Finite Group Databasebeta

← #14927227

Subgroups — #14927227

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×#10623322C211yesmaximal, characteristic, complemented
2#13076964C211yesmaximal, characteristic, complemented
3#13076959C211yesmaximal, characteristic, complemented
4#13076919C211yesmaximal, characteristic, complemented
5#13076915C211yesmaximal, characteristic, complemented
6#13074354C214yesmaximal, complemented
7#13074230C214yesmaximal, complemented
8#13074228C214yesmaximal, complemented
9#13073079C211yesmaximal, characteristic, complemented
10#13073074C211yesmaximal, characteristic, complemented
11#13073070C211yesmaximal, characteristic, complemented
12#13073065C211yesmaximal, characteristic, complemented
13#13072245C211yesmaximal, characteristic, complemented
14#13072240C211yesmaximal, characteristic, complemented
15#13072236C211yesmaximal, characteristic, complemented
16#13072231C211yesmaximal, characteristic, complemented
17#13071314C214yesmaximal, complemented
18C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
19C2×C11×#525C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic
22C22×#4339C2211yescharacteristic
23C11×#525—28no—
24C2×C11×#123C2212yes—
25C2×C11×C22⋊Q8C2211yescharacteristic
26C2×C11×C22⋊Q8C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#121C2211yescharacteristic
29C2×C11×#120C2212yes—
30C2×C4×D4×C11C2212yes—
31C2×C4×D4×C11C2212yes—
32C2×C11×#117C2211yescharacteristic
33C2×#67006C2212yes—
34C22×C22⋊Dic11C2212yes—
35C2×#67000C2211yescharacteristic, complemented
36C2×#66997C2211yescharacteristic, complemented
37C2×#66993C2211yescharacteristic, complemented
38C2×#66992C2214yes—
39C2×#66989C2211yescharacteristic, complemented
40#10623322—28no—
41C2×#66983C2211yescharacteristic
42C2×#66983C2211yescharacteristic
43C2×#66982C2212yes—
44C2×C4×C22⋊D11C2212yes—
45C2×C4×C22⋊D11C2212yes—
46C2×#66979C2211yescharacteristic
47C2×#66977C2211yescharacteristic
48C2×#66977C2211yescharacteristic
49C22×C4×Dic11C2211yescharacteristic
50C22×C4×Dic11C2211yescharacteristic
51#10622843C2211yescharacteristic, complemented
52#10622843C2211yescharacteristic, complemented
53#10622836C2214yes—
54#10622836C2214yes—
55#10622835C2214yes—
56#10622835C2214yes—
57#10622834C2211yescharacteristic, complemented
58#10622834C2211yescharacteristic, complemented
59#10622833C2214yes—
60#10622826C2214yescomplemented
61#10622823C2214yescomplemented
62C4×C22⋊Dic11C2212yes—
63C4×C22⋊Dic11C2212yes—
64C4×C22⋊Dic11C2211yescharacteristic
65C4×C22⋊Dic11C2211yescharacteristic
66C4×C22⋊Dic11C2211yescharacteristic
67C4×C22⋊Dic11C2211yescharacteristic
68C2×C11⋊#95C2212yes—
69#10622603C2214yescomplemented
70#10622602C2214yescomplemented
71#10622601C2211yescharacteristic, complemented
72#10622601C2211yescharacteristic, complemented
73#10622591C2214yescomplemented
74#10622590C2211yescharacteristic, complemented
75#10622590C2211yescharacteristic, complemented
76#10622589C2211yescharacteristic, complemented
77#10622589C2211yescharacteristic, complemented
78#10622587C2211yescharacteristic, complemented
79#10622587C2211yescharacteristic, complemented
80#10622585C2214yescomplemented
81#10622572C2214yes—
82#10622572C2214yes—
83#10622571C2214yes—
84#10622570C2214yescomplemented
85#10622569C2214yescomplemented
86#10622565C2214yes—
87#10622565C2214yes—
88#10622558C2214yescomplemented
