Finite Group Databasebeta

← #14925659

Subgroups — #14925659

Order 2816.

4138 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623363C211yesmaximal, characteristic, complemented
2C2×#10623055C211yesmaximal, characteristic, complemented
3C2×#10623322C211yesmaximal, characteristic, complemented
4C2×#10623359C211yesmaximal, characteristic, complemented
5C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6#13073566C212yesmaximal, complemented
7#13073559C212yesmaximal, complemented
8#13073554C212yesmaximal, complemented
9#13073552C212yesmaximal, complemented
10#13073546C212yesmaximal, complemented
11#13073544C212yesmaximal, complemented
12#13073085C212yesmaximal, complemented
13#13072251C212yesmaximal, complemented
14#13071895C214yesmaximal, complemented
15C4×#66993C214yesmaximal, complemented
16#117×Dic11C211yesmaximal, characteristic, complemented
17C2×C11×#525C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C23×C4×D11C2211yescharacteristic
23C11×#525—28no—
24C2×C11×#123C2212yes—
25C2×C11×C22⋊Q8C2212yescomplemented
26C2×C11×#121C2212yescomplemented
27C2×C11×#120C2212yes—
28C2×C4×D4×C11C2214yescomplemented
29C2×C11×#117C2211yescharacteristic
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2211yescharacteristic
32#10623363—28no—
33#10623359—28no—
34C2×#67000C2211yescharacteristic, complemented
35C2×#66999C2212yescomplemented
36C2×#66997C2211yescharacteristic, complemented
37C2×#66993C2214yes—
38C2×#66993C2211yescharacteristic, complemented
39C2×#66992C2212yes—
40C2×#66992C2212yes—
41C2×#66991C2212yescomplemented
42C2×#66990C2212yes—
43C2×#66989C2211yescharacteristic, complemented
44C2×#66988C2212yes—
45#10623322—28no—
46C2×#66983C2212yescomplemented
47C2×#66982C2212yes—
48C2×C4×C22⋊D11—28no—
49C2×C4×C22⋊D11C2212yes—
50C2×C4×C22⋊D11C2212yes—
51C2×C4×C22⋊D11C2212yes—
52C2×C4×C22⋊D11C2212yes—
53C2×C4×C22⋊D11C2214yescomplemented
54C2×C4×C22⋊D11C2212yescomplemented
55C2×C4×C22⋊D11C2214yescomplemented
56C2×C4×C22⋊D11C2212yescomplemented
57C22×(C2×D11)⋊C4C2211yescharacteristic
58C2×#66979C2211yescharacteristic
59C2×#66977C2212yescomplemented
60C22×Dic11⋊C4C2211yescharacteristic
61C22×C4×Dic11C2211yescharacteristic
62#10623055—28no—
63C2×#66950C2212yescomplemented
64C2×#66948C2212yescomplemented
65C2×#66939C2212yes—
66C2×#66935C2212yes—
67C2×C4×D44C2214yescomplemented
68#10622836C2214yes—
69#10622836C2214yescomplemented
70#10622834C2214yescomplemented
71#10622605C2214yescomplemented
72#10622605C2214yescomplemented
73#10622601C2214yescomplemented
74#10622589C2214yescomplemented
75C4⋊C4×Dic11C2212yescomplemented
76C4⋊C4×Dic11C2212yescomplemented
77#10622573C2214yes—
78#10622573C2214yescomplemented
79#10622570C2214yes—
80#10622570C2214yescomplemented
81#10622570C2214yescomplemented
82#10622570C2214yescomplemented
