Finite Group Databasebeta

← #14917224

Subgroups — #14917224

Order 2816.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623056C211yesmaximal, characteristic
2#13071792C212yesmaximal, complemented
3#13071756C212yesmaximal, complemented
4#13071680C212yesmaximal, complemented
5#13071656C211yesmaximal, characteristic, complemented
6#13071653C211yesmaximal, characteristic, complemented
7#13071634C211yesmaximal, characteristic, complemented
8#13071631C211yesmaximal, characteristic, complemented
9#13071594C212yesmaximal, complemented
10#13071509C211yesmaximal, characteristic, complemented
11C22⋊C4×D44C211yesmaximal, characteristic, complemented
12#13071436C211yesmaximal, characteristic, complemented
13#13071429C212yesmaximal, complemented
14#13071426C212yesmaximal, complemented
15#13071310C211yesmaximal, characteristic, complemented
16#13071307C211yesmaximal, characteristic, complemented
17#13071278C212yesmaximal, complemented
18#13071269C212yesmaximal, complemented
19#13071205C211yesmaximal, characteristic, complemented
20C4×#66948C211yesmaximal, characteristic, complemented
21#13071124C211yesmaximal, characteristic, complemented
22#13071102C211yesmaximal, characteristic, complemented
23C11×#2347C211yesmaximal, characteristic, complemented
24C22×#4339C2211yescharacteristic
25C23×D44C2211yescharacteristic
26C2×C11×#117C2211yescharacteristic
27#10623056C4116yescomplemented
28C2×#66948C2211yescharacteristic
29C2×#66948C2211yescharacteristic
30C2×#66948C2211yescharacteristic
31C2×#66948C2211yescharacteristic
32C2×#66946C2211yescharacteristic
33C2×#66946C2211yescharacteristic
34C2×#66946C2212yescomplemented
35C2×#66946C2212yescomplemented
36C2×#66945C2211yescharacteristic, complemented
37C2×C4⋊C4×D11C2211yescharacteristic, complemented
38C2×#66935C2212yes—
39C2×#66935C2212yes—
40C2×C22⋊C4×D11C2212yes—
41C2×C22⋊C4×D11C2212yes—
42C2×#66928C2212yes—
43C2×#66927C2212yes—
44C2×C4×D44C2211yescharacteristic
45C2×C4×D44C2211yescharacteristic
46C2×C4×D44C2212yescomplemented
47C2×C4×D44C2212yescomplemented
48C2×#66925C2211yescharacteristic, complemented
49C2×C42×D11C2211yescharacteristic, complemented
50C11×#389C2211yescharacteristic, complemented
51C11×#389C2211yescharacteristic, complemented
52C11×#388C2212yes—
53C11×#388C2212yes—
54C11×#383C2212yescomplemented
55C11×#380C2211yescharacteristic
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C4⋊C4C2211yescharacteristic, complemented
58C4×C11×C4⋊C4C2212yescomplemented
59C4×C11×C22⋊C4C2211yescharacteristic
60#10622825C2211yescharacteristic
61C4×C22⋊Dic11C2211yescharacteristic
62#10622603C2212yescomplemented
63#10622603C2212yescomplemented
64#10622602C2212yescomplemented
65#10622602C2212yescomplemented
66#10622601C2211yescharacteristic
67#10622601C2211yescharacteristic
68#10622601C2212yescomplemented
69#10622601C2212yescomplemented
70#10622600C2211yescharacteristic, complemented
71#10622600C2211yescharacteristic, complemented
72#10622598C2211yescharacteristic, complemented
73#10622598C2211yescharacteristic, complemented
74C4⋊C4×Dic11C2211yescharacteristic, complemented
75C4⋊C4×Dic11C2211yescharacteristic, complemented
76#10622570C2212yes—
77#10622570C2211yescharacteristic
78#10622570C2211yescharacteristic
79#10622569C2212yes—
80#10622569C2211yescharacteristic
81#10622569C2211yescharacteristic
82#10622568C2212yes—
