Finite Group Databasebeta

← #14926303

Subgroups — #14926303

Order 2816.

7786 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic, complemented
2C2×#10623184C211yesmaximal, characteristic, complemented
3C2×#10623120C211yesmaximal, characteristic, complemented
4C2×D11×#120C211yesmaximal, characteristic, complemented
5#13076909C211yesmaximal, characteristic, complemented
6#13076905C211yesmaximal, characteristic, complemented
7#13076894C211yesmaximal, characteristic, complemented
8#13076892C211yesmaximal, characteristic, complemented
9#13074331C211yesmaximal, characteristic, complemented
10#13074330C211yesmaximal, characteristic, complemented
11#13074328C211yesmaximal, characteristic, complemented
12#13071985C214yesmaximal, complemented
13#13071983C214yesmaximal, complemented
14#13071938C214yesmaximal, complemented
15#13071925C214yesmaximal, complemented
16#13071193C211yesmaximal, characteristic, complemented
17#13071192C211yesmaximal, characteristic, complemented
18D11×#379C211yesmaximal, characteristic, complemented
19C11×#2613C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic
21C25×D11C2211yescharacteristic, complemented
22C23×D4×C11C2211yescharacteristic, complemented
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic, complemented
25C22×D4×D11—28no—
26C22×D4×D11—28no—
27C22×D4×D11—28no—
28C22×D4×D11C2214yes—
29C22×D4×D11C2214yescomplemented
30C22×D4×D11C2212yescomplemented
31C22×D4×D11C2211yescharacteristic, complemented
32C23×D44C2211yescharacteristic
33C23×C4×D11C2211yescharacteristic, complemented
34C2×C11×#123C2211yescharacteristic, complemented
35C2×C11×#120C2211yescharacteristic, complemented
36C2×C11×#120C2211yescharacteristic, complemented
37C2×#67006C2211yescharacteristic, complemented
38C2×#67006C2211yescharacteristic, complemented
39C2×#66991C2212yescomplemented
40C2×#66990C2211yescharacteristic
41C2×#66990C2212yescomplemented
42C2×#66990C2214yescomplemented
43C2×#66990C2211yescharacteristic, complemented
44C2×#66990C2212yescomplemented
45C2×#66988C2211yescharacteristic, complemented
46C2×#66982C2211yescharacteristic, complemented
47#10623184—28no—
48#10623120—28no—
49D11×#120—28no—
50C2×#66948C2212yescomplemented
51C2×#66947C2212yescomplemented
52C2×#66939C2211yescharacteristic, complemented
53C2×#66937C2212yescomplemented
54C2×#66937C2212yescomplemented
55C2×#66936C2212yescomplemented
56C2×#66935C2211yescharacteristic
57C2×#66935C2212yescomplemented
58C2×#66935C2211yescharacteristic, complemented
59C2×#66935C2212yescomplemented
60C2×#66935C2214yescomplemented
61C2×C22⋊C4×D11C2212yescomplemented
62C2×C22⋊C4×D11C2211yescharacteristic, complemented
63C2×C22⋊C4×D11C2211yescharacteristic, complemented
64C2×C22⋊C4×D11C2211yescharacteristic, complemented
65C2×C22⋊C4×D11C2214yescomplemented
66C11×#394C2214yescomplemented
67C11×#392C2214yescomplemented
68C11×#381C2211yescharacteristic, complemented
69C11×#379C2211yescharacteristic, complemented
70C11×#379C2211yescharacteristic, complemented
71#10622860C2211yescharacteristic, complemented
72#10622860C2211yescharacteristic, complemented
73#10622836C2214yescomplemented
74#10622836C2214yescomplemented
75#10622835C2214yescomplemented
76#10622824C2211yescharacteristic, complemented
77#10622602C2214yescomplemented
78#10622574C2214yescomplemented
79#10622573C2214yescomplemented
80#10622572C2214yescomplemented
81#10622569C2214yescomplemented
82#10622569C2214yescomplemented
83#10622569C2214yescomplemented
84#10622568C2211yescharacteristic, complemented
85#10622568C2211yescharacteristic, complemented
86#10622568C2214yescomplemented
87#10622568C2214yescomplemented
88#10622568C2214yescomplemented
89#10622568C2211yescharacteristic, complemented
90#10622568C2211yescharacteristic, complemented
