Finite Group Databasebeta

← #15618606

Subgroups — #15618606

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081946C211yesmaximal, characteristic
2#13077690C212yesmaximal, complemented
3#13077688C212yesmaximal, complemented
4#13077684C212yesmaximal, complemented
5#13077679C212yesmaximal, complemented
6#13077678C211yesmaximal, characteristic, complemented
7#13077674C211yesmaximal, characteristic, complemented
8#13077668C211yesmaximal, characteristic, complemented
9#13077662C212yesmaximal, complemented
10#13077661C212yesmaximal, complemented
11#13077339C212yesmaximal, complemented
12#13077336C212yesmaximal, complemented
13#13077314C212yesmaximal, complemented
14#13077305C212yesmaximal, complemented
15#13077272C212yesmaximal, complemented
16#13077062C212yesmaximal, complemented
17#13077058C211yesmaximal, characteristic, complemented
18D11×#408C211yesmaximal, characteristic, complemented
19C11×#2977C211yesmaximal, characteristic, complemented
20C2×#41×D11C2211yescharacteristic
21C22×#4339C2211yescharacteristic
22C11×#525C2211yescharacteristic
23#10623359C2211yescharacteristic
24#10623322C2211yescharacteristic
25C2×M16×D11C2211yescharacteristic, complemented
26C2×M16×D11C2211yescharacteristic, complemented
27C2×#66954C2212yes—
28C2×#66954C2212yes—
29C22×#4313C2211yescharacteristic, complemented
30C22×C8×D11C2211yescharacteristic, complemented
31#10623184C411yescharacteristic
32#10623184C411yescharacteristic
33#10623179C411yescharacteristic
34#10623179C411yescharacteristic
35#10623160C412yes—
36#10623159C412yes—
37#10623139C412yes—
38#10623138C412yes—
39#10623123C411yescharacteristic
40#10623123C411yescharacteristic
41#10623120C411yescharacteristic
42#10623120C411yescharacteristic
43#10623079C2212yes—
44#10623079C2212yes—
45#10623078C2212yes—
46#10623078C2212yes—
47#10623055C2211yescharacteristic
48D11×#117C2211yescharacteristic
49C11×#435C2212yescomplemented
50C11×#435C2212yescomplemented
51C8×D4×C11C2212yescomplemented
52C8×D4×C11C2212yescomplemented
53C11×#433C2212yescomplemented
54C11×#408C2211yescharacteristic
55C11×#408C2211yescharacteristic
56C2×C11×C22⋊C8C2212yescomplemented
57#10622847C2211yescharacteristic
58#10622847C2211yescharacteristic
59#10622820C2212yescomplemented
60#10622742C2211yescharacteristic, complemented
61#10622742C2211yescharacteristic, complemented
62#10622741C2212yescomplemented
63#10622740C2212yescomplemented
64#10622724C2212yescomplemented
65#10622724C2212yescomplemented
66#10622724C2212yescomplemented
67#10622723C2211yescharacteristic, complemented
68#10622723C2211yescharacteristic, complemented
69#10622723C2212yescomplemented
70#10622723C2212yescomplemented
71C8×C22⋊D11C2212yescomplemented
72C8×C22⋊D11C2212yescomplemented
73C8×C22⋊D11C2212yescomplemented
74#10622625C2212yescomplemented
75#10622625C2212yescomplemented
76#10622624C2212yescomplemented
77#10622624C2212yescomplemented
78#10622613C2212yescomplemented
79#10622452C2212yescomplemented
80#10622452C2212yescomplemented
81#10622451C2212yescomplemented
82#10622449C2212yescomplemented
83#10622449C2212yescomplemented
84#10622448C2212yescomplemented
85#10622447C2212yescomplemented
86#10622446C2212yescomplemented
87#10622343C2212yescomplemented
88#10622342C2212yescomplemented
89#10622342C2212yescomplemented
90#10622342C2212yescomplemented
91#10622341C2212yescomplemented
92#10622341C2212yescomplemented
93#10622341C2212yescomplemented
94#10622340C2212yes—
95#10622340C2212yes—
96#10622340C2212yes—
97#10622340C2212yes—
98#10622340C2212yescomplemented
99#10622340C2212yescomplemented
100#10622340C2212yescomplemented
101#10622340C2212yescomplemented
102#10622339C2212yes—
103#10622339C2212yescomplemented
104#10622339C2212yescomplemented
