Finite Group Databasebeta

← #14926349

Subgroups — #14926349

Order 2816.

3690 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2C2×#10623335C211yesmaximal, characteristic, complemented
3C2×#10623335C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13076944C212yesmaximal, complemented
6#13076897C212yesmaximal, complemented
7#13074364C212yesmaximal, complemented
8#13074356C212yesmaximal, complemented
9#13072169C214yesmaximal, complemented
10#13072167C214yesmaximal, complemented
11#13072154C214yesmaximal, complemented
12#13072152C214yesmaximal, complemented
13#13071228C211yesmaximal, characteristic, complemented
14C2×#10622826C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic, complemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2212yescomplemented
23C2×#67006C2212yescomplemented
24C2×#67006C2212yescomplemented
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27#10623335—28no—
28#10623335—28no—
29C2×#66992C2214yes—
30C2×#66992C2212yes—
31C2×#66992C2212yes—
32C2×#66990C2212yescomplemented
33C2×#66990C2212yescomplemented
34C2×#66988C2212yescomplemented
35C2×#66988C2212yescomplemented
36C2×#66983C2214yes—
37C2×#66982C2212yescomplemented
38C2×#66982C2212yescomplemented
39C2×C4×C22⋊D11—28no—
40C2×C4×C22⋊D11C2214yescomplemented
41C2×C4×C22⋊D11C2214yescomplemented
42C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D11)⋊C4C2212yescomplemented
44C22×Dic11⋊C4C2211yescharacteristic, complemented
45C22×C4×Dic11C2211yescharacteristic, complemented
46#10623024—28no—
47C2×#66939C2212yescomplemented
48C2×#66939C2212yescomplemented
49C2×#66937C2214yescomplemented
50C2×#66935C2212yescomplemented
51C2×#66935C2212yescomplemented
52C11×#386C2214yescomplemented
53C11×#386C2212yescomplemented
54C11×#386C2212yescomplemented
55C2×C11×#95C2212yescomplemented
56#10622826C2214yescomplemented
57#10622826C2212yescomplemented
58#10622826C2212yescomplemented
59#10622823C2214yescomplemented
60C2×C11⋊#95C2212yescomplemented
61#10622573C2214yescomplemented
62#10622572C2214yescomplemented
63#10622572C2214yescomplemented
64#10622570C2214yescomplemented
65#10622569C2214yescomplemented
66#10622564C2214yescomplemented
67#10622561C2214yescomplemented
68#10622559C2214yescomplemented
69#10622555C2212yescomplemented
70#10622555C2212yescomplemented
71#10622289C2214yescomplemented
72#10622288C2214yescomplemented
73#10622285C2214yescomplemented
74#10622282C2214yescomplemented
75#10622280C2214yescomplemented
76#10622278C2214yescomplemented
77#10622270C2214yescomplemented
78#10622260C2214yescomplemented
79C25×C11C2311yescharacteristic
80C25×C11C2311yescharacteristic
81C24×D11C2311yescharacteristic
82C24×D11C2311yescharacteristic
83C22×D4×C11—24no—
84C22×D4×C11—24no—
85C22×D4×C11—24no—
86C22×D4×C11C2312yes—
87C22×D4×C11C2312yes—
88C23×C4×C11—24no—
89C23×C4×C11—44no—
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2312yes—
93C23×C4×C11C2312yes—
94C23×C4×C11C2311yescharacteristic
95C23×C4×C11C2312yes—
96C22×C22⋊D11—24no—
97C22×C22⋊D11—24no—
98C22×C22⋊D11—24no—
99C22×C22⋊D11—24no—
100C22×C22⋊D11—24no—
101C22×C22⋊D11D418yescomplemented
102C22×C22⋊D11C2312yes—
103C22×C22⋊D11C2312yes—
104C22×C22⋊D11C2312yes—
105C22×C22⋊D11C2312yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2314yes—
108C22×C22⋊D11C2312yes—
109C23×Dic11C2311yescharacteristic
110C23×Dic11C2311yescharacteristic
111C23×Dic11C2312yes—
