Finite Group Databasebeta

← #15620164

Subgroups — #15620164

Order 2816.

5098 conjugacy classes of subgroups.

The subgroup lattice has 1358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D11C211yesmaximal, characteristic, complemented
2C2×#10623308C211yesmaximal, characteristic, complemented
3C2×#10623304C211yesmaximal, characteristic, complemented
4D11×#525C211yesmaximal, characteristic, complemented
5#13077873C214yesmaximal, complemented
6#13077865C214yesmaximal, complemented
7#13077861C211yesmaximal, characteristic, complemented
8#13077858C211yesmaximal, characteristic, complemented
9#13077856C211yesmaximal, characteristic, complemented
10#13077852C211yesmaximal, characteristic, complemented
11#13077848C211yesmaximal, characteristic, complemented
12#13077845C211yesmaximal, characteristic, complemented
13#13077841C211yesmaximal, characteristic, complemented
14#13077837C214yesmaximal, complemented
15#13077831C214yesmaximal, complemented
16#13077134C211yesmaximal, characteristic, complemented
17#13077130C211yesmaximal, characteristic, complemented
18D11×#407C211yesmaximal, characteristic, complemented
19C11×#3005C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic, complemented
21C2×#41×D11—28no—
22C2×#41×D11—28no—
23C2×#41×D11—22no—
24C2×#41×D11—22no—
25C2×#41×D11C2214yes—
26C2×#41×D11C2214yescomplemented
27C2×#41×D11C2211yescharacteristic, complemented
28C22×#4343C2211yescharacteristic
29C22×Q8×D11C2211yescharacteristic, complemented
30C22×#4341—21no—
31C22×#4341C2211yescharacteristic
32C22×D4×D11—21no—
33C22×D4×D11C2211yescharacteristic, complemented
34C22×#4339—21no—
35C22×#4339C2211yescharacteristic, complemented
36C23×C4×D11—21no—
37C23×C4×D11C2211yescharacteristic
38C2×C11×#137C2211yescharacteristic, complemented
39C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
40C11×#525C2211yescharacteristic, complemented
41#10623359C2211yescharacteristic
42C2×#67004C2211yescharacteristic, complemented
43C2×#67002C2211yescharacteristic, complemented
44C2×#66995C2211yescharacteristic, complemented
45C2×#66985C2211yescharacteristic, complemented
46#10623322C2211yescharacteristic, complemented
47#10623308—28no—
48#10623304—28no—
49C2×#66972C2212yescomplemented
50C2×#66971C2212yescomplemented
51C2×#66969C2212yescomplemented
52C2×#66969C2212yescomplemented
53C2×#66968C2212yescomplemented
54C2×#66967C2212yescomplemented
55C2×#66965C2212yescomplemented
56C2×#66964C2212yescomplemented
57C2×#66962C2211yescharacteristic, complemented
58C2×#66961C2211yescharacteristic, complemented
59C2×M16×D11C2211yescharacteristic, complemented
60C2×M16×D11C2211yescharacteristic, complemented
61#10623187—21no—
62D11×#123—21no—
63#10623158C2212yescomplemented
