Finite Group Databasebeta

← #15618902

Subgroups — #15618902

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#529C211yesmaximal, characteristic
2#13077787C212yesmaximal, complemented
3#13077780C212yesmaximal, complemented
4#13077779C211yesmaximal, characteristic, complemented
5#13077777C211yesmaximal, characteristic, complemented
6#13077775C211yesmaximal, characteristic, complemented
7#13077771C211yesmaximal, characteristic, complemented
8#13077767C211yesmaximal, characteristic, complemented
9#13077765C211yesmaximal, characteristic, complemented
10#13077761C211yesmaximal, characteristic, complemented
11#13077753C212yesmaximal, complemented
12#13077750C212yesmaximal, complemented
13#13077568C211yesmaximal, characteristic, complemented
14Q8×#4313C211yesmaximal, characteristic, complemented
15#13077352C212yesmaximal, complemented
16#13077352C211yesmaximal, characteristic, complemented
17#13077349C212yesmaximal, complemented
18D4×#4313C211yesmaximal, characteristic, complemented
19#13077250C212yesmaximal, complemented
20#13077244C211yesmaximal, characteristic, complemented
21#13077177C212yesmaximal, complemented
22D11×#423C211yesmaximal, characteristic, complemented
23C11×#2993C211yesmaximal, characteristic, complemented
24C11×#529C2211yescharacteristic
25C2×M16×D11C2212yes—
26C2×M16×D11C2212yes—
27C22×#4313C2212yes—
28#10623237C412yes—
29D11×#126C412yes—
30#10623222C411yescharacteristic
31D11×#125C411yescharacteristic
32#10623211C411yescharacteristic
33D11×#124C411yescharacteristic
34D11×#123C412yes—
35#10623180C412yes—
36D11×C22⋊Q8C411yescharacteristic
37#10623155C411yescharacteristic
38D11×#121C411yescharacteristic
39#10623131C411yescharacteristic
40#10623111C2211yescharacteristic
41C4×Q8×D11C2211yescharacteristic
42#10623088C2211yescharacteristic
43C4×D4×D11C2211yescharacteristic
44C4×D4×D11C2212yes—
45#10623069C2212yes—
46#10623059C2212yes—
47D11×#117C2212yes—
48#10623010C2211yescharacteristic
49C2×C42×D11C2211yescharacteristic
50C11×#446C2211yescharacteristic, complemented
51C8×Q8×C11C2211yescharacteristic, complemented
52C11×#436C2211yescharacteristic, complemented
53C11×#436C2212yescomplemented
54C11×#435C2212yescomplemented
55C8×D4×C11C2211yescharacteristic, complemented
56C11×#433C2212yescomplemented
57C11×#431C2211yescharacteristic, complemented
58C11×#424C2212yescomplemented
59C11×#423C2211yescharacteristic, complemented
60#10622741C2212yescomplemented
61#10622740C2212yescomplemented
62#10622740C2212yescomplemented
63#10622740C2212yescomplemented
64#10622732C2212yescomplemented
65#10622731C2212yescomplemented
66#10622724C2212yescomplemented
67C8×C22⋊D11C2212yescomplemented
68#10622715C2212yescomplemented
69#10622637C2211yescharacteristic, complemented
70Q8×C11⋊C8C2211yescharacteristic, complemented
71#10622625C2211yescharacteristic, complemented
72#10622625C2212yescomplemented
73#10622624C2212yescomplemented
74D4×C11⋊C8C2211yescharacteristic, complemented
75#10622613C2212yescomplemented
76#10622612C2212yescomplemented
77#10622538C2211yescharacteristic, complemented
78#10622537C2211yescharacteristic, complemented
79#10622453C2212yescomplemented
80#10622453C2212yescomplemented
81#10622452C2212yescomplemented
82#10622452C2212yescomplemented
83#10622452C2212yescomplemented
84#10622452C2212yescomplemented
85#10622451C2211yescharacteristic, complemented
86#10622450C2211yescharacteristic
87#10622450C2212yes—
88#10622450C2212yes—
89#10622450C2211yescharacteristic
90#10622450C2211yescharacteristic
91#10622450C2212yes—
92#10622450C2211yescharacteristic
93#10622449C2212yescomplemented
94#10622448C2211yescharacteristic, complemented
95#10622448C2211yescharacteristic, complemented
96#10622447C2211yescharacteristic, complemented
97#10622447C2212yescomplemented