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C22×D44C2314yes—
115C22×C4×D11—24no—
116C22×C4×D11—44no—
117C22×C4×D11C2314yes—
118C2×C11×C22⋊C4—24no—
119C2×C11×C22⋊C4—44no—
120C2×C11×C22⋊C4C2312yes—
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2314yes—
123C2×C11×C22⋊C4C2314yes—
124#67006—28no—
125#67006—28no—
126C2×C22⋊Dic11—24no—
127C2×C22⋊Dic11D418yescomplemented
128C2×C22⋊Dic11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2312yes—
131C2×C22⋊Dic11C2314yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135#66992—216no—
136#66992—28no—
137#66992—28no—
138#66990—28no—
139#66990—28no—
140#66988—28no—
141#66988—28no—
142#66983—216no—
143#66982—28no—
144#66982—28no—
145C4×C22⋊D11—216no—
146C4×C22⋊D11—216no—
147C2×(C2×D11)⋊C4—24no—
148C2×(C2×D11)⋊C4—44no—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2314yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×(C2×D11)⋊C4C2314yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×C4⋊Dic11C2314yes—
158C2×Dic11⋊C4—24no—
159C2×Dic11⋊C4C2312yes—
160C2×Dic11⋊C4C2314yes—
161C2×Dic11⋊C4C2312yes—
162C2×Dic11⋊C4C2314yes—
163C2×Dic11⋊C4C2314yes—
164C2×Dic11⋊C4C2314yes—
165C2×C4×Dic11—24no—
166C2×C4×Dic11C2314yes—
167#66939—28no—
168#66939—28no—
169#66937—48no—
170#66935—28no—
171#66935—28no—
172C11×#95C2314yes—
173C11×#95C2314yes—
174C11⋊#95C2314yes—
175C11⋊#95C2314yes—
176C11⋊#95C2314yes—
177C11⋊#95C2314yes—
178#34984—111nomaximal, Sylow
179C24×C11—22no—
180C24×C11—22no—
181C24×C11—22no—
182C24×C11—42no—
183C24×C11—42no—
184C24×C11—42no—
185C24×C11—42no—
186C24×C11C2×D414yes—
187C24×C11C2×D414yes—
188C24×C11#4114yes—
189C24×C11C2412yes—
190C24×C11C2411yescharacteristic
191C24×C11C2411yescharacteristic
192C24×C11C2411yescharacteristic
193C23×D11—22no—
194C23×D11—22no—
195C23×D11—22no—
196C23×D11—22no—
197C23×D11—22no—
198C23×D11—42no—
199C23×D11—42no—
200C23×D11—42no—
201C23×D11—42no—
202C23×D11C2×D414yes—
203C23×D11C2412yes—
204C23×D11C2412yes—
205C2×D4×C11—24no—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—24no—
209C2×D4×C11—24no—
210C2×D4×C11—24no—
211C2×D4×C11—416no—
212C22×C4×C11—22no—
213C22×C4×C11—24no—
214C22×C4×C11—22no—
215C22×C4×C11—24no—
216C22×C4×C11—24no—
217C22×C4×C11—22no—
218C22×C4×C11—22no—
219C22×C4×C11—22no—
220C22×C4×C11—24no—
221C22×C4×C11—24no—
222C22×C4×C11—24no—
223C22×C4×C11—42no—
224C22×C4×C11—42no—
225C22×C4×C11—42no—
226C22×C4×C11—42no—
227C22×C4×C11—42no—
228C22×C4×C11—416no—
229C22×C4×C11C2414yes—
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2412yes—
233C2×C22⋊D11—24no—
234C2×C22⋊D11—24no—
235C2×C22⋊D11—232no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—24no—
245C2×C22⋊D11—24no—
246C2×C22⋊D11—28no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—416no—
252C2×C22⋊D11C2×D418yes—
253C2×C22⋊D11C2×D418yes—
254C22×Dic11—22no—
255C22×Dic11—22no—
256C22×Dic11—22no—
257C22×Dic11—24no—
258C22×Dic11—22no—
259C22×Dic11—22no—
260C22×Dic11—42no—
261C22×Dic11—42no—
262C22×Dic11—42no—
263C22×Dic11—42no—
264C22×Dic11C2×D414yes—
265C22×Dic11C2×D414yes—
266C22×Dic11C2×D414yes—
267C22×Dic11C2414yes—
268C22×Dic11C2412yes—
269C22×Dic11C2412yes—
270C22×Dic11C2412yes—
271C22×Dic11C2412yes—
272C2×D44—28no—
273C2×D44—44no—
274C2×D44—44no—
275C2×C4×D11—28no—
276C2×C4×D11—28no—
277C2×C4×D11—44no—
278C2×C4×D11—416no—
279C11×C22⋊C4—24no—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—28no—