64D11×C22⋊Q8C2212yescomplemented
65#10623137C2212yescomplemented
66D11×#121C2212yescomplemented
67D11×#120—21no—
68#10623117—21no—
69#10623078—22no—
70C4×D4×D11—22no—
71#10623055C2211yescharacteristic
72D11×#117C2211yescharacteristic, complemented
73C11×#452C2214yescomplemented
74C11×#449C2214yescomplemented
75C11×#419C2211yescharacteristic, complemented
76C11×#418C2211yescharacteristic, complemented
77C11×#407C2211yescharacteristic, complemented
78#10622852C2214yescomplemented
79#10622851C2214yescomplemented
80#10622838C2211yescharacteristic, complemented
81#10622828C2211yescharacteristic, complemented
82#10622820C2211yescharacteristic, complemented
83#10622799C2214yescomplemented
84#10622783C2214yescomplemented
85#10622782C2214yescomplemented
86#10622769C2214yescomplemented
87#10622744C2211yescharacteristic, complemented
88#10622739C2211yescharacteristic, complemented
89#10622739C2211yescharacteristic, complemented
90#10622733C2211yescharacteristic, complemented
91#10622660C2214yescomplemented
92#10622650C2214yescomplemented
93#10622617C2211yescharacteristic, complemented
94#10622614C2211yescharacteristic, complemented
95#10622421C2214yescomplemented
96#10622419C2214yescomplemented
97#10622417C2214yescomplemented
98#10622416C2214yescomplemented
99#10622389C2214yescomplemented
100#10622386C2214yescomplemented
101#10622385C2214yescomplemented
102#10622384C2214yescomplemented
103#10622347C2214yescomplemented
104#10622346C2214yescomplemented
105#10622339C2214yescomplemented
106D11×C22⋊C8C2214yescomplemented
107C24×D11—21no—
108C24×D11D411yescharacteristic
109C2×C11×#41—24no—
110C2×C11×#41—24no—
111C2×C11×#41—22no—
112C2×C11×#41C2311yescharacteristic
113C2×C11×#41C2314yes—
114C22×Q8×C11C2311yescharacteristic
115C22×D4×C11—21no—
116C22×D4×C11C2311yescharacteristic
117C23×C4×C11—21no—
118C23×C4×C11C2311yescharacteristic
119C22×C22⋊D11—21no—
120C22×C22⋊D11—21no—
121C22×C22⋊D11—21no—
122C23×Dic11—21no—
123C23×Dic11D411yescharacteristic
124#41×D11—232no—
125#41×D11—232no—
126#41×D11—216no—
127#41×D11—216no—
128#41×D11—216no—
129#41×D11—216no—
130#41×D11—24no—
131#41×D11—24no—
132C2×#4343—24no—
133C2×#4343—21no—
134C2×#4343—21no—
135C2×#4343D418yescomplemented
136C2×#4343C2312yes—
137C2×#4343C2312yes—
138C2×#4343C2311yescharacteristic, complemented
139C2×Q8×D11—24no—
140C2×Q8×D11—22no—
141C2×Q8×D11—24no—
142C2×Q8×D11C2314yes—
143C2×Q8×D11C2311yescharacteristic, complemented
144C2×#4341—216no—
145C2×#4341—24no—
146C2×#4341—24no—
147C2×#4341—21no—
148C2×#4341—24no—
149C2×#4341—21no—
150C2×#4341—21no—
151C2×#4341D418yescomplemented
152C2×#4341C2312yes—
153C2×#4341C2312yes—
154C2×#4341C2311yescharacteristic, complemented
155C2×D4×D11—216no—
156C2×D4×D11—24no—
