Finite Group Databasebeta

← #14960699

Subgroups — #14960699

Order 2816.

4170 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623184C211yesmaximal, characteristic, complemented
2C2×D11×#120C211yesmaximal, characteristic, complemented
3#13076894C212yesmaximal, complemented
4#13075180C212yesmaximal, complemented
5#13075175C211yesmaximal, characteristic, complemented
6#13074951C211yesmaximal, characteristic, complemented
7#13074950C211yesmaximal, characteristic, complemented
8#13074949C212yesmaximal, complemented
9#13074946C212yesmaximal, complemented
10#13074945C212yesmaximal, complemented
11#13074940C212yesmaximal, complemented
12#13074939C212yesmaximal, complemented
13#13074390C212yesmaximal, complemented
14#13072000C212yesmaximal, complemented
15#13071996C212yesmaximal, complemented
16#13071938C212yesmaximal, complemented
17#13071928C212yesmaximal, complemented
18#13071195C211yesmaximal, characteristic, complemented
19C11×#2697C211yesmaximal, characteristic, complemented
20C25×D11C2211yescharacteristic, complemented
21C22×D4×D11C2212yes—
22C22×D4×D11C2211yescharacteristic
23C23×D44C2211yescharacteristic, complemented
24C2×C11×#123C2211yescharacteristic, complemented
25C2×C11×#120C2211yescharacteristic
26C2×#67006C2211yescharacteristic, complemented
27C2×#67006C2212yescomplemented
28C2×#66990C2212yes—
29C2×#66990C2211yescharacteristic
30C2×#66990C2211yescharacteristic, complemented
31C2×#66990C2212yescomplemented
32C2×#66982C2211yescharacteristic, complemented
33#10623184—28no—
34D11×#120—28no—
35C2×#66948C2212yescomplemented
36C2×#66947C2212yescomplemented
37C2×#66947C2212yescomplemented
38C2×#66945C2211yescharacteristic, complemented
39C2×#66937C2212yescomplemented
40C2×#66936C2212yescomplemented
41C2×#66935C2212yes—
42C2×#66935C2212yes—
43C2×#66935C2212yes—
44C2×#66935C2212yescomplemented
45C2×#66935C2211yescharacteristic, complemented
46C2×#66935C2211yescharacteristic, complemented
47C2×#66935C2212yescomplemented
48C2×#66935C2212yescomplemented
49C2×#66935C2212yescomplemented
50C2×#66935C2212yescomplemented
51C2×C22⋊C4×D11C2212yescomplemented
52C2×C22⋊C4×D11C2211yescharacteristic, complemented
53C2×C22⋊C4×D11C2211yescharacteristic, complemented
54C2×#66925C2211yescharacteristic, complemented
55C11×#397C2212yescomplemented
56C11×#396C2212yescomplemented
57C11×#394C2212yescomplemented
58C11×#390C2211yescharacteristic, complemented
59C11×#388C2212yescomplemented
60C11×#386C2212yescomplemented
61C11×#379C2212yescomplemented
62#10622835C2212yescomplemented
63#10622834C2211yescharacteristic, complemented
64#10622826C2212yescomplemented
65#10622607C2212yescomplemented
66#10622604C2212yescomplemented
67#10622604C2212yescomplemented
68#10622603C2212yescomplemented
69#10622602C2212yescomplemented
70#10622601C2211yescharacteristic, complemented
71#10622601C2212yescomplemented
72#10622574C2212yescomplemented
73#10622574C2212yescomplemented
74#10622574C2212yescomplemented
75#10622573C2212yescomplemented
76#10622573C2212yescomplemented
77#10622572C2212yescomplemented
78#10622572C2212yescomplemented
79#10622572C2212yescomplemented
80#10622570C2212yescomplemented
81#10622570C2212yescomplemented
82#10622570C2212yescomplemented
83#10622570C2212yescomplemented
84#10622569C2212yescomplemented
85#10622568C2212yescomplemented
86#10622568C2212yescomplemented
87#10622568C2212yescomplemented
88#10622568C2212yescomplemented
89#10622568C2212yescomplemented
90#10622568C2212yescomplemented
91#10622568C2212yescomplemented
92#10622565C2212yescomplemented
93#10622561C2212yescomplemented