282C11×C22⋊C4—44no—
283C22⋊Dic11—24no—
284C22⋊Dic11—24no—
285C22⋊Dic11—28no—
286C22⋊Dic11—24no—
287C22⋊Dic11—24no—
288C22⋊Dic11C2×D418yes—
289C22⋊Dic11C2×D418yes—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—28no—
292(C2×D11)⋊C4—24no—
293(C2×D11)⋊C4—24no—
294(C2×D11)⋊C4—28no—
295(C2×D11)⋊C4—28no—
296(C2×D11)⋊C4—28no—
297(C2×D11)⋊C4—44no—
298C4⋊Dic11—28no—
299Dic11⋊C4—28no—
300Dic11⋊C4—24no—
301Dic11⋊C4—24no—
302Dic11⋊C4—28no—
303Dic11⋊C4—44no—
304Dic11⋊C4—44no—
305C4×Dic11—28no—
306C2×#534—111no—
307C2×#534—111no—
308C2×#534—111no—
309C22×C4×D4—111no—
310#2854—112no—
311#2847—112no—
312#2618—112no—
313#2617—112no—
314#2425—114no—
315#2425—114no—
316#2424—114no—
317#2424—114no—
318#2315—111no—
319C2×#386—111no—
320C2×#386D1111yescharacteristic, complemented
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—24no—
331C23×C11—24no—
332C23×C11—44no—
333C23×C11—44no—
334C23×C11—48no—
335C23×C11—48no—
336C23×C11—48no—
337C23×C11—44no—
338C23×C11—82no—
339C23×C11—82no—
340C23×C11—84no—
341C23×C11#121116yescomplemented
342C23×C11C22×D412yes—
343C23×C11C22×D412yes—
344C23×C11C22×D412yes—
345C23×C11C22×D412yes—
346C23×C11C22×D412yes—
347C23×C11C22×D412yes—
348C23×C11C2×#4112yes—
349C23×C11C2×#4112yes—
350C23×C11C2×#4112yes—
351C23×C11C2511yescharacteristic
352C22×D11—28no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—24no—
356C22×D11—24no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—24no—
361C22×D11—24no—
362C22×D11—48no—
363C22×D11—44no—
364C22×D11—48no—
365C22×D11—44no—
366C22×D11—48no—
367C22×D11—44no—
368C22×D11—82no—
369C22×D11—82no—
370C22×D11—84no—
371C22×D11C22×D414yes—
372D4×C11—48no—
373D4×C11—48no—
374C2×C4×C11—28no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—24no—
381C2×C4×C11—22no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—24no—
386C2×C4×C11—48no—
387C2×C4×C11—48no—
388C2×C4×C11—44no—
389C2×C4×C11—44no—
390C2×C4×C11—84no—
391C2×C4×C11H(5,𝔽2)14yes—
392C22⋊D11—216no—
393C22⋊D11—216no—
394C22⋊D11—48no—
395C22⋊D11—48no—
396C22⋊D11—84no—
397C22⋊D11—84no—
398C22⋊D11—88no—
399C2×Dic11—28no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—24no—
403C2×Dic11—24no—
404C2×Dic11—22no—
405C2×Dic11—24no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—24no—
409C2×Dic11—24no—
410C2×Dic11—44no—
411C2×Dic11—44no—
412C2×Dic11—44no—
413C2×Dic11—84no—
414C2×Dic11C22×D414yes—
415C2×Dic11C22×D414yes—
416C2×Dic11C22×D414yes—
417D44—88no—
418C4×D11—416no—
419C23×D4—111no—
420C23×D4—111no—
421C23×D4C2×D1111yescharacteristic
422C24×C4—111no—
423C24×C4C2×D1111yescharacteristic
424#534—228no—
425#534—228no—
426#534—228no—
427C2×#123—112no—
428C2×#123—112no—
429C2×#123—112no—
430C2×#123—112no—
431C2×#123—112no—
432C2×#123—112no—
433C2×#121—112no—
434C2×#121—112no—
435C2×#121—114no—
436C2×#121—114no—
437C2×#121—114no—
438C2×#120—112no—
439C2×#120—112no—
440C2×#120—112no—
441C2×#120—112no—
442C2×#120—112no—
443C2×#120—112no—
444C2×C4×D4—114no—
445C2×C4×D4—114no—
446C2×C4×D4—228no—
447C22×C4⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—112no—
452C22×C22⋊C4C2×D1111yescharacteristic
453C22×C22⋊C4C2×D1112yescomplemented
454C22×C42—111no—
455#398—114no—
456#397—114no—
457#396—114no—
458#396—114no—
459#394—114no—
460#394—114no—
461#394—114no—
462#392—114no—
463#390—114no—
464#389—114no—
465#388—114no—
466#388—114no—
467#386—112no—
468#386—112no—
469#386—114no—
470#386—114no—