91#10622556C2211yescharacteristic, complemented
92#10622556C2211yescharacteristic, complemented
93#10622281C2214yescomplemented
94#10622278C2214yescomplemented
95#10622278C2214yescomplemented
96#10622278C2214yescomplemented
97C25×C11C2311yescharacteristic
98C25×C11C2311yescharacteristic
99C24×D11—24no—
100C24×D11—24no—
101C24×D11—24no—
102C24×D11—24no—
103C24×D11—24no—
104C24×D11—48no—
105C24×D11—48no—
106C24×D11D418yescomplemented
107C24×D11C2311yescharacteristic
108C24×D11C2314yes—
109C24×D11C2312yes—
110C24×D11C2312yes—
111C24×D11C2311yescharacteristic
112C24×D11C2311yescharacteristic
113C24×D11C2311yescharacteristic, complemented
114C22×D4×C11—24no—
115C22×D4×C11—24no—
116C22×D4×C11—24no—
117C22×D4×C11C2311yescharacteristic
118C22×D4×C11C2314yes—
119C22×D4×C11C2312yescomplemented
120C22×D4×C11C2312yescomplemented
121C23×C4×C11C2311yescharacteristic
122C22×C22⋊D11—24no—
123C22×C22⋊D11—24no—
124C22×C22⋊D11—24no—
125C22×C22⋊D11—24no—
126C22×C22⋊D11—24no—
127C22×C22⋊D11D418yescomplemented
128C22×C22⋊D11C2311yescharacteristic
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2314yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2311yescharacteristic, complemented
134C22×C22⋊D11C2312yescomplemented
135C22×C22⋊D11C2312yescomplemented
136C22×C22⋊D11C2312yescomplemented
137C23×Dic11C2311yescharacteristic
138C2×D4×D11—2128no—
139C2×D4×D11—216no—
140C2×D4×D11—216no—
141C2×D4×D11—216no—
142C2×D4×D11—216no—
143C2×D4×D11—28no—
144C2×D4×D11—24no—
145C2×D4×D11—24no—
146C2×D4×D11—24no—
147C2×D4×D11—216no—
148C2×D4×D11—216no—
149C2×D4×D11—48no—
150C22×D44—24no—
151C22×D44—24no—
152C22×D44D418yescomplemented
153C22×D44C2312yes—
154C22×D44C2312yes—
155C22×D44C2312yes—
156C22×D44C2311yescharacteristic, complemented
157C22×D44C2312yescomplemented
158C22×C4×D11—24no—
159C22×C4×D11—24no—
160C22×C4×D11—24no—
161C22×C4×D11C2314yes—
162C22×C4×D11C2311yescharacteristic, complemented
163C22×C4×D11C2312yescomplemented
164C22×C4×D11C2312yescomplemented
165C22×C4×D11C2312yescomplemented
166C11×#123—24no—
167C11×#120—24no—
168C11×#120—24no—
169C2×C11×C4⋊C4C2312yescomplemented
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yescomplemented
174C2×C11×C22⋊C4C2312yescomplemented
175C2×C11×C22⋊C4C2312yescomplemented
176C2×C11×C22⋊C4C2314yescomplemented
177C2×C11×C22⋊C4C2314yescomplemented
178#67006—24no—
179#67006—24no—
180C2×C22⋊Dic11C2311yescharacteristic
181C2×C22⋊Dic11C2311yescharacteristic
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2312yescomplemented
184C2×C22⋊Dic11C2312yescomplemented
185C2×C22⋊Dic11C2312yescomplemented
186C2×C22⋊Dic11C2314yescomplemented
187C2×C22⋊Dic11C2314yescomplemented
188#66991—28no—
189#66990—24no—
190#66990—28no—
191#66990—24no—
192#66990—28no—
193#66990—48no—
194#66988—24no—
195#66982—24no—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2314yes—
199C2×(C2×D11)⋊C4C2314yes—
200C2×(C2×D11)⋊C4C2312yescomplemented
201C2×(C2×D11)⋊C4C2312yescomplemented
202C2×(C2×D11)⋊C4C2312yescomplemented
203C2×(C2×D11)⋊C4C2312yescomplemented
204C2×(C2×D11)⋊C4C2312yescomplemented
205C2×(C2×D11)⋊C4C2312yescomplemented
206C2×(C2×D11)⋊C4C2312yescomplemented
207C2×(C2×D11)⋊C4C2314yescomplemented
208C2×(C2×D11)⋊C4C2314yescomplemented
209C2×C4⋊Dic11C2312yescomplemented
210C2×Dic11⋊C4C2312yescomplemented
211C2×Dic11⋊C4C2312yescomplemented
212#66948—28no—
213#66947—28no—
214#66939—24no—
215#66937—28no—
216#66937—28no—
217#66936—28no—
218#66935—24no—
219#66935—28no—
220#66935—24no—
221#66935—28no—
222#66935—48no—
223C22⋊C4×D11—28no—
224C22⋊C4×D11—24no—
225C22⋊C4×D11—24no—
226C22⋊C4×D11—24no—
227C22⋊C4×D11—48no—
228C11×#95C2314yescomplemented
229C11⋊#95C2314yescomplemented
230C11⋊#95C2314yescomplemented
231C11⋊#95C2314yescomplemented
232#34980—111nomaximal, Sylow
233C24×C11—22no—
234C24×C11—22no—