83#10622562C2214yescomplemented
84#10622562C2214yescomplemented
85C22⋊C4×Dic11C2212yes—
86C22⋊C4×Dic11C2212yes—
87#10622545C2212yescomplemented
88C42×Dic11C2212yescomplemented
89C25×C11C2311yescharacteristic
90C24×D11C2311yescharacteristic
91C2×C11×#41—24no—
92C2×C11×#41—24no—
93C2×C11×#41—24no—
94C22×Q8×C11C2311yescharacteristic
95C22×D4×C11C2312yes—
96C22×D4×C11C2311yescharacteristic
97C22×D4×C11C2314yes—
98C23×C4×C11—24no—
99C23×C4×C11—24no—
100C23×C4×C11—24no—
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2312yes—
103C23×C4×C11C2312yes—
104C23×C4×C11C2312yes—
105C23×C4×C11C2311yescharacteristic
106C22×C22⋊D11—28no—
107C22×C22⋊D11—24no—
108C22×C22⋊D11C2312yes—
109C22×C22⋊D11C2312yes—
110C22×C22⋊D11C2312yes—
111C22×C22⋊D11C2314yes—
112C22×C22⋊D11C2314yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2312yes—
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2311yescharacteristic
118C2×#4339—24no—
119C2×#4339—24no—
120C2×#4339—24no—
121C22×D44C2311yescharacteristic
122C22×D44C2314yes—
123C22×C4×D11—24no—
124C22×C4×D11—24no—
125C22×C4×D11—24no—
126C22×C4×D11C2312yes—
127C22×C4×D11C2312yes—
128C22×C4×D11C2312yes—
129C22×Dic22C2311yescharacteristic
130C11×#123—28no—
131C11×C22⋊Q8—28no—
132C11×#121—28no—
133C11×#120—28no—
134C4×D4×C11—216no—
135C11×#117D418yescomplemented
136C2×C11×C4⋊C4C2314yes—
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C11×C22⋊C4C2314yes—
140C2×C11×C22⋊C4C2312yes—
141C2×C42×C11C2312yes—
142#67006—28no—
143C2×C22⋊Dic11—24no—
144C2×C22⋊Dic11C2314yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2314yes—
148C2×C22⋊Dic11C2312yes—
149C2×C22⋊Dic11C2312yes—
150C2×C22⋊Dic11C2312yes—
151#67000—24no—
152#66999—28no—
153#66997—24no—
154#66993—216no—
155#66993—24no—
156#66992—28no—
157#66992—28no—
158#66991—28no—
159#66990—28no—
160#66989—24no—
161#66988—28no—
162#66983—28no—
163#66982—28no—
164C4×C22⋊D11—28no—
165C4×C22⋊D11—28no—
166C4×C22⋊D11—28no—
167C4×C22⋊D11—28no—
168C4×C22⋊D11—28no—
169C4×C22⋊D11—28no—
170C4×C22⋊D11—216no—
171C4×C22⋊D11—216no—
172C2×(C2×D11)⋊C4—24no—
173C2×(C2×D11)⋊C4C2314yes—
174C2×(C2×D11)⋊C4C2314yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2314yes—
178C2×(C2×D11)⋊C4C2314yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181#66979D418yescomplemented
182C2×C4⋊Dic11C2314yes—
183C2×C4⋊Dic11C2312yes—
184#66977—28no—
185C2×Dic11⋊C4—24no—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2314yes—
189C2×Dic11⋊C4C2314yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×C4×Dic11D418yescomplemented
193C2×C4×Dic11C2314yes—
194C2×C4×Dic11C2314yes—
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200#66950—28no—
201#66948—28no—
202#66939—28no—
203#66935—28no—
204C4×D44—216no—
205C11⋊#95C2314yes—
206C11⋊#95C2314yes—
207#34936—111nomaximal, Sylow
208C24×C11—22no—