471#386—114no—
472#386C2×D1112yescomplemented
473#386C2×D1112yescomplemented
474#386C2×D1114yescomplemented
475#385—114no—
476#385—114no—
477#380—112no—
478#380—112no—
479#380—114no—
480C2×#95—112no—
481C2×#95C2×D1112yescomplemented
482C22×C11—24no—
483C22×C11—24no—
484C22×C11—24no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—22no—
488C22×C11—22no—
489C22×C11—22no—
490C22×C11—22no—
491C22×C11—24no—
492C22×C11—24no—
493C22×C11—24no—
494C22×C11—416no—
495C22×C11—42no—
496C22×C11—44no—
497C22×C11—42no—
498C22×C11—42no—
499C22×C11—44no—
500C22×C11—88no—
501C22×C11C2×#12114yes—
502C22×C11C2×#12114yes—
503C22×C11C2×#12114yes—
504C22×C11C23×D411yescharacteristic
505C22×C11C23×D411yescharacteristic
506C22×C11C22×#4111yescharacteristic
507C22×C11C2×H(5,𝔽2)12yes—
508C22×C11#58512yes—
509C2×D11—24no—
510C2×D11—28no—
511C2×D11—416no—
512C2×D11—44no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—44no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—44no—
520C2×D11—88no—
521C4×C11—24no—
522C4×C11—42no—
523C4×C11—42no—
524C4×C11—44no—
525Dic11—24no—
526Dic11—24no—
527Dic11—24no—
528Dic11—42no—
529Dic11—44no—
530C25—111no—
531C25—111no—
532C25C22×D1111yescharacteristic
533C25C22×D1111yescharacteristic
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—24no—
537C22×D4—118no—
538C22×D4—112no—
539C22×D4—112no—
540C22×D4—112no—
541C22×D4—112no—
542C22×D4—112no—
543C22×D4—114no—
544C22×D4—112no—
545C22×D4—114no—
546C22×D4—224no—
547C22×D4—224no—
548C22×D4—224no—
549C22×D4—224no—
550C22×D4—224no—
551C22×D4C22×D1112yes—
552C22×D4C22×D1112yes—
553C23×C4—24no—
554C23×C4—44no—
555C23×C4—111no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—112no—
560C23×C4—114no—
561C23×C4—224no—
562C23×C4—444no—
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1112yes—
566C23×C4C22×D1112yes—
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1112yes—
569#123—228no—
570#123—228no—
571#123—228no—
572#123—228no—
573#123—228no—
574#123—228no—
575#121—2216no—
576#121—228no—
577#121—228no—
578#121—2216no—
579#121—448no—
580#120—228no—
581#120—228no—
582#120—228no—
583#120—228no—
584#120—228no—
585#120—228no—
586C4×D4—2216no—
587C4×D4—2216no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—112no—
590C2×C4⋊C4—114no—
591C2×C4⋊C4—114no—
592C2×C4⋊C4—112no—
593C2×C4⋊C4—114no—
594C2×C4⋊C4—114no—
595C2×C4⋊C4—224no—
596C2×C22⋊C4—24no—
597C2×C22⋊C4—44no—
598C2×C22⋊C4—118no—
599C2×C22⋊C4—112no—
600C2×C22⋊C4—112no—
601C2×C22⋊C4—112no—
602C2×C22⋊C4—112no—
603C2×C22⋊C4—112no—
604C2×C22⋊C4—112no—
605C2×C22⋊C4—114no—
606C2×C22⋊C4—114no—
607C2×C22⋊C4—114no—
608C2×C22⋊C4—114no—
609C2×C22⋊C4—114no—
610C2×C22⋊C4—112no—
611C2×C22⋊C4—112no—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—114no—
614C2×C22⋊C4—224no—
615C2×C22⋊C4—224no—
616C2×C22⋊C4—444no—
617C2×C22⋊C4C22×D1112yes—
618C2×C22⋊C4C22×D1112yes—
619C2×C22⋊C4C22×D1114yes—
620C2×C22⋊C4C22×D1114yes—
621C2×C42—114no—
622C2×C42—224no—
623#95—114no—
624#95—114no—
625#95—114no—
626#95—114no—
627#95C22×D1114yes—
628#95C22×D1114yes—
629C2×C11—24no—
630C2×C11—24no—
631C2×C11—24no—
632C2×C11—82no—
633C2×C11C22×#12111yescharacteristic
634C2×C11#345912yes—
635C2×C11#348411yescharacteristic
636C2×C11#348511yescharacteristic
637C2×C11#349612yes—
638D11—44no—
639D11—82no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—42no—
644C24—42no—
645C24—42no—
646C24—42no—