235C24×C11—22no—
236C24×C11—22no—
237C24×C11—44no—
238C24×C11—44no—
239C24×C11C2×D414yes—
240C24×C11C2×D414yescomplemented
241C24×C11C2411yescharacteristic
242C24×C11C2412yes—
243C24×C11C2412yes—
244C24×C11C2411yescharacteristic
245C23×D11—22no—
246C23×D11—22no—
247C23×D11—28no—
248C23×D11—232no—
249C23×D11—22no—
250C23×D11—22no—
251C23×D11—28no—
252C23×D11—232no—
253C23×D11—28no—
254C23×D11—24no—
255C23×D11—24no—
256C23×D11—24no—
257C23×D11—24no—
258C23×D11—28no—
259C23×D11—28no—
260C23×D11—28no—
261C23×D11—22no—
262C23×D11—28no—
263C23×D11—28no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—432no—
267C23×D11—44no—
268C23×D11—44no—
269C23×D11—44no—
270C23×D11—44no—
271C23×D11—44no—
272C23×D11—44no—
273C23×D11—44no—
274C23×D11—432no—
275C23×D11—432no—
276C23×D11—432no—
277C23×D11—432no—
278C23×D11—432no—
279C23×D11C2×D414yes—
280C23×D11C2×D418yes—
281C23×D11C2×D418yes—
282C23×D11C2×D414yes—
283C23×D11C2×D414yes—
284C23×D11C2×D414yes—
285C23×D11C2×D414yescomplemented
286C23×D11C2411yescharacteristic
287C23×D11C2412yes—
288C23×D11C2411yescharacteristic
289C23×D11C2411yescharacteristic
290C23×D11C2412yes—
291C2×D4×C11—232no—
292C2×D4×C11—28no—
293C2×D4×C11—28no—
294C2×D4×C11—22no—
295C2×D4×C11—22no—
296C2×D4×C11—24no—
297C2×D4×C11—22no—
298C2×D4×C11—24no—
299C2×D4×C11—28no—
300C2×D4×C11—44no—
301C2×D4×C11—44no—
302C22×C4×C11—22no—
303C22×C4×C11—22no—
304C22×C4×C11C2×D414yescomplemented
305C22×C4×C11C2412yes—
306C22×C4×C11C2412yes—
307C22×C4×C11C2412yes—
308C22×C4×C11C2411yescharacteristic
309C22×C4×C11C2412yes—
310C2×C22⋊D11—232no—
311C2×C22⋊D11—28no—
312C2×C22⋊D11—28no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—232no—
319C2×C22⋊D11—28no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—24no—
323C2×C22⋊D11—24no—
324C2×C22⋊D11—22no—
325C2×C22⋊D11—24no—
326C2×C22⋊D11—22no—
327C2×C22⋊D11—22no—
328C2×C22⋊D11—24no—
329C2×C22⋊D11—28no—
330C2×C22⋊D11—44no—
331C2×C22⋊D11—44no—
332C2×C22⋊D11—44no—
333C2×C22⋊D11C2×D418yes—
334C2×C22⋊D11C2×D418yescomplemented
335C22×Dic11—22no—
336C22×Dic11—22no—
337C22×Dic11C2×D414yescomplemented
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340C22×Dic11C2412yes—
341C22×Dic11C2411yescharacteristic
342C22×Dic11C2412yes—
343D4×D11—2128no—
344D4×D11—2128no—
345D4×D11—432no—
346D4×D11—416no—
347C2×D44—232no—
348C2×D44—24no—
349C2×D44—24no—
350C2×D44—24no—
351C2×D44—24no—
352C2×D44—24no—
353C2×D44—22no—
354C2×D44—22no—
355C2×D44—22no—
356C2×D44—24no—
357C2×D44—28no—
358C2×D44—44no—
359C2×D44C2×D418yes—
360C2×D44C2×D418yescomplemented
361C2×C4×D11—232no—
362C2×C4×D11—28no—
363C2×C4×D11—28no—
364C2×C4×D11—24no—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—22no—
368C2×C4×D11—24no—
369C2×C4×D11—24no—
370C2×C4×D11—28no—
371C2×C4×D11—44no—
372C2×C4×D11—44no—
373C2×C4×D11—44no—
374C11×C4⋊C4—24no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—24no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—24no—
380C11×C22⋊C4—24no—
381C11×C22⋊C4—44no—
382C11×C22⋊C4—44no—
383C22⋊Dic11—24no—
384C22⋊Dic11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—24no—
388C22⋊Dic11—24no—
389C22⋊Dic11—44no—
390C22⋊Dic11—44no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—24no—
394(C2×D11)⋊C4—24no—
395(C2×D11)⋊C4—24no—
396(C2×D11)⋊C4—24no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—28no—
400(C2×D11)⋊C4—28no—
401(C2×D11)⋊C4—24no—
402(C2×D11)⋊C4—44no—
403(C2×D11)⋊C4—44no—
404C4⋊Dic11—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—24no—
407C24×D4—111no—
408C2×#534—111no—
409C2×#534—111no—
410C22×#120—111no—
411#2849—111no—
412#2849—111no—
413#2846—111no—
414#2846—111no—
415#2613—111no—
416#2613—111no—
417#2613—111no—
418#2613D1111yescharacteristic, complemented
419#2410—114no—
420#2410—114no—
421#2405—114no—