209C24×C11—24no—
210C24×C11—22no—
211C24×C11—22no—
212C24×C11—42no—
213C24×C11C2412yes—
214C24×C11C2412yes—
215C24×C11C2411yescharacteristic
216C23×D11—22no—
217C23×D11—24no—
218C23×D11—22no—
219C23×D11—22no—
220C23×D11—42no—
221C23×D11C2412yes—
222C23×D11C2412yes—
223C11×#41—416no—
224C2×Q8×C11—22no—
225C2×Q8×C11—22no—
226C2×Q8×C11—22no—
227C2×D4×C11—24no—
228C2×D4×C11—24no—
229C2×D4×C11—24no—
230C2×D4×C11—28no—
231C2×D4×C11—22no—
232C2×D4×C11—22no—
233C2×D4×C11—28no—
234C2×D4×C11—22no—
235C2×D4×C11—44no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—22no—
239C22×C4×C11—24no—
240C22×C4×C11—24no—
241C22×C4×C11—24no—
242C22×C4×C11—24no—
243C22×C4×C11—24no—
244C22×C4×C11—24no—
245C22×C4×C11—24no—
246C22×C4×C11—24no—
247C22×C4×C11—24no—
248C22×C4×C11—416no—
249C22×C4×C11C2×D414yes—
250C22×C4×C11C2×D414yes—
251C22×C4×C11C2×D414yes—
252C22×C4×C11C2412yes—
253C22×C4×C11C2412yes—
254C22×C4×C11C2414yes—
255C22×C4×C11C2411yescharacteristic
256C22×C4×C11C2411yescharacteristic
257C2×C22⋊D11—232no—
258C2×C22⋊D11—24no—
259C2×C22⋊D11—24no—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—24no—
263C2×C22⋊D11—24no—
264C2×C22⋊D11—24no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11—24no—
267C2×C22⋊D11—24no—
268C2×C22⋊D11—24no—
269C2×C22⋊D11—24no—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—24no—
272C2×C22⋊D11—28no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11#4118yescomplemented
277C22×Dic11—24no—
278C22×Dic11—22no—
279C22×Dic11—22no—
280C22×Dic11—22no—
281C22×Dic11—42no—
282C22×Dic11C2×D414yes—
283C22×Dic11C2×D414yes—
284C22×Dic11C2412yes—
285C22×Dic11C2412yes—
286C22×Dic11C2411yescharacteristic
287C22×Dic11C2411yescharacteristic
288C22×Dic11C2414yes—
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291#4339—416no—
292C2×D44—28no—
293C2×D44—28no—
294C2×D44—22no—
295C2×D44—22no—
296C2×D44—22no—
297C2×D44—44no—
298C2×C4×D11—24no—
299C2×C4×D11—24no—
300C2×C4×D11—24no—
301C2×C4×D11—24no—
302C2×C4×D11—24no—
303C2×C4×D11—24no—
304C2×C4×D11—24no—
305C2×C4×D11—24no—
306C2×C4×D11—24no—
307C2×C4×D11—416no—
308C2×Dic22—22no—
309C2×Dic22—22no—
310C2×Dic22—22no—
311C11×C4⋊C4—28no—
312C11×C4⋊C4C2×D418yescomplemented
313C11×C22⋊C4—28no—
314C11×C22⋊C4—28no—
315C11×C22⋊C4C2×D418yes—
316C42×C11C2×D418yescomplemented
317C22⋊Dic11—28no—
318C22⋊Dic11—24no—
319C22⋊Dic11—24no—
320C22⋊Dic11—28no—
321C22⋊Dic11—24no—
322C22⋊Dic11—24no—
323C22⋊Dic11C2×D418yes—
324(C2×D11)⋊C4—24no—
325(C2×D11)⋊C4—24no—
326(C2×D11)⋊C4—28no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—24no—
329(C2×D11)⋊C4—24no—
330(C2×D11)⋊C4—28no—
331(C2×D11)⋊C4—28no—
332C4⋊Dic11—28no—
333C4⋊Dic11C2×D418yescomplemented
334Dic11⋊C4—24no—
335Dic11⋊C4—24no—
336Dic11⋊C4—28no—
337Dic11⋊C4—28no—
338Dic11⋊C4—24no—
339Dic11⋊C4—24no—
340C4×Dic11—28no—
