Finite Group Databasebeta

← #15618608

Subgroups — #15618608

Order 2816.

2094 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081943C211yesmaximal, characteristic
2#13077691C212yesmaximal, complemented
3#13077689C212yesmaximal, complemented
4#13077687C211yesmaximal, characteristic, complemented
5#13077685C211yesmaximal, characteristic, complemented
6#13077680C211yesmaximal, characteristic, complemented
7#13077673C212yesmaximal, complemented
8#13077669C212yesmaximal, complemented
9#13077660C212yesmaximal, complemented
10#13077658C212yesmaximal, complemented
11#13077345C212yesmaximal, complemented
12#13077336C212yesmaximal, complemented
13#13077316C212yesmaximal, complemented
14#13077305C212yesmaximal, complemented
15#13077269C212yesmaximal, complemented
16#13077064C212yesmaximal, complemented
17#13077058C211yesmaximal, characteristic, complemented
18D11×#408C211yesmaximal, characteristic, complemented
19C11×#2979C211yesmaximal, characteristic, complemented
20C2×#41×D11C2211yescharacteristic
21C2×#41×D11C2211yescharacteristic
22C11×#532C2211yescharacteristic
23#10623363C2211yescharacteristic
24#10623363C2211yescharacteristic
25C2×#66960C2212yes—
26C2×M16×D11C2211yescharacteristic, complemented
27C2×M16×D11C2211yescharacteristic, complemented
28C2×#66954C2212yes—
29C22×#4313C2211yescharacteristic, complemented
30C22×C8×D11C2211yescharacteristic, complemented
31#10623255C411yescharacteristic
32#10623255C411yescharacteristic
33#10623246C411yescharacteristic
34#10623246C411yescharacteristic
35#10623206C411yescharacteristic
36#10623206C411yescharacteristic
37#10623205C411yescharacteristic
38#10623205C411yescharacteristic
39#10623136C412yes—
40#10623136C412yes—
41#10623128C412yes—
42#10623128C412yes—
43#10623078C2212yes—
44#10623078C2212yes—
45#10623078C2212yes—
46#10623078C2212yes—
47#10623008C2211yescharacteristic
48C2×#66925C2211yescharacteristic
49C11×#436C2212yescomplemented
50C11×#436C2212yescomplemented
51C8×D4×C11C2212yescomplemented
52C8×D4×C11C2212yescomplemented
53C11×#431C2212yescomplemented
54C11×#408C2211yescharacteristic, complemented
55C11×#408C2211yescharacteristic, complemented
56C11×#408C2212yescomplemented
57#10622847C2211yescharacteristic, complemented
58#10622847C2211yescharacteristic, complemented
59#10622847C2212yescomplemented
60#10622742C2211yescharacteristic
61#10622742C2211yescharacteristic
62#10622741C2212yescomplemented
63#10622741C2212yescomplemented
64#10622740C2212yescomplemented
65#10622740C2212yescomplemented
66#10622739C2212yescomplemented
67#10622724C2212yescomplemented
68#10622724C2212yescomplemented
69#10622723C2211yescharacteristic
70#10622723C2211yescharacteristic
71C8×C22⋊D11C2212yescomplemented
72C8×C22⋊D11C2212yescomplemented
73C2×(C2×D11)⋊C8C2212yescomplemented
74#10622624C2212yescomplemented
75#10622624C2212yescomplemented
76#10622624C2212yescomplemented
77#10622624C2212yescomplemented
78#10622539C2212yescomplemented
79#10622453C2212yescomplemented
80#10622453C2212yescomplemented
81#10622452C2212yescomplemented
82#10622452C2212yescomplemented
83#10622449C2212yescomplemented
84#10622449C2212yescomplemented
85#10622449C2212yescomplemented
86#10622449C2212yescomplemented
87#10622343C2212yescomplemented
88#10622343C2212yescomplemented