98D11×C4⋊C8C2211yescharacteristic, complemented
99D11×C4⋊C8C2211yescharacteristic, complemented
100D11×C4⋊C8C2212yescomplemented
101#10622444C2211yescharacteristic, complemented
102#10622444C2212yescomplemented
103#10622443C2211yescharacteristic, complemented
104#10622441C2212yescomplemented
105#10622343C2212yescomplemented
106#10622342C2212yescomplemented
107#10622341C2212yescomplemented
108#10622341C2212yescomplemented
109#10622341C2212yescomplemented
110#10622339C2212yes—
111#10622339C2212yes—
112#10622339C2211yescharacteristic
113#10622339C2211yescharacteristic
114(C22⋊D11)⋊C8C2212yescomplemented
115#10622333C2212yescomplemented
116#10622333C2212yescomplemented
117#10622332C2211yescharacteristic, complemented
118#10622332C2211yescharacteristic, complemented
119#10622322C2212yescomplemented
120#10622320C2212yes—
121#10622319C2212yescomplemented
122#10622314C2212yescomplemented
123#10622303C2212yescomplemented
124#10622301C2211yescharacteristic, complemented
125C4×#4313C2212yes—
126C4×#4313C2211yescharacteristic
127C4×#4313C2211yescharacteristic
128C8×D44C2211yescharacteristic, complemented
129C8×D44C2212yescomplemented
130#10622298C2211yescharacteristic, complemented
131#10622298C2211yescharacteristic, complemented
132#10622292C2211yescharacteristic, complemented
133#10622292C2212yescomplemented
134C8×Dic22C2211yescharacteristic, complemented
135C2×Q8×D11C2×C411yescharacteristic
136C2×D4×D11C2×C412yes—
137C2×D4×D11C2×C411yescharacteristic
138C22×C4×D11C2×C411yescharacteristic
139C22×C4×D11C2×C411yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C2×C11×M16C2312yes—
143C2×C11×M16C2312yes—
144C22×C8×C11C2312yes—
145C11×#126C2×C412yes—
146C11×#125C2×C411yescharacteristic
147C11×#124C2×C411yescharacteristic
148C11×#123C2×C412yes—
149C11×C22⋊Q8C2×C411yescharacteristic
150C11×#121C2×C411yescharacteristic
151C4×Q8×C11C2311yescharacteristic
152C4×D4×C11C2312yes—
153C4×D4×C11C2311yescharacteristic
154C11×#117C2312yes—
155C2×C42×C11C2311yescharacteristic
156#67000C2×C411yescharacteristic
157#66999C2×C411yescharacteristic
158Q8×Dic11C2×C411yescharacteristic
159#66992C2×C412yes—
160#66991C2×C411yescharacteristic
161#66989C2×C411yescharacteristic
162#66988C2×C412yes—
163D4×Dic11C2×C412yes—
164D4×Dic11C2×C411yescharacteristic
165#66983C2×C411yescharacteristic
166#66982C2×C412yes—
167C4×C22⋊D11C2312yes—
168C4×C22⋊D11C2312yes—
169C4×C22⋊D11C2312yes—
170#66979C2312yes—
171#66977C2×C411yescharacteristic
172C2×C4×Dic11C2×C411yescharacteristic
173C2×C4×Dic11C2×C411yescharacteristic
174C2×C4×Dic11C2311yescharacteristic
175C2×#4318C2312yes—
176C2×#4318C2312yes—
177C22×C11⋊C8C2312yes—
178M16×D11—44no—
179M16×D11—44no—
180C2×#4313—44no—
181C2×#4313C2311yescharacteristic
182C2×#4313C2312yes—
183C2×#4313C2312yes—
184C2×#4313C2311yescharacteristic
185C2×#4313C2311yescharacteristic
186C2×#4313C2311yescharacteristic
187C2×#4313C2312yes—
188C2×#4313C2312yes—
189C2×C8×D11C2312yes—
190C2×C8×D11C2312yes—
191C2×C8×D11C2312yes—
192C2×C8×D11C2312yes—
193#66951C2×C412yes—
194#66951C2×C412yes—
195#66951C2×C412yes—
196#66950C2×C411yescharacteristic
197#66949C2×C412yes—
198#66948C2×C411yescharacteristic
199#66947C2×C412yes—
200#66947C2×C412yes—
201#66946C2×C412yes—
202#66946C2×C411yescharacteristic
203#66945C2×C412yes—
204#66945C2×C412yes—
205C4⋊C4×D11C2×C412yes—
206C4⋊C4×D11C2×C412yes—
207C4⋊C4×D11C2×C412yes—
208C4⋊C4×D11C2×C412yes—
209C4⋊C4×D11C2×C411yescharacteristic
210C4⋊C4×D11C2×C411yescharacteristic
211#66943C2×C411yescharacteristic
212#66943C2×C411yescharacteristic
213#66942C2×C412yes—
214#66942C2×C412yes—
215#66940C2×C412yes—
216#66940C2×C411yescharacteristic
217#66939C2×C412yes—
218#66938C2×C412yes—
219#66938C2×C412yes—
220#66937C2×C412yes—
221#66936C2×C412yes—
222#66936C2×C412yes—
