Finite Group Databasebeta

← #13082640

Subgroups — #13082640

Order 1408.

1252 conjugacy classes of subgroups.

The subgroup lattice has 1096 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#538C211yesmaximal, characteristic, complemented
2#10623240C211yesmaximal, characteristic, complemented
3#10623240C211yesmaximal, characteristic, complemented
4#10623237C211yesmaximal, characteristic, complemented
5#10623235C211yesmaximal, characteristic, complemented
6#10623209C211yesmaximal, characteristic, complemented
7#10623207C211yesmaximal, characteristic, complemented
8#10623201C211yesmaximal, characteristic, complemented
9#10623199C211yesmaximal, characteristic, complemented
10#10623194C211yesmaximal, characteristic, complemented
11#10623192C211yesmaximal, characteristic, complemented
12#10623187C211yesmaximal, characteristic, complemented
13#10623185C211yesmaximal, characteristic, complemented
14#10623167C211yesmaximal, characteristic, complemented
15#10623161C211yesmaximal, characteristic, complemented
16#10623146C211yesmaximal, characteristic, complemented
17#10623141C211yesmaximal, characteristic, complemented
18#10623140C211yesmaximal, characteristic, complemented
19D11×#121C211yesmaximal, characteristic, complemented
20#10623132C211yesmaximal, characteristic, complemented
21#10623130C211yesmaximal, characteristic, complemented
22#10623122C211yesmaximal, characteristic, complemented
23#10623122C211yesmaximal, characteristic, complemented
24#10623121C211yesmaximal, characteristic, complemented
25#10623121C211yesmaximal, characteristic, complemented
26#10623091C211yesmaximal, characteristic, complemented
27#10623078C211yesmaximal, characteristic, complemented
28#10623076C211yesmaximal, characteristic, complemented
29C4×D4×D11C211yesmaximal, characteristic, complemented
30C2×#66937C211yesmaximal, characteristic, complemented
31#10623017C211yesmaximal, characteristic, complemented
32C22×C22⋊D11C2211yescharacteristic
33C22×C22⋊D11C2211yescharacteristic, complemented
34C22×C22⋊D11C2211yescharacteristic, complemented
35C2×#4343C2211yescharacteristic, complemented
36C2×#4341C2211yescharacteristic, complemented
37C2×#4341C2211yescharacteristic, complemented
38C2×D4×D11C2211yescharacteristic
39C2×D4×D11C2211yescharacteristic
40C2×D4×D11C2211yescharacteristic, complemented
41C2×D4×D11C2211yescharacteristic, complemented
42C2×D4×D11C2211yescharacteristic, complemented
43C2×#4339C2211yescharacteristic, complemented
44C22×D44C2211yescharacteristic, complemented
45C22×C4×D11C2211yescharacteristic, complemented
46C22×C4×D11C2211yescharacteristic, complemented
47C11×#126C2211yescharacteristic, complemented
48C11×#126C2211yescharacteristic, complemented
49C11×#124C2211yescharacteristic, complemented
50C11×#124C2211yescharacteristic, complemented
51C11×#123C2211yescharacteristic, complemented
52C11×#123C2211yescharacteristic, complemented
53C11×C22⋊Q8C2211yescharacteristic, complemented
54C11×#121C2211yescharacteristic, complemented
55C11×#121C2211yescharacteristic, complemented
56C11×#121C2211yescharacteristic, complemented
57C11×#120C2211yescharacteristic, complemented
58C11×#120C2211yescharacteristic, complemented
59C4×D4×C11C2211yescharacteristic, complemented
60C4×D4×C11C2211yescharacteristic, complemented
61C2×C11×C22⋊C4C2211yescharacteristic, complemented
62C2×C22⋊Dic11C2211yescharacteristic, complemented
63#67000C2211yescharacteristic, complemented
64#66999C2211yescharacteristic, complemented
65#66997C2211yescharacteristic, complemented
66#66993C2211yescharacteristic, complemented
67#66993C2211yescharacteristic, complemented
68#66993C2211yescharacteristic, complemented
69#66992C2211yescharacteristic, complemented
70#66992C2211yescharacteristic, complemented
71#66992C2211yescharacteristic, complemented
72#66992C2211yescharacteristic, complemented
73#66992C2211yescharacteristic, complemented
74#66992C2211yescharacteristic, complemented
75#66992C2211yescharacteristic, complemented
76#66992C2211yescharacteristic, complemented
77#66992C2211yescharacteristic, complemented
78#66991C2211yescharacteristic, complemented
79#66991C2211yescharacteristic, complemented
80#66990C2211yescharacteristic, complemented
81#66990C2211yescharacteristic, complemented
82#66990C2211yescharacteristic, complemented