83#10622568C2212yes—
84#10622564C2212yes—
85#10622564C2212yes—
86#10622553C2212yescomplemented
87#10622553C2212yescomplemented
88#10622552C2211yescharacteristic
89#10622552C2211yescharacteristic
90#10622552C2212yescomplemented
91#10622552C2212yescomplemented
92C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
93C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
94C4×(C2×D11)⋊C4C2212yescomplemented
95C4×(C2×D11)⋊C4C2212yescomplemented
96#10622550C2212yescomplemented
97C4×C4⋊Dic11C2212yescomplemented
98#10622283C2212yescomplemented
99#10622283C2212yescomplemented
100#10622282C2212yescomplemented
101#10622282C2212yescomplemented
102#10622281C2212yescomplemented
103#10622281C2212yescomplemented
104#10622279C2212yescomplemented
105#10622279C2212yescomplemented
106#10622278C2212yes—
107#10622278C2212yes—
108#10622278C2212yes—
109#10622278C2212yes—
110#10622278C2212yescomplemented
111#10622278C2212yescomplemented
112#10622278C2212yescomplemented
113#10622278C2212yescomplemented
114#10622278C2212yescomplemented
115#10622278C2212yescomplemented
116#10622278C2211yescharacteristic, complemented
117#10622278C2212yescomplemented
118#10622278C2211yescharacteristic, complemented
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622259C2211yescharacteristic, complemented
122#10622259C2212yescomplemented
123#10622259C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11C2311yescharacteristic
127C22×C22⋊D11C2311yescharacteristic
128C2×#4339—42no—
129C2×#4339—42no—
130C2×#4339C2×C418yescomplemented
131C22×D44—42no—
132C22×D44—42no—
133C22×D44C2×C418yescomplemented
134C22×D44C2311yescharacteristic
135C22×D44C2311yescharacteristic
136C22×D44C2312yes—
137C22×D44C2312yes—
138C22×D44C2311yescharacteristic
139C22×D44C2312yes—
140C22×D44C2312yes—
141C22×D44C2312yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×Dic22C2311yescharacteristic
152C11×#117C2×C418yescomplemented
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165C2×C42×C11C2312yes—
166C2×C42×C11C2312yes—
167C2×C42×C11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2311yescharacteristic
171C2×(C2×D11)⋊C4C2311yescharacteristic
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2311yescharacteristic
175C2×(C2×D11)⋊C4C2311yescharacteristic
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2312yes—
200C2×Dic11⋊C4C2311yescharacteristic
201C2×Dic11⋊C4C2311yescharacteristic
202C2×Dic11⋊C4C2312yes—
203C2×C4×Dic11C2311yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2311yescharacteristic
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2312yes—
210#66948C2×C418yescomplemented
211#66948C2×C418yescomplemented
212#66948C2×C418yescomplemented
213#66948C2×C418yescomplemented
214#66946—42no—
215#66946—42no—
216#66946—44no—
217#66946—44no—
218#66945—42no—
219C4⋊C4×D11—42no—
220#66935C2×C4116yescomplemented
221#66935C2×C4116yescomplemented
222C22⋊C4×D11—44no—
223C22⋊C4×D11—44no—
224#66928C2×C4116yescomplemented
225#66927C2×C4116yescomplemented
226C4×D44—44no—
227C4×D44—44no—
228C4×D44—42no—
229C4×D44—42no—
230#66925—42no—
231C42×D11—42no—
232C11×#95C2311yescharacteristic
233C11×#95C2311yescharacteristic
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11⋊#95C2311yescharacteristic
240C11⋊#95C2312yes—
241C11⋊#95C2311yescharacteristic
242C11⋊#95C2311yescharacteristic
243C11⋊#95C2312yes—