223(C22⋊D11)⋊C4C2×C412yes—
224(C22⋊D11)⋊C4C2×C412yes—
225(C22⋊D11)⋊C4C2×C412yes—
226C22⋊C4×D11C2×C412yes—
227C22⋊C4×D11C2×C412yes—
228C22⋊C4×D11C2×C412yes—
229C22⋊C4×D11C2×C412yes—
230C22⋊C4×D11C2×C412yes—
231#66932C2×C412yes—
232#66932C2×C412yes—
233#66932C2×C412yes—
234#66931C2×C412yes—
235#66930C2×C412yes—
236#66930C2×C412yes—
237#66929C2×C412yes—
238#66928C2×C411yescharacteristic
239C4×D44C2311yescharacteristic
240C4×D44C2312yes—
241#66925C2312yes—
242#66925C2312yes—
243C42×D11C2×C411yescharacteristic
244C42×D11C2×C411yescharacteristic
245C42×D11C2×C411yescharacteristic
246C42×D11C2×C411yescharacteristic
247C42×D11C2311yescharacteristic
248C42×D11C2311yescharacteristic
249C42×D11C2311yescharacteristic
250C42×D11C2311yescharacteristic
251C42×D11C2312yes—
252#66923C2×C411yescharacteristic
253C4×Dic22C2311yescharacteristic
254C4×Dic22C2312yes—
255C11×C4⋊C8C2312yes—
256C11×C4⋊C8C2311yescharacteristic
257C11×C4⋊C8C2311yescharacteristic
258C11×C4⋊C8C2311yescharacteristic
259C11×C4⋊C8C2312yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2311yescharacteristic
262C11×C22⋊C8C2311yescharacteristic
263C11×C22⋊C8C2311yescharacteristic
264C11×C22⋊C8C2312yes—
265C11×C22⋊C8C2312yes—
266C11×#97C2312yes—
267C4×C8×C11C2311yescharacteristic
268C4×C8×C11C2311yescharacteristic
269C4×C8×C11C2312yes—
270C22⋊(C11⋊C8)C2312yes—
271C22⋊(C11⋊C8)C2312yes—
272C22⋊(C11⋊C8)C2311yescharacteristic
273C22⋊(C11⋊C8)C2311yescharacteristic
274(C2×D11)⋊C8C2311yescharacteristic
275(C2×D11)⋊C8C2312yes—
276(C2×D11)⋊C8C2311yescharacteristic
277(C2×D11)⋊C8C2312yes—
278(C2×D11)⋊C8C2311yescharacteristic
279(C2×D11)⋊C8C2311yescharacteristic
280(C2×D11)⋊C8C2312yes—
281(C2×D11)⋊C8C2312yes—
282#66879C2311yescharacteristic
283#66879C2311yescharacteristic
284#66879C2312yes—
285#66879C2311yescharacteristic
286#66879C2312yes—
287#66879C2311yescharacteristic
288Dic11⋊C8C2312yes—
289Dic11⋊C8C2312yes—
290Dic11⋊C8C2312yes—
291Dic11⋊C8C2312yes—
292Dic11⋊C8C2312yes—
293Dic11⋊C8C2311yescharacteristic
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2311yescharacteristic
298Dic11⋊C8C2311yescharacteristic
299Dic11⋊C8C2311yescharacteristic
300C8×Dic11C2312yes—
301C8×Dic11C2312yes—
302C4⋊(C11⋊C8)C2311yescharacteristic
303C4⋊(C11⋊C8)C2311yescharacteristic
304C4⋊(C11⋊C8)C2312yes—
305C4⋊(C11⋊C8)C2311yescharacteristic
306C4⋊(C11⋊C8)C2311yescharacteristic
307C4⋊(C11⋊C8)C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309#66867C2312yes—
310C4×C11⋊C8C2311yescharacteristic
311C4×C11⋊C8C2311yescharacteristic
312C4×C11⋊C8C2312yes—
313#60264—111nomaximal, Sylow
314C23×D11C22×C411yescharacteristic
315C23×D11C22×C412yes—
316C2×Q8×C11C22×C411yescharacteristic
317C2×D4×C11C22×C411yescharacteristic
318C2×D4×C11C22×C412yes—
319C22×C4×C11C22×C411yescharacteristic
320C22×C4×C11C22×C411yescharacteristic
321C22×C4×C11C2412yes—
322C22×C4×C11C2411yescharacteristic
323C2×C22⋊D11C22×C412yes—
324C2×C22⋊D11C22×C412yes—
325C2×C22⋊D11C22×C412yes—
326C22×Dic11C22×C412yes—
327C22×Dic11C22×C411yescharacteristic
328C22×Dic11C22×C411yescharacteristic
329C22×Dic11C22×C411yescharacteristic
330Q8×D11—42no—
331D4×D11—42no—
332D4×D11—44no—
333C2×D44C22×C411yescharacteristic
334C2×D44C22×C412yes—
335C2×C4×D11—24no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11C22×C411yescharacteristic
342C2×C4×D11C22×C411yescharacteristic
343C2×C4×D11C22×C411yescharacteristic
344C2×C4×D11C22×C411yescharacteristic
345C2×C4×D11C22×C411yescharacteristic
346C2×C4×D11C22×C411yescharacteristic
347C2×C4×D11C22×C412yes—
348C2×C4×D11C22×C412yes—
349C2×C4×D11C22×C411yescharacteristic
350C2×C4×D11C22×C411yescharacteristic
351C2×C4×D11C22×C411yescharacteristic
352C2×C4×D11C22×C411yescharacteristic
353C2×C4×D11C22×C412yes—
354C2×C4×D11C22×C412yes—