105(C22⋊D11)⋊C8C2212yescomplemented
106D11×C22⋊C8C2212yes—
107D11×C22⋊C8C2212yescomplemented
108D11×C22⋊C8C2212yescomplemented
109#10622333C2212yescomplemented
110#10622333C2212yescomplemented
111#10622321C2212yescomplemented
112#10622319C2212yescomplemented
113#10622319C2212yescomplemented
114#10622318C2212yescomplemented
115#10622302C2212yescomplemented
116#10622301C2212yescomplemented
117C8×D44C2212yescomplemented
118#10622298C2212yescomplemented
119C2×C11×#41C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C22×C22⋊D11C2×C411yescharacteristic
122C22×C22⋊D11C2×C411yescharacteristic
123#41×D11—42no—
124#41×D11—42no—
125C2×#4343C2×C411yescharacteristic
126C2×Q8×D11C2×C411yescharacteristic
127C2×#4341C2×C411yescharacteristic
128C2×#4341C2×C411yescharacteristic
129C2×#4341C2×C411yescharacteristic
130C2×D4×D11C2×C411yescharacteristic
131C2×D4×D11C2×C411yescharacteristic
132C2×D4×D11C2×C411yescharacteristic
133C2×#4339—42no—
134C2×#4339—42no—
135C2×#4339C2×C412yes—
136C2×#4339C2×C412yes—
137C2×#4339C2312yes—
138C2×#4339C2312yes—
139C2×#4339C2311yescharacteristic
140C2×#4339C2311yescharacteristic
141C2×#4339C2311yescharacteristic
142C22×D44C2×C411yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×Dic22C2×C411yescharacteristic
148C2×C11×M16C2311yescharacteristic
149C2×C11×M16C2311yescharacteristic
150C22×C8×C11C2311yescharacteristic
151C22×C8×C11C2312yes—
152C22×C8×C11C2311yescharacteristic
153C22×C8×C11C2312yes—
154C11×#123C2×C411yescharacteristic
155C11×#123C2×C411yescharacteristic
156C11×C22⋊Q8C2×C412yes—
157C11×#121C2×C412yes—
158C11×#120C2×C411yescharacteristic
159C11×#120C2×C411yescharacteristic
160C4×D4×C11C2312yes—
161C4×D4×C11C2312yes—
162C11×#117C2311yescharacteristic
163#67006C2×C411yescharacteristic
164#67006C2×C411yescharacteristic
165#66999C2×C412yes—
166#66993C2×C412yes—
167#66993C2×C412yes—
168#66992C2×C412yes—
169#66992C2×C412yes—
170#66991C2×C412yes—
171#66991C2×C412yes—
172#66991C2×C412yes—
173#66990C2×C412yes—
174#66990C2×C412yes—
175#66990C2×C411yescharacteristic
176#66990C2×C411yescharacteristic
177#66988C2×C411yescharacteristic
178#66988C2×C411yescharacteristic
179#66983C2×C412yes—
180#66982C2×C411yescharacteristic
181#66982C2×C411yescharacteristic
182C4×C22⋊D11C2312yes—
183C4×C22⋊D11C2312yes—
184C4×C22⋊D11C2312yes—
185C4×C22⋊D11C2312yes—
186#66979C2311yescharacteristic
187#66977C2×C412yes—
188C2×#4318C2312yes—
189C2×#4318C2312yes—
190C2×#4318C2311yescharacteristic
191C2×#4318C2311yescharacteristic
192C22×C11⋊C8C2311yescharacteristic
193C22×C11⋊C8C2311yescharacteristic
194M16×D11—42no—
195M16×D11—42no—
196#66954—44no—
197#66954—44no—
198C2×#4313—42no—
199C2×#4313C2312yes—
200C2×#4313C2312yes—
201C2×#4313C2312yes—
202C2×#4313C2312yes—
203C2×#4313C2312yes—
204C2×#4313C2312yes—
205C2×C8×D11—42no—
206C2×C8×D11C2312yes—
207C2×C8×D11C2312yes—
208C2×C8×D11C2312yes—
209C2×C8×D11C2312yes—
210C2×C8×D11C2312yes—
211C2×C8×D11C2312yes—
212#66950C2×C412yes—
213#66949C2×C412yes—
214#66949C2×C412yes—
215#66948C2×C412yes—
216#66948C2×C412yes—
217#66948C2×C412yes—
218#66947C2×C412yes—
219#66947C2×C412yes—
220#66945C2×C412yes—
221C4⋊C4×D11C2×C412yes—
222#66941C2×C412yes—
223#66941C2×C412yes—
224#66939C2×C411yescharacteristic
225#66939C2×C411yescharacteristic
226#66938C2×C412yes—
227#66938C2×C412yes—
228#66938C2×C412yes—
229#66938C2×C412yes—
230#66937C2×C412yes—
231#66937C2×C412yes—
232#66937C2×C412yes—
233#66937C2×C412yes—
234#66937C2×C412yes—
235#66937C2×C412yes—
236#66936C2×C412yes—
237#66936C2×C412yes—
238#66935C2×C411yescharacteristic
239#66935C2×C411yescharacteristic
240#66935C2×C412yes—
241#66935C2×C412yes—
242C22⋊C4×D11C2×C411yescharacteristic
243C22⋊C4×D11C2×C411yescharacteristic