89#10622342C2212yescomplemented
90#10622342C2212yescomplemented
91#10622341C2212yescomplemented
92#10622341C2212yescomplemented
93#10622340C2212yes—
94#10622340C2212yes—
95#10622340C2212yes—
96#10622340C2212yes—
97#10622340C2212yescomplemented
98#10622340C2212yescomplemented
99#10622340C2212yescomplemented
100#10622340C2212yescomplemented
101#10622339C2212yes—
102#10622339C2212yescomplemented
103#10622339C2212yescomplemented
104(C22⋊D11)⋊C8C2212yescomplemented
105(C22⋊D11)⋊C8C2212yescomplemented
106D11×C22⋊C8C2212yes—
107D11×C22⋊C8C2212yescomplemented
108D11×C22⋊C8C2212yescomplemented
109#10622332C2212yescomplemented
110#10622331C2212yescomplemented
111#10622303C2212yescomplemented
112#10622303C2212yescomplemented
113#10622302C2212yescomplemented
114#10622302C2212yescomplemented
115#10622301C2212yescomplemented
116#10622301C2212yescomplemented
117C8×D44C2212yescomplemented
118C8×D44C2212yescomplemented
119C2×C11×#41C2311yescharacteristic
120C2×C11×#41C2311yescharacteristic
121#41×D11—42no—
122#41×D11—42no—
123#41×D11—42no—
124#41×D11—42no—
125C2×#4343C2×C411yescharacteristic
126C2×#4343C2×C411yescharacteristic
127C2×Q8×D11C2×C411yescharacteristic
128C2×Q8×D11C2×C411yescharacteristic
129C2×#4341C2×C411yescharacteristic
130C2×#4341C2×C411yescharacteristic
131C2×#4341C2×C412yes—
132C2×#4341C2×C411yescharacteristic
133C2×#4341C2×C411yescharacteristic
134C2×D4×D11C2×C411yescharacteristic
135C2×D4×D11C2×C411yescharacteristic
136C2×D4×D11C2×C411yescharacteristic
137C2×D4×D11C2×C411yescharacteristic
138C2×D4×D11C2×C412yes—
139C2×#4339C2312yes—
140C2×#4339C2311yescharacteristic
141C2×#4339C2311yescharacteristic
142C2×#4339C2311yescharacteristic
143C2×#4339C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C2×C11×M16C2312yes—
149C2×C11×M16C2311yescharacteristic
150C2×C11×M16C2311yescharacteristic
151C22×C8×C11C2312yes—
152C22×C8×C11C2311yescharacteristic
153C22×C8×C11C2311yescharacteristic
154C11×C4⋊Q8C2×C411yescharacteristic
155C11×#127C2×C411yescharacteristic
156C11×#124C2×C411yescharacteristic
157C11×#124C2×C411yescharacteristic
158C11×#121C2×C412yes—
159C11×#121C2×C412yes—
160C4×D4×C11C2312yes—
161C4×D4×C11C2312yes—
162C2×C42×C11C2311yescharacteristic
163#67000C2×C411yescharacteristic
164#67000C2×C411yescharacteristic
165#66997C2×C411yescharacteristic
166#66997C2×C411yescharacteristic
167#66993C2×C411yescharacteristic
168#66993C2×C411yescharacteristic
169#66992C2×C412yes—
170#66992C2×C412yes—
171#66992C2×C412yes—
172#66992C2×C412yes—
173#66992C2×C412yes—
174#66992C2×C412yes—
175#66992C2×C412yes—
176#66992C2×C412yes—
177#66990C2×C412yes—
178#66990C2×C412yes—
179#66990C2×C412yes—
180#66990C2×C412yes—
181#66989C2×C411yescharacteristic
182#66989C2×C411yescharacteristic
183#66983C2×C412yes—
184#66983C2×C412yes—
185C4×C22⋊D11C2312yes—
186C4×C22⋊D11C2312yes—
187C4×C22⋊D11C2312yes—
188C4×C22⋊D11C2312yes—
189C2×(C2×D11)⋊C4C2×C412yes—
190C2×Dic11⋊C4C2×C412yes—
191C2×C4×Dic11C2311yescharacteristic
192C2×#4318C2311yescharacteristic
193C2×#4318C2311yescharacteristic
194C2×#4318C2312yes—
195C22×C11⋊C8C2312yes—
196C22×C11⋊C8C2311yescharacteristic
197C22×C11⋊C8C2311yescharacteristic
198#66960—44no—
199M16×D11—42no—
200M16×D11—42no—
201#66954—44no—
202C2×#4313—42no—
203C2×#4313C2312yes—