355C2×C4×D11C2411yescharacteristic
356C2×C4×D11C2412yes—
357C2×C4×D11C2411yescharacteristic
358C2×Dic22C22×C411yescharacteristic
359C2×Dic22C22×C412yes—
360C11×M16—42no—
361C11×M16—42no—
362C2×C8×C11—42no—
363C2×C8×C11C2411yescharacteristic
364C2×C8×C11C2412yes—
365C2×C8×C11C2412yes—
366C2×C8×C11C2411yescharacteristic
367C2×C8×C11C2411yescharacteristic
368C2×C8×C11C2411yescharacteristic
369C11×C4⋊C4C22×C411yescharacteristic
370C11×C4⋊C4C22×C412yes—
371C11×C4⋊C4C22×C412yes—
372C11×C4⋊C4C22×C412yes—
373C11×C4⋊C4C22×C411yescharacteristic
374C11×C4⋊C4C22×C412yes—
375C11×C22⋊C4C22×C412yes—
376C11×C22⋊C4C22×C412yes—
377C11×C22⋊C4C22×C412yes—
378C11×C22⋊C4C22×C412yes—
379C11×C22⋊C4C22×C412yes—
380C42×C11C22×C411yescharacteristic
381C42×C11C22×C411yescharacteristic
382C42×C11C2411yescharacteristic
383C42×C11C2412yes—
384C42×C11C2411yescharacteristic
385C22⋊Dic11C22×C412yes—
386C22⋊Dic11C22×C412yes—
387C22⋊Dic11C22×C412yes—
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C412yes—
390(C2×D11)⋊C4C22×C412yes—
391(C2×D11)⋊C4C22×C412yes—
392(C2×D11)⋊C4C22×C412yes—
393(C2×D11)⋊C4C22×C412yes—
394(C2×D11)⋊C4C22×C412yes—
395(C2×D11)⋊C4C22×C412yes—
396(C2×D11)⋊C4C22×C412yes—
397(C2×D11)⋊C4C22×C412yes—
398(C2×D11)⋊C4C22×C412yes—
399(C2×D11)⋊C4C22×C412yes—
400C4⋊Dic11C22×C411yescharacteristic
401C4⋊Dic11C22×C412yes—
402C4⋊Dic11C22×C411yescharacteristic
403C4⋊Dic11C22×C412yes—
404C4⋊Dic11C22×C412yes—
405C4⋊Dic11C22×C412yes—
406Dic11⋊C4C22×C412yes—
407Dic11⋊C4C22×C412yes—
408Dic11⋊C4C22×C412yes—
409Dic11⋊C4C22×C412yes—
410Dic11⋊C4C22×C412yes—
411Dic11⋊C4C22×C412yes—
412Dic11⋊C4C22×C412yes—
413Dic11⋊C4C22×C412yes—
414Dic11⋊C4C22×C412yes—
415Dic11⋊C4C22×C412yes—
416C4×Dic11C22×C411yescharacteristic
417C4×Dic11C22×C411yescharacteristic
418C4×Dic11C22×C411yescharacteristic
419C4×Dic11C22×C411yescharacteristic
420C4×Dic11C22×C411yescharacteristic
421C4×Dic11C22×C411yescharacteristic
422C4×Dic11C22×C411yescharacteristic
423C4×Dic11C22×C411yescharacteristic
424C4×Dic11C22×C411yescharacteristic
425C4×Dic11C22×C411yescharacteristic
426C4×Dic11C22×C412yes—
427C4×Dic11C22×C412yes—
428C4×Dic11C2412yes—
429C4×Dic11C2411yescharacteristic
430C4×Dic11C2411yescharacteristic
431#4318—42no—
432#4318—42no—
433C2×C11⋊C8—42no—
434C2×C11⋊C8C2411yescharacteristic
435C2×C11⋊C8C2411yescharacteristic
436C2×C11⋊C8C2411yescharacteristic
437C2×C11⋊C8C2412yes—
438C2×C11⋊C8C2411yescharacteristic
439C2×C11⋊C8C2412yes—
440#4313—22no—
441#4313—24no—
442#4313—24no—
443#4313—22no—
444#4313—22no—
445#4313—22no—
446#4313—42no—
447#4313—42no—
448C8×D11—42no—
449C8×D11—42no—
450C8×D11—42no—
451C8×D11—42no—
452C2×#529—111no—
453#2995—112no—
454#2995—112no—
455#2994—111no—
456#2994—111no—
457#2994—111no—
458#2994—111no—
459#2993—111no—
460#2993—111no—
461#2993—111no—
462#2993D1111yescharacteristic, complemented
463#2992—112no—
464#2992—112no—
465Q8×M16—111no—
466Q8×M16—111no—
467D4×M16—112no—
468D4×M16—111no—
469D4×M16—112no—
470D4×M16—111no—
471#2921—112no—
472#2920—111no—
473#2905—112no—
474C2×#423—111no—
475C23×C11C23×C412yes—
476C23×C11C23×C411yescharacteristic
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—24no—
480C22×D11—41no—
481C22×D11—42no—
482C22×D11—42no—
483C22×D11C23×C412yes—
484C22×D11C23×C411yescharacteristic
485C22×D11C23×C411yescharacteristic
486Q8×C11—22no—
487D4×C11—22no—
488D4×C11—42no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—41no—
495C2×C4×C11C23×C411yescharacteristic
496C2×C4×C11C23×C411yescharacteristic
497C2×C4×C11C23×C411yescharacteristic
498C2×C4×C11C23×C411yescharacteristic
499C2×C4×C11C23×C412yes—
500C2×C4×C11C23×C412yes—
501C2×C4×C11C23×C412yes—
502C2×C4×C11C23×C411yescharacteristic
503C2×C4×C11C2511yescharacteristic
504C22⋊D11—24no—
505C22⋊D11—42no—
506C22⋊D11—42no—
507C2×Dic11—24no—