244C11⋊#95C2311yescharacteristic
245C11⋊#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252#34411—111nomaximal, Sylow
253C24×C11C2411yescharacteristic
254C23×D11—42no—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11C22×C418yes—
261C23×D11C2412yes—
262C23×D11C2412yes—
263C23×D11C2411yescharacteristic
264C23×D11C2411yescharacteristic
265C22×C4×C11—22no—
266C22×C4×C11—22no—
267C22×C4×C11C22×C414yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C22×C4×C11C2412yes—
276C22×C4×C11C2411yescharacteristic
277C22×C4×C11C2411yescharacteristic
278C2×C22⋊D11—41no—
279C2×C22⋊D11—41no—
280C2×C22⋊D11—41no—
281C2×C22⋊D11—41no—
282C2×C22⋊D11C22×C414yes—
283C2×C22⋊D11C22×C414yes—
284C22×Dic11C2411yescharacteristic
285C22×Dic11C2411yescharacteristic
286C22×Dic11C2412yes—
287C22×Dic11C2412yes—
288C22×Dic11C2411yescharacteristic
289C22×Dic11C2411yescharacteristic
290C22×Dic11C2411yescharacteristic
291C22×Dic11C2411yescharacteristic
292#4339—416no—
293C2×D44—22no—
294C2×D44—22no—
295C2×D44—22no—
296C2×D44—22no—
297C2×D44—42no—
298C2×D44—42no—
299C2×D44—42no—
300C2×D44—42no—
301C2×D44—42no—
302C2×D44—42no—
303C2×D44—42no—
304C2×D44—42no—
305C2×D44—42no—
306C2×D44—42no—
307C2×D44—41no—
308C2×D44—41no—
309C2×D44—416no—
310C2×D44C22×C414yes—
311C2×D44C22×C414yes—
312C2×D44C22×C414yes—
313C2×D44C22×C418yes—
314C2×D44C22×C418yes—
315C2×D44C22×C418yes—
316C2×D44C22×C418yes—
317C2×D44C22×C418yes—
318C2×C4×D11—22no—
319C2×C4×D11—24no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—22no—
323C2×C4×D11—22no—
324C2×C4×D11—22no—
325C2×C4×D11—24no—
326C2×C4×D11—41no—
327C2×C4×D11—41no—
328C2×C4×D11—41no—
329C2×C4×D11—41no—
330C2×C4×D11—42no—
331C2×C4×D11—42no—
332C2×C4×D11—42no—
333C2×C4×D11—42no—
334C2×C4×D11—42no—
335C2×C4×D11—42no—
336C2×C4×D11—42no—
337C2×C4×D11—42no—
338C2×C4×D11—42no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11—42no—
342C2×C4×D11—42no—
343C2×C4×D11C22×C414yes—
344C2×C4×D11C22×C414yes—
345C2×Dic22—41no—
346C2×Dic22—41no—
347C2×Dic22C22×C414yes—
348C11×C4⋊C4—22no—
349C11×C4⋊C4—22no—
350C11×C4⋊C4—24no—
351C11×C4⋊C4—42no—
352C11×C4⋊C4C22×C414yes—
353C11×C4⋊C4C22×C414yes—
354C11×C22⋊C4—22no—
355C11×C22⋊C4—42no—
356C11×C22⋊C4—41no—
357C11×C22⋊C4C22×C418yes—
358C42×C11—22no—
359C42×C11—22no—
360C42×C11—42no—
361C42×C11—42no—
362C42×C11C22×C418yes—
363C22⋊Dic11—22no—
364C22⋊Dic11—42no—
365C22⋊Dic11—41no—
366(C2×D11)⋊C4—22no—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—41no—
371(C2×D11)⋊C4—41no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379(C2×D11)⋊C4—42no—
380(C2×D11)⋊C4—42no—
381(C2×D11)⋊C4—42no—
382(C2×D11)⋊C4—42no—
383(C2×D11)⋊C4—42no—
384(C2×D11)⋊C4—41no—
385(C2×D11)⋊C4—42no—
386(C2×D11)⋊C4—41no—
387(C2×D11)⋊C4C22×C418yes—
388(C2×D11)⋊C4C22×C418yes—
389(C2×D11)⋊C4C22×C418yes—
390(C2×D11)⋊C4C22×C418yes—
391C4⋊Dic11—24no—
392C4⋊Dic11—22no—
393C4⋊Dic11—22no—
394C4⋊Dic11—42no—
395Dic11⋊C4—41no—
396Dic11⋊C4—41no—
397Dic11⋊C4—42no—
398C4×Dic11—22no—
399C4×Dic11—22no—
400C4×Dic11—41no—
401C4×Dic11—41no—
402C4×Dic11—42no—
403C4×Dic11—42no—
404C4×Dic11—42no—
405C2×#535—111no—
406#2380—112no—
407#2375—112no—
408#2366—112no—
409#2363—111no—
410#2363—111no—
411#2361—111no—
412#2361—111no—
413#2358—112no—
414#2347—111no—
415#2347D1111yescharacteristic, complemented
416D4×C22⋊C4—111no—
417D4×C22⋊C4—111no—
418#2337—112no—