244#66931C2×C412yes—
245#66931C2×C412yes—
246#66930C2×C411yescharacteristic
247#66930C2×C411yescharacteristic
248C4×D44C2312yes—
249C4×D44C2312yes—
250#66925C2312yes—
251C42×D11C2312yes—
252C11×C4⋊C8C2312yes—
253C11×C4⋊C8C2312yes—
254C11×C22⋊C8C2312yes—
255C11×C22⋊C8C2312yes—
256C11×C22⋊C8C2312yes—
257C11×C22⋊C8C2312yes—
258C11×C22⋊C8C2312yes—
259C11×C22⋊C8C2312yes—
260C11×#97C2312yes—
261C4×C8×C11C2312yes—
262C22⋊(C11⋊C8)C2312yes—
263C22⋊(C11⋊C8)C2312yes—
264C22⋊(C11⋊C8)C2312yes—
265C22⋊(C11⋊C8)C2312yes—
266C22⋊(C11⋊C8)C2312yes—
267C22⋊(C11⋊C8)C2312yes—
268(C2×D11)⋊C8C2312yes—
269(C2×D11)⋊C8C2312yes—
270(C2×D11)⋊C8C2312yes—
271(C2×D11)⋊C8C2312yes—
272(C2×D11)⋊C8C2312yes—
273(C2×D11)⋊C8C2312yes—
274(C2×D11)⋊C8C2312yes—
275(C2×D11)⋊C8C2312yes—
276(C2×D11)⋊C8C2312yes—
277(C2×D11)⋊C8C2312yes—
278(C2×D11)⋊C8C2312yes—
279(C2×D11)⋊C8C2312yes—
280#66879C2312yes—
281#66879C2312yes—
282Dic11⋊C8C2312yes—
283Dic11⋊C8C2312yes—
284Dic11⋊C8C2312yes—
285Dic11⋊C8C2312yes—
286C8×Dic11C2312yes—
287C8×Dic11C2312yes—
288C4⋊(C11⋊C8)C2312yes—
289C4⋊(C11⋊C8)C2312yes—
290#66867C2312yes—
291C4×C11⋊C8C2312yes—
292#60235—111nomaximal, Sylow
293C24×C11C22×C411yescharacteristic
294C23×D11C22×C411yescharacteristic
295C23×D11C22×C411yescharacteristic
296C23×D11C22×C411yescharacteristic
297C23×D11C22×C411yescharacteristic
298C11×#41—41no—
299C11×#41—41no—
300C2×Q8×C11C22×C411yescharacteristic
301C2×D4×C11C22×C411yescharacteristic
302C2×D4×C11C22×C411yescharacteristic
303C2×D4×C11C22×C412yes—
304C2×D4×C11C22×C412yes—
305C2×D4×C11C22×C411yescharacteristic
306C22×C4×C11—41no—
307C22×C4×C11—41no—
308C22×C4×C11C22×C412yes—
309C22×C4×C11C22×C411yescharacteristic
310C22×C4×C11C2411yescharacteristic
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2412yes—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11C22×C412yes—
317C2×C22⋊D11C22×C412yes—
318C2×C22⋊D11C22×C412yes—
319C2×C22⋊D11C22×C412yes—
320C2×C22⋊D11C22×C411yescharacteristic
321C2×C22⋊D11C22×C411yescharacteristic
322C2×C22⋊D11C22×C412yes—
323C2×C22⋊D11C22×C412yes—
324C2×C22⋊D11C22×C412yes—
325C2×C22⋊D11C22×C411yescharacteristic
326C2×C22⋊D11C22×C411yescharacteristic
327C2×C22⋊D11C22×C412yes—
328C2×C22⋊D11C22×C411yescharacteristic
329C2×C22⋊D11C22×C411yescharacteristic
330C22×Dic11C22×C411yescharacteristic
331C22×Dic11C22×C411yescharacteristic
332C22×Dic11C22×C411yescharacteristic
333C22×Dic11C22×C411yescharacteristic
334#4343—42no—
335Q8×D11—42no—
336#4341—42no—
337#4341—42no—
338#4341—42no—
339D4×D11—42no—
340D4×D11—42no—
341D4×D11—42no—
342#4339—24no—
343#4339—24no—
344#4339—42no—
345#4339—42no—
346#4339—41no—
347#4339—41no—
348#4339—41no—
349#4339—41no—
350#4339—41no—
351#4339—41no—
352#4339—44no—
353#4339—44no—
354C2×D44—42no—
355C2×D44C22×C412yes—
356C2×D44C22×C412yes—
357C2×D44C22×C412yes—
358C2×D44C22×C412yes—
359C2×D44C22×C411yescharacteristic
360C2×D44C22×C411yescharacteristic
361C2×D44C22×C411yescharacteristic
362C2×C4×D11—22no—
363C2×C4×D11—22no—
364C2×C4×D11—22no—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—22no—
368C2×C4×D11—41no—
369C2×C4×D11—41no—
370C2×C4×D11C22×C411yescharacteristic
371C2×C4×D11C22×C411yescharacteristic
372C2×C4×D11C22×C411yescharacteristic
373C2×C4×D11C22×C411yescharacteristic
374C2×C4×D11C22×C411yescharacteristic
375C2×C4×D11C22×C411yescharacteristic
376C2×C4×D11C22×C412yes—
377C2×C4×D11C22×C412yes—
378C2×C4×D11C22×C412yes—
379C2×C4×D11C2411yescharacteristic
380C2×C4×D11C2411yescharacteristic
381C2×C4×D11C2411yescharacteristic
382C2×C4×D11C2412yes—
383C2×C4×D11C2411yescharacteristic
384C2×Dic22—42no—
385C2×Dic22C22×C412yes—
386C2×Dic22C22×C412yes—
387C2×Dic22C22×C411yescharacteristic
388C2×Dic22C22×C411yescharacteristic