508C2×Dic11—22no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11C23×C411yescharacteristic
512C2×Dic11C23×C411yescharacteristic
513C2×Dic11C23×C411yescharacteristic
514C2×Dic11C23×C411yescharacteristic
515C2×Dic11C23×C411yescharacteristic
516C2×Dic11C23×C412yes—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C412yes—
519C2×Dic11C23×C411yescharacteristic
520D44—24no—
521D44—22no—
522C4×D11—24no—
523C4×D11—22no—
524C4×D11—22no—
525C4×D11—22no—
526C4×D11—22no—
527C4×D11—22no—
528C4×D11—21no—
529C4×D11—22no—
530C4×D11—21no—
531C4×D11—22no—
532C4×D11—22no—
533C4×D11—24no—
534C4×D11—41no—
535C4×D11—41no—
536C4×D11—41no—
537C4×D11—41no—
538C4×D11—42no—
539C4×D11—42no—
540C4×D11H(5,𝔽2)12yes—
541C4×D112−1+412yes—
542Dic22—22no—
543Dic22—42no—
544C8×C11—21no—
545C8×C11—22no—
546C8×C11—22no—
547C8×C11—21no—
548C8×C11—21no—
549C8×C11—21no—
550C11⋊C8—21no—
551C11⋊C8—22no—
552C11⋊C8—22no—
553C11⋊C8—21no—
554C11⋊C8—21no—
555C11⋊C8—21no—
556C22×M16—112no—
557C22×M16—112no—
558C22×M16—112no—
559#529—112no—
560#529—111no—
561#529—111no—
562#529—112no—
563#529—111no—
564#529—111no—
565#529—111no—
566#529—112no—
567#529—111no—
568#529—112no—
569#529—111no—
570#529C2×D1111yescharacteristic
571C2×#126—112no—
572C2×#125—111no—
573C2×#124—111no—
574C2×#123—112no—
575C2×C22⋊Q8—111no—
576C2×#121—111no—
577C2×C4×Q8—111no—
578C2×C4×D4—112no—
579C2×C4×D4—111no—
580C2×#117—112no—
581C22×C42—111no—
582#446—111no—
583#446—112no—
584#446—112no—
585#446—111no—
586#446—112no—
587#446—112no—
588#446—111no—
589#446C2×D1111yescharacteristic, complemented
590C8×Q8—111no—
591C8×Q8—111no—
592C8×Q8—111no—
593C8×Q8C2×D1111yescharacteristic, complemented
594#436—112no—
595#436—111no—
596#436—112no—
597#436—111no—
598#436—112no—
599#436—111no—
600#436C2×D1111yescharacteristic, complemented
601#436C2×D1112yescomplemented
602#435—112no—
603#435—112no—
604#435—112no—
605#435—112no—
606#435—112no—
607#435—112no—
608#435—112no—
609#435—112no—
610#435—112no—
611#435—112no—
612#435—112no—
613#435C2×D1112yescomplemented
614C8×D4—112no—
615C8×D4—111no—
616C8×D4—112no—
617C8×D4—111no—
618C8×D4—112no—
619C8×D4—112no—
620C8×D4—111no—
621C8×D4C2×D1111yescharacteristic, complemented
622#433—112no—
623#433—112no—
624#433—112no—
625#433—112no—
626#433—112no—
627#433—112no—
628#433—112no—
629#433C2×D1112yescomplemented
630#432—111no—
631#432—111no—
632#432—111no—
633#432—111no—
634#431—111no—
635#431—111no—
636#431—111no—
637#431C2×D1111yescharacteristic, complemented
638#424—112no—
639#424—112no—
640#424—112no—
641#424—112no—
642#424—112no—
643#424—112no—
644#424—112no—
645#424C2×D1112yescomplemented
646#423—112no—
647#423—111no—
648#423—112no—
649#423—111no—
650#423—111no—
651#423—111no—
652#423—112no—
653#423—112no—
654#423—111no—
655#423C2×D1111yescharacteristic, complemented
656C2×C4⋊C8—112no—
657C2×C4⋊C8—111no—
658C2×C4⋊C8—111no—
659#407—111no—
660#407—111no—
661#407—112no—
662#407—112no—
663C4×M16—112no—
664C4×M16—111no—
665C4×M16—111no—
666C4×M16—112no—
667C22×C11—21no—
668C22×C11—22no—
669C22×C11—21no—
670C22×C11—21no—
671C22×C11—22no—
672C22×C11—22no—
673C22×C11C24×C411yescharacteristic
674C2×D11—21no—
675C2×D11—21no—
676C2×D11—21no—
677C2×D11—21no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—44no—
682C2×D11—84no—
683C2×D11#52012yes—
684C2×D11#56812yes—
685C4×C11—22no—
686C4×C11—21no—
687C4×C11—21no—
688C4×C11—21no—
689C4×C11—21no—
690C4×C11—22no—
691C4×C11—22no—
692C4×C11#56812yes—
693C4×C11C2×H(5,𝔽2)11yescharacteristic
694C4×C11C2×2−1+411yescharacteristic
695Dic11—21no—
696Dic11—22no—
697Dic11—22no—
698Dic11—21no—
699Dic11—21no—
700Dic11—21no—
701Dic11—21no—
702Dic11—22no—
703Dic11#52012yes—
704C22×Q8—111no—
705C22×D4—112no—
706C22×D4—111no—
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C2×M16—112no—