94#10622557C2212yescomplemented
95#10622552C2212yescomplemented
96#10622552C2211yescharacteristic, complemented
97#10622289C2212yescomplemented
98#10622288C2212yescomplemented
99#10622287C2212yescomplemented
100#10622285C2212yescomplemented
101#10622285C2212yescomplemented
102#10622284C2212yescomplemented
103#10622284C2212yescomplemented
104#10622282C2212yescomplemented
105#10622281C2212yescomplemented
106#10622278C2212yescomplemented
107#10622278C2212yescomplemented
108#10622278C2212yescomplemented
109C25×C11C2311yescharacteristic
110C24×D11—24no—
111C24×D11—44no—
112C24×D11—42no—
113C24×D11—42no—
114C24×D11—44no—
115C24×D11C2312yes—
116C24×D11C2311yescharacteristic
117C24×D11C2312yes—
118C24×D11C2311yescharacteristic
119C24×D11C2311yescharacteristic
120C24×D11C2311yescharacteristic, complemented
121C22×D4×C11C2312yes—
122C22×D4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic, complemented
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2312yes—
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C2×D4×D11—28no—
132C2×D4×D11—42no—
133C2×D4×D11—42no—
134C2×D4×D11—44no—
135C2×D4×D11—44no—
136C2×D4×D11D418yescomplemented
137C22×D44—24no—
138C22×D44—42no—
139C22×D44—42no—
140C22×D44C2312yes—
141C22×D44C2312yes—
142C22×D44C2312yes—
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×D44C2312yescomplemented
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yescomplemented
150C11×#123—24no—
151C11×#120—24no—
152C2×C11×C4⋊C4C2312yescomplemented
153C2×C11×C4⋊C4C2311yescharacteristic, complemented
154C2×C11×C4⋊C4C2312yescomplemented
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic, complemented
164C2×C11×C22⋊C4C2312yescomplemented
165C2×C42×C11C2311yescharacteristic, complemented
166#67006—24no—
167#67006—44no—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2311yescharacteristic, complemented
174C2×C22⋊Dic11C2312yescomplemented
175#66990—24no—
176#66990—24no—
177#66990—28no—
178#66990—44no—
179#66982—24no—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yescomplemented
196C2×(C2×D11)⋊C4C2312yescomplemented
197C2×(C2×D11)⋊C4C2312yescomplemented
198C2×(C2×D11)⋊C4C2312yescomplemented
199C2×(C2×D11)⋊C4C2312yescomplemented
200C2×(C2×D11)⋊C4C2312yescomplemented
201C2×(C2×D11)⋊C4C2312yescomplemented
202C2×(C2×D11)⋊C4C2312yescomplemented
203C2×C4⋊Dic11C2312yescomplemented
204C2×C4⋊Dic11C2311yescharacteristic, complemented
205C2×Dic11⋊C4C2312yescomplemented
206C2×Dic11⋊C4C2312yescomplemented
207C2×Dic11⋊C4C2312yescomplemented
208C2×Dic11⋊C4C2312yescomplemented
209C2×C4×Dic11C2311yescharacteristic, complemented
210C2×C4×Dic11C2312yescomplemented
211#66948—28no—
212#66947—28no—
213#66947—44no—
214#66945—42no—
215#66937—28no—
216#66936—44no—
217#66935—28no—
218#66935—24no—
219#66935—24no—
220#66935—28no—
221#66935—44no—
222#66935—44no—
223#66935—44no—
224#66935—44no—
225#66935—44no—
226#66935—44no—
227C22⋊C4×D11—24no—
228C22⋊C4×D11—24no—
229C22⋊C4×D11—28no—
230#66925—42no—
231C11×#95C2312yescomplemented
232C11×#95C2312yescomplemented
233C11×#95C2312yescomplemented
234C11⋊#95C2312yescomplemented
235C11⋊#95C2312yescomplemented
236C11⋊#95C2312yescomplemented
237C11⋊#95C2312yescomplemented
238C11⋊#95C2312yescomplemented
239#36714—111nomaximal, Sylow
240C24×C11—22no—
241C24×C11—24no—
242C24×C11—42no—
243C24×C11—41no—
244C24×C11—41no—
245C24×C11C2411yescharacteristic
246C24×C11C2411yescharacteristic
247C24×C11C2412yes—
248C23×D11—24no—
249C23×D11—24no—
250C23×D11—24no—
251C23×D11—22no—
252C23×D11—22no—
253C23×D11—22no—
254C23×D11—22no—
255C23×D11—22no—
256C23×D11—24no—
257C23×D11—22no—