419#2337—112no—
420#2324—111no—
421#2324—111no—
422#2321—112no—
423#2321—112no—
424#2311—111no—
425C4×#121—111no—
426C4×#121—111no—
427#2297—111no—
428C23×C11—21no—
429C23×C11—21no—
430C23×C11—21no—
431C23×C11—21no—
432C23×C11—21no—
433C23×C11—21no—
434C23×C11C23×C412yes—
435C23×C11C2511yescharacteristic
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—21no—
439C22×D11—21no—
440C22×D11—21no—
441C22×D11—21no—
442C22×D11—21no—
443C22×D11—21no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—48no—
461C22×D11—48no—
462C22×D11—48no—
463C22×D11—84no—
464C22×D11—84no—
465C22×D11—84no—
466C22×D11—84no—
467C22×D11C23×C414yes—
468C22×D11C23×C414yes—
469C22×D11C23×C412yes—
470C22×D11C23×C412yes—
471C2×C4×C11—22no—
472C2×C4×C11—21no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—21no—
476C2×C4×C11—21no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—28no—
480C2×C4×C11—21no—
481C2×C4×C11—22no—
482C2×C4×C11—21no—
483C2×C4×C11—21no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—22no—
487C2×C4×C11—21no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11C23×C414yes—
496C2×C4×C11C23×C414yes—
497C2×C4×C11C23×C412yes—
498C2×C4×C11C23×C412yes—
499C2×C4×C11H(5,𝔽2)12yes—
500C2×C4×C11H(5,𝔽2)12yes—
501C2×C4×C11H(5,𝔽2)12yes—
502C22⋊D11—44no—
503C22⋊D11—44no—
504C2×Dic11—21no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—21no—
509C2×Dic11—21no—
510C2×Dic11—21no—
511C2×Dic11—21no—
512C2×Dic11—21no—
513C2×Dic11—21no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—22no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C412yes—
527C2×Dic11H(5,𝔽2)12yes—
528D44—28no—
529D44—28no—
530D44—48no—
531D44—48no—
532D44—48no—
533D44—48no—
534D44—48no—
535D44—44no—
536C4×D11—28no—
537C4×D11—28no—
538C4×D11—44no—
539C4×D11—44no—
540C4×D11—84no—
541C4×D11—84no—
542C4×D11—84no—
543C4×D11—84no—
544C4×D11—84no—
545Dic22—44no—
546C22×#41—111no—
547C23×D4—111no—
548#535—1116no—
549C2×#127—112no—
550C2×#124—112no—
551C2×#121—111no—
552C2×#121—111no—
553C2×#121—111no—
554C2×#121—111no—
555C2×#120—112no—
556C2×#120—112no—
557C2×C4×D4—112no—
558C2×C4×D4—111no—
559C2×C4×D4—111no—
560C2×C4×D4—112no—
561C2×C4×D4—112no—
562C2×C4×D4—111no—
563C2×C4×D4—111no—
564C2×C4×D4—112no—
565C2×#117—111no—
566C2×#117—111no—
567C2×#117C2×D1111yescharacteristic
568C22×C4⋊C4—111no—
569C22×C22⋊C4—112no—
570C22×C22⋊C4—112no—
571C22×C42—111no—
572#391—112no—
573#391—111no—
574#391—111no—
575#390—112no—
576#390—111no—
577#390—112no—
578#390—111no—
579#390—112no—
580#390—111no—
581#390—111no—
582#390—112no—
583#390—111no—
584#390—112no—
585#390—111no—
586#389—111no—
587#389—111no—
588#389C2×D1111yescharacteristic, complemented
589#389C2×D1111yescharacteristic, complemented
590#388—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388—112no—
597#388—112no—
598#388—112no—
599#388—112no—
600#388C2×D1112yes—
601#388C2×D1112yes—
602#386—112no—
603#386—111no—
604#386—111no—
605#386—112no—
606#386—112no—
607#386—112no—
608#386—112no—
609#386—112no—
610#386—112no—
611#386—112no—
612#386—112no—
613#386—112no—
614#386—112no—
615#386—112no—
616#386—111no—
617#386—112no—
618#386—112no—
619#386—111no—
620#385—112no—
621#385—112no—
622#385—112no—
623#385—112no—
624#383—112no—
625#383C2×D1112yescomplemented
626#380—111no—
627#380—111no—
628#380—111no—
629#380C2×D1111yescharacteristic
630#379—112no—