712C2×M16—112no—
713C2×M16—112no—
714C2×M16—112no—
715C2×M16—111no—
716C2×M16—111no—
717C2×M16—111no—
718C2×M16—111no—
719C2×M16—112no—
720C2×M16—112no—
721C2×M16—444no—
722C2×M16—444no—
723C2×M16—444no—
724C2×M16C22×D1112yes—
725C2×M16C22×D1112yes—
726C22×C8—112no—
727C22×C8—112no—
728C22×C8—112no—
729C22×C8—112no—
730C22×C8—112no—
731C22×C8C22×D1112yes—
732#126—112no—
733#126—112no—
734#126—112no—
735#126—112no—
736#126—112no—
737#126—112no—
738#126—112no—
739#126C4×D1112yes—
740#125—112no—
741#125—112no—
742#125—111no—
743#125—111no—
744#125—111no—
745#125C4×D1111yescharacteristic
746#124—111no—
747#124—111no—
748#124—112no—
749#124—112no—
750#124—111no—
751#124C4×D1111yescharacteristic
752#123—112no—
753#123—112no—
754#123—112no—
755#123—112no—
756#123—112no—
757#123—112no—
758#123—112no—
759#123C4×D1112yes—
760C22⋊Q8—111no—
761C22⋊Q8—111no—
762C22⋊Q8—112no—
763C22⋊Q8—111no—
764C22⋊Q8—112no—
765C22⋊Q8C4×D1111yescharacteristic
766#121—111no—
767#121—112no—
768#121—111no—
769#121—111no—
770#121—112no—
771#121C4×D1111yescharacteristic
772C4×Q8—111no—
773C4×Q8—112no—
774C4×Q8—111no—
775C4×Q8—111no—
776C4×Q8—112no—
777C4×Q8C22×D1111yescharacteristic
778C4×D4—111no—
779C4×D4—112no—
780C4×D4—112no—
781C4×D4—112no—
782C4×D4—112no—
783C4×D4—111no—
784C4×D4—112no—
785C4×D4—112no—
786C4×D4—112no—
787C4×D4—112no—
788C4×D4—112no—
789C4×D4—111no—
790C4×D4C22×D1111yescharacteristic
791C4×D4C22×D1112yes—
792#117—112no—
793#117—112no—
794#117—112no—
795#117—112no—
796#117—112no—
797#117—112no—
798#117—112no—
799#117C22×D1112yes—
800C2×C4⋊C4—112no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—111no—
803C2×C4⋊C4—112no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—112no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42C22×D1111yescharacteristic
824C4⋊C8—112no—
825C4⋊C8—112no—
826C4⋊C8—112no—
827C4⋊C8—112no—
828C4⋊C8—111no—
829C4⋊C8—111no—
830C4⋊C8—112no—
831C4⋊C8—112no—
832C4⋊C8—112no—
833C4⋊C8—112no—
834C4⋊C8—111no—
835C4⋊C8—111no—
836C4⋊C8—112no—
837C4⋊C8—111no—
838C4⋊C8—111no—
839C4⋊C8—111no—
840C4⋊C8—112no—
841C4⋊C8—112no—
842C4⋊C8—111no—
843C4⋊C8C22×D1112yes—
844C4⋊C8C22×D1111yescharacteristic
845C4⋊C8C22×D1111yescharacteristic
846C4⋊C8C22×D1111yescharacteristic
847C4⋊C8C22×D1112yes—
848C4⋊C8C22×D1112yes—
849C4⋊C8C22×D1111yescharacteristic
850C22⋊C8—111no—
851C22⋊C8—111no—
852C22⋊C8—112no—
853C22⋊C8—112no—
854C22⋊C8—111no—
855C22⋊C8—111no—
856C22⋊C8—111no—
857C22⋊C8—111no—
858C22⋊C8—112no—
859C22⋊C8—112no—
860C22⋊C8—112no—
861C22⋊C8—112no—
862C22⋊C8C22×D1111yescharacteristic
863C22⋊C8C22×D1111yescharacteristic
864C22⋊C8C22×D1112yes—
865C22⋊C8C22×D1112yes—
866#97—111no—
867#97—111no—
868#97—111no—
869#97—111no—
870#97—112no—
871#97—112no—
872#97—112no—
873#97C22×D1112yes—
874C4×C8—112no—
875C4×C8—112no—
876C4×C8—111no—
877C4×C8—111no—
878C4×C8—112no—
879C4×C8C22×D1111yescharacteristic
880C4×C8C22×D1111yescharacteristic
881C4×C8C22×D1112yes—
882C2×C11—41no—
883C2×C11—42no—
884C2×C11C2×#52011yescharacteristic
885C2×C11C2×#56811yescharacteristic
886C2×C11C2×#56811yescharacteristic
887D11—22no—
888D11—22no—
889D11—42no—
890C24—111no—
891C24—112no—
892C2×Q8—111no—
893C2×Q8—112no—
894C2×Q8—442no—
895C2×Q8C2×C4×D1111yescharacteristic
896C2×D4—112no—
897C2×D4—112no—
898C2×D4—112no—
899C2×D4—112no—
900C2×D4—111no—
901C2×D4—442no—
902C2×D4—444no—
903C2×D4C2×C4×D1111yescharacteristic
904C2×D4C2×C4×D1112yes—
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—112no—
908C22×C4—111no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—111no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—112no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—112no—