83#66990C2211yescharacteristic, complemented
84#66988C2211yescharacteristic, complemented
85D4×Dic11C2211yescharacteristic, complemented
86D4×Dic11C2211yescharacteristic, complemented
87#66983C2211yescharacteristic, complemented
88#66982C2211yescharacteristic, complemented
89C4×C22⋊D11C2211yescharacteristic
90C4×C22⋊D11C2211yescharacteristic
91C4×C22⋊D11C2211yescharacteristic, complemented
92C4×C22⋊D11C2211yescharacteristic, complemented
93C4×C22⋊D11C2211yescharacteristic, complemented
94C4×C22⋊D11C2211yescharacteristic, complemented
95C4×C22⋊D11C2211yescharacteristic, complemented
96C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
97C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
98C2×Dic11⋊C4C2211yescharacteristic, complemented
99#66951C2211yescharacteristic, complemented
100#66951C2211yescharacteristic, complemented
101#66949C2211yescharacteristic, complemented
102#66949C2211yescharacteristic, complemented
103#66949C2211yescharacteristic, complemented
104#66948C2211yescharacteristic, complemented
105#66948C2211yescharacteristic, complemented
106#66948C2211yescharacteristic, complemented
107#66948C2211yescharacteristic, complemented
108#66947C2211yescharacteristic, complemented
109#66947C2211yescharacteristic, complemented
110#66947C2211yescharacteristic, complemented
111#66947C2211yescharacteristic, complemented
112#66946C2211yescharacteristic, complemented
113#66946C2211yescharacteristic, complemented
114#66946C2211yescharacteristic, complemented
115#66946C2211yescharacteristic, complemented
116#66945C2211yescharacteristic, complemented
117C4⋊C4×D11C2211yescharacteristic, complemented
118C4⋊C4×D11C2211yescharacteristic, complemented
119#66942C2211yescharacteristic, complemented
120#66942C2211yescharacteristic, complemented
121#66942C2211yescharacteristic, complemented
122#66940C2211yescharacteristic, complemented
123#66939C2211yescharacteristic, complemented
124#66939C2211yescharacteristic, complemented
125#66938C2211yescharacteristic, complemented
126#66938C2211yescharacteristic, complemented
127#66938C2211yescharacteristic, complemented
128#66937C2211yescharacteristic
129#66937C2211yescharacteristic, complemented
130#66937C2211yescharacteristic, complemented
131#66937C2211yescharacteristic, complemented
132#66937C2211yescharacteristic, complemented
133#66937C2211yescharacteristic, complemented
134#66937C2211yescharacteristic, complemented
135#66937C2211yescharacteristic, complemented
136#66937C2211yescharacteristic, complemented
137#66937C2211yescharacteristic, complemented
138#66937C2211yescharacteristic, complemented
139#66937C2211yescharacteristic, complemented
140#66937C2211yescharacteristic, complemented
141#66937C2211yescharacteristic, complemented
142#66937C2211yescharacteristic, complemented
143#66937C2211yescharacteristic, complemented
144#66936C2211yescharacteristic, complemented
145#66936C2211yescharacteristic, complemented
146#66936C2211yescharacteristic, complemented
147#66936C2211yescharacteristic, complemented
148#66935C2211yescharacteristic, complemented
149#66935C2211yescharacteristic, complemented
150#66935C2211yescharacteristic, complemented
151#66935C2211yescharacteristic, complemented
152#66935C2211yescharacteristic, complemented
153#66935C2211yescharacteristic, complemented
154(C22⋊D11)⋊C4C2211yescharacteristic
155(C22⋊D11)⋊C4C2211yescharacteristic
156(C22⋊D11)⋊C4C2211yescharacteristic, complemented
157(C22⋊D11)⋊C4C2211yescharacteristic, complemented
158(C22⋊D11)⋊C4C2211yescharacteristic, complemented
159(C22⋊D11)⋊C4C2211yescharacteristic, complemented
160(C22⋊D11)⋊C4C2211yescharacteristic, complemented
161(C22⋊D11)⋊C4C2211yescharacteristic, complemented
162(C22⋊D11)⋊C4C2211yescharacteristic, complemented
163(C22⋊D11)⋊C4C2211yescharacteristic, complemented
164(C22⋊D11)⋊C4C2211yescharacteristic, complemented
165(C22⋊D11)⋊C4C2211yescharacteristic, complemented
166(C22⋊D11)⋊C4C2211yescharacteristic, complemented
167C22⋊C4×D11C2211yescharacteristic, complemented
168C22⋊C4×D11C2211yescharacteristic, complemented
169C22⋊C4×D11C2211yescharacteristic, complemented
170C22⋊C4×D11C2211yescharacteristic, complemented
171C22⋊C4×D11C2211yescharacteristic, complemented
172C22⋊C4×D11C2211yescharacteristic, complemented
173#66932C2211yescharacteristic, complemented