157C2×D4×D11—24no—
158C2×D4×D11—24no—
159C2×D4×D11—22no—
160C2×D4×D11—21no—
161C2×D4×D11—24no—
162C2×D4×D11—22no—
163C2×D4×D11C2314yes—
164C2×D4×D11C2311yescharacteristic, complemented
165C2×#4339—216no—
166C2×#4339—22no—
167C2×#4339—24no—
168C2×#4339—24no—
169C2×#4339—24no—
170C2×#4339—21no—
171C2×#4339—24no—
172C2×#4339C2311yescharacteristic
173C2×#4339C2314yes—
174C22×D44—21no—
175C22×D44C2311yescharacteristic
176C22×C4×D11—216no—
177C22×C4×D11—21no—
178C22×C4×D11—21no—
179C22×C4×D11—21no—
180C22×C4×D11—24no—
181C22×C4×D11—24no—
182C22×C4×D11—24no—
183C22×C4×D11—24no—
184C22×C4×D11—21no—
185C22×C4×D11D412yes—
186C22×C4×D11D412yes—
187C22×C4×D11D411yescharacteristic
188C22×C4×D11D411yescharacteristic
189C22×C4×D11C2311yescharacteristic
190C22×C4×D11C2312yes—
191C22×C4×D11C2312yes—
192C22×C4×D11C2311yescharacteristic
193C22×Dic22—21no—
194C22×Dic22C2311yescharacteristic
195C11×#137—24no—
196C11×AGL(1,ℤ/8)—24no—
197C2×C11×Q16C2312yescomplemented
198C2×C11×SD16C2312yescomplemented
199C2×C11×SD16C2312yescomplemented
200C2×C11×D8C2312yescomplemented
201C2×C11×M16C2311yescharacteristic
202C2×C11×M16C2311yescharacteristic
203C11×#123—21no—
204C11×C22⋊Q8C2312yescomplemented
205C11×#121C2312yescomplemented
206C11×#120—21no—
207C4×D4×C11—22no—
208C11×#117C2311yescharacteristic
209#67006—21no—
210#67004—24no—
211#67002—24no—
212#66999C2312yes—
213C2×#4326C2312yescomplemented
214C2×#4326C2312yescomplemented
215#66995—24no—
216C2×#4325C2312yescomplemented
217C2×#4325C2312yescomplemented
218#66992—22no—
219#66991C2312yes—
220#66990—22no—
221#66990—21no—
222#66988—21no—
223D4×Dic11—22no—
224C2×#4324C2312yescomplemented
225C2×#4324C2312yescomplemented
226#66985—24no—
227C2×#4323C2312yescomplemented
228C2×#4323C2312yescomplemented
229#66983C2312yescomplemented
230#66982—21no—
231C4×C22⋊D11—22no—
232C4×C22⋊D11—22no—
233#66979C2311yescharacteristic
234#66977C2312yescomplemented
235C2×#4318C2311yescharacteristic
236C2×#4318C2311yescharacteristic
237#66972—28no—
238#66971—28no—
239#66969—28no—
240#66969—28no—
241#66968—28no—
242#66967—28no—
243#66965—28no—
244#66964—28no—
245#66962—24no—
246#66961—24no—
247M16×D11—24no—
248M16×D11—24no—
249C2×Dic44C2312yescomplemented
250C2×D88C2312yescomplemented
251C2×#4314C2312yescomplemented
252C2×#4314C2312yescomplemented
253C2×#4313C2312yescomplemented
254C2×#4313C2312yescomplemented
255C2×C8×D11C2312yescomplemented
256C2×C8×D11C2312yescomplemented
257#66950C2312yes—
258#66949—22no—
259#66948C2312yes—
260#66947—22no—
261#66946—22no—
262#66945C2312yescomplemented
263C4⋊C4×D11—22no—
264C4⋊C4×D11C2312yescomplemented
265#66939—21no—
266#66937—22no—
267#66936—22no—
268#66935—21no—
269#66935—22no—
270(C22⋊D11)⋊C4—22no—