920C22×C4—111no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—224no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4C2×C4×D1111yescharacteristic
933C22×C4C2×C4×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1112yes—
936M16—42no—
937M16—42no—
938M16—222no—
939M16—224no—
940M16—224no—
941M16—222no—
942M16—222no—
943M16—222no—
944M16—442no—
945M16—442no—
946M16—442no—
947M16—442no—
948C2×C8—42no—
949C2×C8—111no—
950C2×C8—111no—
951C2×C8—112no—
952C2×C8—111no—
953C2×C8—111no—
954C2×C8—112no—
955C2×C8—442no—
956C2×C8—442no—
957C2×C8—442no—
958C2×C8—442no—
959C2×C8—442no—
960C2×C8C23×D1111yescharacteristic
961C2×C8C23×D1112yes—
962C2×C8C23×D1111yescharacteristic
963C2×C8C23×D1111yescharacteristic
964C2×C8C23×D1112yes—
965C2×C8C23×D1111yescharacteristic
966C4⋊C4—112no—
967C4⋊C4—112no—
968C4⋊C4—112no—
969C4⋊C4—112no—
970C4⋊C4—112no—
971C4⋊C4—112no—
972C4⋊C4—112no—
973C4⋊C4—111no—
974C4⋊C4—112no—
975C4⋊C4—112no—
976C4⋊C4—112no—
977C4⋊C4—112no—
978C4⋊C4—111no—
979C4⋊C4—112no—
980C4⋊C4—112no—
981C4⋊C4—112no—
982C4⋊C4C2×C4×D1112yes—
983C4⋊C4C2×C4×D1112yes—
984C4⋊C4C2×C4×D1111yescharacteristic
985C4⋊C4C2×C4×D1112yes—
986C4⋊C4C2×C4×D1111yescharacteristic
987C4⋊C4C2×C4×D1112yes—
988C22⋊C4—112no—
989C22⋊C4—112no—
990C22⋊C4—112no—
991C22⋊C4—112no—
992C22⋊C4—112no—
993C22⋊C4—112no—
994C22⋊C4—112no—
995C22⋊C4—112no—
996C22⋊C4—112no—
997C22⋊C4—112no—
998C22⋊C4—112no—
999C22⋊C4—112no—
1000C22⋊C4—112no—
1001C22⋊C4—112no—
1002C22⋊C4—112no—
1003C22⋊C4C2×C4×D1112yes—
1004C22⋊C4C2×C4×D1112yes—
1005C22⋊C4C2×C4×D1112yes—
1006C22⋊C4C2×C4×D1112yes—
1007C22⋊C4C2×C4×D1112yes—
1008C42—111no—
1009C42—111no—
1010C42—111no—
1011C42—111no—
1012C42—111no—
1013C42—111no—
1014C42—111no—
1015C42—111no—
1016C42—111no—
1017C42—111no—
1018C42—112no—
1019C42—112no—
1020C42—112no—
1021C42—111no—
1022C42—111no—
1023C42C2×C4×D1111yescharacteristic
1024C42C2×C4×D1111yescharacteristic
1025C42C23×D1111yescharacteristic
1026C42C23×D1112yes—
1027C42C23×D1111yescharacteristic
1028C11#6026411yescharacteristic, complemented, Sylow
1029C23—111no—
1030C23—111no—
1031C23—112no—
1032C23—222no—
1033C23—222no—
1034C23—224no—
1035C23—441no—
1036C23—442no—
1037C23—442no—
1038C23C22×C4×D1112yes—
1039C23C22×C4×D1111yescharacteristic
1040Q8—22no—
1041Q8—222no—
1042Q8—442no—
1043D4—22no—
1044D4—42no—
1045D4—224no—
1046D4—224no—
1047D4—222no—
1048D4—442no—
1049D4—442no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—22no—
1055C2×C4—41no—
1056C2×C4—111no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—111no—
1060C2×C4—111no—
1061C2×C4—111no—
1062C2×C4—111no—
1063C2×C4—111no—
1064C2×C4—112no—
1065C2×C4—112no—
1066C2×C4—112no—
1067C2×C4—222no—
1068C2×C4—224no—
1069C2×C4—222no—
1070C2×C4—224no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—224no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—221no—
1078C2×C4—222no—
1079C2×C4—221no—
1080C2×C4—222no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—442no—
1086C2×C4—442no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4C22×C4×D1111yescharacteristic
1090C2×C4C22×C4×D1111yescharacteristic
1091C2×C4C22×C4×D1111yescharacteristic
1092C2×C4C22×C4×D1111yescharacteristic
1093C2×C4C22×C4×D1112yes—
1094C2×C4C22×C4×D1112yes—
1095C2×C4C22×C4×D1112yes—
1096C2×C4C22×C4×D1111yescharacteristic
1097C2×C4C24×D1111yescharacteristic
1098C8—21no—
1099C8—22no—
1100C8—22no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—221no—
1105C8—222no—
1106C8—222no—
1107C8—221no—
1108C8—221no—
1109C8—221no—
1110C22—21no—
1111C22—22no—
1112C22—21no—
1113C22—22no—
1114C22—21no—
1115C22—22no—
1116C22—112no—
1117C22—112no—
1118C22—221no—
1119C22—221no—
1120C22—221no—
1121C22—221no—
1122C22—222no—
1123C22—222no—
1124C22—222no—
1125C22—444no—
1126C22—884no—
1127C22C23×C4×D1111yescharacteristic
1128C4—21no—
1129C4—21no—
1130C4—22no—
1131C4—21no—