631#379—112no—
632C4×C4⋊C4—111no—
633C4×C4⋊C4—111no—
634C4×C4⋊C4—112no—
635C4×C4⋊C4C2×D1111yescharacteristic, complemented
636C4×C4⋊C4C2×D1112yescomplemented
637C4×C4⋊C4C2×D1111yescharacteristic, complemented
638C4×C22⋊C4—111no—
639C4×C22⋊C4—112no—
640C4×C22⋊C4—112no—
641C4×C22⋊C4—111no—
642C4×C22⋊C4—111no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—112no—
645C4×C22⋊C4C2×D1111yescharacteristic
646C22×C11—22no—
647C22×C11—22no—
648C22×C11—22no—
649C22×C11—41no—
650C22×C11—41no—
651C22×C11—41no—
652C22×C11—41no—
653C22×C11C24×C411yescharacteristic
654C22×C11C2×H(5,𝔽2)11yescharacteristic
655C22×C11C2×H(5,𝔽2)11yescharacteristic
656C22×C11C2×H(5,𝔽2)11yescharacteristic
657C22×C11C2×H(5,𝔽2)11yescharacteristic
658C22×C11#58511yescharacteristic
659C22×C11#58511yescharacteristic
660C2×D11—24no—
661C2×D11—24no—
662C2×D11—22no—
663C2×D11—22no—
664C2×D11—24no—
665C2×D11—24no—
666C2×D11—24no—
667C2×D11—24no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—41no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—41no—
680C2×D11—41no—
681C2×D11—41no—
682C2×D11—41no—
683C2×D11—41no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—816no—
689C4×C11—22no—
690C4×C11—24no—
691C4×C11—24no—
692C4×C11—22no—
693C4×C11—42no—
694C4×C11—41no—
695C4×C11—41no—
696C4×C11—42no—
697C4×C11—41no—
698C4×C11#51814yes—
699Dic11—22no—
700Dic11—22no—
701Dic11—22no—
702Dic11—42no—
703Dic11—41no—
704Dic11—41no—
705Dic11—42no—
706Dic11—41no—
707C25—112no—
708C2×#41—118no—
709C2×#41—442no—
710C2×#41—442no—
711C22×Q8—111no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—118no—
715C22×D4—111no—
716C22×D4—111no—
717C22×D4—112no—
718C22×D4—112no—
719C22×D4—112no—
720C22×D4—112no—
721C22×D4—112no—
722C22×D4—111no—
723C22×D4—442no—
724C22×D4—442no—
725C23×C4—111no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—112no—
729C23×C4—112no—
730C23×C4—112no—
731C23×C4—112no—
732C23×C4—112no—
733C23×C4—111no—
734C23×C4C22×D1111yescharacteristic
735#127—1116no—
736#124—1116no—
737#121—118no—
738#121—118no—
739#121—118no—
740#121—118no—
741#120—1116no—
742#120—1116no—
743C4×D4—442no—
744C4×D4—442no—
745C4×D4—444no—
746C4×D4—444no—
747C4×D4—442no—
748C4×D4—442no—
749C4×D4—444no—
750C4×D4—444no—
751#117—442no—
752#117—442no—
753#117C4×D1118yescomplemented
754C2×C4⋊C4—111no—
755C2×C4⋊C4—111no—
756C2×C4⋊C4—112no—
757C2×C4⋊C4—112no—
758C2×C4⋊C4—111no—
759C2×C4⋊C4—111no—
760C2×C4⋊C4—112no—
761C2×C4⋊C4—442no—
762C2×C4⋊C4C22×D1111yescharacteristic
763C2×C4⋊C4C22×D1111yescharacteristic
764C2×C4⋊C4C22×D1112yes—
765C2×C4⋊C4C22×D1112yes—
766C2×C4⋊C4C22×D1111yescharacteristic
767C2×C4⋊C4C22×D1111yescharacteristic
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—111no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—111no—
776C2×C22⋊C4—111no—
777C2×C22⋊C4—112no—
778C2×C22⋊C4—111no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—111no—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—111no—
784C2×C22⋊C4—112no—
785C2×C22⋊C4—112no—
786C2×C22⋊C4—112no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—112no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—112no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—444no—
797C2×C22⋊C4—444no—
798C2×C22⋊C4C22×D1111yescharacteristic
799C2×C22⋊C4C22×D1112yes—
800C2×C22⋊C4C22×D1111yescharacteristic
801C2×C22⋊C4C22×D1112yes—