258C23×D11—24no—
259C23×D11—24no—
260C23×D11—24no—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—41no—
268C23×D11—42no—
269C23×D11—41no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11—41no—
275C23×D11—41no—
276C23×D11—42no—
277C23×D11—42no—
278C23×D11—42no—
279C23×D11—42no—
280C23×D11—432no—
281C23×D11—416no—
282C23×D11—416no—
283C23×D11—432no—
284C23×D11—416no—
285C23×D11C2×D414yes—
286C23×D11C2×D414yes—
287C23×D11C2412yes—
288C23×D11C2411yescharacteristic
289C23×D11C2411yescharacteristic
290C23×D11C2412yes—
291C23×D11C2411yescharacteristic
292C2×D4×C11—24no—
293C2×D4×C11—24no—
294C2×D4×C11—41no—
295C2×D4×C11—41no—
296C2×D4×C11—42no—
297C2×D4×C11C2×D414yes—
298C22×C4×C11—22no—
299C22×C4×C11—41no—
300C22×C4×C11—41no—
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2412yes—
304C22×C4×C11C2412yes—
305C22×C4×C11C2412yes—
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—41no—
316C2×C22⋊D11—41no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—41no—
319C2×C22⋊D11—41no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C2×C22⋊D11—42no—
325C2×C22⋊D11—42no—
326C2×C22⋊D11C2×D414yes—
327C2×C22⋊D11C2×D414yes—
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2412yes—
332C22×Dic11C2411yescharacteristic
333D4×D11—416no—
334D4×D11—432no—
335C2×D44—24no—
336C2×D44—24no—
337C2×D44—24no—
338C2×D44—24no—
339C2×D44—24no—
340C2×D44—24no—
341C2×D44—24no—
342C2×D44—24no—
343C2×D44—24no—
344C2×D44—42no—
345C2×D44—42no—
346C2×D44—41no—
347C2×D44—41no—
348C2×D44—42no—
349C2×D44—42no—
350C2×D44—42no—
351C2×D44—42no—
352C2×D44—42no—
353C2×D44—42no—
354C2×D44—42no—
355C2×D44—416no—
356C2×D44C2×D414yes—
357C2×C4×D11—24no—
358C2×C4×D11—24no—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—42no—
362C2×C4×D11—42no—
363C2×C4×D11—42no—
364C2×C4×D11—42no—
365C2×C4×D11C2×D414yes—
366C11×C4⋊C4—24no—
367C11×C4⋊C4—41no—
368C11×C4⋊C4—42no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—24no—
372C11×C22⋊C4—24no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—42no—
375C11×C22⋊C4—42no—
376C11×C22⋊C4—42no—
377C11×C22⋊C4—42no—
378C11×C22⋊C4—42no—
379C42×C11—41no—
380C22⋊Dic11—24no—
381C22⋊Dic11—22no—
382C22⋊Dic11—22no—
383C22⋊Dic11—24no—
384C22⋊Dic11—42no—
385C22⋊Dic11—42no—
386C22⋊Dic11—42no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
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—42no—
399(C2×D11)⋊C4—42no—
400(C2×D11)⋊C4—42no—
401(C2×D11)⋊C4—42no—
402(C2×D11)⋊C4—42no—
403(C2×D11)⋊C4—42no—
404(C2×D11)⋊C4—42no—
405(C2×D11)⋊C4—42no—
406(C2×D11)⋊C4—42no—
407(C2×D11)⋊C4—42no—
408(C2×D11)⋊C4—42no—
409(C2×D11)⋊C4—42no—
410C4⋊Dic11—42no—
411C4⋊Dic11—41no—
412Dic11⋊C4—24no—
413Dic11⋊C4—42no—
414Dic11⋊C4—42no—
415Dic11⋊C4—42no—
416C4×Dic11—41no—
417C4×Dic11—42no—
418C2×#534—111no—
419C22×#120—111no—
420#2846—112no—
421#2697—112no—
422#2697—111no—
423#2697D1111yescharacteristic, complemented
424#2679—112no—
425#2679—111no—
426#2679—111no—
427#2678—112no—
428#2678—112no—
429#2678—112no—
430#2678—112no—
431#2622—112no—
432#2411—112no—
433#2411—112no—
434#2405—112no—
435#2403—112no—
436#2309—111no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—22no—
451C23×C11—48no—
452C23×C11—44no—
453C23×C11—44no—
454C23×C11—48no—
455C23×C11—44no—
456C23×C11C22×D412yes—
457C23×C11C22×D412yes—
458C23×C11H(5,𝔽2)14yes—
459C23×C11C2511yescharacteristic
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—216no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—21no—
473C22×D11—21no—
474C22×D11—22no—
475C22×D11—21no—
476C22×D11—21no—
477C22×D11—28no—
478C22×D11—28no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—48no—