89#10622557C2214yescomplemented
90#10622555C2214yes—
91#10622553C2214yescomplemented
92#10622546C2214yescomplemented
93C25×C11C2311yescharacteristic
94C2×C11×#41—24no—
95C2×C11×#41—42no—
96C2×C11×#41—42no—
97C22×Q8×C11C2311yescharacteristic
98C22×D4×C11C2311yescharacteristic
99C22×D4×C11C2312yes—
100C22×D4×C11C2312yes—
101C22×D4×C11C2312yes—
102C23×C4×C11—42no—
103C23×C4×C11—42no—
104C23×C4×C11D418yescomplemented
105C23×C4×C11C2311yescharacteristic
106C23×C4×C11C2311yescharacteristic
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2312yes—
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2312yes—
115C22×C22⋊D11C2314yes—
116C23×Dic11C2312yes—
117C23×Dic11C2312yes—
118C2×#4339—24no—
119C2×#4339—42no—
120C2×#4339—42no—
121C22×D44C2311yescharacteristic
122C22×C4×D11C2312yes—
123C22×Dic22C2311yescharacteristic
124C11×#123—28no—
125C11×C22⋊Q8—24no—
126C11×C22⋊Q8—24no—
127C11×#121—24no—
128C11×#121—24no—
129C11×#120—28no—
130C4×D4×C11—28no—
131C4×D4×C11—28no—
132C11×#117—24no—
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2312yes—
137C2×C11×C22⋊C4C2312yes—
138C2×C11×C22⋊C4C2312yes—
139C2×C11×C22⋊C4C2312yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C11×C22⋊C4C2312yes—
142C2×C42×C11C2312yes—
143#67006—28no—
144C2×C22⋊Dic11—28no—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2312yes—
148C2×C22⋊Dic11C2314yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151C2×C22⋊Dic11C2312yes—
152C2×C22⋊Dic11C2312yes—
153C2×C22⋊Dic11C2314yes—
154C2×C22⋊Dic11C2314yes—
155#67000—42no—
156#66997—42no—
157#66993—42no—
158#66992—216no—
159#66989—42no—
160#66983—24no—
161#66983—24no—
162#66982—28no—
163C4×C22⋊D11—28no—
164C4×C22⋊D11—28no—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2312yes—
167C2×(C2×D11)⋊C4C2314yes—
168C2×(C2×D11)⋊C4C2314yes—
169C2×(C2×D11)⋊C4C2314yes—
170#66979—24no—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2311yescharacteristic
173#66977—24no—
174#66977—24no—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2314yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×C4×Dic11—42no—
181C2×C4×Dic11—42no—
182C2×C4×Dic11C2311yescharacteristic
183C2×C4×Dic11C2311yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2311yescharacteristic
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2312yes—
188C2×C4×Dic11C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2314yes—
191C11⋊#95C2314yes—
192C11⋊#95C2314yes—
193C11⋊#95C2312yes—
194C11⋊#95C2314yes—
195C11⋊#95C2314yes—
196C11⋊#95C2312yes—
197C11⋊#95C2314yes—
198C11⋊#95C2312yes—
199#35032—111nomaximal, Sylow
200C24×C11—24no—
201C24×C11—41no—
202C24×C11—41no—
203C24×C11—42no—
204C24×C11C2×D414yes—
205C24×C11C2412yes—
206C24×C11C2411yescharacteristic
207C24×C11C2411yescharacteristic
208C24×C11C2411yescharacteristic
209C23×D11C2412yes—
210C11×#41—416no—
211C2×Q8×C11—22no—
212C2×Q8×C11—22no—
213C2×Q8×C11—22no—
214C2×D4×C11—24no—
215C2×D4×C11—24no—
216C2×D4×C11—24no—
217C2×D4×C11—28no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—22no—
221C2×D4×C11—44no—
222C2×D4×C11—42no—
223C2×D4×C11—42no—
224C22×C4×C11—22no—
225C22×C4×C11—22no—
226C22×C4×C11—22no—
227C22×C4×C11—22no—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—24no—
231C22×C4×C11—416no—
232C22×C4×C11—41no—
233C22×C4×C11—41no—
234C22×C4×C11—41no—
235C22×C4×C11—41no—
236C22×C4×C11—41no—
237C22×C4×C11—41no—
238C22×C4×C11—42no—
239C22×C4×C11—42no—