422#2403—114no—
423#2308—111no—
424#2308—111no—
425C2×#379—111no—
426C23×C11—24no—
427C23×C11—28no—
428C23×C11—28no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—24no—
434C23×C11—24no—
435C23×C11—24no—
436C23×C11—24no—
437C23×C11—21no—
438C23×C11—21no—
439C23×C11—21no—
440C23×C11—24no—
441C23×C11—48no—
442C23×C11—48no—
443C23×C11—48no—
444C23×C11—48no—
445C23×C11—48no—
446C23×C11—48no—
447C23×C11C22×D414yes—
448C23×C11C22×D414yes—
449C23×C11C22×D412yes—
450C23×C11C22×D412yes—
451C23×C11C22×D412yes—
452C23×C11C2511yescharacteristic
453C22×D11—216no—
454C22×D11—216no—
455C22×D11—28no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—24no—
459C22×D11—24no—
460C22×D11—24no—
461C22×D11—216no—
462C22×D11—232no—
463C22×D11—28no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—24no—
467C22×D11—24no—
468C22×D11—216no—
469C22×D11—216no—
470C22×D11—216no—
471C22×D11—216no—
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—21no—
475C22×D11—24no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—48no—
481C22×D11—48no—
482C22×D11—416no—
483C22×D11—416no—
484C22×D11—416no—
485C22×D11—416no—
486C22×D11—416no—
487C22×D11—416no—
488C22×D11—416no—
489C22×D11—416no—
490C22×D11—4128no—
491C22×D11—4128no—
492C22×D11—416no—
493C22×D11—48no—
494C22×D11—48no—
495C22×D11—48no—
496C22×D11—416no—
497C22×D11—44no—
498C22×D11—84no—
499C22×D11—84no—
500C22×D11#120116yescomplemented
501C22×D11C22×D414yes—
502C22×D11C22×D412yes—
503C22×D11C22×D412yes—
504C22×D11C22×D412yes—
505C22×D11C22×D412yes—
506C22×D11C22×D412yes—
507C22×D11C22×D412yes—
508C22×D11C22×D414yes—
509C22×D11H(5,𝔽2)18yes—
510D4×C11—232no—
511D4×C11—48no—
512D4×C11—44no—
513D4×C11—84no—
514C2×C4×C11—28no—
515C2×C4×C11—22no—
516C2×C4×C11—22no—
517C2×C4×C11—21no—
518C2×C4×C11—22no—
519C2×C4×C11—22no—
520C2×C4×C11—21no—
521C2×C4×C11—22no—
522C2×C4×C11—21no—
523C2×C4×C11—24no—
524C2×C4×C11—24no—
525C2×C4×C11—24no—
526C2×C4×C11C22×D414yes—
527C22⋊D11—232no—
528C22⋊D11—216no—
529C22⋊D11—216no—
530C22⋊D11—48no—
531C22⋊D11—44no—
532C22⋊D11—44no—
533C22⋊D11—48no—
534C22⋊D11—84no—
535C22⋊D11—84no—
536C2×Dic11—28no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—21no—
543C2×Dic11—21no—
544C2×Dic11—22no—
545C2×Dic11—24no—
546C2×Dic11—24no—
547C2×Dic11—24no—
548C2×Dic11C22×D414yes—
549D44—216no—
550D44—216no—
551D44—44no—
552D44—48no—
553D44—84no—
554C4×D11—232no—
555C4×D11—48no—
556C4×D11—44no—
557C4×D11—84no—
558C4×D11—84no—
559C26—111no—
560C26—111no—
561C23×D4—111no—
562C23×D4—111no—
563C23×D4—114no—
564C23×D4—114no—
565C23×D4—111no—
566C23×D4—112no—
567C23×D4—111no—
568C23×D4—228no—
569C23×D4—228no—
570C23×D4—228no—
571C23×D4C2×D1111yescharacteristic, complemented
572C24×C4—111no—
573#534—228no—
574#534—228no—
575C2×#123—111no—
576C2×#123—111no—
577C2×#123—112no—
578C2×#123—111no—
579C2×#123—112no—
580C2×#123C2×D1111yescharacteristic, complemented
581C2×#121—112no—
582C2×#121—112no—
583C2×#121—112no—
584C2×#121—112no—
585C2×#120—111no—
586C2×#120—111no—
587C2×#120—111no—
588C2×#120—111no—
589C2×#120—112no—
590C2×#120—112no—
591C2×#120—114no—
592C2×#120—111no—
593C2×#120—111no—
594C2×#120—112no—
595C2×#120—112no—
596C2×#120—114no—
597C2×#120—228no—
598C2×#120C2×D1111yescharacteristic, complemented
599C2×#120C2×D1111yescharacteristic, complemented
600C22×C22⋊C4—111no—
601C22×C22⋊C4—111no—
602C22×C22⋊C4—111no—
603C22×C22⋊C4—112no—
604C22×C22⋊C4—114no—
605#394—114no—
606#394—114no—
607#394—114no—
608#394C2×D1114yescomplemented
609#392—114no—
610#392—114no—
611#392—114no—
612#392C2×D1114yescomplemented
613#386—114no—
614#386—114no—
615#386—114no—
616#386—114no—
617#386—114no—
618#386—114no—
619#385—114no—
620#385—114no—
621#381—111no—
622#381—111no—
623#381—111no—
624#381C2×D1111yescharacteristic, complemented
625#379—111no—