341C4×Dic11—44no—
342C4×Dic11C2×D414yes—
343C4×Dic11C2×D414yes—
344C4×Dic11C2×D414yes—
345C4×Dic11C2×D414yes—
346C4×Dic11C2×D418yescomplemented
347C2×#532—111no—
348C2×#525—111no—
349C2×#525—111no—
350C2×#525—111no—
351C2×#525D1111yescharacteristic, complemented
352C22×C4×D4—111no—
353#2542—112no—
354#2541—112no—
355#2540—112no—
356#2540—112no—
357#2539—112no—
358#2539—112no—
359#2501—112no—
360#2433—112no—
361#2397—114no—
362C4×#127—114no—
363C4×#117—111no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—28no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—24no—
377C23×C11—24no—
378C23×C11—48no—
379C23×C11—48no—
380C23×C11—44no—
381C23×C11—44no—
382C23×C11C22×D412yes—
383C23×C11C22×D412yes—
384C23×C11C22×D412yes—
385C23×C11C2×#4114yes—
386C23×C11C2511yescharacteristic
387C22×D11—28no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—24no—
398C22×D11—24no—
399C22×D11—48no—
400C22×D11—48no—
401C22×D11—44no—
402C22×D11—44no—
403C22×D11C2×#4114yes—
404Q8×C11—44no—
405D4×C11—416no—
406D4×C11—48no—
407D4×C11—44no—
408C2×C4×C11—24no—
409C2×C4×C11—24no—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—44no—
417C2×C4×C11—48no—
418C2×C4×C11—48no—
419C2×C4×C11—48no—
420C2×C4×C11#127116yescomplemented
421C2×C4×C11C22×D412yes—
422C2×C4×C11C22×D412yes—
423C2×C4×C11C22×D412yes—
424C2×C4×C11C22×D412yes—
425C2×C4×C11C22×D418yes—
426C2×C4×C11C22×D412yes—
427C2×C4×C11C22×D412yes—
428C22⋊D11—216no—
429C22⋊D11—216no—
430C22⋊D11—416no—
431C22⋊D11—416no—
432C22⋊D11—48no—
433C22⋊D11—48no—
434C22⋊D11—48no—
435C2×Dic11—24no—
436C2×Dic11—22no—
437C2×Dic11—22no—
438C2×Dic11—24no—
439C2×Dic11—22no—
440C2×Dic11—28no—
441C2×Dic11—22no—
442C2×Dic11—22no—
443C2×Dic11—22no—
444C2×Dic11—22no—
445C2×Dic11—22no—
446C2×Dic11—22no—
447C2×Dic11—44no—
448C2×Dic11—44no—
449C2×Dic11C22×D412yes—
450C2×Dic11C22×D412yes—
451C2×Dic11C22×D412yes—
452C2×Dic11C22×D418yes—
453C2×Dic11C22×D412yes—
454C2×Dic11C2×#4114yes—
455D44—416no—
456D44—44no—
457C4×D11—48no—
458C4×D11—48no—
459C4×D11—48no—
460Dic22—44no—
461C22×#41—111no—
462C22×#41C2×D1111yescharacteristic
463C23×D4—111no—
464C24×C4—111no—
465C24×C4C2×D1111yescharacteristic
466#532—228no—
467C2×C4⋊Q8—111no—
468C2×#127—114no—
469C2×#127—111no—
470C2×#124—111no—
471C2×#124—111no—
472#525—28no—
473#525—228no—
474#525—228no—
475#525—228no—
476C2×#123—112no—
477C2×#123—112no—
478C2×#123—112no—
479C2×#123C2×D1112yes—
480C2×C22⋊Q8—112no—
481C2×C22⋊Q8—112no—
482C2×C22⋊Q8—112no—
483C2×C22⋊Q8C2×D1112yescomplemented
484C2×#121—112no—
485C2×#121—112no—
486C2×#121—112no—
487C2×#121—112no—
488C2×#121—112no—
489C2×#121C2×D1112yescomplemented
490C2×#120—112no—
491C2×#120—112no—
492C2×#120—112no—
493C2×#120C2×D1112yes—
494C2×C4×D4—112no—
495C2×C4×D4—112no—
496C2×C4×D4—114no—
497C2×C4×D4—114no—
498C2×C4×D4—112no—