174#66931C2211yescharacteristic, complemented
175#66931C2211yescharacteristic, complemented
176#66930C2211yescharacteristic, complemented
177#66930C2211yescharacteristic, complemented
178#66930C2211yescharacteristic, complemented
179#66929C2211yescharacteristic, complemented
180#66928C2211yescharacteristic, complemented
181C4×D44C2211yescharacteristic, complemented
182C4×D44C2211yescharacteristic, complemented
183C4×D44C2211yescharacteristic, complemented
184#66925C2211yescharacteristic, complemented
185#66925C2211yescharacteristic, complemented
186C42×D11C2211yescharacteristic, complemented
187C24×C11C2311yescharacteristic
188C23×D11C2311yescharacteristic
189C23×D11C2311yescharacteristic
190C23×D11C2311yescharacteristic
191C23×D11C2311yescharacteristic
192C23×D11C2311yescharacteristic
193C2×Q8×C11C2311yescharacteristic
194C2×D4×C11C2311yescharacteristic
195C2×D4×C11C2311yescharacteristic
196C2×D4×C11C2311yescharacteristic
197C2×D4×C11C2311yescharacteristic
198C2×D4×C11C2311yescharacteristic
199C2×D4×C11C2311yescharacteristic
200C2×D4×C11C2311yescharacteristic
201C22×C4×C11C2311yescharacteristic
202C22×C4×C11C2311yescharacteristic
203C22×C4×C11C2311yescharacteristic
204C22×C4×C11C2311yescharacteristic
205C2×C22⋊D11—24no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11C2311yescharacteristic
209C2×C22⋊D11C2311yescharacteristic
210C2×C22⋊D11C2311yescharacteristic
211C2×C22⋊D11C2311yescharacteristic
212C2×C22⋊D11C2311yescharacteristic
213C2×C22⋊D11C2311yescharacteristic
214C2×C22⋊D11C2311yescharacteristic
215C2×C22⋊D11C2311yescharacteristic
216C2×C22⋊D11C2311yescharacteristic
217C2×C22⋊D11C2311yescharacteristic
218C2×C22⋊D11C2311yescharacteristic
219C2×C22⋊D11C2311yescharacteristic
220C2×C22⋊D11C2311yescharacteristic
221C2×C22⋊D11C2311yescharacteristic
222C2×C22⋊D11C2311yescharacteristic
223C2×C22⋊D11C2311yescharacteristic
224C2×C22⋊D11C2311yescharacteristic
225C2×C22⋊D11C2311yescharacteristic
226C2×C22⋊D11C2311yescharacteristic
227C2×C22⋊D11C2311yescharacteristic
228C22×Dic11C2311yescharacteristic
229C22×Dic11C2311yescharacteristic
230C22×Dic11C2311yescharacteristic
231C22×Dic11C2311yescharacteristic
232C22×Dic11C2311yescharacteristic
233C22×Dic11C2311yescharacteristic
234C22×Dic11C2311yescharacteristic
235#4343—42no—
236#4341—42no—
237#4341—42no—
238D4×D11—24no—
239D4×D11—24no—
240D4×D11—42no—
241D4×D11—42no—
242D4×D11—42no—
243#4339—42no—
244C2×D44—42no—
245C2×D44C2311yescharacteristic
246C2×D44C2311yescharacteristic
247C2×D44C2311yescharacteristic
248C2×D44C2311yescharacteristic
249C2×D44C2311yescharacteristic
250C2×D44C2311yescharacteristic
251C2×D44C2311yescharacteristic
252C2×D44C2311yescharacteristic
253C2×D44C2311yescharacteristic
254C2×D44C2311yescharacteristic
255C2×C4×D11—42no—
256C2×C4×D11—42no—
257C2×C4×D11C2311yescharacteristic
258C2×C4×D11C2311yescharacteristic
259C2×C4×D11C2311yescharacteristic
260C2×C4×D11C2311yescharacteristic
261C2×C4×D11C2311yescharacteristic
262C2×C4×D11C2311yescharacteristic
263C2×C4×D11C2311yescharacteristic
264C2×C4×D11C2311yescharacteristic
265C2×C4×D11C2311yescharacteristic
266C2×C4×D11C2311yescharacteristic
267C2×C4×D11C2311yescharacteristic
268C2×C4×D11C2311yescharacteristic
269C2×C4×D11C2311yescharacteristic
270C2×C4×D11C2311yescharacteristic
271C2×C4×D11C2311yescharacteristic
272C2×C4×D11C2311yescharacteristic
273C2×Dic22C2311yescharacteristic
274C2×Dic22C2311yescharacteristic
275C11×C4⋊C4C2311yescharacteristic
276C11×C4⋊C4C2311yescharacteristic
277C11×C4⋊C4C2311yescharacteristic
278C11×C4⋊C4C2311yescharacteristic
279C11×C4⋊C4C2311yescharacteristic
280C11×C4⋊C4C2311yescharacteristic
281C11×C22⋊C4C2311yescharacteristic
282C11×C22⋊C4C2311yescharacteristic
283C11×C22⋊C4C2311yescharacteristic
284C11×C22⋊C4C2311yescharacteristic
285C11×C22⋊C4C2311yescharacteristic
286C11×C22⋊C4C2311yescharacteristic
287C11×C22⋊C4C2311yescharacteristic
288C11×C22⋊C4C2311yescharacteristic
289C11×C22⋊C4C2311yescharacteristic
290C11×C22⋊C4C2311yescharacteristic
291C11×C22⋊C4C2311yescharacteristic
292C11×C22⋊C4C2311yescharacteristic
293C11×C22⋊C4C2311yescharacteristic
294C11×C22⋊C4C2311yescharacteristic
295C42×C11C2311yescharacteristic
296C42×C11C2311yescharacteristic
297C22⋊Dic11C2311yescharacteristic
298C22⋊Dic11C2311yescharacteristic
299C22⋊Dic11C2311yescharacteristic