204C2×#4313C2312yes—
205C2×#4313C2312yes—
206C2×#4313C2312yes—
207C2×#4313C2312yes—
208C2×#4313C2312yes—
209C2×C8×D11—42no—
210C2×C8×D11C2312yes—
211C2×C8×D11C2312yes—
212C2×C8×D11C2312yes—
213C2×C8×D11C2312yes—
214C2×C8×D11C2312yes—
215C2×C8×D11C2312yes—
216#66949C2×C412yes—
217#66949C2×C412yes—
218#66949C2×C412yes—
219#66949C2×C412yes—
220#66947C2×C412yes—
221#66947C2×C412yes—
222#66947C2×C412yes—
223#66947C2×C412yes—
224#66937C2×C412yes—
225#66937C2×C412yes—
226#66937C2×C412yes—
227#66937C2×C412yes—
228#66936C2×C412yes—
229#66936C2×C412yes—
230#66936C2×C412yes—
231#66936C2×C412yes—
232#66935C2×C412yes—
233#66935C2×C412yes—
234#66935C2×C412yes—
235#66935C2×C412yes—
236#66931C2×C412yes—
237#66931C2×C412yes—
238#66931C2×C412yes—
239#66931C2×C412yes—
240#66928C2×C411yescharacteristic
241#66928C2×C411yescharacteristic
242#66927C2×C411yescharacteristic
243C4×D44C2312yes—
244C4×D44C2312yes—
245#66925C2×C411yescharacteristic
246#66925C2×C411yescharacteristic
247#66925C2×C411yescharacteristic
248#66925C2×C411yescharacteristic
249#66925C2312yes—
250#66925C2312yes—
251#66922C2×C411yescharacteristic
252C11×C4⋊C8C2312yes—
253C11×C4⋊C8C2312yes—
254C11×C22⋊C8C2312yes—
255C11×C22⋊C8C2312yes—
256C11×C22⋊C8C2312yes—
257C11×C22⋊C8C2312yes—
258C11×C22⋊C8C2312yes—
259C11×C22⋊C8C2312yes—
260C4×C8×C11C2312yes—
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—
291#66867C2312yes—
292#60235—111nomaximal, Sylow
293C23×D11C22×C411yescharacteristic
294C23×D11C22×C411yescharacteristic
295C23×D11C22×C411yescharacteristic
296C23×D11C22×C412yes—
297C11×#41—41no—
298C11×#41—41no—
299C11×#41—41no—
300C11×#41—41no—
301C2×Q8×C11C22×C411yescharacteristic
302C2×Q8×C11C22×C411yescharacteristic
303C2×D4×C11C22×C411yescharacteristic
304C2×D4×C11C22×C411yescharacteristic
305C2×D4×C11C22×C412yes—
306C2×D4×C11C22×C412yes—
307C2×D4×C11C22×C412yes—
308C2×D4×C11C22×C411yescharacteristic
309C2×D4×C11C22×C411yescharacteristic
310C22×C4×C11C22×C412yes—
311C22×C4×C11C2411yescharacteristic
312C22×C4×C11C2411yescharacteristic
313C22×C4×C11C2411yescharacteristic
314C22×C4×C11C2412yes—
315C2×C22⋊D11C22×C412yes—
316C2×C22⋊D11C22×C412yes—
317C2×C22⋊D11C22×C412yes—
318C2×C22⋊D11C22×C412yes—
319C2×C22⋊D11C22×C412yes—
320C2×C22⋊D11C22×C412yes—
321C2×C22⋊D11C22×C411yescharacteristic
322C2×C22⋊D11C22×C411yescharacteristic
323C2×C22⋊D11C22×C411yescharacteristic
324C2×C22⋊D11C22×C411yescharacteristic
325C2×C22⋊D11C22×C411yescharacteristic
326C2×C22⋊D11C22×C411yescharacteristic
327C2×C22⋊D11C22×C412yes—
328C22×Dic11C22×C411yescharacteristic
329C22×Dic11C22×C411yescharacteristic
330C22×Dic11C22×C411yescharacteristic
331C22×Dic11C22×C412yes—
332C22×Dic11C22×C412yes—
333#4343—42no—
334#4343—42no—
335Q8×D11—42no—
336Q8×D11—42no—
337#4341—44no—
338#4341—42no—
339#4341—42no—
340#4341—42no—
341#4341—42no—
342D4×D11—42no—
343D4×D11—42no—
344D4×D11—42no—
345D4×D11—44no—
346D4×D11—42no—
347#4339—24no—
348#4339—24no—
349#4339—41no—
350#4339—41no—
351#4339—41no—
352#4339—41no—
353#4339—41no—
354#4339—41no—
355#4339—41no—
356#4339—41no—
357C2×D44C22×C412yes—
358C2×D44C22×C412yes—
359C2×D44C22×C412yes—
360C2×D44C22×C411yescharacteristic
361C2×D44C22×C411yescharacteristic
362C2×D44C22×C411yescharacteristic
363C2×D44C22×C411yescharacteristic