1132C4—22no—
1133C4—22no—
1134C4—21no—
1135C4—112no—
1136C4—221no—
1137C4—221no—
1138C4—222no—
1139C4—221no—
1140C4—221no—
1141C4—222no—
1142C4—221no—
1143C4—222no—
1144C4#1062328112yes—
1145C4D11×H(5,𝔽2)11yescharacteristic
1146C4D11×2−1+411yescharacteristic
1147C2—41no—
1148C2—42no—
1149C2—222no—
1150C2—222no—
1151C2—442no—
1152C2D11×#52011yescharacteristic
1153C2D11×#56811yescharacteristic
1154C2C2×#1062328111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2993C2
prime radicalD11×#121C4
cosocleC2×C4×C11C25
hypercenter#2993D11
hypocenterC11#60264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #13077787C2semidirect
3. #13077780C2semidirect
4. #13077779C2semidirect
5. #13077777C2semidirect
6. #13077775C2semidirect
7. #13077771C2semidirect
8. #13077767C2semidirect
9. #13077765C2semidirect
10. #13077761C2semidirect
11. #13077753C2semidirect
12. #13077750C2semidirect
13. #13077568C2semidirect
14. Q8×#4313C2semidirect
15. #13077352C2semidirect
16. #13077352C2semidirect
17. #13077349C2semidirect
18. D4×#4313C2semidirect
19. #13077250C2semidirect
20. #13077244C2semidirect
21. #13077177C2semidirect
22. D11×#423C2semidirect
23. C11×#2993C2semidirect
50. C11×#446C22semidirect
51. C8×Q8×C11C22semidirect
52. C11×#436C22semidirect
53. C11×#436C22semidirect
54. C11×#435C22semidirect
55. C8×D4×C11C22semidirect
56. C11×#433C22semidirect
57. C11×#431C22semidirect
58. C11×#424C22semidirect
59. C11×#423C22semidirect
60. #10622741C22semidirect
61. #10622740C22semidirect
62. #10622740C22semidirect
63. #10622740C22semidirect
64. #10622732C22semidirect
65. #10622731C22semidirect
66. #10622724C22semidirect
67. C8×C22⋊D11C22semidirect
68. #10622715C22semidirect
69. #10622637C22semidirect
70. Q8×C11⋊C8C22semidirect
71. #10622625C22semidirect
72. #10622625C22semidirect
73. #10622624C22semidirect
74. D4×C11⋊C8C22semidirect
75. #10622613C22semidirect
76. #10622612C22semidirect
77. #10622538C22semidirect
78. #10622537C22semidirect
79. #10622453C22semidirect
80. #10622453C22semidirect
81. #10622452C22semidirect
82. #10622452C22semidirect
83. #10622452C22semidirect
84. #10622452C22semidirect
85. #10622451C22semidirect
93. #10622449C22semidirect
94. #10622448C22semidirect
95. #10622448C22semidirect
96. #10622447C22semidirect
97. #10622447C22semidirect
98. D11×C4⋊C8C22semidirect
99. D11×C4⋊C8C22semidirect
100. D11×C4⋊C8C22semidirect
101. #10622444C22semidirect
102. #10622444C22semidirect
103. #10622443C22semidirect
104. #10622441C22semidirect
105. #10622343C22semidirect
106. #10622342C22semidirect
107. #10622341C22semidirect
108. #10622341C22semidirect
109. #10622341C22semidirect
114. (C22⋊D11)⋊C8C22semidirect
115. #10622333C22semidirect
116. #10622333C22semidirect
117. #10622332C22semidirect
118. #10622332C22semidirect
119. #10622322C22semidirect
121. #10622319C22semidirect
122. #10622314C22semidirect
123. #10622303C22semidirect
124. #10622301C22semidirect
128. C8×D44C22semidirect
129. C8×D44C22semidirect
130. #10622298C22semidirect
131. #10622298C22semidirect
132. #10622292C22semidirect
133. #10622292C22semidirect
134. C8×Dic22C22semidirect
462. #2993D11semidirect
589. #446C2×D11semidirect
593. C8×Q8C2×D11semidirect
600. #436C2×D11semidirect
601. #436C2×D11semidirect
613. #435C2×D11semidirect
621. C8×D4C2×D11semidirect
629. #433C2×D11semidirect
637. #431C2×D11semidirect
645. #424C2×D11semidirect
655. #423C2×D11semidirect
1028. C11#60264semidirect

Maximal subgroups

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

subgroupindex
D11×#5292
#130777872
#130777802
#130777792
#130777772
#130777752
#130777712
#130777672
#130777652
#130777612
#130777532
#130777502
#130775682
Q8×#43132
#130773522
#130773492
D4×#43132
#130772502
#130772442
#130771772
D11×#4232
C11×#29932
#6026411