499C2×C4×D4—112no—
500C2×C4×D4—112no—
501C2×C4×D4—112no—
502C2×C4×D4—114no—
503C2×C4×D4—228no—
504C2×C4×D4C2×D1114yescomplemented
505C2×#117—111no—
506C2×#117C2×D1111yescharacteristic
507C22×C4⋊C4—111no—
508C22×C22⋊C4—111no—
509C22×C22⋊C4—111no—
510C22×C42—111no—
511#399—114no—
512#399—114no—
513#399—114no—
514#399—114no—
515#392—114no—
516#392—114no—
517#392—114no—
518#392—114no—
519#390—114no—
520#390—114no—
521#390—114no—
522#390—114no—
523#390—114no—
524#390—114no—
525#384—114no—
526C4×C4⋊C4—112no—
527C4×C4⋊C4—112no—
528C4×C22⋊C4—112no—
529C4×C22⋊C4—112no—
530#376—112no—
531C43—112no—
532C22×C11—22no—
533C22×C11—22no—
534C22×C11—24no—
535C22×C11—24no—
536C22×C11—24no—
537C22×C11—24no—
538C22×C11—24no—
539C22×C11—416no—
540C22×C11—42no—
541C22×C11—42no—
542C22×C11—42no—
543C22×C11—42no—
544C22×C11—42no—
545C22×C11—42no—
546C22×C11—42no—
547C22×C11—44no—
548C22×C11—44no—
549C22×C11C2×#12714yes—
550C22×C11C23×D411yescharacteristic
551C22×C11C23×D411yescharacteristic
552C22×C11C23×D411yescharacteristic
553C22×C11C22×#4112yes—
554C22×C11#58512yes—
555C2×D11—24no—
556C2×D11—24no—
557C2×D11—24no—
558C2×D11—416no—
559C2×D11—42no—
560C2×D11—42no—
561C2×D11—42no—
562C2×D11—42no—
563C2×D11—42no—
564C2×D11—42no—
565C2×D11—42no—
566C2×D11—44no—
567C2×D11—44no—
568C4×C11—28no—
569C4×C11—42no—
570C4×C11—42no—
571C4×C11C2×#12714yes—
572C4×C11C2×#12714yes—
573Dic11—22no—
574Dic11—22no—
575Dic11—22no—
576Dic11—28no—
577Dic11—42no—
578Dic11—42no—
579Dic11#52514yescomplemented
580C25—111no—
581C25C22×D1111yescharacteristic
582C2×#41—24no—
583C2×#41—24no—
584C2×#41—24no—
585C2×#41—224no—
586C2×#41—224no—
587C2×#41—224no—
588C22×Q8—111no—
589C22×Q8C22×D1111yescharacteristic
590C22×D4—112no—
591C22×D4—112no—
592C22×D4—112no—
593C22×D4—112no—
594C22×D4—114no—
595C22×D4—114no—
596C22×D4—112no—
597C22×D4—111no—
598C22×D4—114no—
599C22×D4—224no—
600C22×D4—228no—
601C22×D4C22×D1112yes—
602C22×D4C22×D1111yescharacteristic
603C22×D4C22×D1114yes—
604C23×C4—24no—
605C23×C4—24no—
606C23×C4—24no—
607C23×C4—111no—
608C23×C4—111no—
609C23×C4—111no—
610C23×C4—112no—
611C23×C4—112no—
612C23×C4—112no—
613C23×C4—224no—
614C23×C4—224no—
615C23×C4—224no—
616C23×C4C22×D1111yescharacteristic
617C23×C4C22×D1112yes—
618C23×C4C22×D1112yes—
619C23×C4C22×D1112yes—
620C23×C4C22×D1111yescharacteristic
621C4⋊Q8—224no—
622#127—224no—
623#127—2216no—
624#124—224no—
625#124—224no—
626#123—28no—
627#123—228no—
628#123—228no—
629#123—228no—
630C22⋊Q8—28no—
631C22⋊Q8—228no—
632C22⋊Q8—228no—
633C22⋊Q8—228no—
634#121—28no—
635#121—228no—
636#121—228no—
637#121—228no—
638#121—228no—
639#121—228no—
640#120—28no—
641#120—228no—
642#120—228no—
643#120—228no—
644C4×D4—216no—
645C4×D4—228no—
646C4×D4—228no—
647C4×D4—228no—
648C4×D4—228no—
649C4×D4—2216no—
650C4×D4—2216no—
651C4×D4—228no—