364C2×C4×D11—22no—
365C2×C4×D11—22no—
366C2×C4×D11—22no—
367C2×C4×D11—22no—
368C2×C4×D11—22no—
369C2×C4×D11—22no—
370C2×C4×D11—42no—
371C2×C4×D11—42no—
372C2×C4×D11C22×C411yescharacteristic
373C2×C4×D11C22×C411yescharacteristic
374C2×C4×D11C22×C411yescharacteristic
375C2×C4×D11C22×C411yescharacteristic
376C2×C4×D11C22×C411yescharacteristic
377C2×C4×D11C22×C411yescharacteristic
378C2×C4×D11C22×C412yes—
379C2×C4×D11C22×C412yes—
380C2×C4×D11C2411yescharacteristic
381C2×C4×D11C2411yescharacteristic
382C2×C4×D11C2411yescharacteristic
383C2×C4×D11C2412yes—
384C2×C4×D11C2411yescharacteristic
385C2×Dic22C22×C412yes—
386C2×Dic22C22×C411yescharacteristic
387C2×Dic22C22×C411yescharacteristic
388C2×Dic22C22×C411yescharacteristic
389C2×Dic22C22×C411yescharacteristic
390C11×M16—41no—
391C11×M16—41no—
392C11×M16—42no—
393C2×C8×C11—41no—
394C2×C8×C11—41no—
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×C22⋊C4C22×C412yes—
403C11×C22⋊C4C22×C412yes—
404C11×C22⋊C4C22×C412yes—
405C11×C22⋊C4C22×C412yes—
406C42×C11C22×C411yescharacteristic
407C42×C11C22×C411yescharacteristic
408C42×C11C2412yes—
409C22⋊Dic11C22×C412yes—
410C22⋊Dic11C22×C412yes—
411C22⋊Dic11C22×C412yes—
412C22⋊Dic11C22×C412yes—
413(C2×D11)⋊C4C22×C412yes—
414(C2×D11)⋊C4C22×C412yes—
415(C2×D11)⋊C4C22×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—
425C4⋊Dic11C22×C412yes—
426C4⋊Dic11C22×C412yes—
427Dic11⋊C4C22×C412yes—
428Dic11⋊C4C22×C412yes—
429Dic11⋊C4C22×C412yes—
430Dic11⋊C4C22×C412yes—
431Dic11⋊C4C22×C412yes—
432Dic11⋊C4C22×C412yes—
433Dic11⋊C4C22×C412yes—
434Dic11⋊C4C22×C412yes—
435C4×Dic11C22×C411yescharacteristic
436C4×Dic11C22×C411yescharacteristic
437C4×Dic11C2412yes—
438#4318—42no—
439#4318—41no—
440#4318—41no—
441C2×C11⋊C8—41no—
442C2×C11⋊C8—41no—
443C2×C11⋊C8—42no—
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—111no—
464#2980—111no—
465#2979—111no—
466#2979D1111yescharacteristic, complemented
467#2978—112no—
468#2977—112no—
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×C11C23×C411yescharacteristic
480C23×C11C23×C411yescharacteristic
481C23×C11C23×C412yes—
482C23×C11C23×C411yescharacteristic
483C22×D11—22no—
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—42no—
487C22×D11—42no—
488C22×D11—42no—
489C22×D11—42no—
490C22×D11—42no—
491C22×D11—42no—
492C22×D11C23×C411yescharacteristic
493C22×D11C23×C411yescharacteristic
494C22×D11C23×C411yescharacteristic
495C22×D11C23×C412yes—
496C22×D11C23×C411yescharacteristic
497Q8×C11—41no—
498Q8×C11—41no—
499D4×C11—41no—
500D4×C11—41no—
501D4×C11—42no—
502D4×C11—41no—
503D4×C11—41no—
504D4×C11—42no—
505D4×C11—42no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11—22no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—21no—
514C2×C4×C11—42no—
515C2×C4×C11C23×C411yescharacteristic
516C2×C4×C11C23×C412yes—
517C2×C4×C11C23×C412yes—
518C2×C4×C11C23×C412yes—
519C2×C4×C11C23×C411yescharacteristic
520C2×C4×C11C23×C411yescharacteristic
521C2×C4×C11C2511yescharacteristic
522C22⋊D11—24no—
523C22⋊D11—24no—
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—42no—
539C2×Dic11—42no—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C411yescharacteristic
543C2×Dic11C23×C412yes—
544C2×Dic11C23×C411yescharacteristic
545C2×Dic11C23×C411yescharacteristic