487C22×D11—48no—
488C22×D11—48no—
489C22×D11—48no—
490C22×D11—44no—
491C22×D11—48no—
492C22×D11—48no—
493C22×D11—48no—
494C22×D11—48no—
495C22×D11—48no—
496C22×D11—48no—
497C22×D11—48no—
498C22×D11—48no—
499C22×D11—44no—
500C22×D11—44no—
501C22×D11—48no—
502C22×D11—48no—
503C22×D11—48no—
504C22×D11—44no—
505C22×D11—48no—
506C22×D11—4128no—
507C22×D11—48no—
508C22×D11—44no—
509C22×D11—48no—
510C22×D11—44no—
511C22×D11—84no—
512C22×D11—82no—
513C22×D11—82no—
514C22×D11—84no—
515C22×D11—82no—
516C22×D11—84no—
517C22×D11—82no—
518C22×D11C22×D412yes—
519C22×D11C22×D412yes—
520C22×D11C22×D412yes—
521C22×D11H(5,𝔽2)14yes—
522C22×D11H(5,𝔽2)12yes—
523C22×D11H(5,𝔽2)12yes—
524D4×C11—44no—
525D4×C11—48no—
526C2×C4×C11—21no—
527C2×C4×C11—21no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—22no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—22no—
538C2×C4×C11—22no—
539C2×C4×C11—22no—
540C2×C4×C11—22no—
541C2×C4×C11—22no—
542C2×C4×C11—22no—
543C2×C4×C11—44no—
544C2×C4×C11C22×D412yes—
545C22⋊D11—44no—
546C22⋊D11—44no—
547C22⋊D11—48no—
548C22⋊D11—48no—
549C22⋊D11—84no—
550C22⋊D11—84no—
551C22⋊D11—84no—
552C2×Dic11—21no—
553C2×Dic11—21no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—22no—
558C2×Dic11—22no—
559C2×Dic11—22no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11C22×D412yes—
567D44—44no—
568D44—48no—
569D44—48no—
570D44—48no—
571D44—84no—
572D44—84no—
573D44—84no—
574C4×D11—28no—
575C4×D11—48no—
576C4×D11—84no—
577C26—111no—
578C23×D4—111no—
579C23×D4—112no—
580C23×D4—111no—
581#534—228no—
582C2×#123—111no—
583C2×#123—112no—
584C2×#123—112no—
585C2×#123—112no—
586C2×#123C2×D1111yescharacteristic, complemented
587C2×#121—112no—
588C2×#121—112no—
589C2×#120—111no—
590C2×#120—112no—
591C2×#120—111no—
592C2×#120—111no—
593C2×#120—112no—
594C2×#120—112no—
595C2×#120—112no—
596C2×#120—111no—
597C2×#120—112no—
598C2×#120—112no—
599C2×#120—112no—
600C2×#120—112no—
601C2×#120—112no—
602C2×#120—112no—
603C2×#120—111no—
604C2×#120—112no—
605C2×#120—228no—
606C2×#120C2×D1111yescharacteristic
607C2×#117—111no—
608C2×#117—111no—
609C22×C22⋊C4—111no—
610C22×C22⋊C4—112no—
611C22×C22⋊C4—111no—
612#397—112no—
613#397—112no—
614#397—112no—
615#397C2×D1112yescomplemented
616#396—112no—
617#396—112no—
618#396—112no—
619#396C2×D1112yescomplemented
620#394—112no—
621#394—112no—
622#394—112no—
623#394—112no—
624#394—112no—
625#394—112no—
626#394—112no—
627#394—112no—
628#394—112no—
629#394—112no—
630#394—112no—
631#394C2×D1112yescomplemented
632#392—112no—
633#392—112no—
634#392—112no—
635#392—112no—
636#390—111no—
637#390—111no—
638#390—112no—
639#390—112no—
640#390—112no—
641#390—112no—
642#390—112no—
643#390—111no—
644#390—112no—
645#390C2×D1111yescharacteristic, complemented
646#388—112no—
647#388—112no—
648#388—112no—
649#388C2×D1112yescomplemented
650#386—112no—
651#386—112no—
652#386—112no—
653#386—112no—
654#386—112no—
655#386C2×D1112yescomplemented
656#385—112no—
657#385—112no—
658#379—112no—
659#379—112no—
660#379—112no—
661#379—112no—
662#379—112no—
663#379—112no—
664#379—112no—
665#379C2×D1112yescomplemented
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—24no—
669C22×C11—24no—
670C22×C11—24no—
671C22×C11—24no—
672C22×C11—24no—
673C22×C11—416no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—41no—
679C22×C11—42no—
680C22×C11—41no—
681C22×C11—42no—
682C22×C11—41no—
683C22×C11—41no—
684C22×C11C23×D411yescharacteristic
685C22×C11C2×H(5,𝔽2)12yes—
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11C2×H(5,𝔽2)12yes—