240C22×C4×C11C2×D414yes—
241C22×C4×C11C2×D414yes—
242C22×C4×C11C2×D414yes—
243C22×C4×C11C2×D414yes—
244C22×C4×C11C2×D414yes—
245C22×C4×C11C2×D414yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×C4×C11C2411yescharacteristic
252C22×C4×C11C2411yescharacteristic
253C2×C22⋊D11—28no—
254C2×C22⋊D11—24no—
255C2×C22⋊D11—24no—
256C2×C22⋊D11—24no—
257C2×C22⋊D11—28no—
258C2×C22⋊D11—42no—
259C2×C22⋊D11—42no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C22×Dic11—24no—
264C22×Dic11—42no—
265C22×Dic11—42no—
266C22×Dic11—42no—
267C22×Dic11—42no—
268C22×Dic11#4118yescomplemented
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C22×Dic11C2412yes—
273C22×Dic11C2412yes—
274C22×Dic11C2412yes—
275C22×Dic11C2412yes—
276#4339—416no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—22no—
280C2×C4×D11—24no—
281C2×C4×D11—42no—
282C2×C4×D11—42no—
283C2×Dic22—22no—
284C2×Dic22—22no—
285C2×Dic22—22no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4—24no—
289C11×C4⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—24no—
294C11×C22⋊C4—24no—
295C42×C11—24no—
296C22⋊Dic11—28no—
297C22⋊Dic11—24no—
298C22⋊Dic11—24no—
299C22⋊Dic11—24no—
300C22⋊Dic11—24no—
301C22⋊Dic11—24no—
302C22⋊Dic11—24no—
303C22⋊Dic11—24no—
304C22⋊Dic11—44no—
305C22⋊Dic11—44no—
306(C2×D11)⋊C4—28no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—44no—
310(C2×D11)⋊C4—44no—
311C4⋊Dic11—22no—
312C4⋊Dic11—22no—
313Dic11⋊C4—28no—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4—44no—
317Dic11⋊C4—44no—
318C4×Dic11—24no—
319C4×Dic11—22no—
320C4×Dic11—22no—
321C4×Dic11—22no—
322C4×Dic11—22no—
323C4×Dic11—42no—
324C4×Dic11—42no—
325C2×#525—111no—
326C2×#525D1111yescharacteristic, complemented
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#2499—111no—
338#2432—111no—
339#2432—111no—
340#2431—111no—
341#2431—111no—
342#2325—114no—
343C2×C4×C22⋊C4—111no—
344C23×C11—21no—
345C23×C11—21no—
346C23×C11—22no—
347C23×C11—28no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—21no—
351C23×C11—21no—
352C23×C11—21no—
353C23×C11—21no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—24no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—24no—
361C23×C11—44no—
362C23×C11—44no—
363C23×C11—48no—
364C23×C11—48no—
365C23×C11C22×D412yes—
366C23×C11C22×D412yes—
367C23×C11C22×D412yes—
368C23×C11C2×#4114yes—
369C23×C11C2511yescharacteristic
370C22×D11—22no—
371C22×D11—24no—
372C22×D11—22no—
373C22×D11—22no—
374C22×D11—24no—
375Q8×C11—44no—
376D4×C11—48no—
377D4×C11—48no—
378D4×C11—48no—
379D4×C11—44no—
380C2×C4×C11—21no—
381C2×C4×C11—21no—
382C2×C4×C11—21no—
383C2×C4×C11—21no—
384C2×C4×C11—21no—
385C2×C4×C11—21no—
386C2×C4×C11—28no—
387C2×C4×C11—28no—
388C2×C4×C11—28no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—24no—
393C2×C4×C11—22no—
394C2×C4×C11—22no—
395C2×C4×C11—24no—
396C2×C4×C11—44no—
397C2×C4×C11—44no—
398C2×C4×C11—44no—
399C2×C4×C11—48no—
400C2×C4×C11C22×D412yes—
401C2×C4×C11C22×D412yes—
402C2×C4×C11C22×D412yes—
403C2×C4×C11C22×D412yes—
404C2×C4×C11H(5,𝔽2)12yes—
405C2×C4×C11H(5,𝔽2)12yes—
406C22⋊D11—48no—
407C22⋊D11—48no—
408C22⋊D11—48no—
409C22⋊D11—88no—
410C2×Dic11—22no—
411C2×Dic11—22no—
412C2×Dic11—22no—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—24no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—24no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—48no—
428C2×Dic11—48no—
