2×C11—42no—
659C2×C11C2×#53211yescharacteristic
660C2×C11C2×#53411yescharacteristic
661C2×C11#344911yescharacteristic
662C2×C11#350512yes—
663C2×C11#350612yes—
664D11—24no—
665D11—42no—
666D11—82no—
667D11—82no—
668C24—111no—
669C24—111no—
670C24—114no—
671C24—112no—
672C24—112no—
673C24—224no—
674C24—441no—
675C24—441no—
676C24—442no—
677C24C23×D1111yescharacteristic
678#41—4416no—
679#41—4416no—
680C2×Q8—22no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—222no—
684C2×Q8—222no—
685C2×Q8—222no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—224no—
689C2×D4—224no—
690C2×D4—228no—
691C2×D4—228no—
692C2×D4—224no—
693C2×D4—224no—
694C2×D4—222no—
695C2×D4—222no—
696C2×D4—228no—
697C2×D4—222no—
698C2×D4—222no—
699C2×D4—222no—
700C2×D4—222no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—444no—
704C2×D4—444no—
705C2×D4—444no—
706C2×D4—442no—
707C2×D4—442no—
708C2×D4—444no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—111no—
712C22×C4—112no—
713C22×C4—111no—
714C22×C4—114no—
715C22×C4—114no—
716C22×C4—114no—
717C22×C4—114no—
718C22×C4—114no—
719C22×C4—118no—
720C22×C4—112no—
721C22×C4—112no—
722C22×C4—112no—
723C22×C4—224no—
724C22×C4—224no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—224no—
730C22×C4—4416no—
731C22×C4—442no—
732C22×C4—442no—
733C22×C4—441no—
734C22×C4—441no—
735C22×C4—441no—
736C22×C4—441no—
737C22×C4—442no—
738C22×C4—442no—
739C22×C4—442no—
740C22×C4—442no—
741C22×C4—442no—
742C22×C4—442no—
743C22×C4—441no—
744C22×C4—441no—
745C22×C4D4×D1114yes—
746C22×C4C23×D1112yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C22×C4C23×D1112yes—
751C22×C4C23×D1111yescharacteristic
752C22×C4C23×D1112yes—
753C22×C4C23×D1111yescharacteristic
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—22no—
757C4⋊C4—24no—
758C4⋊C4—28no—
759C4⋊C4—224no—
760C4⋊C4—224no—
761C4⋊C4—224no—
762C4⋊C4—222no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C22⋊C4—224no—
771C22⋊C4—224no—
772C22⋊C4—228no—
773C22⋊C4—228no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C22⋊C4—224no—
780C22⋊C4—224no—
781C22⋊C4—444no—
782C22⋊C4—444no—
783C22⋊C4—444no—
784C22⋊C4—444no—
785C42—24no—
786C42—22no—
787C42—22no—
788C42—224no—
789C42—222no—
790C42—222no—
791C42—442no—
792C42—442no—
793C11#3503211yescharacteristic, complemented, Sylow
794C23—22no—
795C23—21no—
796C23—21no—
797C23—22no—
798C23—112no—
799C23—114no—
800C23—112no—
801C23—228no—
802C23—221no—
803C23—221no—
804C23—222no—
805C23—222no—
806C23—221no—
807C23—221no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—224no—
812C23—224no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—224no—
818C23—224no—
819C23—444no—
820C23—444no—
821C23—448no—
822C23—448no—
823C23C2×D4×D1112yes—
824C23C24×D1111yescharacteristic
825Q8—44no—
826Q8—444no—
827D4—448no—
828D4—448no—
829D4—448no—
830D4—448no—
831D4—448no—
832D4—448no—
833D4—444no—
834D4—444no—
835D4—888no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—28no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—24no—
853C2×C4—112no—
854C2×C4—112no—
855C2×C4—114no—
856C2×C4—222no—
857C2×C4—221no—
858C2×C4—221no—
859C2×C4—221no—
860C2×C4—221no—
861C2×C4—222no—
862C2×C4—228no—
863C2×C4—228no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—224no—
872C2×C4—444no—
873C2×C4—444no—
874C2×C4—448no—
875C2×C4—448no—
876C2×C4—448no—
877C2×C4—448no—
878C2×C4—444no—
879C2×C4C2×D4×D1112yes—
880C2×C4C2×D4×D1112yes—
881C2×C4#41×D1114yes—
882C2×C4#6704212yes—
883C2×C4#6704212yes—
884C22—22no—
885C22—22no—
886C22—22no—
887C22—42no—
888C22—42no—
889C22—114no—
890C22—222no—
891C22—224no—
892C22—222no—
893C22—224no—
894C22—222no—
895C22—222no—
896C22—222no—
897C22—4416no—
898C22—442no—
899C22—442no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—444no—
905C22—444no—
906C22—442no—
907C22—442no—
908C22—444no—
909C22—444no—
910C22C22×D4×D1111yescharacteristic
911C22C2×#41×D1112yes—
912C22C2×#6704211yescharacteristic
913C22C2×#6704211yescharacteristic
914C22#1062345712yes—
915C4—22no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—42no—
921C4—42no—
922C4—222no—
923C4—222no—
924C4—224no—
925C4—442no—
926C4—442no—
927C4—442no—
928C4#1062318414yes—
929C2—42no—
930C2—224no—
931C2—442no—
932C2—882no—
933C2—882no—
934C2D11×#53211yescharacteristic
935C2C2×#1062318411yescharacteristic
936C2#1308194811yescharacteristic
937C2#1308245612yes—
938C2#1308246912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2499C2
hypercenter#2499D11
hypocenterC11#35032
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2499