300C22⋊Dic11C2311yescharacteristic
301C22⋊Dic11C2311yescharacteristic
302C22⋊Dic11C2311yescharacteristic
303C22⋊Dic11C2311yescharacteristic
304C22⋊Dic11C2311yescharacteristic
305(C2×D11)⋊C4C2311yescharacteristic
306(C2×D11)⋊C4C2311yescharacteristic
307(C2×D11)⋊C4C2311yescharacteristic
308(C2×D11)⋊C4C2311yescharacteristic
309(C2×D11)⋊C4C2311yescharacteristic
310(C2×D11)⋊C4C2311yescharacteristic
311(C2×D11)⋊C4C2311yescharacteristic
312(C2×D11)⋊C4C2311yescharacteristic
313(C2×D11)⋊C4C2311yescharacteristic
314(C2×D11)⋊C4C2311yescharacteristic
315(C2×D11)⋊C4C2311yescharacteristic
316(C2×D11)⋊C4C2311yescharacteristic
317(C2×D11)⋊C4C2311yescharacteristic
318(C2×D11)⋊C4C2311yescharacteristic
319(C2×D11)⋊C4C2311yescharacteristic
320(C2×D11)⋊C4C2311yescharacteristic
321(C2×D11)⋊C4C2311yescharacteristic
322(C2×D11)⋊C4C2311yescharacteristic
323(C2×D11)⋊C4C2311yescharacteristic
324(C2×D11)⋊C4C2311yescharacteristic
325(C2×D11)⋊C4C2311yescharacteristic
326(C2×D11)⋊C4C2311yescharacteristic
327(C2×D11)⋊C4C2311yescharacteristic
328(C2×D11)⋊C4C2311yescharacteristic
329C4⋊Dic11C2311yescharacteristic
330C4⋊Dic11C2311yescharacteristic
331C4⋊Dic11C2311yescharacteristic
332C4⋊Dic11C2311yescharacteristic
333Dic11⋊C4C2311yescharacteristic
334Dic11⋊C4C2311yescharacteristic
335Dic11⋊C4C2311yescharacteristic
336Dic11⋊C4C2311yescharacteristic
337Dic11⋊C4C2311yescharacteristic
338Dic11⋊C4C2311yescharacteristic
339Dic11⋊C4C2311yescharacteristic
340Dic11⋊C4C2311yescharacteristic
341Dic11⋊C4C2311yescharacteristic
342Dic11⋊C4C2311yescharacteristic
343Dic11⋊C4C2311yescharacteristic
344Dic11⋊C4C2311yescharacteristic
345Dic11⋊C4C2311yescharacteristic
346Dic11⋊C4C2311yescharacteristic
347Dic11⋊C4C2311yescharacteristic
348Dic11⋊C4C2311yescharacteristic
349C4×Dic11C2311yescharacteristic
350C4×Dic11C2311yescharacteristic
351C4×Dic11C2311yescharacteristic
352C4×Dic11C2311yescharacteristic
353C4×Dic11C2311yescharacteristic
354C4×Dic11C2311yescharacteristic
355C4×Dic11C2311yescharacteristic
356C4×Dic11C2311yescharacteristic
357#3519—111nomaximal, Sylow
358C23×C11—22no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11C2411yescharacteristic
362C23×C11C2411yescharacteristic
363C23×C11C2411yescharacteristic
364C23×C11C2411yescharacteristic
365C23×C11C2411yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—22no—
373C22×D11—41no—
374C22×D11—41no—
375C22×D11—41no—
376C22×D11—41no—
377C22×D11—41no—
378C22×D11—41no—
379C22×D11—41no—
380C22×D11—41no—
381C22×D11C2411yescharacteristic
382C22×D11C2411yescharacteristic
383C22×D11C2411yescharacteristic
384C22×D11C2411yescharacteristic
385C22×D11C2411yescharacteristic
386C22×D11C2411yescharacteristic
387Q8×C11—41no—
388D4×C11—22no—
389D4×C11—22no—
390D4×C11—41no—
391D4×C11—41no—
392D4×C11—41no—
393D4×C11—41no—
394D4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11C2411yescharacteristic
400C2×C4×C11C2411yescharacteristic
401C2×C4×C11C2411yescharacteristic
402C2×C4×C11C2411yescharacteristic
403C2×C4×C11C2411yescharacteristic
404C2×C4×C11C2411yescharacteristic
405C2×C4×C11C2411yescharacteristic
406C2×C4×C11C2411yescharacteristic
407C2×C4×C11C2411yescharacteristic
408C2×C4×C11C2411yescharacteristic
409C22⋊D11—22no—
410C22⋊D11—22no—
411C22⋊D11—22no—
412C22⋊D11—22no—
413C22⋊D11—22no—
414C22⋊D11—22no—
415C22⋊D11—22no—
416C22⋊D11—22no—
417C22⋊D11—22no—
418C22⋊D11—22no—
419C22⋊D11—22no—
420C22⋊D11—41no—
421C22⋊D11—41no—
422C22⋊D11—41no—
423C22⋊D11—41no—
424C22⋊D11—41no—
425C22⋊D11—41no—
426C22⋊D11—41no—
427C22⋊D11—41no—
428C22⋊D11#4114yescomplemented
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11C2411yescharacteristic
437C2×Dic11C2411yescharacteristic
438C2×Dic11C2411yescharacteristic
439C2×Dic11C2411yescharacteristic
440C2×Dic11C2411yescharacteristic
441C2×Dic11C2411yescharacteristic
442C2×Dic11C2411yescharacteristic
443C2×Dic11C2411yescharacteristic
444C2×Dic11C2411yescharacteristic
445C2×Dic11C2411yescharacteristic
446D44—22no—
447D44—22no—
448D44—22no—
449D44—22no—
450D44—22no—
451D44—41no—
452D44—41no—
453D44—41no—
454D44—41no—
455D44—41no—
456C4×D11—22no—
457C4×D11—22no—
458C4×D11—22no—
459C4×D11—22no—
460C4×D11—22no—
461C4×D11—22no—
462C4×D11—41no—
463C4×D11—41no—
464C4×D11—41no—
465C4×D11—41no—
466C4×D11—41no—
467C4×D11—41no—
468C4×D11—41no—
469C4×D11—41no—
470C4×D11—41no—