802C2×C42—111no—
803C2×C42—111no—
804C2×C42—112no—
805C2×C42—112no—
806C2×C42—112no—
807C2×C42—111no—
808C2×C42—111no—
809C2×C42—442no—
810C2×C42C22×D1111yescharacteristic
811C2×C42C22×D1111yescharacteristic
812C2×C42C22×D1112yes—
813C2×C42C22×D1112yes—
814C2×C42C22×D1112yes—
815#95—111no—
816#95—111no—
817#95—111no—
818#95—112no—
819#95—112no—
820#95—111no—
821#95—112no—
822#95—112no—
823#95—111no—
824#95—111no—
825#95—112no—
826#95—112no—
827#95—112no—
828#95C22×D1112yes—
829#95C22×D1112yes—
830#95C22×D1111yescharacteristic
831#95C22×D1111yescharacteristic
832#95C22×D1112yes—
833#95C22×D1112yes—
834#95C22×D1112yes—
835C2×C11—42no—
836C2×C11C2×#51811yescharacteristic
837C2×C11C4×H(5,𝔽2)11yescharacteristic
838C2×C11C4×H(5,𝔽2)11yescharacteristic
839C2×C11#353711yescharacteristic
840C2×C11#354011yescharacteristic
841C2×C11#354611yescharacteristic
842C2×C11#354611yescharacteristic
843D11—42no—
844D11—42no—
845D11—44no—
846D11—44no—
847C24—112no—
848C24—112no—
849C24—111no—
850C24—111no—
851C24—118no—
852C24—442no—
853C24—442no—
854C24—442no—
855C24—442no—
856C24—442no—
857C24—442no—
858C24C23×D1111yescharacteristic
859#41—4416no—
860C2×Q8—114no—
861C2×Q8—441no—
862C2×Q8—441no—
863C2×D4—114no—
864C2×D4—114no—
865C2×D4—114no—
866C2×D4—114no—
867C2×D4—118no—
868C2×D4—118no—
869C2×D4—118no—
870C2×D4—118no—
871C2×D4—118no—
872C2×D4—114no—
873C2×D4—222no—
874C2×D4—222no—
875C2×D4—222no—
876C2×D4—222no—
877C2×D4—4416no—
878C2×D4—442no—
879C2×D4—442no—
880C2×D4—442no—
881C2×D4—442no—
882C2×D4—442no—
883C2×D4—442no—
884C2×D4—441no—
885C2×D4—441no—
886C2×D4—442no—
887C2×D4—442no—
888C2×D4—442no—
889C2×D4—442no—
890C2×D4—441no—
891C2×D4—441no—
892C2×D4—441no—
893C2×D4—441no—
894C22×C4—22no—
895C22×C4—22no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—111no—
899C22×C4—114no—
900C22×C4—114no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—111no—
906C22×C4—222no—
907C22×C4—224no—
908C22×C4—222no—
909C22×C4—222no—
910C22×C4—222no—
911C22×C4—222no—
912C22×C4—222no—
913C22×C4—224no—
914C22×C4—441no—
915C22×C4—441no—
916C22×C4—441no—
917C22×C4—441no—
918C22×C4—442no—
919C22×C4—442no—
920C22×C4—442no—
921C22×C4—442no—
922C22×C4—442no—
923C22×C4—442no—
924C22×C4—442no—
925C22×C4—442no—
926C22×C4—442no—
927C22×C4—442no—
928C22×C4—442no—
929C22×C4—442no—
930C22×C4—442no—
931C22×C4C2×C4×D1114yes—
932C22×C4C23×D1111yescharacteristic
933C22×C4C23×D1111yescharacteristic
934C22×C4C23×D1112yes—
935C22×C4C23×D1112yes—
936C22×C4C23×D1111yescharacteristic
937C22×C4C23×D1111yescharacteristic
938C22×C4C23×D1112yes—
939C22×C4C23×D1112yes—
940C22×C4C23×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—42no—
946C4⋊C4—224no—
947C4⋊C4—222no—
948C4⋊C4—222no—
949C4⋊C4—442no—
950C4⋊C4—441no—
951C4⋊C4—441no—
952C4⋊C4—442no—
953C4⋊C4C2×C4×D1114yes—
954C4⋊C4C2×C4×D1114yes—
955C22⋊C4—22no—
956C22⋊C4—42no—
957C22⋊C4—41no—
958C22⋊C4—118no—
959C22⋊C4—118no—
960C22⋊C4—118no—
961C22⋊C4—118no—
962C22⋊C4—224no—
963C22⋊C4—222no—
964C22⋊C4—222no—
965C22⋊C4—224no—
966C22⋊C4—222no—
967C22⋊C4—442no—
968C22⋊C4—442no—
969C22⋊C4—441no—
970C22⋊C4—441no—
971C22⋊C4—442no—
972C22⋊C4—442no—
973C22⋊C4—442no—
974C22⋊C4—442no—
975C22⋊C4—442no—
976C22⋊C4—442no—
977C22⋊C4—442no—
978C22⋊C4—442no—
979C22⋊C4—442no—
980C22⋊C4—441no—
981C22⋊C4—442no—
982C22⋊C4—442no—
983C22⋊C4—441no—
984C22⋊C4—442no—