389C2×Dic22C22×C411yescharacteristic
390C11×M16—41no—
391C11×M16—41no—
392C2×C8×C11—41no—
393C2×C8×C11—41no—
394C2×C8×C11—42no—
395C2×C8×C11—42no—
396C2×C8×C11C2412yes—
397C2×C8×C11C2412yes—
398C2×C8×C11C2412yes—
399C2×C8×C11C2412yes—
400C11×C4⋊C4C22×C412yes—
401C11×C4⋊C4C22×C412yes—
402C11×C4⋊C4C22×C412yes—
403C11×C22⋊C4C22×C411yescharacteristic
404C11×C22⋊C4C22×C411yescharacteristic
405C11×C22⋊C4C22×C412yes—
406C11×C22⋊C4C22×C412yes—
407C11×C22⋊C4C22×C412yes—
408C11×C22⋊C4C22×C412yes—
409C42×C11C2412yes—
410C22⋊Dic11C22×C411yescharacteristic
411C22⋊Dic11C22×C411yescharacteristic
412C22⋊Dic11C22×C412yes—
413C22⋊Dic11C22×C412yes—
414C22⋊Dic11C22×C412yes—
415C22⋊Dic11C22×C412yes—
416(C2×D11)⋊C4C22×C412yes—
417(C2×D11)⋊C4C22×C412yes—
418(C2×D11)⋊C4C22×C412yes—
419(C2×D11)⋊C4C22×C412yes—
420(C2×D11)⋊C4C22×C412yes—
421(C2×D11)⋊C4C22×C412yes—
422(C2×D11)⋊C4C22×C412yes—
423(C2×D11)⋊C4C22×C412yes—
424(C2×D11)⋊C4C22×C412yes—
425(C2×D11)⋊C4C22×C412yes—
426C4⋊Dic11C22×C412yes—
427C4⋊Dic11C22×C412yes—
428C4⋊Dic11C22×C412yes—
429Dic11⋊C4C22×C412yes—
430Dic11⋊C4C22×C412yes—
431Dic11⋊C4C22×C412yes—
432Dic11⋊C4C22×C412yes—
433Dic11⋊C4C22×C412yes—
434Dic11⋊C4C22×C412yes—
435C4×Dic11C22×C412yes—
436C4×Dic11C22×C412yes—
437C4×Dic11C2412yes—
438#4318—42no—
439#4318—42no—
440#4318—41no—
441#4318—41no—
442C2×C11⋊C8—41no—
443C2×C11⋊C8—41no—
444C2×C11⋊C8C2412yes—
445C2×C11⋊C8C2412yes—
446C2×C11⋊C8C2412yes—
447C2×C11⋊C8C2412yes—
448#4313—24no—
449#4313—24no—
450#4313—42no—
451#4313—42no—
452#4313—42no—
453#4313—42no—
454C8×D11—24no—
455C8×D11—24no—
456C8×D11—42no—
457C8×D11—42no—
458C8×D11—42no—
459C8×D11—42no—
460#3449—111no—
461#2981—112no—
462#2981—112no—
463#2980—112no—
464#2979—112no—
465#2978—111no—
466#2978—111no—
467#2977—111no—
468#2977D1111yescharacteristic, complemented
469#2976—112no—
470#2976—112no—
471#2933—112no—
472#2933—112no—
473#2930—112no—
474#2929—112no—
475#2924—112no—
476#2880—112no—
477#2879—111no—
478C2×#408—111no—
479C23×C11—41no—
480C23×C11—42no—
481C23×C11C23×C411yescharacteristic
482C23×C11C23×C411yescharacteristic
483C23×C11C23×C411yescharacteristic
484C23×C11C23×C412yes—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—42no—
489C22×D11—41no—
490C22×D11—42no—
491C22×D11—42no—
492C22×D11—42no—
493C22×D11C23×C411yescharacteristic
494C22×D11C23×C411yescharacteristic
495C22×D11C23×C412yes—
496C22×D11C23×C411yescharacteristic
497C22×D11C23×C411yescharacteristic
498Q8×C11—41no—
499D4×C11—41no—
500D4×C11—41no—
501D4×C11—41no—
502D4×C11—42no—
503D4×C11—42no—
504C2×C4×C11—21no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—41no—
513C2×C4×C11—42no—
514C2×C4×C11C23×C412yes—
515C2×C4×C11C23×C412yes—
516C2×C4×C11C23×C412yes—
517C2×C4×C11C23×C411yescharacteristic
518C2×C4×C11C23×C411yescharacteristic
519C2×C4×C11C23×C411yescharacteristic
520C2×C4×C11C2511yescharacteristic
521C22⋊D11—24no—
522C22⋊D11—24no—
523C22⋊D11—42no—
524C22⋊D11—42no—
525C22⋊D11—41no—
526C22⋊D11—41no—
527C22⋊D11—41no—
528C22⋊D11—41no—
529C22⋊D11—41no—
530C22⋊D11—41no—
531C22⋊D11—42no—
532C22⋊D11—42no—
533C22⋊D11—42no—
534C22⋊D11—42no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—41no—
539C2×Dic11C23×C411yescharacteristic
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C412yes—
543C2×Dic11C23×C411yescharacteristic
544C2×Dic11C23×C411yescharacteristic
545C2×Dic11C23×C411yescharacteristic
546D44—24no—
547D44—42no—
548D44—42no—
549D44—42no—
550D44—41no—
551D44—41no—
552D44—41no—
553C4×D11—22no—
554C4×D11—22no—
555C4×D11—22no—
556C4×D11—21no—
557C4×D11—21no—
558C4×D11—22no—
559C4×D11—22no—
560C4×D11—21no—
561C4×D11—21no—
562C4×D11—21no—
563C4×D11—21no—
564C4×D11—22no—
565C4×D11—22no—
566C4×D11—22no—