471C4×D11—41no—
472Dic22—22no—
473Dic22—41no—
474#555—111no—
475#554—111no—
476#553—111no—
477#553—111no—
478#553—111no—
479#553—111no—
480#550—111no—
481#546—111no—
482#546—111no—
483#546—111no—
484#546—111no—
485#546—111no—
486#546—111no—
487D42—111no—
488D42—111no—
489D42—111no—
490#540—111no—
491#540—111no—
492#538—111no—
493#538—111no—
494#538—111no—
495#538D1111yescharacteristic, complemented
496#532—111no—
497#529—111no—
498#525—111no—
499#525—111no—
500C2×#121—111no—
501C2×#121—111no—
502#518—111no—
503#518—111no—
504C2×C4×D4—111no—
505C22×C11—21no—
506C22×C11—21no—
507C22×C11—21no—
508C22×C11—21no—
509C22×C11—21no—
510C22×C11—21no—
511C22×C11—21no—
512C22×C11—21no—
513C22×C11—21no—
514C22×C11—21no—
515C22×C11—21no—
516C22×C11—21no—
517C22×C11—21no—
518C22×C11—21no—
519C22×C11—82no—
520C22×C11C2×#4112yes—
521C22×C11C2511yescharacteristic
522C2×D11—21no—
523C2×D11—21no—
524C2×D11—21no—
525C2×D11—21no—
526C2×D11—21no—
527C2×D11—21no—
528C2×D11—21no—
529C2×D11—21no—
530C2×D11—21no—
531C2×D11—21no—
532C2×D11—21no—
533C2×D11—21no—
534C2×D11—21no—
535C2×D11—21no—
536C2×D11—21no—
537C2×D11—21no—
538C2×D11—44no—
539C2×D11—44no—
540C2×D11—82no—
541C2×D11—82no—
542C2×D11—82no—
543C2×D11C2×#4112yes—
544C2×D11H(5,𝔽2)12yes—
545C4×C11—21no—
546C4×C11—21no—
547C4×C11—21no—
548C4×C11—21no—
549C4×C11—21no—
550C4×C11—21no—
551C4×C11—21no—
552C4×C11—21no—
553C4×C11—21no—
554C4×C11—21no—
555Dic11—21no—
556Dic11—21no—
557Dic11—21no—
558Dic11—21no—
559Dic11—21no—
560Dic11—21no—
561Dic11—21no—
562Dic11—21no—
563Dic11C2×#4112yes—
564Dic11H(5,𝔽2)12yes—
565C2×#41—111no—
566C2×#41—111no—
567C2×#41—111no—
568C2×#41—111no—
569C22×D4—111no—
570C22×D4—111no—
571C22×D4—111no—
572C22×D4—111no—
573C22×D4—111no—
574C22×D4—111no—
575C22×D4—111no—
576C22×D4—111no—
577C22×D4—111no—
578C23×C4—111no—
579C23×C4—111no—
580C4⋊Q8—111no—
581#127—111no—
582#127—111no—
583#127—111no—
584#126—111no—
585#126—111no—
586#126—111no—
587#126—111no—
588#126C2×D1111yescharacteristic, complemented
589#126C2×D1111yescharacteristic, complemented
590#125—111no—
591#125—111no—
592#125—111no—
593#124—111no—
594#124—111no—
595#124—111no—
596#124—111no—
597#124—111no—
598#124C2×D1111yescharacteristic, complemented
599#124C2×D1111yescharacteristic, complemented
600#123—111no—
601#123—111no—
602#123—111no—
603#123—111no—
604#123—111no—
605#123—111no—
606#123—111no—
607#123—111no—
608#123—111no—
609#123—111no—
610#123—111no—
611#123—111no—
612#123C2×D1111yescharacteristic, complemented
613#123C2×D1111yescharacteristic, complemented
614C22⋊Q8—111no—
615C22⋊Q8—111no—
616C22⋊Q8—111no—
617C22⋊Q8—111no—
618C22⋊Q8—111no—
619C22⋊Q8—111no—
620C22⋊Q8C2×D1111yescharacteristic, complemented
621#121—111no—
622#121—111no—
623#121—111no—
624#121—111no—
625#121—111no—
626#121—111no—
627#121—111no—
628#121—111no—
629#121—111no—
630#121—111no—
631#121—111no—
632#121—111no—
633#121—111no—
634#121—111no—
635#121—111no—
636#121—111no—
637#121—111no—
638#121—111no—
639#121—111no—
640#121—111no—
641#121—111no—
642#121—111no—
643#121—111no—
644#121—111no—
645#121—111no—
646#121—111no—
647#121—111no—
648#121—111no—
649#121—111no—
650#121—111no—
651#121—111no—
652#121—111no—
653#121C2×D1111yescharacteristic, complemented
654#121C2×D1111yescharacteristic, complemented
655#121C2×D1111yescharacteristic, complemented
656#120—111no—
657#120—111no—
658#120—111no—
659#120—111no—
660#120—111no—
661#120—111no—
662#120—111no—
663#120—111no—
664#120—111no—
665#120—111no—
666#120C2×D1111yescharacteristic, complemented
667#120C2×D1111yescharacteristic, complemented
668C4×Q8—111no—
669C4×D4—111no—
670C4×D4—111no—
671C4×D4—111no—
672C4×D4—111no—
673C4×D4—111no—
674C4×D4—111no—
675C4×D4—111no—
676C4×D4—111no—
677C4×D4—111no—
678C4×D4—111no—
679C4×D4—111no—
680C4×D4—111no—
681C4×D4—111no—
682C4×D4—111no—
683C4×D4—111no—
684C4×D4—111no—
685C4×D4—111no—
686C4×D4—111no—
687C4×D4—111no—
688C4×D4—111no—
689C4×D4—111no—
690C4×D4—111no—
691C4×D4—111no—
692C4×D4—111no—
693C4×D4—111no—
694C4×D4—111no—
695C4×D4—111no—
696C4×D4—111no—
697C4×D4—111no—
698C4×D4C2×D1111yescharacteristic, complemented
699C4×D4C2×D1111yescharacteristic, complemented
700#117—111no—
701#117—111no—
702#117—111no—
703#117—111no—
704#117—111no—
705#117—111no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—111no—
708C2×C4⋊C4—111no—