985C22⋊C4—441no—
986C22⋊C4C2×C4×D1118yes—
987C42—22no—
988C42—22no—
989C42—42no—
990C42—42no—
991C42—222no—
992C42—222no—
993C42—441no—
994C42—441no—
995C42—442no—
996C42—442no—
997C42—442no—
998C42C2×C4×D1118yes—
999C11#3441111yescharacteristic, complemented, Sylow
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—114no—
1007C23—114no—
1008C23—112no—
1009C23—112no—
1010C23—222no—
1011C23—221no—
1012C23—221no—
1013C23—221no—
1014C23—221no—
1015C23—222no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—221no—
1021C23—221no—
1022C23—221no—
1023C23—222no—
1024C23—221no—
1025C23—222no—
1026C23—222no—
1027C23—221no—
1028C23—221no—
1029C23—222no—
1030C23—221no—
1031C23—222no—
1032C23—221no—
1033C23—222no—
1034C23—448no—
1035C23—448no—
1036C23—448no—
1037C23—884no—
1038C23—884no—
1039C23—884no—
1040C23—884no—
1041C23C22×C4×D1112yes—
1042C23C24×D1111yescharacteristic
1043Q8—444no—
1044D4—228no—
1045D4—228no—
1046D4—448no—
1047D4—444no—
1048D4—448no—
1049D4—448no—
1050D4—448no—
1051D4—448no—
1052D4—444no—
1053D4—444no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—21no—
1061C2×C4—22no—
1062C2×C4—28no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—21no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
1073C2×C4—21no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—112no—
1079C2×C4—112no—
1080C2×C4—112no—
1081C2×C4—221no—
1082C2×C4—221no—
1083C2×C4—221no—
1084C2×C4—221no—
1085C2×C4—221no—
1086C2×C4—221no—
1087C2×C4—228no—
1088C2×C4—228no—
1089C2×C4—221no—
1090C2×C4—221no—
1091C2×C4—221no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—222no—
1101C2×C4—221no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—444no—
1105C2×C4—444no—
1106C2×C4—884no—
1107C2×C4—884no—
1108C2×C4—884no—
1109C2×C4—884no—
1110C2×C4—884no—
1111C2×C4C22×C4×D1112yes—
1112C2×C4C22×C4×D1114yes—
1113C2×C4C22×C4×D1114yes—
1114C2×C4C22×C4×D1112yes—
1115C2×C4#6704212yes—
1116C2×C4#6704212yes—
1117C2×C4#6704212yes—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—222no—
1126C22—222no—
1127C22—224no—
1128C22—224no—
1129C22—222no—
1130C22—222no—
1131C22—224no—
1132C22—224no—
1133C22—222no—
1134C22—222no—
1135C22—224no—
1136C22—224no—
1137C22—441no—
1138C22—442no—
1139C22—442no—
1140C22—441no—
1141C22—442no—
1142C22—442no—
1143C22—441no—
1144C22—441no—
1145C22—442no—
1146C22—442no—
1147C22—441no—
1148C22—441no—
1149C22—441no—
1150C22—441no—
1151C22—442no—
1152C22—442no—
1153C22—8816no—
1154C22C23×C4×D1111yescharacteristic
1155C22C2×#6704211yescharacteristic
1156C22C2×#6704211yescharacteristic
1157C22C2×#6704211yescharacteristic
1158C22#1062345311yescharacteristic
1159C22D11×H(5,𝔽2)11yescharacteristic
1160C22#1062345711yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—24no—
1164C4—22no—
1165C4—41no—
1166C4—42no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—222no—
1171C4—222no—
1172C4—222no—
1173C4—441no—
1174C4—441no—
1175C4—442no—
1176C4—441no—
1177C4—442no—
1178C4#1062305214yes—
1179C2—42no—
1180C2—444no—
1181C2—444no—
1182C2—442no—
1183C2—442no—
1184C2C2×#1062305211yescharacteristic
1185C2#1308182211yescharacteristic
1186C2C4×#6704211yescharacteristic
1187C2#1308285211yescharacteristic
1188C2#1308289211yescharacteristic
1189C2#1308298711yescharacteristic
1190C2#1308299111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2347C2
socle, cosocleC23×C11C25