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C2×D11—24no—
696C2×D11—24no—
697C2×D11—24no—
698C2×D11—24no—
699C2×D11—24no—
700C2×D11—432no—
701C2×D11—416no—
702C2×D11—432no—
703C2×D11—416no—
704C2×D11—42no—
705C2×D11—42no—
706C2×D11—42no—
707C2×D11—42no—
708C2×D11—41no—
709C2×D11—42no—
710C2×D11—41no—
711C2×D11—42no—
712C2×D11—41no—
713C2×D11—41no—
714C2×D11—42no—
715C2×D11—42no—
716C2×D11—42no—
717C2×D11—42no—
718C2×D11—42no—
719C2×D11—42no—
720C2×D11—42no—
721C2×D11—88no—
722C2×D11—88no—
723C2×D11#53414yes—
724C4×C11—22no—
725C4×C11—42no—
726C4×C11—42no—
727C4×C11—42no—
728C4×C11—42no—
729C4×C11—42no—
730Dic11—22no—
731Dic11—42no—
732Dic11—42no—
733Dic11—42no—
734Dic11—42no—
735C25—111no—
736C25—111no—
737C25—112no—
738C25—112no—
739C25—111no—
740C25—111no—
741C25—224no—
742C25—444no—
743C25—442no—
744C25—444no—
745C25—442no—
746C25C22×D1111yescharacteristic
747C22×D4—111no—
748C22×D4—111no—
749C22×D4—118no—
750C22×D4—112no—
751C22×D4—112no—
752C22×D4—112no—
753C22×D4—112no—
754C22×D4—112no—
755C22×D4—111no—
756C22×D4—112no—
757C22×D4—112no—
758C22×D4—112no—
759C22×D4—112no—
760C22×D4—112no—
761C22×D4—112no—
762C22×D4—224no—
763C22×D4—228no—
764C22×D4—442no—
765C22×D4—442no—
766C22×D4—442no—
767C22×D4—442no—
768C22×D4—444no—
769C22×D4—444no—
770C22×D4C22×D1112yes—
771C22×D4C22×D1111yescharacteristic
772C23×C4—111no—
773C23×C4—112no—
774C23×C4—112no—
775C23×C4C22×D1111yescharacteristic, complemented
776#123—24no—
777#123—228no—
778#123—224no—
779#123—444no—
780#123—444no—
781#121—228no—
782#121—228no—
783#120—24no—
784#120—224no—
785#120—228no—
786#120—224no—
787#120—228no—
788#120—228no—
789#120—224no—
790#120—224no—
791#120—224no—
792#120—444no—
793#120—444no—
794#120—444no—
795#120—444no—
796#120—444no—
797#120—444no—
798#120—444no—
799#120—444no—
800#117—442no—
801#117—442no—
802C2×C4⋊C4—112no—
803C2×C4⋊C4—112no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—112no—
806C2×C4⋊C4—112no—
807C2×C4⋊C4—112no—
808C2×C4⋊C4C22×D1112yescomplemented
809C2×C4⋊C4C22×D1111yescharacteristic, complemented
810C2×C4⋊C4C22×D1112yescomplemented
811C2×C22⋊C4—112no—
812C2×C22⋊C4—111no—
813C2×C22⋊C4—111no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—112no—
821C2×C22⋊C4—112no—
822C2×C22⋊C4—112no—
823C2×C22⋊C4—112no—
824C2×C22⋊C4—112no—
825C2×C22⋊C4—112no—
826C2×C22⋊C4—112no—
827C2×C22⋊C4—112no—
828C2×C22⋊C4—112no—
829C2×C22⋊C4—112no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
838C2×C22⋊C4—112no—
839C2×C22⋊C4—112no—
840C2×C22⋊C4—112no—
841C2×C22⋊C4—228no—
842C2×C22⋊C4—224no—
843C2×C22⋊C4—224no—
844C2×C22⋊C4C22×D1112yes—
845C2×C22⋊C4C22×D1111yescharacteristic
846C2×C22⋊C4C22×D1112yes—
847C2×C22⋊C4C22×D1112yes—
848C2×C22⋊C4C22×D1112yes—
849C2×C22⋊C4C22×D1112yes—
850C2×C22⋊C4C22×D1112yes—
851C2×C22⋊C4C22×D1112yes—
852C2×C22⋊C4C22×D1111yescharacteristic, complemented
853C2×C22⋊C4C22×D1112yescomplemented
854C2×C42—112no—
855C2×C42—111no—
856C2×C42C22×D1111yescharacteristic, complemented
857#95—112no—
858#95—112no—
859#95—112no—
860#95—112no—
861#95—112no—
862#95C22×D1112yescomplemented
863#95C22×D1112yescomplemented
864#95C22×D1112yescomplemented
865C2×C11—42no—
866C2×C11—44no—
867C2×C11—42no—
868C2×C11C2×#53411yescharacteristic
869C2×C11#348412yes—
870C2×C11#353212yes—
871C2×C11#353211yescharacteristic
872C2×C11#353211yescharacteristic
873D11—24no—
874D11—42no—
875D11—44no—
876D11—42no—
877D11—82no—
878C24—22no—
879C24—24no—
880C24—42no—
881C24—41no—
882C24—41no—
883C24—111no—
884C24—111no—
885C24—112no—
886C24—111no—
887C24—114no—
888C24—114no—
889C24—112no—
890C24—224no—
891C24—222no—
892C24—222no—