652C4×D4—228no—
653C4×D4—2216no—
654#117—118no—
655#117C22⋊D1118yescomplemented
656C2×C4⋊C4—112no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—112no—
660C2×C4⋊C4—112no—
661C2×C4⋊C4—114no—
662C2×C4⋊C4—114no—
663C2×C4⋊C4—114no—
664C2×C4⋊C4—224no—
665C2×C4⋊C4C22×D1114yes—
666C2×C4⋊C4C22×D1112yes—
667C2×C22⋊C4—112no—
668C2×C22⋊C4—112no—
669C2×C22⋊C4—112no—
670C2×C22⋊C4—114no—
671C2×C22⋊C4—114no—
672C2×C22⋊C4—112no—
673C2×C22⋊C4—112no—
674C2×C22⋊C4—112no—
675C2×C22⋊C4—112no—
676C2×C22⋊C4—114no—
677C2×C22⋊C4—114no—
678C2×C22⋊C4—114no—
679C2×C22⋊C4—114no—
680C2×C22⋊C4—112no—
681C2×C22⋊C4—112no—
682C2×C22⋊C4—224no—
683C2×C22⋊C4—224no—
684C2×C22⋊C4C22×D1114yes—
685C2×C22⋊C4C22×D1114yes—
686C2×C22⋊C4C22×D1112yes—
687C2×C42—118no—
688C2×C42—111no—
689C2×C42—111no—
690C2×C42—112no—
691C2×C42—111no—
692C2×C42—111no—
693C2×C42—114no—
694C2×C42—114no—
695C2×C42C22×D1112yes—
696#95—114no—
697#95—114no—
698C2×C11—24no—
699C2×C11—44no—
700C2×C11—82no—
701C2×C11C2×#52511yescharacteristic
702C2×C11C22×#12711yescharacteristic
703C2×C11#344911yescharacteristic
704C2×C11D4×#4112yes—
705C2×C11D4×#4112yes—
706D11—44no—
707D11—82no—
708C24—22no—
709C24—24no—
710C24—22no—
711C24—22no—
712C24—42no—
713C24—112no—
714C24—112no—
715C24—224no—
716C24—222no—
717C24—222no—
718C24—222no—
719C24—442no—
720C24C23×D1112yes—
721C24C23×D1112yes—
722C24C23×D1111yescharacteristic
723#41—416no—
724#41—4416no—
725C2×Q8—22no—
726C2×Q8—22no—
727C2×Q8—22no—
728C2×Q8—222no—
729C2×Q8—222no—
730C2×Q8—222no—
731C2×D4—24no—
732C2×D4—24no—
733C2×D4—28no—
734C2×D4—24no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—28no—
738C2×D4—22no—
739C2×D4—44no—
740C2×D4—118no—
741C2×D4—228no—
742C2×D4—224no—
743C2×D4—224no—
744C2×D4—224no—
745C2×D4—228no—
746C2×D4—228no—
747C2×D4—224no—
748C2×D4—224no—
749C2×D4—228no—
750C2×D4—224no—
751C2×D4—2232no—
752C2×D4—224no—
753C2×D4—228no—
754C2×D4—224no—
755C2×D4—224no—
756C2×D4—228no—
757C2×D4—224no—
758C2×D4—222no—
759C2×D4—222no—
760C2×D4—228no—
761C2×D4—222no—
762C2×D4—444no—
763C2×D4—444no—
764C2×D4—444no—
765C2×D4—444no—
766C22×C4—22no—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—24no—
770C22×C4—24no—
771C22×C4—24no—
772C22×C4—24no—
773C22×C4—24no—
774C22×C4—24no—
775C22×C4—24no—
776C22×C4—24no—
777C22×C4—24no—
778C22×C4—416no—
779C22×C4—111no—
780C22×C4—114no—
781C22×C4—111no—
782C22×C4—111no—
783C22×C4—114no—
784C22×C4—111no—
785C22×C4—114no—
786C22×C4—112no—
787C22×C4—112no—
788C22×C4—224no—
789C22×C4—222no—
790C22×C4—222no—
791C22×C4—222no—
792C22×C4—224no—
793C22×C4—224no—
794C22×C4—224no—
795C22×C4—224no—
796C22×C4—224no—
797C22×C4—224no—
798C22×C4—224no—
799C22×C4—224no—
800C22×C4—224no—
801C22×C4—442no—
802C22×C4—4416no—
803C22×C4D4×D1114yes—
804C22×C4D4×D1114yes—
805C22×C4C2×C22⋊D1114yes—