429C2×Dic11C2×#4114yes—
430C2×Dic11C2×#4114yes—
431D44—44no—
432C4×D11—48no—
433Dic22—44no—
434C22×#41—111no—
435C22×#41C2×D1111yescharacteristic
436C24×C4C2×D1111yescharacteristic
437C2×C4⋊Q8—111no—
438C2×#127—111no—
439C2×#124—111no—
440C2×#124—111no—
441#525—28no—
442#525—228no—
443C2×#123—112no—
444C2×#123C2×D1112yes—
445C2×C22⋊Q8—111no—
446C2×C22⋊Q8—111no—
447C2×C22⋊Q8C2×D1111yescharacteristic
448C2×C22⋊Q8C2×D1111yescharacteristic
449C2×#121—114no—
450C2×#121—111no—
451C2×#121—111no—
452C2×#121C2×D1111yescharacteristic
453C2×#121C2×D1111yescharacteristic
454C2×#120—112no—
455C2×#120C2×D1112yes—
456C2×C4×D4—112no—
457C2×C4×D4—112no—
458C2×C4×D4C2×D1112yes—
459C2×C4×D4C2×D1112yes—
460C2×#117—111no—
461C2×#117C2×D1111yescharacteristic
462C22×C22⋊C4—112no—
463C22×C42—111no—
464C22×C42—111no—
465#397—114no—
466#397—114no—
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#391—111no—
476#391—111no—
477#390—111no—
478#390—111no—
479#390—111no—
480#390—111no—
481#390—114no—
482#389—114no—
483#388—114no—
484#388—114no—
485#388—114no—
486#388—114no—
487#387—114no—
488#387—114no—
489#386—114no—
490#386—114no—
491#386—114no—
492#386—114no—
493#385—114no—
494#385—114no—
495#384—111no—
496#384—111no—
497#382—111no—
498#382—111no—
499#380—114no—
500C4×C22⋊C4—112no—
501C4×C22⋊C4—112no—
502C4×C22⋊C4—111no—
503C4×C22⋊C4—111no—
504C4×C22⋊C4—111no—
505C4×C22⋊C4—111no—
506C2×#95—112no—
507C22×C11—22no—
508C22×C11—22no—
509C22×C11—24no—
510C22×C11—24no—
511C22×C11—22no—
512C22×C11—22no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—22no—
516C22×C11—22no—
517C22×C11—416no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—42no—
524C22×C11—42no—
525C22×C11—44no—
526C22×C11—44no—
527C22×C11#53214yes—
528C22×C11C23×D411yescharacteristic
529C22×C11C22×#4112yes—
530C22×C11C2×H(5,𝔽2)11yescharacteristic
531C22×C11C2×H(5,𝔽2)11yescharacteristic
532C22×C11#58512yes—
533C2×D11—42no—
534C2×D11—42no—
535C2×D11—42no—
536C2×D11—44no—
537C2×D11—44no—
538C4×C11—22no—
539C4×C11—22no—
540C4×C11—22no—
541C4×C11—42no—
542C4×C11—42no—
543C4×C11—42no—
544C4×C11#53414yes—
545Dic11—24no—
546Dic11—24no—
547Dic11—42no—
548Dic11—42no—
549Dic11—42no—
550Dic11—42no—
551Dic11—42no—
552C25C22×D1111yescharacteristic
553C2×#41—24no—
554C2×#41—42no—
555C2×#41—42no—
556C2×#41—224no—
557C2×#41—442no—
558C2×#41—442no—
559C22×Q8—111no—
560C22×Q8C22×D1111yescharacteristic
561C22×D4—112no—
562C22×D4—112no—
563C22×D4—112no—
564C22×D4—114no—
565C22×D4—111no—
566C22×D4C22×D1112yes—
567C22×D4C22×D1111yescharacteristic
568C22×D4C22×D1112yes—
569C22×D4C22×D1112yes—
570C23×C4—42no—
571C23×C4—42no—
572C23×C4—112no—
573C23×C4—112no—
574C23×C4—112no—
575C23×C4C22⋊D1118yescomplemented
576C23×C4C22×D1111yescharacteristic
577C23×C4C22×D1111yescharacteristic
578C23×C4C22×D1111yescharacteristic
579C23×C4C22×D1112yes—
580C23×C4C22×D1111yescharacteristic
581C23×C4C22×D1111yescharacteristic
582C23×C4C22×D1111yescharacteristic
583C4⋊Q8—442no—
584#127—442no—
585#124—442no—
586#124—442no—
587#123—28no—
588#123—228no—
589C22⋊Q8—24no—
590C22⋊Q8—24no—
591C22⋊Q8—224no—
592C22⋊Q8—224no—
593#121—24no—
594#121—24no—
595#121—2216no—
596#121—224no—
597#121—224no—
598#120—28no—
599#120—228no—
600C4×D4—28no—
601C4×D4—28no—
602C4×D4—228no—
603C4×D4—228no—
604#117—24no—
605#117—224no—
606C2×C4⋊C4—111no—
607C2×C4⋊C4—111no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—114no—