546C2×Dic11C23×C411yescharacteristic
547D44—24no—
548D44—42no—
549D44—42no—
550D44—41no—
551D44—41no—
552D44—41no—
553D44—41no—
554C4×D11—22no—
555C4×D11—22no—
556C4×D11—22no—
557C4×D11—21no—
558C4×D11—21no—
559C4×D11—22no—
560C4×D11—22no—
561C4×D11—21no—
562C4×D11—21no—
563C4×D11—21no—
564C4×D11—21no—
565C4×D11—22no—
566C4×D11—22no—
567C4×D11—22no—
568C4×D11—42no—
569C4×D11—42no—
570C4×D11H(5,𝔽2)12yes—
571C4×D11H(5,𝔽2)12yes—
572Dic22—24no—
573Dic22—41no—
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—111no—
598#536—111no—
599#535—111no—
600#535—111no—
601#535—111no—
602#535—111no—
603#534—112no—
604#534—112no—
605#532—111no—
606#532—111no—
607#532—111no—
608#532C2×D1111yescharacteristic
609#525—112no—
610#525—112no—
611#525—112no—
612#525—112no—
613C2×#117—111no—
614#436—112no—
615#436—112no—
616#436—112no—
617#436—112no—
618#436—112no—
619#436—112no—
620#436C2×D1112yescomplemented
621#436C2×D1112yescomplemented
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#435—112no—
637#435—112no—
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#433—112no—
650#432—112no—
651#432—112no—
652#431—112no—
653#431C2×D1112yescomplemented
654#424—112no—
655#424—112no—
656#408—111no—
657#408—111no—
658#408—112no—
659#408—111no—
660#408—111no—
661#408—111no—
662#408—111no—
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#408C2×D1111yescharacteristic, complemented
672#408C2×D1111yescharacteristic, complemented
673#408C2×D1112yescomplemented
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⋊C8—112no—
682#405—112no—
683#405—112no—
684C22×C11—21no—
685C22×C11—21no—
686C22×C11—21no—
687C22×C11—22no—
688C22×C11—22no—
689C22×C11—22no—
690C22×C11—22no—
691C22×C11—22no—
692C22×C11—22no—
693C22×C11C24×C411yescharacteristic
694C2×D11—22no—
695C2×D11—21no—
696C2×D11—21no—
697C2×D11—21no—
698C2×D11—22no—
699C2×D11—22no—
700C2×D11—22no—
701C2×D11—22no—
702C2×D11—22no—
703C2×D11—22no—
704C2×D11—44no—
705C2×D11—82no—
706C2×D11—82no—
707C2×D11—84no—
708C2×D11#51812yes—
709C4×C11—21no—
710C4×C11—22no—
711C4×C11—21no—
712C4×C11—21no—
713C4×C11—22no—
714C4×C11—22no—
715C4×C11C2×H(5,𝔽2)11yescharacteristic
716C4×C11C2×H(5,𝔽2)11yescharacteristic
717Dic11—22no—
718Dic11—21no—
719Dic11—21no—
720Dic11—21no—
721Dic11—22no—
722Dic11—22no—
723Dic11#51812yes—
724C2×#41—111no—
725C2×#41—111no—
726C2×#41—111no—
727C2×#41—111no—
728C2×#41—111no—
729C2×#41—111no—
730C2×#41—112no—
731C2×#41—112no—
732C2×#41—111no—
733C2×#41—111no—
734C2×#41—111no—
735C2×#41—111no—
736C2×#41—442no—
737C2×#41—442no—
738C2×#41—442no—
739C2×#41—442no—
740C2×#41C22×D1111yescharacteristic
741C2×#41C22×D1111yescharacteristic
742C22×Q8—111no—
743C22×Q8—111no—
744C22×D4—111no—
745C22×D4—111no—
746C22×D4—112no—
747C22×D4—111no—
748C22×D4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—112no—
753#131—444no—
754#131—444no—
755C2×M16—111no—
756C2×M16—111no—
757C2×M16—112no—
758C2×M16—112no—
759C2×M16—112no—
760C2×M16—112no—
761C2×M16—112no—
762C2×M16—112no—
763C2×M16—112no—
764C2×M16—442no—
765C2×M16—442no—
766C2×M16—442no—
767C2×M16C22×D1111yescharacteristic
768C2×M16C22×D1111yescharacteristic
769C2×M16C22×D1112yes—
770C22×C8—111no—
771C22×C8—111no—
772C22×C8—112no—
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—