prime radicalC2×#10623056C2
hypercenter#2347D11
hypocenterC11#34411
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2347

Complements

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

NH ≅ G/Ntype
2. #13071792C2semidirect
3. #13071756C2semidirect
4. #13071680C2semidirect
5. #13071656C2semidirect
6. #13071653C2semidirect
7. #13071634C2semidirect
8. #13071631C2semidirect
9. #13071594C2semidirect
10. #13071509C2semidirect
11. C22⋊C4×D44C2semidirect
12. #13071436C2semidirect
13. #13071429C2semidirect
14. #13071426C2semidirect
15. #13071310C2semidirect
16. #13071307C2semidirect
17. #13071278C2semidirect
18. #13071269C2semidirect
19. #13071205C2semidirect
20. C4×#66948C2semidirect
21. #13071124C2semidirect
22. #13071102C2semidirect
23. C11×#2347C2semidirect
27. #10623056C4semidirect
34. C2×#66946C22semidirect
35. C2×#66946C22semidirect
36. C2×#66945C22semidirect
37. C2×C4⋊C4×D11C22semidirect
46. C2×C4×D44C22semidirect
47. C2×C4×D44C22semidirect
48. C2×#66925C22semidirect
49. C2×C42×D11C22semidirect
50. C11×#389C22semidirect
51. C11×#389C22semidirect
54. C11×#383C22semidirect
56. C4×C11×C4⋊C4C22semidirect
57. C4×C11×C4⋊C4C22semidirect
58. C4×C11×C4⋊C4C22semidirect
62. #10622603C22semidirect
63. #10622603C22semidirect
64. #10622602C22semidirect
65. #10622602C22semidirect
68. #10622601C22semidirect
69. #10622601C22semidirect
70. #10622600C22semidirect
71. #10622600C22semidirect
72. #10622598C22semidirect
73. #10622598C22semidirect
74. C4⋊C4×Dic11C22semidirect
75. C4⋊C4×Dic11C22semidirect
86. #10622553C22semidirect
87. #10622553C22semidirect
90. #10622552C22semidirect
91. #10622552C22semidirect
92. C4×(C2×D11)⋊C4C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. C4×(C2×D11)⋊C4C22semidirect
95. C4×(C2×D11)⋊C4C22semidirect
96. #10622550C22semidirect
97. C4×C4⋊Dic11C22semidirect
98. #10622283C22semidirect
99. #10622283C22semidirect
100. #10622282C22semidirect
101. #10622282C22semidirect
102. #10622281C22semidirect
103. #10622281C22semidirect
104. #10622279C22semidirect
105. #10622279C22semidirect
110. #10622278C22semidirect
111. #10622278C22semidirect
112. #10622278C22semidirect
113. #10622278C22semidirect
114. #10622278C22semidirect
115. #10622278C22semidirect
116. #10622278C22semidirect
117. #10622278C22semidirect
118. #10622278C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622259C22semidirect
122. #10622259C22semidirect
123. #10622259C22semidirect
130. C2×#4339C2×C4semidirect
133. C22×D44C2×C4semidirect
152. C11×#117C2×C4semidirect
210. #66948C2×C4semidirect
211. #66948C2×C4semidirect
212. #66948C2×C4semidirect
213. #66948C2×C4semidirect
220. #66935C2×C4semidirect
221. #66935C2×C4semidirect
224. #66928C2×C4semidirect
225. #66927C2×C4semidirect
415. #2347D11semidirect
588. #389C2×D11semidirect
589. #389C2×D11semidirect
625. #383C2×D11semidirect
635. C4×C4⋊C4C2×D11semidirect
636. C4×C4⋊C4C2×D11semidirect
637. C4×C4⋊C4C2×D11semidirect
753. #117C4×D11semidirect
999. C11#34411semidirect

Maximal subgroups

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

subgroupindex
C2×#106230562
#130717922
#130717562
#130716802
#130716562
#130716532
#130716342
#130716312
#130715942
#130715092
C22⋊C4×D442
#130714362
#130714292
#130714262
#130713102
#130713072
#130712782
#130712692
#130712052
C4×#669482
#130711242
#130711022
C11×#23472
#3441111