Complements

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

NH ≅ G/Ntype
1. C2×#10623158C2semidirect
2. C2×#10623055C2semidirect
3. #13076965C2semidirect
4. #13076962C2semidirect
5. #13076920C2semidirect
6. #13076918C2semidirect
7. #13074351C2semidirect
8. #13074226C2semidirect
9. #13074223C2semidirect
10. #13073081C2semidirect
11. #13073074C2semidirect
12. #13073066C2semidirect
13. #13072245C2semidirect
14. #13072243C2semidirect
15. #13072237C2semidirect
16. #13072235C2semidirect
17. #13071315C2semidirect
18. C4×C22⋊C4×D11C2semidirect
19. C11×#2499C2semidirect
25. C2×#67000C22semidirect
27. C2×#66997C22semidirect
45. C2×#66928C22semidirect
46. C2×#66927C22semidirect
52. C11×#391C22semidirect
53. C11×#391C22semidirect
54. C11×#387C22semidirect
55. C11×#384C22semidirect
56. C11×#382C22semidirect
60. #10622602C22semidirect
61. #10622601C22semidirect
62. #10622601C22semidirect
63. #10622601C22semidirect
64. #10622601C22semidirect
65. #10622594C22semidirect
66. #10622590C22semidirect
67. #10622589C22semidirect
68. #10622587C22semidirect
73. #10622553C22semidirect
74. #10622552C22semidirect
77. #10622542C22semidirect
81. #10622283C22semidirect
82. #10622282C22semidirect
83. #10622282C22semidirect
84. #10622281C22semidirect
89. #10622278C22semidirect
90. #10622278C22semidirect
92. #10622260C22semidirect
114. C22×C4×D11D4semidirect
282. C2×C4×D11#41semidirect
337. #2499D11semidirect
475. #391C2×D11semidirect
476. #391C2×D11semidirect
488. #387C2×D11semidirect
496. #384C2×D11semidirect
498. #382C2×D11semidirect
793. C11#35032semidirect

Maximal subgroups

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

subgroupindex
C2×#106231582
C2×#106230552
#130769652
#130769622
#130769202
#130769182
#130743512
#130742262
#130742232
#130730812
#130730742
#130730662
#130722452
#130722432
#130722372
#130722352
#130713152
C4×C22⋊C4×D112
C11×#24992
#3503211