783C4⋊Q8—111no—
784C4⋊Q8—111no—
785C4⋊Q8—111no—
786C4⋊Q8C4×D1111yescharacteristic
787#127—111no—
788#127—111no—
789#127—111no—
790#127C4×D1111yescharacteristic
791#124—111no—
792#124—111no—
793#124—111no—
794#124—111no—
795#124—111no—
796#124—111no—
797#124C4×D1111yescharacteristic
798#124C4×D1111yescharacteristic
799#123—112no—
800#123—112no—
801#123—112no—
802#123—112no—
803#123—112no—
804#123—112no—
805#123—112no—
806#123—112no—
807C22⋊Q8—112no—
808C22⋊Q8—112no—
809C22⋊Q8—112no—
810C22⋊Q8—112no—
811C22⋊Q8—112no—
812C22⋊Q8—112no—
813C22⋊Q8—112no—
814C22⋊Q8—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#121—112no—
828#121—112no—
829#121C4×D1112yes—
830#121C4×D1112yes—
831#120—112no—
832#120—112no—
833#120—112no—
834#120—112no—
835#120—112no—
836#120—112no—
837#120—112no—
838#120—112no—
839C4×D4—112no—
840C4×D4—112no—
841C4×D4—112no—
842C4×D4—112no—
843C4×D4—112no—
844C4×D4—112no—
845C4×D4C22×D1112yes—
846C4×D4C22×D1112yes—
847#117—111no—
848#117—111no—
849#117—111no—
850#117—111no—
851#117—112no—
852#117—112no—
853C2×C4⋊C4—112no—
854C2×C22⋊C4—112no—
855C2×C42—111no—
856C2×C42C22×D1111yescharacteristic
857C4⋊C8—112no—
858C4⋊C8—112no—
859C4⋊C8—112no—
860C4⋊C8—112no—
861C4⋊C8—112no—
862C4⋊C8—112no—
863C4⋊C8C22×D1112yes—
864C4⋊C8C22×D1112yes—
865C22⋊C8—112no—
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⋊C8C22×D1112yes—
884C22⋊C8C22×D1112yes—
885C22⋊C8C22×D1112yes—
886C22⋊C8C22×D1112yes—
887C22⋊C8C22×D1112yes—
888C22⋊C8C22×D1112yes—
889#97—112no—
890#97—112no—
891#97—112no—
892#97—112no—
893C4×C8—112no—
894C4×C8—112no—
895C4×C8C22×D1112yes—
896C4×C8C22×D1112yes—
897C2×C11—41no—
898C2×C11—41no—
899C2×C11—41no—
900C2×C11—42no—
901C2×C11C2×#51811yescharacteristic
902C2×C11#357312yes—
903D11—22no—
904D11—41no—
905D11—41no—
906D11—42no—
907D11—41no—
908C24—111no—
909C24—111no—
910C24—111no—
911C24—112no—
912#41—41no—
913#41—41no—
914#41—41no—
915#41—41no—
916#41—224no—
917#41—224no—
918#41—441no—
919#41—441no—
920#41—441no—
921#41—441no—
922#41—441no—
923#41—441no—
924#41—441no—
925#41—441no—
926#41—442no—
927#41—442no—
928#41—442no—
929#41—442no—
930#41—442no—
931#41—444no—
932#41—442no—
933C2×Q8—112no—
934C2×Q8—111no—
935C2×Q8—111no—
936C2×Q8—111no—
937C2×Q8—111no—
938C2×Q8—442no—
939C2×Q8—442no—
940C2×Q8C2×C4×D1111yescharacteristic
941C2×Q8C2×C4×D1111yescharacteristic
942C2×D4—112no—
943C2×D4—112no—
944C2×D4—112no—
945C2×D4—112no—
946C2×D4—112no—
947C2×D4—112no—
948C2×D4—111no—
949C2×D4—111no—
950C2×D4—111no—
951C2×D4—111no—
952C2×D4—112no—
953C2×D4—111no—
954C2×D4—111no—
955C2×D4—112no—
956C2×D4—112no—
957C2×D4—112no—
958C2×D4—111no—
959C2×D4—111no—
960C2×D4—111no—
961C2×D4—111no—
962C2×D4—442no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—442no—
966C2×D4—444no—
967C2×D4C2×C4×D1112yes—
968C2×D4C2×C4×D1112yes—
969C2×D4C2×C4×D1111yescharacteristic
970C2×D4C2×C4×D1111yescharacteristic
971C2×D4C2×C4×D1112yes—
972C2×D4C2×C4×D1111yescharacteristic
973C2×D4C2×C4×D1111yescharacteristic
974C22×C4—111no—
975C22×C4—111no—
976C22×C4—111no—
977C22×C4—111no—
978C22×C4—112no—
979C22×C4—112no—
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—111no—
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—442no—
999C22×C4—442no—
1000C22×C4C2×C4×D1112yes—