806C22×C4C23×D1112yes—
807C22×C4C23×D1112yes—
808C22×C4C23×D1114yes—
809C22×C4C23×D1111yescharacteristic
810C22×C4C23×D1111yescharacteristic
811C4⋊C4—28no—
812C4⋊C4—118no—
813C4⋊C4—224no—
814C4⋊C4—224no—
815C4⋊C4—224no—
816C4⋊C4—224no—
817C4⋊C4—228no—
818C4⋊C4—228no—
819C4⋊C4—228no—
820C4⋊C4C2×C22⋊D1118yescomplemented
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—118no—
824C22⋊C4—224no—
825C22⋊C4—224no—
826C22⋊C4—228no—
827C22⋊C4—228no—
828C22⋊C4—224no—
829C22⋊C4—224no—
830C22⋊C4—224no—
831C22⋊C4—224no—
832C22⋊C4—228no—
833C22⋊C4—228no—
834C22⋊C4—224no—
835C22⋊C4—224no—
836C22⋊C4—228no—
837C22⋊C4—228no—
838C22⋊C4C2×C22⋊D1118yes—
839C42—114no—
840C42—114no—
841C42—114no—
842C42—114no—
843C42—118no—
844C42—228no—
845C42—444no—
846C42C2×C22⋊D1118yescomplemented
847C11#3493611yescharacteristic, complemented, Sylow
848C23—22no—
849C23—22no—
850C23—28no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—24no—
860C23—24no—
861C23—22no—
862C23—48no—
863C23—48no—
864C23—44no—
865C23—44no—
866C23—114no—
867C23—228no—
868C23—222no—
869C23—222no—
870C23—222no—
871C23—222no—
872C23—222no—
873C23—222no—
874C23—222no—
875C23—222no—
876C23—224no—
877C23—224no—
878C23—222no—
879C23—448no—
880C23—448no—
881C23—444no—
882C23—444no—
883C23C2×D4×D1112yes—
884C23C2×D4×D1112yes—
885C23#41×D1114yes—
886C23C22×C22⋊D1112yes—
887C23C24×D1111yescharacteristic
888Q8—44no—
889Q8—444no—
890D4—416no—
891D4—48no—
892D4—44no—
893D4—2216no—
894D4—2216no—
895D4—4416no—
896D4—448no—
897D4—4416no—
898D4—4416no—
899D4—448no—
900D4—448no—
901D4—444no—
902C2×C4—24no—
903C2×C4—24no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—44no—
911C2×C4—48no—
912C2×C4—48no—
913C2×C4—48no—
914C2×C4—112no—
915C2×C4—114no—
916C2×C4—112no—
917C2×C4—112no—
918C2×C4—112no—
919C2×C4—118no—
920C2×C4—228no—
921C2×C4—224no—
922C2×C4—222no—
923C2×C4—222no—
924C2×C4—224no—
925C2×C4—222no—
926C2×C4—222no—
927C2×C4—222no—
928C2×C4—222no—
929C2×C4—222no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—444no—
933C2×C4—444no—
934C2×C4—448no—
935C2×C4—448no—
936C2×C4—448no—
937C2×C4#66993116yescomplemented
938C2×C4C2×D4×D1112yes—
939C2×C4C2×D4×D1112yes—
940C2×C4C2×D4×D1112yes—
941C2×C4C2×D4×D1112yes—
942C2×C4C22×C22⋊D1118yes—
943C2×C4C22×C22⋊D1112yes—
944C2×C4C22×C22⋊D1112yes—
945C22—22no—
946C22—24no—
947C22—24no—
948C22—22no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—416no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—44no—
961C22—42no—
962C22—224no—
963C22—224no—
964C22—224no—
965C22—4416no—
966C22—442no—
967C22—442no—
968C22—442no—
969C22—442no—
970C22—442no—
971C22—442no—
972C22—444no—
973C22—444no—
974C22—442no—
975C22C2×#6699314yes—
976C22C22×D4×D1111yescharacteristic
977C22C22×D4×D1111yescharacteristic
978C22C2×#41×D1112yes—
979C22#1062345312yes—