271(C22⋊D11)⋊C4—22no—
272C22⋊C4×D11—21no—
273C22⋊C4×D11—22no—
274C22⋊C4×D11—22no—
275#66931—22no—
276#66930—21no—
277C4×D44—22no—
278#66925—21no—
279C42×D11—21no—
280C11×#103C2314yescomplemented
281C11×#102C2314yescomplemented
282C11×C22⋊C8C2314yescomplemented
283#66899C2314yescomplemented
284#66896C2314yescomplemented
285C22⋊(C11⋊C8)C2314yescomplemented
286#66885C2314yescomplemented
287(C2×D11)⋊C8C2314yes—
288(C2×D11)⋊C8C2314yes—
289#66880C2314yescomplemented
290#66874C2314yescomplemented
291#66873C2314yescomplemented
292#60359—111nomaximal, Sylow
293C24×C11—21no—
294C24×C11C2×D411yescharacteristic
295C23×D11—28no—
296C23×D11—21no—
297C23×D11—24no—
298C23×D11—24no—
299C23×D11—21no—
300C23×D11—44no—
301C23×D11—48no—
302C23×D11C2×D411yescharacteristic
303C23×D11C2×D412yes—
304C23×D11C2×D412yes—
305C23×D11C2×D411yescharacteristic
306C11×#41—216no—
307C11×#41—28no—
308C11×#41—28no—
309C11×#41—22no—
310C11×#41—22no—
311C2×Q8×C11—22no—
312C2×Q8×C11—21no—
313C2×Q8×C11C2×D414yescomplemented
314C2×Q8×C11C2411yescharacteristic
315C2×Q8×C11C2412yes—
316C2×D4×C11—28no—
317C2×D4×C11—24no—
318C2×D4×C11—22no—
319C2×D4×C11—21no—
320C2×D4×C11—21no—
321C2×D4×C11—22no—
322C2×D4×C11C2×D414yescomplemented
323C2×D4×C11C2411yescharacteristic
324C2×D4×C11C2412yes—
325C22×C4×C11—28no—
326C22×C4×C11—21no—
327C22×C4×C11—24no—
328C22×C4×C11—22no—
329C22×C4×C11—22no—
330C22×C4×C11—21no—
331C22×C4×C11C2×D412yes—
332C22×C4×C11C2×D411yescharacteristic
333C22×C4×C11C2412yes—
334C22×C4×C11C2411yescharacteristic
335C2×C22⋊D11—28no—
336C2×C22⋊D11—28no—
337C2×C22⋊D11—24no—
338C2×C22⋊D11—21no—
339C2×C22⋊D11—24no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—21no—
342C2×C22⋊D11—28no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—22no—
345C2×C22⋊D11—22no—
346C2×C22⋊D11—21no—
347C22×Dic11—24no—
348C22×Dic11—28no—
349C22×Dic11—22no—
350C22×Dic11—22no—
351C22×Dic11—21no—
352C22×Dic11—21no—
353C22×Dic11C2×D412yes—
354C22×Dic11C2×D412yes—
355C22×Dic11C2×D411yescharacteristic
356C22×Dic11C2×D411yescharacteristic
357#4343—28no—
358#4343—28no—
359#4343—24no—
360#4343—24no—
361#4343—22no—
362#4343—22no—
363#4343C2×D418yes—
364#4343C2×D418yescomplemented
365Q8×D11—216no—
366Q8×D11—28no—
367Q8×D11—22no—
368Q8×D11—22no—
369Q8×D11—28no—
370#4341—232no—
371#4341—232no—
372#4341—28no—
373#4341—28no—
374#4341—24no—
375#4341—24no—
376#4341—22no—
377#4341—22no—
378#4341—44no—
379#4341C2×D418yes—
380#4341C2×D418yescomplemented
381D4×D11—232no—
382D4×D11—232no—
383D4×D11—216no—
384D4×D11—28no—
385D4×D11—22no—
386D4×D11—22no—
387D4×D11—28no—
388D4×D11—48no—
389D4×D11—44no—
390#4339—232no—
391#4339—232no—
392#4339—216no—
393#4339—28no—
394#4339—28no—
395#4339—22no—
396#4339—22no—
397#4339—44no—