626#379—111no—
627#379—111no—
628#379—111no—
629#379—111no—
630#379—111no—
631#379—114no—
632#379—114no—
633#379—114no—
634#379C2×D1111yescharacteristic, complemented
635#379C2×D1111yescharacteristic, complemented
636C22×C11—24no—
637C22×C11—24no—
638C22×C11—24no—
639C22×C11—24no—
640C22×C11—24no—
641C22×C11—24no—
642C22×C11—24no—
643C22×C11—24no—
644C22×C11—24no—
645C22×C11—416no—
646C22×C11—416no—
647C22×C11—44no—
648C22×C11—44no—
649C22×C11—44no—
650C22×C11—44no—
651C22×C11—41no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—42no—
655C22×C11C2×#12014yes—
656C22×C11C23×D411yescharacteristic
657C22×C11C23×D411yescharacteristic
658C22×C11C23×D411yescharacteristic
659C22×C11C2×H(5,𝔽2)14yes—
660C2×D11—232no—
661C2×D11—24no—
662C2×D11—24no—
663C2×D11—24no—
664C2×D11—24no—
665C2×D11—28no—
666C2×D11—28no—
667C2×D11—24no—
668C2×D11—24no—
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—24no—
672C2×D11—24no—
673C2×D11—24no—
674C2×D11—416no—
675C2×D11—432no—
676C2×D11—432no—
677C2×D11—464no—
678C2×D11—416no—
679C2×D11—44no—
680C2×D11—44no—
681C2×D11—41no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—88no—
686C2×D11C2×#12014yes—
687C2×D11C2×#12014yes—
688C2×D11#53418yescomplemented
689C4×C11—24no—
690C4×C11—41no—
691C4×C11—42no—
692C4×C11—42no—
693C4×C11—42no—
694Dic11—24no—
695Dic11—41no—
696Dic11—42no—
697Dic11—42no—
698Dic11—42no—
699C25—111no—
700C25—111no—
701C25—112no—
702C25—112no—
703C25—118no—
704C25—111no—
705C25—114no—
706C25—111no—
707C25—224no—
708C25—224no—
709C25—224no—
710C25—224no—
711C25—224no—
712C25—448no—
713C25—448no—
714C25C22×D1111yescharacteristic
715C25C22×D1111yescharacteristic
716C22×D4—24no—
717C22×D4—24no—
718C22×D4—24no—
719C22×D4—118no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—111no—
725C22×D4—114no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—118no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—112no—
733C22×D4—111no—
734C22×D4—112no—
735C22×D4—224no—
736C22×D4—224no—
737C22×D4—224no—
738C22×D4—2216no—
739C22×D4—2216no—
740C22×D4—2216no—
741C22×D4—2216no—
742C22×D4—2216no—
743C22×D4—2216no—
744C22×D4—22128no—
745C22×D4—224no—
746C22×D4—228no—
747C22×D4—224no—
748C22×D4—224no—
749C22×D4—224no—
750C22×D4—224no—
751C22×D4—224no—
752C22×D4—224no—
753C22×D4—448no—
754C22×D4C22×D1111yescharacteristic
755C22×D4C22×D1114yes—
756C22×D4C22×D1112yescomplemented
757C22×D4C22×D1112yescomplemented
758C23×C4—111no—
759C23×C4—111no—
760C23×C4—114no—
761C23×C4—112no—
762C23×C4—112no—
763C23×C4—112no—
764C23×C4—224no—
765C23×C4—224no—
766C23×C4—224no—
767C23×C4C22×D1111yescharacteristic
768#123—24no—
769#123—224no—
770#123—228no—
771#123—228no—
772#123—224no—
773#123—224no—
774#121—228no—
775#121—228no—
776#121—228no—
777#121—228no—
778#120—24no—
779#120—24no—
780#120—228no—
781#120—224no—
782#120—228no—
783#120—224no—
784#120—228no—
785#120—224no—
786#120—228no—
787#120—224no—
788#120—224no—
789#120—224no—
790#120—448no—
791#120—448no—
792C2×C4⋊C4—112no—
793C2×C4⋊C4—112no—
794C2×C4⋊C4—112no—
795C2×C4⋊C4C22×D1112yescomplemented
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—114no—
808C2×C22⋊C4—114no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—114no—
814C2×C22⋊C4—114no—
815C2×C22⋊C4—114no—
816C2×C22⋊C4—114no—
817C2×C22⋊C4—224no—
818C2×C22⋊C4—228no—
819C2×C22⋊C4—224no—
820C2×C22⋊C4—224no—
821C2×C22⋊C4—448no—
822C2×C22⋊C4C22×D1111yescharacteristic
823C2×C22⋊C4C22×D1111yescharacteristic
824C2×C22⋊C4C22×D1111yescharacteristic
825C2×C22⋊C4C22×D1112yescomplemented
826C2×C22⋊C4C22×D1112yescomplemented
827C2×C22⋊C4C22×D1112yescomplemented
828C2×C22⋊C4C22×D1114yescomplemented
829C2×C22⋊C4C22×D1114yescomplemented
830#95—114no—
831#95—114no—
832#95—114no—
833#95C22×D1114yescomplemented
834C2×C11—24no—
835C2×C11—44no—