611C2×C4⋊C4—114no—
612C2×C4⋊C4—114no—
613C2×C4⋊C4C22×D1111yescharacteristic
614C2×C4⋊C4C22×D1111yescharacteristic
615C2×C4⋊C4C22×D1112yes—
616C2×C4⋊C4C22×D1112yes—
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—114no—
625C2×C22⋊C4—112no—
626C2×C22⋊C4—112no—
627C2×C22⋊C4—114no—
628C2×C22⋊C4—114no—
629C2×C22⋊C4—114no—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—228no—
633C2×C22⋊C4C22×D1112yes—
634C2×C22⋊C4C22×D1112yes—
635C2×C22⋊C4C22×D1112yes—
636C2×C22⋊C4C22×D1112yes—
637C2×C22⋊C4C22×D1112yes—
638C2×C42—112no—
639C2×C42—111no—
640C2×C42—111no—
641C2×C42—111no—
642C2×C42—111no—
643C2×C42—112no—
644C2×C42—112no—
645C2×C42—442no—
646C2×C42—442no—
647C2×C42C22×D1112yes—
648#95—112no—
649#95—112no—
650#95—112no—
651#95—112no—
652#95—114no—
653#95—114no—
654#95—114no—
655#95—114no—
656#95—114no—
657#95—114no—
658C2×C11—24no—
659C2×C11—42no—
660C2×C11—42no—
661C2×C11—82no—
662C2×C11C2×#53211yescharacteristic
663C2×C11C2×#53411yescharacteristic
664C2×C11#344911yescharacteristic
665C2×C11#350512yes—
666C2×C11#350612yes—
667D11—82no—
668C24—24no—
669C24—41no—
670C24—41no—
671C24—42no—
672C24—112no—
673C24C2×C22⋊D1114yes—
674C24C23×D1112yes—
675C24C23×D1111yescharacteristic
676C24C23×D1111yescharacteristic
677C24C23×D1111yescharacteristic
678#41—416no—
679#41—4416no—
680C2×Q8—22no—
681C2×Q8—22no—
682C2×Q8—22no—
683C2×Q8—222no—
684C2×Q8—222no—
685C2×Q8—222no—
686C2×D4—28no—
687C2×D4—24no—
688C2×D4—24no—
689C2×D4—24no—
690C2×D4—22no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—44no—
696C2×D4—228no—
697C2×D4—228no—
698C2×D4—224no—
699C2×D4—224no—
700C2×D4—224no—
701C2×D4—222no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—442no—
705C2×D4—442no—
706C2×D4—444no—
707C2×D4—444no—
708C2×D4—444no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—416no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—112no—
726C22×C4—112no—
727C22×C4—118no—
728C22×C4—112no—
729C22×C4—112no—
730C22×C4—112no—
731C22×C4—112no—
732C22×C4—112no—
733C22×C4—224no—
734C22×C4—224no—
735C22×C4—442no—
736C22×C4—442no—
737C22×C4—442no—
738C22×C4—442no—
739C22×C4—442no—
740C22×C4—442no—
741C22×C4C2×C22⋊D1114yes—
742C22×C4C2×C22⋊D1114yes—
743C22×C4C2×C22⋊D1114yes—
744C22×C4C2×C22⋊D1114yes—
745C22×C4C2×C22⋊D1114yes—
746C22×C4C2×C22⋊D1114yes—
747C22×C4C23×D1112yes—
748C22×C4C23×D1112yes—
749C22×C4C23×D1112yes—
750C22×C4C23×D1111yescharacteristic
751C22×C4C23×D1111yescharacteristic
752C22×C4C23×D1111yescharacteristic
753C22×C4C23×D1111yescharacteristic
754C4⋊C4—22no—
755C4⋊C4—22no—
756C4⋊C4—24no—
757C4⋊C4—24no—
758C4⋊C4—228no—
759C4⋊C4—222no—
760C4⋊C4—222no—
761C4⋊C4—224no—
762C4⋊C4—224no—
763C4⋊C4—444no—
764C4⋊C4—444no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—228no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—228no—
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—222no—
787C42—222no—
788C42—222no—
789C42—222no—
790C42—224no—
791C42—442no—
792C42—442no—
793C11#3503211yescharacteristic, complemented, Sylow
794C23—21no—
795C23—21no—
796C23—22no—
797C23—28no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—24no—
809C23—24no—
810C23—22no—
811C23—44no—
812C23—44no—
813C23—48no—
814C23—48no—
815C23—222no—
816C23—222no—
817C23—224no—
818C23—224no—
819C23—222no—
820C23#41×D1114yes—
821C23C22×C22⋊D1112yes—
822C23C22×C22⋊D1112yes—
823C23C22×C22⋊D1112yes—