567C4×D11—42no—
568C4×D11—42no—
569C4×D11—42no—
570C4×D11H(5,𝔽2)12yes—
571C4×D11H(5,𝔽2)12yes—
572Dic22—24no—
573Dic22—42no—
574Dic22—41no—
575Dic22—41no—
576Dic22—41no—
577C8×C11—22no—
578C8×C11—22no—
579C8×C11—22no—
580C8×C11—22no—
581C11⋊C8—22no—
582C11⋊C8—22no—
583C11⋊C8—22no—
584C11⋊C8—22no—
585C22×#41—111no—
586C22×#41—111no—
587C2×#131—112no—
588C2×#131—112no—
589C22×M16—111no—
590C22×M16—111no—
591C22×M16—111no—
592C23×C8—111no—
593#537—112no—
594#537—112no—
595#536—111no—
596#536—111no—
597#536—112no—
598#535—112no—
599#535—111no—
600#535—111no—
601#534—111no—
602#534—111no—
603#534—111no—
604#534—111no—
605#532—112no—
606#532—112no—
607#525—111no—
608#525—111no—
609#525—112no—
610#525—112no—
611#525—111no—
612#525C2×D1111yescharacteristic
613C2×#117—111no—
614#436—112no—
615#436—112no—
616#436—112no—
617#436—112no—
618#436—112no—
619#436—112no—
620#436—112no—
621#436—112no—
622#435—112no—
623#435—112no—
624#435—112no—
625#435—112no—
626#435—112no—
627#435—112no—
628#435—112no—
629#435—112no—
630#435—112no—
631#435—112no—
632#435—112no—
633#435—112no—
634#435—112no—
635#435—112no—
636#435C2×D1112yescomplemented
637#435C2×D1112yescomplemented
638C8×D4—112no—
639C8×D4—112no—
640C8×D4—112no—
641C8×D4—112no—
642C8×D4—112no—
643C8×D4—112no—
644C8×D4C2×D1112yescomplemented
645C8×D4C2×D1112yescomplemented
646#433—112no—
647#433—112no—
648#433—112no—
649#433C2×D1112yescomplemented
650#432—112no—
651#432—112no—
652#431—112no—
653#431—112no—
654#424—112no—
655#424—112no—
656#408—111no—
657#408—111no—
658#408—111no—
659#408—111no—
660#408—111no—
661#408—111no—
662#408—112no—
663#408—112no—
664#408—112no—
665#408—112no—
666#408—112no—
667#408—112no—
668#408—112no—
669#408—112no—
670#408—112no—
671#408—112no—
672#408C2×D1111yescharacteristic
673#408C2×D1111yescharacteristic
674#407—112no—
675#407—112no—
676#407—112no—
677#407—112no—
678C2×C22⋊C8—112no—
679C2×C22⋊C8—112no—
680C2×C22⋊C8—112no—
681C2×C22⋊C8C2×D1112yescomplemented
682#405—112no—
683#405—112no—
684C22×C11—21no—
685C22×C11—22no—
686C22×C11—21no—
687C22×C11—21no—
688C22×C11—22no—
689C22×C11—22no—
690C22×C11—22no—
691C22×C11—22no—
692C22×C11—22no—
693C22×C11—82no—
694C22×C11C24×C411yescharacteristic
695C2×D11—22no—
696C2×D11—21no—
697C2×D11—21no—
698C2×D11—21no—
699C2×D11—22no—
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—22no—
705C2×D11—44no—
706C2×D11—82no—
707C2×D11—82no—
708C2×D11—82no—
709C2×D11#51812yes—
710C4×C11—21no—
711C4×C11—22no—
712C4×C11—21no—
713C4×C11—21no—
714C4×C11—22no—
715C4×C11—22no—
716C4×C11C2×H(5,𝔽2)11yescharacteristic
717C4×C11C2×H(5,𝔽2)11yescharacteristic
718Dic11—22no—
719Dic11—21no—
720Dic11—21no—
721Dic11—21no—
722Dic11—22no—
723Dic11—22no—
724Dic11#51812yes—
725C2×#41—111no—
726C2×#41—111no—
727C2×#41—111no—
728C2×#41—111no—
729C2×#41—112no—
730C2×#41—112no—
731C2×#41—112no—
732C2×#41—111no—
733C2×#41—111no—
734C2×#41—111no—
735C2×#41—112no—
736C2×#41—442no—
737C2×#41—442no—
738C2×#41—442no—
739C2×#41—442no—
740C2×#41C22×D1111yescharacteristic
741C22×Q8—111no—
742C22×Q8—111no—
743C22×D4—111no—
744C22×D4—111no—
745C22×D4—111no—
746C22×D4—111no—
747C22×D4—111no—
748C22×D4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—111no—
753C23×C4C22×D1111yescharacteristic
754#131—444no—
755#131—444no—
756C2×M16—111no—
757C2×M16—111no—
758C2×M16—112no—
759C2×M16—112no—
760C2×M16—112no—
761C2×M16—112no—
762C2×M16—112no—
763C2×M16—112no—
764C2×M16—112no—
765C2×M16—112no—
766C2×M16—442no—
767C2×M16—442no—
768C2×M16—442no—
769C2×M16C22×D1111yescharacteristic
770C2×M16C22×D1111yescharacteristic
771C22×C8—111no—
772C22×C8—111no—
773C22×C8—112no—
774C22×C8—112no—
775C22×C8—112no—
776C22×C8—112no—
777C22×C8—112no—
778C22×C8—112no—