893C24—224no—
894C24—222no—
895C24—222no—
896C24—224no—
897C24—224no—
898C24—224no—
899C24—224no—
900C24—224no—
901C24—224no—
902C24—222no—
903C24—224no—
904C24—222no—
905C24—442no—
906C24—442no—
907C24—442no—
908C24—442no—
909C24—442no—
910C24—442no—
911C24—442no—
912C24—442no—
913C24—442no—
914C24—441no—
915C24—441no—
916C24—442no—
917C24—442no—
918C24—441no—
919C24—441no—
920C24—442no—
921C24—442no—
922C24—4432no—
923C24—4416no—
924C24—4416no—
925C24—4432no—
926C24—4416no—
927C24C23×D1111yescharacteristic
928C24C23×D1111yescharacteristic
929C24C23×D1112yes—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—41no—
933C2×D4—41no—
934C2×D4—42no—
935C2×D4—114no—
936C2×D4—114no—
937C2×D4—114no—
938C2×D4—224no—
939C2×D4—224no—
940C2×D4—224no—
941C2×D4—224no—
942C2×D4—224no—
943C2×D4—224no—
944C2×D4—224no—
945C2×D4—224no—
946C2×D4—224no—
947C2×D4—224no—
948C2×D4—224no—
949C2×D4—224no—
950C2×D4—224no—
951C2×D4—224no—
952C2×D4—224no—
953C2×D4—224no—
954C2×D4—441no—
955C2×D4—441no—
956C2×D4—442no—
957C2×D4—442no—
958C2×D4—442no—
959C2×D4—442no—
960C2×D4—442no—
961C2×D4—442no—
962C2×D4—442no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—4416no—
966C2×D4—4416no—
967C2×D4—441no—
968C2×D4—441no—
969C2×D4—441no—
970C2×D4—441no—
971C2×D4—442no—
972C2×D4—442no—
973C2×D4—442no—
974C2×D4—442no—
975C2×D4—442no—
976C2×D4—442no—
977C2×D4—442no—
978C2×D4—442no—
979C2×D4—4432no—
980C2×D4D4×D1114yes—
981C22×C4—22no—
982C22×C4—41no—
983C22×C4—41no—
984C22×C4—111no—
985C22×C4—114no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—222no—
991C22×C4—222no—
992C22×C4—224no—
993C22×C4—224no—
994C22×C4—442no—
995C22×C4—442no—
996C22×C4—442no—
997C22×C4—442no—
998C22×C4C23×D1112yes—
999C22×C4C23×D1112yes—
1000C22×C4C23×D1112yes—
1001C22×C4C23×D1112yes—
1002C22×C4C23×D1112yes—
1003C22×C4C23×D1111yescharacteristic
1004C4⋊C4—24no—
1005C4⋊C4—41no—
1006C4⋊C4—42no—
1007C4⋊C4—224no—
1008C4⋊C4—442no—
1009C4⋊C4—441no—
1010C4⋊C4—442no—
1011C4⋊C4—442no—
1012C4⋊C4—442no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—24no—
1016C22⋊C4—24no—
1017C22⋊C4—24no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—224no—
1024C22⋊C4—224no—
1025C22⋊C4—224no—
1026C22⋊C4—224no—
1027C22⋊C4—224no—
1028C22⋊C4—224no—
1029C22⋊C4—224no—
1030C22⋊C4—224no—
1031C22⋊C4—224no—
1032C22⋊C4—224no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—224no—
1036C22⋊C4—224no—
1037C22⋊C4—224no—
1038C22⋊C4—442no—
1039C22⋊C4—442no—
1040C22⋊C4—442no—
1041C22⋊C4—442no—
1042C22⋊C4—442no—
1043C22⋊C4—442no—
1044C22⋊C4—442no—
1045C22⋊C4—442no—
1046C22⋊C4—442no—
1047C22⋊C4—442no—
1048C22⋊C4—442no—
1049C22⋊C4—442no—
1050C22⋊C4—442no—
1051C22⋊C4—442no—
1052C22⋊C4—442no—
1053C42—41no—
1054C42—441no—
1055C42—442no—
1056C11#3671411yescharacteristic, complemented, Sylow
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—22no—
1071C23—48no—
1072C23—44no—
1073C23—44no—
1074C23—48no—
1075C23—44no—
1076C23—112no—
1077C23—112no—
1078C23—112no—
1079C23—112no—
1080C23—112no—
1081C23—114no—
1082C23—228no—
1083C23—228no—
1084C23—2216no—
1085C23—222no—
1086C23—222no—
1087C23—222no—
1088C23—222no—
1089C23—222no—
1090C23—222no—
1091C23—222no—
1092C23—222no—
1093C23—222no—
1094C23—222no—
1095C23—222no—
1096C23—222no—
1097C23—221no—
1098C23—221no—
1099C23—221no—
1100C23—221no—
1101C23—222no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—448no—
1109C23—448no—
1110C23—448no—
1111C23—448no—
1112C23—448no—
1113C23—448no—
1114C23—448no—
1115C23—444no—
1116C23—448no—
1117C23—444no—
1118C23—448no—
1119C23—448no—
1120C23—448no—
1121C23—448no—
1122C23—444no—