836C2×C11—44no—
837C2×C11—81no—
838C2×C11C22×#12011yescharacteristic
839C2×C11C2×#53412yes—
840C2×C11#348412yes—
841C2×C11#348412yes—
842D11—28no—
843D11—24no—
844D11—24no—
845D11—44no—
846D11—81no—
847C24—22no—
848C24—22no—
849C24—22no—
850C24—22no—
851C24—44no—
852C24—44no—
853C24—112no—
854C24—111no—
855C24—111no—
856C24—114no—
857C24—114no—
858C24—114no—
859C24—114no—
860C24—112no—
861C24—118no—
862C24—118no—
863C24—114no—
864C24—111no—
865C24—228no—
866C24—228no—
867C24—2232no—
868C24—228no—
869C24—224no—
870C24—224no—
871C24—224no—
872C24—224no—
873C24—228no—
874C24—228no—
875C24—228no—
876C24—228no—
877C24—222no—
878C24—222no—
879C24—222no—
880C24—2232no—
881C24—222no—
882C24—222no—
883C24—228no—
884C24—222no—
885C24—222no—
886C24—444no—
887C24—444no—
888C24—444no—
889C24—444no—
890C24—444no—
891C24—444no—
892C24—444no—
893C24—4432no—
894C24—4432no—
895C24—4432no—
896C24—4432no—
897C24—4432no—
898C24—4432no—
899C24D4×D1114yes—
900C24D4×D1114yescomplemented
901C24C23×D1111yescharacteristic
902C24C23×D1112yes—
903C24C23×D1112yes—
904C24C23×D1111yescharacteristic
905C2×D4—232no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—22no—
909C2×D4—24no—
910C2×D4—22no—
911C2×D4—22no—
912C2×D4—24no—
913C2×D4—28no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—118no—
917C2×D4—118no—
918C2×D4—118no—
919C2×D4—118no—
920C2×D4—2232no—
921C2×D4—224no—
922C2×D4—224no—
923C2×D4—224no—
924C2×D4—224no—
925C2×D4—224no—
926C2×D4—222no—
927C2×D4—228no—
928C2×D4—222no—
929C2×D4—222no—
930C2×D4—224no—
931C2×D4—228no—
932C2×D4—22128no—
933C2×D4—22128no—
934C2×D4—2232no—
935C2×D4—224no—
936C2×D4—224no—
937C2×D4—224no—
938C2×D4—224no—
939C2×D4—228no—
940C2×D4—2232no—
941C2×D4—228no—
942C2×D4—224no—
943C2×D4—222no—
944C2×D4—228no—
945C2×D4—222no—
946C2×D4—222no—
947C2×D4—224no—
948C2×D4—222no—
949C2×D4—222no—
950C2×D4—222no—
951C2×D4—224no—
952C2×D4—224no—
953C2×D4—444no—
954C2×D4—444no—
955C2×D4—444no—
956C2×D4—444no—
957C2×D4—4416no—
958C2×D4—4432no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—114no—
962C22×C4—112no—
963C22×C4—112no—
964C22×C4—112no—
965C22×C4—112no—
966C22×C4—111no—
967C22×C4—228no—
968C22×C4—228no—
969C22×C4—2232no—
970C22×C4—222no—
971C22×C4—224no—
972C22×C4—222no—
973C22×C4—222no—
974C22×C4—224no—
975C22×C4—224no—
976C22×C4—222no—
977C22×C4—222no—
978C22×C4—228no—
979C22×C4—444no—
980C22×C4—444no—
981C22×C4—444no—
982C22×C4D4×D1114yescomplemented
983C22×C4C23×D1112yes—
984C22×C4C23×D1112yes—
985C22×C4C23×D1112yes—
986C22×C4C23×D1111yescharacteristic
987C22×C4C23×D1112yes—
988C4⋊C4—24no—
989C4⋊C4—224no—
990C4⋊C4—224no—
991C4⋊C4—224no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—22no—
995C22⋊C4—24no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—44no—
999C22⋊C4—44no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—228no—
1007C22⋊C4—228no—
1008C22⋊C4—224no—
1009C22⋊C4—224no—
1010C22⋊C4—224no—
1011C22⋊C4—224no—
1012C22⋊C4—222no—
1013C22⋊C4—222no—
1014C22⋊C4—222no—
1015C22⋊C4—224no—
1016C22⋊C4—224no—
1017C22⋊C4—444no—
1018C22⋊C4—444no—
1019C22⋊C4—444no—
1020C22⋊C4—444no—
1021C11#3498011yescharacteristic, complemented, Sylow
1022C23—24no—
1023C23—28no—
1024C23—28no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—24no—
1030C23—24no—
1031C23—24no—
1032C23—24no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—24no—
1037C23—48no—
1038C23—48no—
1039C23—48no—
1040C23—48no—
1041C23—48no—
1042C23—48no—
1043C23—114no—
1044C23—112no—
1045C23—112no—
1046C23—112no—
1047C23—112no—
1048C23—112no—
1049C23—112no—
1050C23—118no—
1051C23—1116no—
1052C23—114no—
1053C23—2216no—
1054C23—2216no—
1055C23—2216no—
1056C23—2216no—
1057C23—2216no—
1058C23—2216no—
1059C23—2216no—
1060C23—2232no—
1061C23—228no—
1062C23—222no—
1063C23—222no—
1064C23—224no—