779C22×C8—442no—
780C22×C8C22×D1111yescharacteristic
781C22×C8C22×D1111yescharacteristic
782C22×C8C22×D1112yes—
783C22×C8C22×D1112yes—
784C4⋊Q8—112no—
785C4⋊Q8—112no—
786#127—112no—
787#127—112no—
788#124—112no—
789#124—112no—
790#124—112no—
791#124—112no—
792#123—111no—
793#123—111no—
794#123—111no—
795#123—111no—
796#123—112no—
797#123—112no—
798#123—112no—
799#123—112no—
800#123—111no—
801#123—111no—
802#123C4×D1111yescharacteristic
803#123C4×D1111yescharacteristic
804C22⋊Q8—112no—
805C22⋊Q8—112no—
806C22⋊Q8—112no—
807C22⋊Q8—112no—
808C22⋊Q8—112no—
809C22⋊Q8—112no—
810C22⋊Q8—112no—
811C22⋊Q8C4×D1112yes—
812#121—112no—
813#121—112no—
814#121—112no—
815#121—112no—
816#121—112no—
817#121—112no—
818#121—112no—
819#121—112no—
820#121—112no—
821#121—112no—
822#121—112no—
823#121—112no—
824#121—112no—
825#121—112no—
826#121—112no—
827#121C4×D1112yes—
828#120—111no—
829#120—111no—
830#120—111no—
831#120—111no—
832#120—112no—
833#120—112no—
834#120—112no—
835#120—112no—
836#120—111no—
837#120—111no—
838#120C4×D1111yescharacteristic
839#120C4×D1111yescharacteristic
840C4×D4—112no—
841C4×D4—112no—
842C4×D4—112no—
843C4×D4—112no—
844C4×D4—112no—
845C4×D4—112no—
846C4×D4C22×D1112yes—
847C4×D4C22×D1112yes—
848#117—111no—
849#117—112no—
850#117—111no—
851#117—111no—
852#117—112no—
853#117C22×D1111yescharacteristic
854C2×C4⋊C4—112no—
855C2×C22⋊C4—111no—
856C2×C22⋊C4—111no—
857C2×C42—112no—
858C4⋊C8—112no—
859C4⋊C8—112no—
860C4⋊C8—112no—
861C4⋊C8—112no—
862C4⋊C8—112no—
863C4⋊C8—112no—
864C4⋊C8C22×D1112yes—
865C4⋊C8C22×D1112yes—
866C22⋊C8—112no—
867C22⋊C8—112no—
868C22⋊C8—112no—
869C22⋊C8—112no—
870C22⋊C8—112no—
871C22⋊C8—112no—
872C22⋊C8—112no—
873C22⋊C8—112no—
874C22⋊C8—112no—
875C22⋊C8—112no—
876C22⋊C8—112no—
877C22⋊C8—112no—
878C22⋊C8—112no—
879C22⋊C8—112no—
880C22⋊C8—112no—
881C22⋊C8—112no—
882C22⋊C8—112no—
883C22⋊C8—112no—
884C22⋊C8C22×D1112yes—
885C22⋊C8C22×D1112yes—
886C22⋊C8C22×D1112yes—
887C22⋊C8C22×D1112yes—
888C22⋊C8C22×D1112yes—
889C22⋊C8C22×D1112yes—
890#97—112no—
891#97—112no—
892#97—112no—
893#97C22×D1112yes—
894C4×C8—112no—
895C4×C8—112no—
896C4×C8—112no—
897C4×C8C22×D1112yes—
898C2×C11—41no—
899C2×C11—41no—
900C2×C11—41no—
901C2×C11—42no—
902C2×C11C2×#51811yescharacteristic
903C2×C11#357312yes—
904D11—22no—
905D11—41no—
906D11—41no—
907D11—41no—
908D11—42no—
909C24—111no—
910C24—111no—
911C24—111no—
912C24—111no—
913C24C2×C4×D1111yescharacteristic
914#41—41no—
915#41—41no—
916#41—224no—
917#41—224no—
918#41—441no—
919#41—441no—
920#41—442no—
921#41—442no—
922#41—441no—
923#41—441no—
924#41—441no—
925#41—441no—
926#41—444no—
927#41—444no—
928#41—442no—
929#41—442no—
930#41—442no—
931#41—442no—
932C2×Q8—112no—
933C2×Q8—111no—
934C2×Q8—111no—
935C2×Q8—111no—
936C2×Q8—112no—
937C2×Q8—442no—
938C2×Q8—442no—
939C2×Q8C2×C4×D1111yescharacteristic
940C2×D4—112no—
941C2×D4—112no—
942C2×D4—112no—
943C2×D4—112no—
944C2×D4—112no—
945C2×D4—112no—
946C2×D4—111no—
947C2×D4—111no—
948C2×D4—111no—
949C2×D4—111no—
950C2×D4—112no—
951C2×D4—111no—
952C2×D4—111no—
953C2×D4—112no—
954C2×D4—112no—
955C2×D4—112no—
956C2×D4—112no—
957C2×D4—111no—
958C2×D4—111no—
959C2×D4—112no—
960C2×D4—111no—
961C2×D4—442no—
962C2×D4—442no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—442no—
966C2×D4—442no—
967C2×D4C2×C4×D1112yes—
968C2×D4C2×C4×D1112yes—
969C2×D4C2×C4×D1111yescharacteristic
970C2×D4C2×C4×D1111yescharacteristic
971C2×D4C2×C4×D1111yescharacteristic
972C22×C4—41no—
973C22×C4—41no—
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—111no—
977C22×C4—111no—
978C22×C4—111no—
979C22×C4—111no—
980C22×C4—111no—
981C22×C4—111no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—111no—
985C22×C4—111no—