1123C23—448no—
1124C23—448no—
1125C23—448no—
1126C23—448no—
1127C23—444no—
1128C23—448no—
1129C23—444no—
1130C23—44128no—
1131C23—448no—
1132C23—444no—
1133C23—884no—
1134C23—884no—
1135C23—882no—
1136C23—882no—
1137C23—884no—
1138C23—882no—
1139C23—882no—
1140C23C2×D4×D1112yes—
1141C23C2×D4×D1112yes—
1142C23#6704214yes—
1143C23C24×D1111yescharacteristic
1144D4—44no—
1145D4—48no—
1146D4—444no—
1147D4—448no—
1148D4—448no—
1149D4—448no—
1150D4—444no—
1151D4—444no—
1152D4—448no—
1153D4—448no—
1154D4—884no—
1155D4—884no—
1156D4—884no—
1157D4—884no—
1158D4—884no—
1159D4—884no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—44no—
1178C2×C4—112no—
1179C2×C4—228no—
1180C2×C4—221no—
1181C2×C4—221no—
1182C2×C4—222no—
1183C2×C4—222no—
1184C2×C4—222no—
1185C2×C4—222no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—222no—
1190C2×C4—222no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—448no—
1195C2×C4—884no—
1196C2×C4C2×D4×D1112yes—
1197C22—22no—
1198C22—22no—
1199C22—24no—
1200C22—24no—
1201C22—24no—
1202C22—24no—
1203C22—24no—
1204C22—416no—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—41no—
1211C22—42no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—114no—
1216C22—224no—
1217C22—224no—
1218C22—222no—
1219C22—222no—
1220C22—222no—
1221C22—222no—
1222C22—224no—
1223C22—224no—
1224C22—224no—
1225C22—224no—
1226C22—224no—
1227C22—4416no—
1228C22—4432no—
1229C22—4416no—
1230C22—4432no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—442no—
1235C22—442no—
1236C22—441no—
1237C22—441no—
1238C22—441no—
1239C22—442no—
1240C22—441no—
1241C22—442no—
1242C22—442no—
1243C22—442no—
1244C22—442no—
1245C22—442no—
1246C22—442no—
1247C22—442no—
1248C22—888no—
1249C22—888no—
1250C22C22×D4×D1111yescharacteristic
1251C22C2×#6704212yes—
1252C22D11×H(5,𝔽2)11yescharacteristic
1253C22D11×H(5,𝔽2)11yescharacteristic
1254C22D11×H(5,𝔽2)12yes—
1255C4—22no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—42no—
1260C4—42no—
1261C4—222no—
1262C4—442no—
1263C4—442no—
1264C4—442no—
1265C4—442no—
1266C2—42no—
1267C2—44no—
1268C2—42no—
1269C2—224no—
1270C2—442no—
1271C2—444no—
1272C2—442no—
1273C2—882no—
1274C2D11×#53411yescharacteristic
1275C2#1308224612yes—
1276C2#1308276712yes—
1277C2#1308276911yescharacteristic
1278C2#1308277211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2697C2
hypercenter#2697D11
hypocenterC11#36714
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2697

Complements

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

NH ≅ G/Ntype
1. C2×#10623184C2semidirect
2. C2×D11×#120C2semidirect
3. #13076894C2semidirect
4. #13075180C2semidirect
5. #13075175C2semidirect
6. #13074951C2semidirect
7. #13074950C2semidirect
8. #13074949C2semidirect
9. #13074946C2semidirect
10. #13074945C2semidirect
11. #13074940C2semidirect
12. #13074939C2semidirect
13. #13074390C2semidirect
14. #13072000C2semidirect
15. #13071996C2semidirect
16. #13071938C2semidirect
17. #13071928C2semidirect
18. #13071195C2semidirect
19. C11×#2697C2semidirect
20. C25×D11C22semidirect
23. C23×D44C22semidirect
24. C2×C11×#123C22semidirect
26. C2×#67006C22semidirect
27. C2×#67006C22semidirect
30. C2×#66990C22semidirect
31. C2×#66990C22semidirect
32. C2×#66982C22semidirect
35. C2×#66948C22semidirect
36. C2×#66947C22semidirect
37. C2×#66947C22semidirect
38. C2×#66945C22semidirect
39. C2×#66937C22semidirect
40. C2×#66936C22semidirect
44. C2×#66935C22semidirect
45. C2×#66935C22semidirect
46. C2×#66935C22semidirect
47. C2×#66935C22semidirect
48. C2×#66935C22semidirect
49. C2×#66935C22semidirect
50. C2×#66935C22semidirect