1001C22×C4C23×D1111yescharacteristic
1002C22×C4C23×D1111yescharacteristic
1003C22×C4C23×D1111yescharacteristic
1004C22×C4C23×D1112yes—
1005M16—41no—
1006M16—41no—
1007M16—42no—
1008M16—224no—
1009M16—224no—
1010M16—442no—
1011M16—442no—
1012M16—442no—
1013M16—442no—
1014M16—441no—
1015M16—441no—
1016M16—442no—
1017C2×C8—41no—
1018C2×C8—41no—
1019C2×C8—42no—
1020C2×C8—112no—
1021C2×C8—112no—
1022C2×C8—112no—
1023C2×C8—112no—
1024C2×C8—224no—
1025C2×C8—224no—
1026C2×C8—442no—
1027C2×C8—442no—
1028C2×C8—442no—
1029C2×C8—442no—
1030C2×C8—441no—
1031C2×C8—441no—
1032C2×C8—442no—
1033C2×C8C23×D1112yes—
1034C2×C8C23×D1112yes—
1035C2×C8C23×D1112yes—
1036C2×C8C23×D1112yes—
1037C4⋊C4—112no—
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—
1049C22⋊C4—112no—
1050C22⋊C4—112no—
1051C22⋊C4—112no—
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⋊C4C2×C4×D1112yes—
1066C22⋊C4C2×C4×D1112yes—
1067C22⋊C4C2×C4×D1112yes—
1068C22⋊C4C2×C4×D1112yes—
1069C42—111no—
1070C42—111no—
1071C42—112no—
1072C42C2×C4×D1111yescharacteristic
1073C42C2×C4×D1111yescharacteristic
1074C42C23×D1112yes—
1075C11#6023511yescharacteristic, complemented, Sylow
1076C23—111no—
1077C23—111no—
1078C23—111no—
1079C23—111no—
1080C23—112no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—442no—
1085C23—442no—
1086C23—442no—
1087C23—442no—
1088C23—442no—
1089C23—442no—
1090C23C22×C4×D1111yescharacteristic
1091C23C22×C4×D1111yescharacteristic
1092C23C22×C4×D1112yes—
1093C23C22×C4×D1111yescharacteristic
1094Q8—41no—
1095Q8—41no—
1096Q8—224no—
1097Q8—441no—
1098Q8—441no—
1099Q8—441no—
1100Q8—441no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—42no—
1106D4—42no—
1107D4—42no—
1108D4—224no—
1109D4—224no—
1110D4—224no—
1111D4—441no—
1112D4—441no—
1113D4—441no—
1114D4—441no—
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—42no—
1137C2×C4—111no—
1138C2×C4—112no—
1139C2×C4—112no—
1140C2×C4—112no—
1141C2×C4—112no—
1142C2×C4—111no—
1143C2×C4—111no—
1144C2×C4—112no—
1145C2×C4—111no—
1146C2×C4—222no—
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—221no—
1156C2×C4—221no—
1157C2×C4—222no—
1158C2×C4—222no—
1159C2×C4—221no—
1160C2×C4—221no—
1161C2×C4—221no—
1162C2×C4—221no—
1163C2×C4—442no—
1164C2×C4—442no—
1165C2×C4—442no—
1166C2×C4—442no—
1167C2×C4C22×C4×D1111yescharacteristic
1168C2×C4C22×C4×D1112yes—
1169C2×C4C22×C4×D1112yes—
1170C2×C4C22×C4×D1111yescharacteristic
1171C2×C4C22×C4×D1111yescharacteristic
1172C2×C4C22×C4×D1112yes—
1173C2×C4C24×D1111yescharacteristic
1174C8—22no—
1175C8—22no—
1176C8—22no—
1177C8—22no—
1178C8—222no—
1179C8—222no—
1180C8—222no—
1181C8—222no—
1182C22—22no—
1183C22—22no—
1184C22—22no—
1185C22—22no—
1186C22—22no—
1187C22—21no—
1188C22—21no—
1189C22—21no—
1190C22—22no—
1191C22—112no—
1192C22—222no—
1193C22—222no—
1194C22—222no—
1195C22—222no—
1196C22—222no—
1197C22—222no—
1198C22—221no—
1199C22—221no—
1200C22—221no—
1201C22—222no—
1202C22—444no—
1203C22—882no—
1204C22—882no—
1205C22—884no—
1206C22C23×C4×D1111yescharacteristic
1207C4—22no—
1208C4—22no—
1209C4—21no—
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—112no—
1214C4—222no—
1215C4—222no—
1216C4—221no—
1217C4—221no—
1218C4—221no—
1219C4—222no—
1220C4D11×H(5,𝔽2)11yescharacteristic
1221C4D11×H(5,𝔽2)11yescharacteristic
1222C2—41no—