1065C23—224no—
1066C23—224no—
1067C23—228no—
1068C23—222no—
1069C23—222no—
1070C23—224no—
1071C23—224no—
1072C23—221no—
1073C23—221no—
1074C23—221no—
1075C23—224no—
1076C23—448no—
1077C23—448no—
1078C23—448no—
1079C23—448no—
1080C23—448no—
1081C23—448no—
1082C23—4416no—
1083C23—4416no—
1084C23—448no—
1085C23—448no—
1086C23—4416no—
1087C23—444no—
1088C23—4416no—
1089C23—4416no—
1090C23—4416no—
1091C23—4416no—
1092C23—4416no—
1093C23—4416no—
1094C23—44128no—
1095C23—44128no—
1096C23—4416no—
1097C23—448no—
1098C23—884no—
1099C23—884no—
1100C23C2×D4×D1114yes—
1101C23C2×D4×D1114yes—
1102C23C2×D4×D1112yes—
1103C23C2×D4×D1112yes—
1104C23C2×D4×D1112yes—
1105C23C24×D1111yescharacteristic
1106D4—232no—
1107D4—48no—
1108D4—44no—
1109D4—84no—
1110D4—2216no—
1111D4—2216no—
1112D4—2216no—
1113D4—2216no—
1114D4—2232no—
1115D4—448no—
1116D4—444no—
1117D4—448no—
1118D4—448no—
1119D4—444no—
1120D4—444no—
1121D4—884no—
1122D4—884no—
1123D4—884no—
1124C2×C4—28no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—24no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—114no—
1137C2×C4—2232no—
1138C2×C4—228no—
1139C2×C4—222no—
1140C2×C4—222no—
1141C2×C4—222no—
1142C2×C4—222no—
1143C2×C4—222no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—224no—
1148C2×C4—224no—
1149C2×C4—224no—
1150C2×C4—444no—
1151C2×C4—448no—
1152C2×C4—884no—
1153C2×C4—884no—
1154C2×C4C2×D4×D1114yes—
1155C22—24no—
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—24no—
1160C22—24no—
1161C22—24no—
1162C22—24no—
1163C22—24no—
1164C22—416no—
1165C22—416no—
1166C22—44no—
1167C22—44no—
1168C22—44no—
1169C22—44no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—41no—
1174C22—118no—
1175C22—114no—
1176C22—114no—
1177C22—2232no—
1178C22—224no—
1179C22—224no—
1180C22—224no—
1181C22—224no—
1182C22—228no—
1183C22—224no—
1184C22—224no—
1185C22—228no—
1186C22—224no—
1187C22—224no—
1188C22—224no—
1189C22—224no—
1190C22—224no—
1191C22—4416no—
1192C22—4416no—
1193C22—4432no—
1194C22—4432no—
1195C22—4464no—
1196C22—444no—
1197C22—444no—
1198C22—442no—
1199C22—442no—
1200C22—442no—
1201C22—441no—
1202C22—888no—
1203C22D11×#12014yes—
1204C22C22×D4×D1111yescharacteristic
1205C22C22×D4×D1111yescharacteristic
1206C22C22×D4×D1111yescharacteristic
1207C22D11×H(5,𝔽2)14yes—
1208C4—24no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C4—41no—
1213C4—224no—
1214C4—442no—
1215C4—442no—
1216C4—442no—
1217C4—441no—
1218C2—24no—
1219C2—44no—
1220C2—44no—
1221C2—81no—
1222C2—228no—
1223C2—224no—
1224C2—224no—
1225C2—444no—
1226C2—881no—
1227C2C2×D11×#12011yescharacteristic
1228C2D11×#53412yes—
1229C2#1308224812yes—
1230C2#1308225012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2613C2
hypercenter#2613D11
hypocenterC11#34980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2613

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C2×#10623184C2semidirect
3. C2×#10623120C2semidirect
4. C2×D11×#120C2semidirect
5. #13076909C2semidirect
6. #13076905C2semidirect
7. #13076894C2semidirect
8. #13076892C2semidirect
9. #13074331C2semidirect
10. #13074330C2semidirect
11. #13074328C2semidirect
12. #13071985C2semidirect
13. #13071983C2semidirect
14. #13071938C2semidirect
15. #13071925C2semidirect
16. #13071193C2semidirect
17. #13071192C2semidirect
18. D11×#379C2semidirect
19. C11×#2613C2semidirect
21. C25×D11C22semidirect
22. C23×D4×C11C22semidirect
24. C23×C22⋊D11C22semidirect
29. C22×D4×D11C22semidirect
30. C22×D4×D11C22semidirect
31. C22×D4×D11C22semidirect
33. C23×C4×D11C22semidirect
34. C2×C11×#123C22semidirect
35. C2×C11×#120C22semidirect
36. C2×C11×#120C22semidirect
37. C2×#67006C22semidirect
38. C2×#67006C22semidirect
39. C2×#66991C22semidirect
41. C2×#66990C22semidirect
42. C2×#66990C22semidirect
43. C2×#66990C22semidirect