986C22×C4—111no—
987C22×C4—111no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—112no—
991C22×C4—112no—
992C22×C4—222no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—222no—
996C22×C4—222no—
997C22×C4—222no—
998C22×C4—441no—
999C22×C4—441no—
1000C22×C4C2×C4×D1112yes—
1001C22×C4C2×C4×D1111yescharacteristic
1002C22×C4C23×D1111yescharacteristic
1003C22×C4C23×D1111yescharacteristic
1004C22×C4C23×D1111yescharacteristic
1005C22×C4C23×D1112yes—
1006M16—41no—
1007M16—41no—
1008M16—224no—
1009M16—224no—
1010M16—442no—
1011M16—442no—
1012M16—442no—
1013M16—442no—
1014M16—441no—
1015M16—441no—
1016M16—442no—
1017M16—442no—
1018C2×C8—41no—
1019C2×C8—41no—
1020C2×C8—42no—
1021C2×C8—42no—
1022C2×C8—112no—
1023C2×C8—112no—
1024C2×C8—112no—
1025C2×C8—112no—
1026C2×C8—224no—
1027C2×C8—224no—
1028C2×C8—442no—
1029C2×C8—442no—
1030C2×C8—442no—
1031C2×C8—442no—
1032C2×C8—441no—
1033C2×C8—441no—
1034C2×C8C23×D1112yes—
1035C2×C8C23×D1112yes—
1036C2×C8C23×D1112yes—
1037C2×C8C23×D1112yes—
1038C4⋊C4—112no—
1039C4⋊C4—112no—
1040C4⋊C4—112no—
1041C4⋊C4—112no—
1042C4⋊C4—112no—
1043C4⋊C4—112no—
1044C4⋊C4—112no—
1045C4⋊C4—112no—
1046C4⋊C4—112no—
1047C4⋊C4C2×C4×D1112yes—
1048C4⋊C4C2×C4×D1112yes—
1049C4⋊C4C2×C4×D1112yes—
1050C22⋊C4—111no—
1051C22⋊C4—111no—
1052C22⋊C4—112no—
1053C22⋊C4—112no—
1054C22⋊C4—112no—
1055C22⋊C4—112no—
1056C22⋊C4—112no—
1057C22⋊C4—112no—
1058C22⋊C4—112no—
1059C22⋊C4—112no—
1060C22⋊C4—112no—
1061C22⋊C4—112no—
1062C22⋊C4—112no—
1063C22⋊C4—112no—
1064C22⋊C4—112no—
1065C22⋊C4—112no—
1066C22⋊C4C2×C4×D1111yescharacteristic
1067C22⋊C4C2×C4×D1111yescharacteristic
1068C22⋊C4C2×C4×D1112yes—
1069C22⋊C4C2×C4×D1112yes—
1070C22⋊C4C2×C4×D1112yes—
1071C22⋊C4C2×C4×D1112yes—
1072C42—112no—
1073C42—112no—
1074C42—112no—
1075C42C23×D1112yes—
1076C11#6023511yescharacteristic, complemented, Sylow
1077C23—41no—
1078C23—42no—
1079C23—111no—
1080C23—111no—
1081C23—111no—
1082C23—112no—
1083C23—111no—
1084C23—222no—
1085C23—222no—
1086C23—222no—
1087C23—442no—
1088C23—441no—
1089C23—442no—
1090C23—442no—
1091C23—442no—
1092C23C22×C4×D1111yescharacteristic
1093C23C22×C4×D1111yescharacteristic
1094C23C22×C4×D1111yescharacteristic
1095C23C22×C4×D1112yes—
1096Q8—41no—
1097Q8—224no—
1098Q8—441no—
1099Q8—442no—
1100Q8—441no—
1101Q8—441no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—224no—
1108D4—224no—
1109D4—224no—
1110D4—441no—
1111D4—442no—
1112D4—441no—
1113D4—441no—
1114D4—442no—
1115D4—442no—
1116D4—442no—
1117D4—441no—
1118D4—441no—
1119D4—441no—
1120D4—441no—
1121D4—441no—
1122D4—441no—
1123D4—442no—
1124D4—442no—
1125D4—442no—
1126D4—442no—
1127D4—442no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—41no—
1137C2×C4—42no—
1138C2×C4—111no—
1139C2×C4—112no—
1140C2×C4—112no—
1141C2×C4—111no—
1142C2×C4—112no—
1143C2×C4—112no—
1144C2×C4—111no—
1145C2×C4—111no—
1146C2×C4—112no—
1147C2×C4—222no—
1148C2×C4—222no—
1149C2×C4—222no—
1150C2×C4—222no—
1151C2×C4—222no—
1152C2×C4—222no—
1153C2×C4—222no—
1154C2×C4—222no—
1155C2×C4—222no—
1156C2×C4—221no—
1157C2×C4—221no—
1158C2×C4—222no—
1159C2×C4—222no—
1160C2×C4—221no—
1161C2×C4—221no—
1162C2×C4—221no—
1163C2×C4—221no—
1164C2×C4—442no—
1165C2×C4—442no—
1166C2×C4—442no—
1167C2×C4—441no—
1168C2×C4C22×C4×D1112yes—
1169C2×C4C22×C4×D1112yes—
1170C2×C4C22×C4×D1111yescharacteristic
1171C2×C4C22×C4×D1111yescharacteristic
1172C2×C4C22×C4×D1112yes—
1173C2×C4C22×C4×D1111yescharacteristic
1174C2×C4C24×D1111yescharacteristic
1175C8—22no—
1176C8—22no—
1177C8—22no—
1178C8—22no—
1179C8—222no—
1180C8—222no—
1181C8—222no—
1182C8—222no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—22no—
1188C22—21no—
1189C22—22no—
1190C22—21no—
1191C22—21no—
1192C22—82no—
1193C22—112no—
1194C22—222no—