647C24—112no—
648C24—114no—
649C24—112no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24—442no—
656C24—442no—
657C24—442no—
658C24—442no—
659C24#433914yes—
660C24D4×D1114yes—
661C24D4×D1114yes—
662C24C23×D1112yes—
663C24C23×D1111yescharacteristic
664C24C23×D1111yescharacteristic
665C24C23×D1111yescharacteristic
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—416no—
673C2×D4—118no—
674C2×D4—118no—
675C2×D4—228no—
676C2×D4—224no—
677C2×D4—224no—
678C2×D4—2232no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—224no—
686C2×D4—224no—
687C2×D4—224no—
688C2×D4—224no—
689C2×D4—228no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—444no—
693C2×D4—444no—
694C2×D4—444no—
695C2×D4—444no—
696C2×D4—4416no—
697C22×C4—22no—
698C22×C4—24no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
702C22×C4—24no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—24no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—42no—
709C22×C4—42no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4—42no—
713C22×C4—416no—
714C22×C4—114no—
715C22×C4—112no—
716C22×C4—112no—
717C22×C4—112no—
718C22×C4—114no—
719C22×C4—114no—
720C22×C4—114no—
721C22×C4—112no—
722C22×C4—228no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—224no—
729C22×C4—228no—
730C22×C4—444no—
731C22×C4—4416no—
732C22×C4—442no—
733C22×C4—442no—
734C22×C4—442no—
735C22×C4—442no—
736C22×C4C23×D1112yes—
737C22×C4C23×D1114yes—
738C22×C4C23×D1112yes—
739C22×C4C23×D1112yes—
740C4⋊C4—228no—
741C4⋊C4—224no—
742C4⋊C4—224no—
743C4⋊C4—228no—
744C4⋊C4—228no—
745C4⋊C4—444no—
746C4⋊C4—444no—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—28no—
750C22⋊C4—44no—
751C22⋊C4—118no—
752C22⋊C4—118no—
753C22⋊C4—228no—
754C22⋊C4—228no—
755C22⋊C4—224no—
756C22⋊C4—224no—
757C22⋊C4—228no—
758C22⋊C4—228no—
759C22⋊C4—224no—
760C22⋊C4—224no—
761C22⋊C4—228no—
762C22⋊C4—224no—
763C22⋊C4—224no—
764C22⋊C4—228no—
765C22⋊C4—444no—
766C42—228no—
767C11#3498411yescharacteristic, complemented, Sylow
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—44no—
780C23—48no—
781C23—48no—
782C23—44no—
783C23—48no—
784C23—44no—
785C23—84no—
786C23—82no—
787C23—82no—
788C23—114no—
789C23—228no—
790C23—222no—
791C23—222no—
792C23—224no—
793C23—224no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—224no—
798C23—224no—
799C23—448no—
800C23—444no—
801C23—444no—
802C23—448no—
803C23—448no—
804C23—444no—
805C23—884no—
806C23—882no—
807C23—882no—
808C23#66937116yescomplemented
809C23C2×#433912yes—
810C23C2×#433912yes—
811C23C2×#433912yes—
812C23C2×D4×D1112yes—
813C23C2×D4×D1112yes—
814C23C2×D4×D1112yes—
815C23C2×D4×D1112yes—
816C23C2×D4×D1112yes—
817C23C2×D4×D1112yes—
818C23C24×D1111yescharacteristic
819D4—48no—
820D4—48no—
821D4—2216no—
822D4—2216no—
823D4—448no—
824D4—448no—
825D4—888no—
826D4—884no—
827D4—884no—
828D4—888no—
829C2×C4—28no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—24no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—24no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—24no—
841C2×C4—48no—
842C2×C4—48no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—84no—
846C2×C4—114no—
847C2×C4—114no—
848C2×C4—114no—
849C2×C4—228no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—224no—
853C2×C4—224no—
854C2×C4—222no—
855C2×C4—224no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—224no—
859C2×C4—224no—
860C2×C4—4416no—
861C2×C4—444no—