824C23C24×D1111yescharacteristic
825Q8—44no—
826Q8—444no—
827D4—48no—
828D4—48no—
829D4—48no—
830D4—44no—
831D4—448no—
832D4—448no—
833D4—448no—
834D4—444no—
835D4—888no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—28no—
843C2×C4—28no—
844C2×C4—28no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—44no—
853C2×C4—44no—
854C2×C4—44no—
855C2×C4—48no—
856C2×C4—114no—
857C2×C4—114no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—224no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—224no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—448no—
876C2×C4—448no—
877C2×C4—448no—
878C2×C4#6703712yes—
879C2×C4#6703712yes—
880C2×C4C22×C22⋊D1112yes—
881C2×C4C22×C22⋊D1112yes—
882C2×C4C22×C22⋊D1112yes—
883C2×C4C22×C22⋊D1112yes—
884C22—22no—
885C22—24no—
886C22—22no—
887C22—24no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—416no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—44no—
902C22—42no—
903C22—44no—
904C22—442no—
905C22—442no—
906C22—444no—
907C22—442no—
908C22—444no—
909C22#1062336314yes—
910C22C2×#6703711yescharacteristic
911C22C2×#6703711yescharacteristic
912C22C2×#41×D1112yes—
913C22#1062345312yes—
914C22C23×C22⋊D1111yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—42no—
919C4—42no—
920C4—42no—
921C4—224no—
922C4—224no—
923C4—442no—
924C4—442no—
925C4—442no—
926C4—442no—
927C4—442no—
928C4#1062333514yes—
929C2—24no—
930C2—42no—
931C2—42no—
932C2—82no—
933C2—882no—
934C2C2×#1062336311yescharacteristic
935C2C2×#1062333511yescharacteristic
936C2#1308194511yescharacteristic
937C2#1308244412yes—
938C2#1308245912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#525C2
hypercenterC2×#525D11
hypocenterC11#35032
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13076964C2semidirect
3. #13076959C2semidirect
4. #13076919C2semidirect
5. #13076915C2semidirect
6. #13074354C2semidirect
7. #13074230C2semidirect
8. #13074228C2semidirect
9. #13073079C2semidirect
10. #13073074C2semidirect
11. #13073070C2semidirect
12. #13073065C2semidirect
13. #13072245C2semidirect
14. #13072240C2semidirect
15. #13072236C2semidirect
16. #13072231C2semidirect
17. #13071314C2semidirect
18. C2×C4×C22⋊Dic11C2semidirect
19. C2×C11×#525C2semidirect
35. C2×#67000C22semidirect
36. C2×#66997C22semidirect
37. C2×#66993C22semidirect
39. C2×#66989C22semidirect
51. #10622843C22semidirect
52. #10622843C22semidirect
57. #10622834C22semidirect
58. #10622834C22semidirect
60. #10622826C22semidirect
61. #10622823C22semidirect
69. #10622603C22semidirect
70. #10622602C22semidirect
71. #10622601C22semidirect
72. #10622601C22semidirect
73. #10622591C22semidirect
74. #10622590C22semidirect
75. #10622590C22semidirect
76. #10622589C22semidirect
77. #10622589C22semidirect
78. #10622587C22semidirect
79. #10622587C22semidirect
80. #10622585C22semidirect
84. #10622570C22semidirect
85. #10622569C22semidirect
88. #10622558C22semidirect
89. #10622557C22semidirect
91. #10622553C22semidirect
92. #10622546C22semidirect
104. C23×C4×C11D4semidirect
268. C22×Dic11#41semidirect
326. C2×#525D11semidirect
575. C23×C4C22⋊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×#106233222
#130769642
#130769592
#130769192
#130769152
#130743542
#130742302
#130742282
#130730792
#130730742
#130730702
#130730652
#130722452
#130722402
#130722362
#130722312
#130713142
C2×C4×C22⋊Dic112
C2×C11×#5252
#3503211