1195C22—222no—
1196C22—222no—
1197C22—222no—
1198C22—222no—
1199C22—222no—
1200C22—221no—
1201C22—221no—
1202C22—221no—
1203C22—222no—
1204C22—444no—
1205C22—882no—
1206C22—882no—
1207C22—882no—
1208C22C23×C4×D1111yescharacteristic
1209C4—22no—
1210C4—22no—
1211C4—21no—
1212C4—22no—
1213C4—21no—
1214C4—21no—
1215C4—112no—
1216C4—222no—
1217C4—222no—
1218C4—221no—
1219C4—221no—
1220C4—221no—
1221C4—222no—
1222C4D11×H(5,𝔽2)11yescharacteristic
1223C4D11×H(5,𝔽2)11yescharacteristic
1224C2—41no—
1225C2—42no—
1226C2—41no—
1227C2—41no—
1228C2—222no—
1229C2—441no—
1230C2—441no—
1231C2—441no—
1232C2—442no—
1233C2D11×#51811yescharacteristic
1234C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2977C2
prime radical#13081946C2
cosocleC2×C4×C11C25
hypercenter#2977D11
hypocenterC11#60235
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2977

Complements

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

NH ≅ G/Ntype
2. #13077690C2semidirect
3. #13077688C2semidirect
4. #13077684C2semidirect
5. #13077679C2semidirect
6. #13077678C2semidirect
7. #13077674C2semidirect
8. #13077668C2semidirect
9. #13077662C2semidirect
10. #13077661C2semidirect
11. #13077339C2semidirect
12. #13077336C2semidirect
13. #13077314C2semidirect
14. #13077305C2semidirect
15. #13077272C2semidirect
16. #13077062C2semidirect
17. #13077058C2semidirect
18. D11×#408C2semidirect
19. C11×#2977C2semidirect
25. C2×M16×D11C22semidirect
26. C2×M16×D11C22semidirect
29. C22×#4313C22semidirect
30. C22×C8×D11C22semidirect
49. C11×#435C22semidirect
50. C11×#435C22semidirect
51. C8×D4×C11C22semidirect
52. C8×D4×C11C22semidirect
53. C11×#433C22semidirect
56. C2×C11×C22⋊C8C22semidirect
59. #10622820C22semidirect
60. #10622742C22semidirect
61. #10622742C22semidirect
62. #10622741C22semidirect
63. #10622740C22semidirect
64. #10622724C22semidirect
65. #10622724C22semidirect
66. #10622724C22semidirect
67. #10622723C22semidirect
68. #10622723C22semidirect
69. #10622723C22semidirect
70. #10622723C22semidirect
71. C8×C22⋊D11C22semidirect
72. C8×C22⋊D11C22semidirect
73. C8×C22⋊D11C22semidirect
74. #10622625C22semidirect
75. #10622625C22semidirect
76. #10622624C22semidirect
77. #10622624C22semidirect
78. #10622613C22semidirect
79. #10622452C22semidirect
80. #10622452C22semidirect
81. #10622451C22semidirect
82. #10622449C22semidirect
83. #10622449C22semidirect
84. #10622448C22semidirect
85. #10622447C22semidirect
86. #10622446C22semidirect
87. #10622343C22semidirect
88. #10622342C22semidirect
89. #10622342C22semidirect
90. #10622342C22semidirect
91. #10622341C22semidirect
92. #10622341C22semidirect
93. #10622341C22semidirect
98. #10622340C22semidirect
99. #10622340C22semidirect
100. #10622340C22semidirect
101. #10622340C22semidirect
103. #10622339C22semidirect
104. #10622339C22semidirect
105. (C22⋊D11)⋊C8C22semidirect
107. D11×C22⋊C8C22semidirect
108. D11×C22⋊C8C22semidirect
109. #10622333C22semidirect
110. #10622333C22semidirect
111. #10622321C22semidirect
112. #10622319C22semidirect
113. #10622319C22semidirect
114. #10622318C22semidirect
115. #10622302C22semidirect
116. #10622301C22semidirect
117. C8×D44C22semidirect
118. #10622298C22semidirect
468. #2977D11semidirect
636. #435C2×D11semidirect
637. #435C2×D11semidirect
644. C8×D4C2×D11semidirect
645. C8×D4C2×D11semidirect
649. #433C2×D11semidirect
681. C2×C22⋊C8C2×D11semidirect
1076. C11#60235semidirect

Maximal subgroups

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

subgroupindex
#130819462
#130776902
#130776882
#130776842
#130776792
#130776782
#130776742
#130776682
#130776622
#130776612
#130773392
#130773362
#130773142
#130773052
#130772722
#130770622
#130770582
D11×#4082
C11×#29772
#6023511