709C2×C22⋊C4—111no—
710C2×C22⋊C4—111no—
711C2×C22⋊C4—111no—
712C2×C22⋊C4—111no—
713C2×C22⋊C4—111no—
714C2×C22⋊C4—111no—
715C2×C22⋊C4—111no—
716C2×C22⋊C4—111no—
717C2×C22⋊C4—111no—
718C2×C22⋊C4C2×D1111yescharacteristic, complemented
719C2×C42—111no—
720C2×C11—22no—
721C2×C11—41no—
722C2×C11—41no—
723C2×C11—41no—
724C2×C11—41no—
725C2×C11C22×#4111yescharacteristic
726C2×C11C2×H(5,𝔽2)11yescharacteristic
727C2×C11C2×H(5,𝔽2)11yescharacteristic
728D11—22no—
729D11—22no—
730D11—41no—
731D11—41no—
732D11—41no—
733D11—41no—
734C24—111no—
735C24—111no—
736C24—111no—
737C24—111no—
738C24—111no—
739C24C22×D1111yescharacteristic
740#41—442no—
741#41—442no—
742#41—442no—
743#41—442no—
744C2×Q8—111no—
745C2×Q8—111no—
746C2×Q8C22×D1111yescharacteristic
747C2×D4—111no—
748C2×D4—111no—
749C2×D4—111no—
750C2×D4—111no—
751C2×D4—111no—
752C2×D4—111no—
753C2×D4—111no—
754C2×D4—111no—
755C2×D4—111no—
756C2×D4—111no—
757C2×D4—111no—
758C2×D4—111no—
759C2×D4—111no—
760C2×D4—111no—
761C2×D4—111no—
762C2×D4—111no—
763C2×D4—111no—
764C2×D4—111no—
765C2×D4—111no—
766C2×D4—111no—
767C2×D4—111no—
768C2×D4—111no—
769C2×D4—111no—
770C2×D4—111no—
771C2×D4—111no—
772C2×D4—111no—
773C2×D4—111no—
774C2×D4—111no—
775C2×D4—111no—
776C2×D4—111no—
777C2×D4—224no—
778C2×D4—224no—
779C2×D4—224no—
780C2×D4—442no—
781C2×D4—442no—
782C2×D4—442no—
783C2×D4—442no—
784C2×D4—442no—
785C2×D4—442no—
786C2×D4C22×D1111yescharacteristic
787C2×D4C22×D1111yescharacteristic
788C2×D4C22×D1111yescharacteristic
789C2×D4C22×D1111yescharacteristic
790C2×D4C22×D1111yescharacteristic
791C2×D4C22×D1111yescharacteristic
792C2×D4C22×D1111yescharacteristic
793C22×C4—111no—
794C22×C4—111no—
795C22×C4—111no—
796C22×C4—111no—
797C22×C4—111no—
798C22×C4—111no—
799C22×C4—111no—
800C22×C4—111no—
801C22×C4—111no—
802C22×C4—111no—
803C22×C4—111no—
804C22×C4—111no—
805C22×C4—111no—
806C22×C4—111no—
807C22×C4—111no—
808C22×C4—111no—
809C22×C4—111no—
810C22×C4—111no—
811C22×C4—111no—
812C22×C4—111no—
813C22×C4—111no—
814C22×C4—111no—
815C22×C4—111no—
816C22×C4—442no—
817C22×C4—442no—
818C22×C4C22×D1111yescharacteristic
819C22×C4C22×D1111yescharacteristic
820C22×C4C22×D1111yescharacteristic
821C22×C4C22×D1111yescharacteristic
822C4⋊C4—111no—
823C4⋊C4—111no—
824C4⋊C4—111no—
825C4⋊C4—111no—
826C4⋊C4—111no—
827C4⋊C4—111no—
828C4⋊C4—111no—
829C4⋊C4—111no—
830C4⋊C4—111no—
831C4⋊C4—111no—
832C4⋊C4—111no—
833C4⋊C4—111no—
834C4⋊C4—111no—
835C4⋊C4—111no—
836C4⋊C4—111no—
837C4⋊C4—111no—
838C4⋊C4—111no—
839C4⋊C4—111no—
840C4⋊C4—111no—
841C4⋊C4—111no—
842C4⋊C4C22×D1111yescharacteristic
843C4⋊C4C22×D1111yescharacteristic
844C4⋊C4C22×D1111yescharacteristic
845C4⋊C4C22×D1111yescharacteristic
846C4⋊C4C22×D1111yescharacteristic
847C4⋊C4C22×D1111yescharacteristic
848C22⋊C4—111no—
849C22⋊C4—111no—
850C22⋊C4—111no—
851C22⋊C4—111no—
852C22⋊C4—111no—
853C22⋊C4—111no—
854C22⋊C4—111no—
855C22⋊C4—111no—
856C22⋊C4—111no—
857C22⋊C4—111no—
858C22⋊C4—111no—
859C22⋊C4—111no—
860C22⋊C4—111no—
861C22⋊C4—111no—
862C22⋊C4—111no—
863C22⋊C4—111no—
864C22⋊C4—111no—
865C22⋊C4—111no—
866C22⋊C4—111no—
867C22⋊C4—111no—
868C22⋊C4—111no—
869C22⋊C4—111no—
870C22⋊C4—111no—
871C22⋊C4—111no—
872C22⋊C4—111no—
873C22⋊C4—111no—
874C22⋊C4—111no—
875C22⋊C4—111no—
876C22⋊C4—111no—
877C22⋊C4—111no—
878C22⋊C4—111no—
879C22⋊C4—111no—
880C22⋊C4C22×D1111yescharacteristic
881C22⋊C4C22×D1111yescharacteristic
882C22⋊C4C22×D1111yescharacteristic
883C22⋊C4C22×D1111yescharacteristic
884C22⋊C4C22×D1111yescharacteristic
885C22⋊C4C22×D1111yescharacteristic
886C22⋊C4C22×D1111yescharacteristic
887C22⋊C4C22×D1111yescharacteristic
888C22⋊C4C22×D1111yescharacteristic
889C22⋊C4C22×D1111yescharacteristic
890C22⋊C4C22×D1111yescharacteristic
891C22⋊C4C22×D1111yescharacteristic
892C22⋊C4C22×D1111yescharacteristic
893C22⋊C4C22×D1111yescharacteristic
894C42—111no—
895C42—111no—
896C42—111no—
897C42—111no—
898C42—111no—
899C42—111no—
900C42—111no—
901C42—111no—
902C42C22×D1111yescharacteristic
903C42C22×D1111yescharacteristic
904C11#351911yescharacteristic, complemented, Sylow
905C23—22no—
906C23—41no—
907C23—41no—
908C23—111no—
909C23—111no—
910C23—111no—
911C23—111no—
912C23—111no—
913C23—111no—
914C23—222no—
915C23—222no—
916C23—222no—
917C23—222no—
918C23—222no—
919C23—222no—
920C23—222no—
921C23—441no—
922C23—441no—
923C23—441no—