862C2×C4—444no—
863C2×C4—444no—
864C2×C4—884no—
865C2×C4#6703714yes—
866C22—24no—
867C22—24no—
868C22—24no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—24no—
876C22—24no—
877C22—24no—
878C22—416no—
879C22—44no—
880C22—42no—
881C22—42no—
882C22—44no—
883C22—42no—
884C22—88no—
885C22—228no—
886C22—224no—
887C22—4416no—
888C22—442no—
889C22—442no—
890C22—444no—
891C22—444no—
892C22—442no—
893C22—442no—
894C22—444no—
895C22—442no—
896C22—888no—
897C22C2×#6693714yes—
898C22C2×#6693714yes—
899C22C2×#6693714yes—
900C22C22×#433911yescharacteristic
901C22C22×D4×D1111yescharacteristic
902C22C22×D4×D1111yescharacteristic
903C22C2×#6703712yes—
904C22#1062345312yes—
905C4—24no—
906C4—44no—
907C4—42no—
908C4—42no—
909C4—224no—
910C4—224no—
911C4—224no—
912C4—444no—
913C4—442no—
914C2—24no—
915C2—24no—
916C2—24no—
917C2—82no—
918C2—444no—
919C2—882no—
920C2C22×#6693711yescharacteristic
921C2#1308202512yes—
922C2#1308224511yescharacteristic
923C2#1308225411yescharacteristic
924C2#1308237312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#386C2
hypercenterC2×#386D11
hypocenterC11#34984
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C2×#10623335C2semidirect
3. C2×#10623335C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. #13076944C2semidirect
6. #13076897C2semidirect
7. #13074364C2semidirect
8. #13074356C2semidirect
9. #13072169C2semidirect
10. #13072167C2semidirect
11. #13072154C2semidirect
12. #13072152C2semidirect
13. #13071228C2semidirect
14. C2×#10622826C2semidirect
15. C2×C11×#386C2semidirect
20. C23×C4×D11C22semidirect
22. C22×C11×C22⋊C4C22semidirect
23. C2×#67006C22semidirect
24. C2×#67006C22semidirect
32. C2×#66990C22semidirect
33. C2×#66990C22semidirect
34. C2×#66988C22semidirect
35. C2×#66988C22semidirect
37. C2×#66982C22semidirect
38. C2×#66982C22semidirect
40. C2×C4×C22⋊D11C22semidirect
41. C2×C4×C22⋊D11C22semidirect
42. C22×(C2×D11)⋊C4C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. C22×C4×Dic11C22semidirect
47. C2×#66939C22semidirect
48. C2×#66939C22semidirect
49. C2×#66937C22semidirect
50. C2×#66935C22semidirect
51. C2×#66935C22semidirect
52. C11×#386C22semidirect
53. C11×#386C22semidirect
54. C11×#386C22semidirect
55. C2×C11×#95C22semidirect
56. #10622826C22semidirect
57. #10622826C22semidirect
58. #10622826C22semidirect
59. #10622823C22semidirect
60. C2×C11⋊#95C22semidirect
61. #10622573C22semidirect
62. #10622572C22semidirect
63. #10622572C22semidirect
64. #10622570C22semidirect
65. #10622569C22semidirect
66. #10622564C22semidirect
67. #10622561C22semidirect
68. #10622559C22semidirect
69. #10622555C22semidirect
70. #10622555C22semidirect
71. #10622289C22semidirect
72. #10622288C22semidirect
73. #10622285C22semidirect
74. #10622282C22semidirect
75. #10622280C22semidirect
76. #10622278C22semidirect
77. #10622270C22semidirect
78. #10622260C22semidirect
101. C22×C22⋊D11D4semidirect
127. C2×C22⋊Dic11D4semidirect
320. C2×#386D11semidirect
341. C23×C11#121semidirect
453. C22×C22⋊C4C2×D11semidirect
472. #386C2×D11semidirect
473. #386C2×D11semidirect
474. #386C2×D11semidirect
481. C2×#95C2×D11semidirect
767. C11#34984semidirect
808. C23#66937semidirect

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106233352
C22×C4×C22⋊D112
#130769442
#130768972
#130743642
#130743562
#130721692
#130721672
#130721542
#130721522
#130712282
C2×#106228262
C2×C11×#3862
#3498411