980C22C23×C22⋊D1111yescharacteristic
981C4—28no—
982C4—42no—
983C4—42no—
984C4—114no—
985C4—222no—
986C4—222no—
987C4—228no—
988C4—222no—
989C4—442no—
990C4—442no—
991C4C2×#6699314yes—
992C4C2×#6699314yes—
993C2—24no—
994C2—44no—
995C2—82no—
996C2—444no—
997C2—882no—
998C2D11×#52511yescharacteristic
999C2C22×#6699311yescharacteristic
1000C2#1308194611yescharacteristic
1001C2#1308209912yes—
1002C2#41×C22⋊D1112yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#525C2
hypercenterC2×#525D11
hypocenterC11#34936
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623363C2semidirect
2. C2×#10623055C2semidirect
3. C2×#10623322C2semidirect
4. C2×#10623359C2semidirect
5. C22×C4×C22⋊D11C2semidirect
6. #13073566C2semidirect
7. #13073559C2semidirect
8. #13073554C2semidirect
9. #13073552C2semidirect
10. #13073546C2semidirect
11. #13073544C2semidirect
12. #13073085C2semidirect
13. #13072251C2semidirect
14. #13071895C2semidirect
15. C4×#66993C2semidirect
16. #117×Dic11C2semidirect
17. C2×C11×#525C2semidirect
25. C2×C11×C22⋊Q8C22semidirect
26. C2×C11×#121C22semidirect
28. C2×C4×D4×C11C22semidirect
34. C2×#67000C22semidirect
35. C2×#66999C22semidirect
36. C2×#66997C22semidirect
38. C2×#66993C22semidirect
41. C2×#66991C22semidirect
43. C2×#66989C22semidirect
46. C2×#66983C22semidirect
53. C2×C4×C22⋊D11C22semidirect
54. C2×C4×C22⋊D11C22semidirect
55. C2×C4×C22⋊D11C22semidirect
56. C2×C4×C22⋊D11C22semidirect
59. C2×#66977C22semidirect
63. C2×#66950C22semidirect
64. C2×#66948C22semidirect
67. C2×C4×D44C22semidirect
69. #10622836C22semidirect
70. #10622834C22semidirect
71. #10622605C22semidirect
72. #10622605C22semidirect
73. #10622601C22semidirect
74. #10622589C22semidirect
75. C4⋊C4×Dic11C22semidirect
76. C4⋊C4×Dic11C22semidirect
78. #10622573C22semidirect
80. #10622570C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622562C22semidirect
84. #10622562C22semidirect
87. #10622545C22semidirect
88. C42×Dic11C22semidirect
135. C11×#117D4semidirect
181. #66979D4semidirect
192. C2×C4×Dic11D4semidirect
276. C2×C22⋊D11#41semidirect
312. C11×C4⋊C4C2×D4semidirect
316. C42×C11C2×D4semidirect
333. C4⋊Dic11C2×D4semidirect
346. C4×Dic11C2×D4semidirect
351. C2×#525D11semidirect
420. C2×C4×C11#127semidirect
483. C2×C22⋊Q8C2×D11semidirect
489. C2×#121C2×D11semidirect
504. C2×C4×D4C2×D11semidirect
579. Dic11#525semidirect
655. #117C22⋊D11semidirect
820. C4⋊C4C2×C22⋊D11semidirect
846. C42C2×C22⋊D11semidirect
847. C11#34936semidirect
937. C2×C4#66993semidirect

Maximal subgroups

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

subgroupindex
C2×#106233632
C2×#106230552
C2×#106233222
C2×#106233592
C22×C4×C22⋊D112
#130735662
#130735592
#130735542
#130735522
#130735462
#130735442
#130730852
#130722512
#130718952
C4×#669932
#117×Dic112
C2×C11×#5252
#3493611