44. C2×#66990C22semidirect
45. C2×#66988C22semidirect
46. C2×#66982C22semidirect
50. C2×#66948C22semidirect
51. C2×#66947C22semidirect
52. C2×#66939C22semidirect
53. C2×#66937C22semidirect
54. C2×#66937C22semidirect
55. C2×#66936C22semidirect
57. C2×#66935C22semidirect
58. C2×#66935C22semidirect
59. C2×#66935C22semidirect
60. C2×#66935C22semidirect
61. C2×C22⋊C4×D11C22semidirect
62. C2×C22⋊C4×D11C22semidirect
63. C2×C22⋊C4×D11C22semidirect
64. C2×C22⋊C4×D11C22semidirect
65. C2×C22⋊C4×D11C22semidirect
66. C11×#394C22semidirect
67. C11×#392C22semidirect
68. C11×#381C22semidirect
69. C11×#379C22semidirect
70. C11×#379C22semidirect
71. #10622860C22semidirect
72. #10622860C22semidirect
73. #10622836C22semidirect
74. #10622836C22semidirect
75. #10622835C22semidirect
76. #10622824C22semidirect
77. #10622602C22semidirect
78. #10622574C22semidirect
79. #10622573C22semidirect
80. #10622572C22semidirect
81. #10622569C22semidirect
82. #10622569C22semidirect
83. #10622569C22semidirect
84. #10622568C22semidirect
85. #10622568C22semidirect
86. #10622568C22semidirect
87. #10622568C22semidirect
88. #10622568C22semidirect
89. #10622568C22semidirect
90. #10622568C22semidirect
91. #10622556C22semidirect
92. #10622556C22semidirect
93. #10622281C22semidirect
94. #10622278C22semidirect
95. #10622278C22semidirect
96. #10622278C22semidirect
106. C24×D11D4semidirect
113. C24×D11C23semidirect
119. C22×D4×C11C23semidirect
120. C22×D4×C11C23semidirect
127. C22×C22⋊D11D4semidirect
133. C22×C22⋊D11C23semidirect
134. C22×C22⋊D11C23semidirect
135. C22×C22⋊D11C23semidirect
136. C22×C22⋊D11C23semidirect
152. C22×D44D4semidirect
156. C22×D44C23semidirect
157. C22×D44C23semidirect
162. C22×C4×D11C23semidirect
163. C22×C4×D11C23semidirect
164. C22×C4×D11C23semidirect
165. C22×C4×D11C23semidirect
169. C2×C11×C4⋊C4C23semidirect
173. C2×C11×C22⋊C4C23semidirect
174. C2×C11×C22⋊C4C23semidirect
175. C2×C11×C22⋊C4C23semidirect
176. C2×C11×C22⋊C4C23semidirect
177. C2×C11×C22⋊C4C23semidirect
183. C2×C22⋊Dic11C23semidirect
184. C2×C22⋊Dic11C23semidirect
185. C2×C22⋊Dic11C23semidirect
186. C2×C22⋊Dic11C23semidirect
187. C2×C22⋊Dic11C23semidirect
200. C2×(C2×D11)⋊C4C23semidirect
201. C2×(C2×D11)⋊C4C23semidirect
202. C2×(C2×D11)⋊C4C23semidirect
203. C2×(C2×D11)⋊C4C23semidirect
204. C2×(C2×D11)⋊C4C23semidirect
205. C2×(C2×D11)⋊C4C23semidirect
206. C2×(C2×D11)⋊C4C23semidirect
207. C2×(C2×D11)⋊C4C23semidirect
208. C2×(C2×D11)⋊C4C23semidirect
209. C2×C4⋊Dic11C23semidirect
210. C2×Dic11⋊C4C23semidirect
211. C2×Dic11⋊C4C23semidirect
228. C11×#95C23semidirect
229. C11⋊#95C23semidirect
230. C11⋊#95C23semidirect
231. C11⋊#95C23semidirect
240. C24×C11C2×D4semidirect
285. C23×D11C2×D4semidirect
304. C22×C4×C11C2×D4semidirect
334. C2×C22⋊D11C2×D4semidirect
337. C22×Dic11C2×D4semidirect
360. C2×D44C2×D4semidirect
418. #2613D11semidirect
500. C22×D11#120semidirect
571. C23×D4C2×D11semidirect
580. C2×#123C2×D11semidirect
598. C2×#120C2×D11semidirect
599. C2×#120C2×D11semidirect
608. #394C2×D11semidirect
612. #392C2×D11semidirect
624. #381C2×D11semidirect
634. #379C2×D11semidirect
635. #379C2×D11semidirect
688. C2×D11#534semidirect
756. C22×D4C22×D11semidirect
757. C22×D4C22×D11semidirect
795. C2×C4⋊C4C22×D11semidirect
825. C2×C22⋊C4C22×D11semidirect
826. C2×C22⋊C4C22×D11semidirect
827. C2×C22⋊C4C22×D11semidirect
828. C2×C22⋊C4C22×D11semidirect
829. C2×C22⋊C4C22×D11semidirect
833. #95C22×D11semidirect
900. C24D4×D11semidirect
982. C22×C4D4×D11semidirect
1021. C11#34980semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D112
C2×#106231842
C2×#106231202
C2×D11×#1202
#130769092
#130769052
#130768942
#130768922
#130743312
#130743302
#130743282
#130719852
#130719832
#130719382
#130719252
#130711932
#130711922
D11×#3792
C11×#26132
#3498011