51. C2×C22⋊C4×D11C22semidirect
52. C2×C22⋊C4×D11C22semidirect
53. C2×C22⋊C4×D11C22semidirect
54. C2×#66925C22semidirect
55. C11×#397C22semidirect
56. C11×#396C22semidirect
57. C11×#394C22semidirect
58. C11×#390C22semidirect
59. C11×#388C22semidirect
60. C11×#386C22semidirect
61. C11×#379C22semidirect
62. #10622835C22semidirect
63. #10622834C22semidirect
64. #10622826C22semidirect
65. #10622607C22semidirect
66. #10622604C22semidirect
67. #10622604C22semidirect
68. #10622603C22semidirect
69. #10622602C22semidirect
70. #10622601C22semidirect
71. #10622601C22semidirect
72. #10622574C22semidirect
73. #10622574C22semidirect
74. #10622574C22semidirect
75. #10622573C22semidirect
76. #10622573C22semidirect
77. #10622572C22semidirect
78. #10622572C22semidirect
79. #10622572C22semidirect
80. #10622570C22semidirect
81. #10622570C22semidirect
82. #10622570C22semidirect
83. #10622570C22semidirect
84. #10622569C22semidirect
85. #10622568C22semidirect
86. #10622568C22semidirect
87. #10622568C22semidirect
88. #10622568C22semidirect
89. #10622568C22semidirect
90. #10622568C22semidirect
91. #10622568C22semidirect
92. #10622565C22semidirect
93. #10622561C22semidirect
94. #10622557C22semidirect
95. #10622552C22semidirect
96. #10622552C22semidirect
97. #10622289C22semidirect
98. #10622288C22semidirect
99. #10622287C22semidirect
100. #10622285C22semidirect
101. #10622285C22semidirect
102. #10622284C22semidirect
103. #10622284C22semidirect
104. #10622282C22semidirect
105. #10622281C22semidirect
106. #10622278C22semidirect
107. #10622278C22semidirect
108. #10622278C22semidirect
120. C24×D11C23semidirect
123. C23×C4×C11C23semidirect
136. C2×D4×D11D4semidirect
146. C22×D44C23semidirect
149. C22×C4×D11C23semidirect
152. C2×C11×C4⋊C4C23semidirect
153. C2×C11×C4⋊C4C23semidirect
154. C2×C11×C4⋊C4C23semidirect
163. C2×C11×C22⋊C4C23semidirect
164. C2×C11×C22⋊C4C23semidirect
165. C2×C42×C11C23semidirect
173. C2×C22⋊Dic11C23semidirect
174. C2×C22⋊Dic11C23semidirect
195. C2×(C2×D11)⋊C4C23semidirect
196. C2×(C2×D11)⋊C4C23semidirect
197. C2×(C2×D11)⋊C4C23semidirect
198. C2×(C2×D11)⋊C4C23semidirect
199. C2×(C2×D11)⋊C4C23semidirect
200. C2×(C2×D11)⋊C4C23semidirect
201. C2×(C2×D11)⋊C4C23semidirect
202. C2×(C2×D11)⋊C4C23semidirect
203. C2×C4⋊Dic11C23semidirect
204. C2×C4⋊Dic11C23semidirect
205. C2×Dic11⋊C4C23semidirect
206. C2×Dic11⋊C4C23semidirect
207. C2×Dic11⋊C4C23semidirect
208. C2×Dic11⋊C4C23semidirect
209. C2×C4×Dic11C23semidirect
210. C2×C4×Dic11C23semidirect
231. C11×#95C23semidirect
232. C11×#95C23semidirect
233. C11×#95C23semidirect
234. C11⋊#95C23semidirect
235. C11⋊#95C23semidirect
236. C11⋊#95C23semidirect
237. C11⋊#95C23semidirect
238. C11⋊#95C23semidirect
423. #2697D11semidirect
586. C2×#123C2×D11semidirect
615. #397C2×D11semidirect
619. #396C2×D11semidirect
631. #394C2×D11semidirect
645. #390C2×D11semidirect
649. #388C2×D11semidirect
655. #386C2×D11semidirect
665. #379C2×D11semidirect
775. C23×C4C22×D11semidirect
808. C2×C4⋊C4C22×D11semidirect
809. C2×C4⋊C4C22×D11semidirect
810. C2×C4⋊C4C22×D11semidirect
852. C2×C22⋊C4C22×D11semidirect
853. C2×C22⋊C4C22×D11semidirect
856. C2×C42C22×D11semidirect
862. #95C22×D11semidirect
863. #95C22×D11semidirect
864. #95C22×D11semidirect
1056. C11#36714semidirect

Maximal subgroups

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

subgroupindex
C2×#106231842
C2×D11×#1202
#130768942
#130751802
#130751752
#130749512
#130749502
#130749492
#130749462
#130749452
#130749402
#130749392
#130743902
#130720002
#130719962
#130719382
#130719282
#130711952
C11×#26972
#3671411