1223C2—41no—
1224C2—41no—
1225C2—42no—
1226C2—222no—
1227C2—441no—
1228C2—441no—
1229C2—441no—
1230C2—442no—
1231C2D11×#51811yescharacteristic
1232C2#1308332712yes—
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2979C2
prime radical#13081943C2
cosocleC2×C4×C11C25
hypercenter#2979D11
hypocenterC11#60235
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2979

Complements

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

NH ≅ G/Ntype
2. #13077691C2semidirect
3. #13077689C2semidirect
4. #13077687C2semidirect
5. #13077685C2semidirect
6. #13077680C2semidirect
7. #13077673C2semidirect
8. #13077669C2semidirect
9. #13077660C2semidirect
10. #13077658C2semidirect
11. #13077345C2semidirect
12. #13077336C2semidirect
13. #13077316C2semidirect
14. #13077305C2semidirect
15. #13077269C2semidirect
16. #13077064C2semidirect
17. #13077058C2semidirect
18. D11×#408C2semidirect
19. C11×#2979C2semidirect
26. C2×M16×D11C22semidirect
27. C2×M16×D11C22semidirect
29. C22×#4313C22semidirect
30. C22×C8×D11C22semidirect
49. C11×#436C22semidirect
50. C11×#436C22semidirect
51. C8×D4×C11C22semidirect
52. C8×D4×C11C22semidirect
53. C11×#431C22semidirect
54. C11×#408C22semidirect
55. C11×#408C22semidirect
56. C11×#408C22semidirect
57. #10622847C22semidirect
58. #10622847C22semidirect
59. #10622847C22semidirect
62. #10622741C22semidirect
63. #10622741C22semidirect
64. #10622740C22semidirect
65. #10622740C22semidirect
66. #10622739C22semidirect
67. #10622724C22semidirect
68. #10622724C22semidirect
71. C8×C22⋊D11C22semidirect
72. C8×C22⋊D11C22semidirect
73. C2×(C2×D11)⋊C8C22semidirect
74. #10622624C22semidirect
75. #10622624C22semidirect
76. #10622624C22semidirect
77. #10622624C22semidirect
78. #10622539C22semidirect
79. #10622453C22semidirect
80. #10622453C22semidirect
81. #10622452C22semidirect
82. #10622452C22semidirect
83. #10622449C22semidirect
84. #10622449C22semidirect
85. #10622449C22semidirect
86. #10622449C22semidirect
87. #10622343C22semidirect
88. #10622343C22semidirect
89. #10622342C22semidirect
90. #10622342C22semidirect
91. #10622341C22semidirect
92. #10622341C22semidirect
97. #10622340C22semidirect
98. #10622340C22semidirect
99. #10622340C22semidirect
100. #10622340C22semidirect
102. #10622339C22semidirect
103. #10622339C22semidirect
104. (C22⋊D11)⋊C8C22semidirect
105. (C22⋊D11)⋊C8C22semidirect
107. D11×C22⋊C8C22semidirect
108. D11×C22⋊C8C22semidirect
109. #10622332C22semidirect
110. #10622331C22semidirect
111. #10622303C22semidirect
112. #10622303C22semidirect
113. #10622302C22semidirect
114. #10622302C22semidirect
115. #10622301C22semidirect
116. #10622301C22semidirect
117. C8×D44C22semidirect
118. C8×D44C22semidirect
466. #2979D11semidirect
620. #436C2×D11semidirect
621. #436C2×D11semidirect
644. C8×D4C2×D11semidirect
645. C8×D4C2×D11semidirect
653. #431C2×D11semidirect
671. #408C2×D11semidirect
672. #408C2×D11semidirect
673. #408C2×D11semidirect
1075. C11#60235semidirect

Maximal subgroups

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

subgroupindex
#130819432
#130776912
#130776892
#130776872
#130776852
#130776802
#130776732
#130776692
#130776602
#130776582
#130773452
#130773362
#130773162
#130773052
#130772692
#130770642
#130770582
D11×#4082
C11×#29792
#6023511