924C23—441no—
925C23—441no—
926C23—441no—
927C23—441no—
928C23—441no—
929C23C23×D1111yescharacteristic
930C23C23×D1111yescharacteristic
931C23C23×D1111yescharacteristic
932C23C23×D1111yescharacteristic
933C23C23×D1111yescharacteristic
934Q8—41no—
935Q8—222no—
936Q8—441no—
937D4—22no—
938D4—22no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943D4—41no—
944D4—114no—
945D4—222no—
946D4—222no—
947D4—222no—
948D4—222no—
949D4—222no—
950D4—222no—
951D4—222no—
952D4—222no—
953D4—222no—
954D4—222no—
955D4—222no—
956D4—222no—
957D4—222no—
958D4—222no—
959D4—222no—
960D4—222no—
961D4—441no—
962D4—441no—
963D4—441no—
964D4—441no—
965D4—441no—
966D4—441no—
967D4—441no—
968D4—441no—
969D4—441no—
970D4—441no—
971D4—441no—
972D4—441no—
973D4—441no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—111no—
979C2×C4—111no—
980C2×C4—111no—
981C2×C4—111no—
982C2×C4—111no—
983C2×C4—111no—
984C2×C4—111no—
985C2×C4—111no—
986C2×C4—111no—
987C2×C4—111no—
988C2×C4—222no—
989C2×C4—222no—
990C2×C4—222no—
991C2×C4—222no—
992C2×C4—222no—
993C2×C4—222no—
994C2×C4—222no—
995C2×C4—222no—
996C2×C4—222no—
997C2×C4—441no—
998C2×C4—441no—
999C2×C4—441no—
1000C2×C4—441no—
1001C2×C4—441no—
1002C2×C4—441no—
1003C2×C4—441no—
1004C2×C4—441no—
1005C2×C4—441no—
1006C2×C4—441no—
1007C2×C4—441no—
1008C2×C4—441no—
1009C2×C4—441no—
1010C2×C4—441no—
1011C2×C4C23×D1111yescharacteristic
1012C2×C4C23×D1111yescharacteristic
1013C2×C4C23×D1111yescharacteristic
1014C2×C4C23×D1111yescharacteristic
1015C2×C4C23×D1111yescharacteristic
1016C2×C4C23×D1111yescharacteristic
1017C2×C4C23×D1111yescharacteristic
1018C2×C4C23×D1111yescharacteristic
1019C2×C4C23×D1111yescharacteristic
1020C2×C4C23×D1111yescharacteristic
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—21no—
1030C22—21no—
1031C22—21no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—82no—
1036C22—112no—
1037C22—112no—
1038C22—221no—
1039C22—221no—
1040C22—221no—
1041C22—221no—
1042C22—221no—
1043C22—221no—
1044C22—221no—
1045C22—221no—
1046C22—221no—
1047C22—221no—
1048C22—221no—
1049C22—221no—
1050C22—221no—
1051C22—221no—
1052C22—221no—
1053C22—221no—
1054C22—444no—
1055C22—444no—
1056C22—882no—
1057C22—882no—
1058C22—882no—
1059C22#41×D1112yes—
1060C22C24×D1111yescharacteristic
1061C4—21no—
1062C4—21no—
1063C4—21no—
1064C4—21no—
1065C4—21no—
1066C4—21no—
1067C4—21no—
1068C4—21no—
1069C4—21no—
1070C4—21no—
1071C4—112no—
1072C4—112no—
1073C4—221no—
1074C4—221no—
1075C4—221no—
1076C4—221no—
1077C4—221no—
1078C4—221no—
1079C4—221no—
1080C4—221no—
1081C2—22no—
1082C2—41no—
1083C2—41no—
1084C2—41no—
1085C2—41no—
1086C2—222no—
1087C2—222no—
1088C2—441no—
1089C2—441no—
1090C2—441no—
1091C2—441no—
1092C2C2×#41×D1111yescharacteristic
1093C2D11×H(5,𝔽2)11yescharacteristic
1094C2D11×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C24×D11
commutator, socle, cosocleC22×C11C25
FittingC11×#538C2
hypercenter#538D11
hypocenterC11#3519
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ #538

Complements

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

NH ≅ G/Ntype
1. C11×#538C2semidirect
2. #10623240C2semidirect
3. #10623240C2semidirect
4. #10623237C2semidirect
5. #10623235C2semidirect
6. #10623209C2semidirect
7. #10623207C2semidirect
8. #10623201C2semidirect
9. #10623199C2semidirect
10. #10623194C2semidirect
11. #10623192C2semidirect
12. #10623187C2semidirect
13. #10623185C2semidirect
14. #10623167C2semidirect
15. #10623161C2semidirect
16. #10623146C2semidirect
17. #10623141C2semidirect
18. #10623140C2semidirect
19. D11×#121C2semidirect
20. #10623132C2semidirect
21. #10623130C2semidirect
22. #10623122C2semidirect
23. #10623122C2semidirect
24. #10623121C2semidirect
25. #10623121C2semidirect
26. #10623091C2semidirect
27. #10623078C2semidirect
28. #10623076C2semidirect
29. C4×D4×D11C2semidirect
30. C2×#66937C2semidirect
31. #10623017C2semidirect
33. C22×C22⋊D11C22semidirect
34. C22×C22⋊D11C22semidirect
35. C2×#4343C22semidirect
36. C2×#4341C22semidirect
37. C2×#4341C22semidirect
40. C2×D4×D11C22semidirect
41. C2×D4×D11C22semidirect
42. C2×D4×D11C22semidirect
43. C2×#4339C22semidirect
44. C22×D44C22semidirect
45. C22×C4×D11C22semidirect
46. C22×C4×D11C22semidirect
47. C11×#126C22semidirect
48. C11×#126C22semidirect
49. C11×#124C22semidirect
50. C11×#124C22semidirect
51. C11×#123C22semidirect
52. C11×#123C22semidirect
53. C11×C22⋊Q8C22semidirect
54. C11×#121C22semidirect
55. C11×#121C22semidirect
56. C11×#121C22semidirect
57. C11×#120C22semidirect
58. C11×#120C22semidirect
59. C4×D4×C11C22semidirect
60. C4×D4×C11C22semidirect
61. C2×C11×C22⋊C4C22semidirect
62. C2×C22⋊Dic11C22semidirect
63. #67000C22semidirect
64. #66999C22semidirect
65. #66997C22semidirect
66. #66993C22semidirect
67. #66993C22semidirect
68. #66993C22semidirect
69. #66992C22semidirect
70. #66992C22semidirect
71. #66992C22semidirect
72. #66992C22semidirect
73. #66992C22semidirect
74. #66992C22semidirect
75. #66992C22semidirect
76. #66992C22semidirect
77. #66992C22semidirect
78. #66991C22semidirect
79. #66991C22semidirect
80. #66990C22semidirect
81. #66990C22semidirect
82. #66990C22semidirect
83. #66990C22semidirect
84. #66988C22semidirect
85. D4×Dic11C22semidirect
86. D4×Dic11C22semidirect
87. #66983C22semidirect
88. #66982C22semidirect
91. C4×C22⋊D11C22semidirect
92. C4×C22⋊D11C22semidirect
93. C4×C22⋊D11C22semidirect
94. C4×C22⋊D11C22semidirect
95. C4×C22⋊D11C22semidirect
96. C2×(C2×D11)⋊C4C22semidirect
97. C2×(C2×D11)⋊C4C22semidirect
98. C2×Dic11⋊C4C22semidirect
99. #66951C22semidirect
100. #66951C22semidirect
101. #66949C22semidirect
102. #66949C22semidirect
103. #66949C22semidirect
104. #66948C22semidirect
105. #66948C22semidirect
106. #66948C22semidirect
107. #66948C22semidirect
108. #66947C22semidirect
109. #66947C22semidirect
110. #66947C22semidirect
111. #66947C22semidirect
112. #66946C22semidirect
113. #66946C22semidirect
114. #66946C22semidirect
115. #66946C22semidirect
116. #66945C22semidirect
117. C4⋊C4×D11C22semidirect
118. C4⋊C4×D11C22semidirect
119. #66942C22semidirect
120. #66942C22semidirect
121. #66942C22semidirect
122. #66940C22semidirect
123. #66939C22semidirect
124. #66939C22semidirect
125. #66938C22semidirect
126. #66938C22semidirect
127. #66938C22semidirect
129. #66937C22semidirect
130. #66937C22semidirect
131. #66937C22semidirect
132. #66937C22semidirect
133. #66937C22semidirect
134. #66937C22semidirect
135. #66937C22semidirect
136. #66937C22semidirect
137. #66937C22semidirect
138. #66937C22semidirect
139. #66937C22semidirect
140. #66937C22semidirect
141. #66937C22semidirect
142. #66937C22semidirect
143. #66937C22semidirect
144. #66936C22semidirect
145. #66936C22semidirect
146. #66936C22semidirect
147. #66936C22semidirect
148. #66935C22semidirect
149. #66935C22semidirect
150. #66935C22semidirect
151. #66935C22semidirect
152. #66935C22semidirect
153. #66935C22semidirect
156. (C22⋊D11)⋊C4C22semidirect
157. (C22⋊D11)⋊C4C22semidirect
158. (C22⋊D11)⋊C4C22semidirect
159. (C22⋊D11)⋊C4C22semidirect
160. (C22⋊D11)⋊C4C22semidirect
161. (C22⋊D11)⋊C4C22semidirect
162. (C22⋊D11)⋊C4C22semidirect
163. (C22⋊D11)⋊C4C22semidirect
164. (C22⋊D11)⋊C4C22semidirect
165. (C22⋊D11)⋊C4C22semidirect
166. (C22⋊D11)⋊C4C22semidirect
167. C22⋊C4×D11C22semidirect
168. C22⋊C4×D11C22semidirect
169. C22⋊C4×D11C22semidirect
170. C22⋊C4×D11C22semidirect
171. C22⋊C4×D11C22semidirect
172. C22⋊C4×D11C22semidirect
173. #66932C22semidirect
174. #66931C22semidirect
175. #66931C22semidirect
176. #66930C22semidirect
177. #66930C22semidirect
178. #66930C22semidirect
179. #66929C22semidirect
180. #66928C22semidirect
181. C4×D44C22semidirect
182. C4×D44C22semidirect
183. C4×D44C22semidirect
184. #66925C22semidirect
185. #66925C22semidirect
186. C42×D11C22semidirect
428. C22⋊D11#41semidirect
495. #538D11semidirect
588. #126C2×D11semidirect
589. #126C2×D11semidirect
598. #124C2×D11semidirect
599. #124C2×D11semidirect
612. #123C2×D11semidirect
613. #123C2×D11semidirect
620. C22⋊Q8C2×D11semidirect
653. #121C2×D11semidirect
654. #121C2×D11semidirect
655. #121C2×D11semidirect
666. #120C2×D11semidirect
667. #120C2×D11semidirect
698. C4×D4C2×D11semidirect
699. C4×D4C2×D11semidirect
718. C2×C22⋊C4C2×D11semidirect
904. C11#3519semidirect

Maximal subgroups

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

subgroupindex
C11×#5382
#106232402
#106232372
#106232352
#106232092
#106232072
#106232012
#106231992
#106231942
#106231922
#106231872
#106231852
#106231672
#106231612
#106231462
#106231412
#106231402
D11×#1212
#106231322
#106231302
#106231222
#106231212
#106230912
#106230782
#106230762
C4×D4×D112
C2×#669372
#106230172
#351911