398C2×D44—28no—
399C2×D44—22no—
400C2×D44—22no—
401C2×D44—22no—
402C2×D44—21no—
403C2×D44—21no—
404C2×D44—22no—
405C2×D44C2×D414yescomplemented
406C2×D44C2411yescharacteristic
407C2×D44C2412yes—
408C2×C4×D11—28no—
409C2×C4×D11—28no—
410C2×C4×D11—232no—
411C2×C4×D11—232no—
412C2×C4×D11—24no—
413C2×C4×D11—28no—
414C2×C4×D11—22no—
415C2×C4×D11—22no—
416C2×C4×D11—28no—
417C2×C4×D11—28no—
418C2×C4×D11—24no—
419C2×C4×D11—24no—
420C2×C4×D11—24no—
421C2×C4×D11—24no—
422C2×C4×D11—21no—
423C2×C4×D11—24no—
424C2×C4×D11—24no—
425C2×C4×D11—22no—
426C2×C4×D11—21no—
427C2×C4×D11—24no—
428C2×C4×D11—22no—
429C2×C4×D11—22no—
430C2×C4×D11—21no—
431C2×C4×D11—44no—
432C2×C4×D11C2×D414yes—
433C2×C4×D11C2×D414yes—
434C2×C4×D11C2×D412yes—
435C2×C4×D11C2×D412yes—
436C2×C4×D11C2×D412yes—
437C2×C4×D11C2×D412yes—
438C2×C4×D11C2×D412yes—
439C2×C4×D11C2×D411yescharacteristic
440C2×C4×D11C2×D411yescharacteristic
441C2×C4×D11C2412yes—
442C2×C4×D11C2411yescharacteristic
443C2×C4×D11C2411yescharacteristic
444C2×Dic22—28no—
445C2×Dic22—24no—
446C2×Dic22—21no—
447C2×Dic22—21no—
448C2×Dic22—22no—
449C2×Dic22C2×D414yescomplemented
450C2×Dic22C2411yescharacteristic
451C2×Dic22C2412yes—
452C11×Q16—24no—
453C11×SD16—24no—
454C11×SD16—24no—
455C11×D8—24no—
456C11×M16—22no—
457C11×M16—22no—
458C2×C8×C11C2412yes—
459C2×C8×C11C2412yes—
460C11×C4⋊C4—22no—
461C11×C4⋊C4C2412yes—
462C11×C22⋊C4—21no—
463C11×C22⋊C4—22no—
464C11×C22⋊C4—22no—
465C42×C11—21no—
466C22⋊Dic11—22no—
467C22⋊Dic11—21no—
468C22⋊Dic11—22no—
469#4326—24no—
470#4326—24no—
471#4325—24no—
472#4325—24no—
473#4324—24no—
474#4324—24no—
475#4323—24no—
476#4323—24no—
477(C2×D11)⋊C4—22no—
478(C2×D11)⋊C4—22no—
479(C2×D11)⋊C4—22no—
480(C2×D11)⋊C4—22no—
481(C2×D11)⋊C4—22no—
482C4⋊Dic11—22no—
483C4⋊Dic11C2412yes—
484Dic11⋊C4—22no—
485Dic11⋊C4—22no—
486Dic11⋊C4—22no—
487C4×Dic11—22no—
488C4×Dic11—21no—
489#4318—22no—
490#4318—22no—
491C2×C11⋊C8C2412yes—
492C2×C11⋊C8C2412yes—
493Dic44—24no—
494D88—24no—
495#4314—24no—
496#4314—24no—
497#4313—24no—
498#4313—24no—
499C8×D11—24no—
500C8×D11—24no—
501C23×#41—111no—
502C2×#575—111no—
503C2×#575—111no—
504C2×#525—111no—
505#3007—114no—
506#3006—114no—
507#3005—111no—
508#3005—111no—
509#3005—111no—
510#3005D1111yescharacteristic, complemented
511#3004—111no—
512#3004—111no—
513#3003—111no—
514#3003—111no—
515#3002—114no—
516#3002—114no—
517#2896—111no—
518#2896—111no—
519C2×#407—111no—
520C23×C11—22no—
521C23×C11—24no—
522C23×C11—22no—
523C23×C11—21no—
524C23×C11—42no—
525C23×C11—44no—
526C23×C11C22×D412yes—
527C23×C11C22×D411yescharacteristic
528C22×D11—22no—
529C22×D11—24no—
530C22×D11—216no—
531C22×D11—24no—
532C22×D11—22no—
533C22×D11—24no—
534C22×D11—24no—
535C22×D11—24no—
536C22×D11—24no—
537C22×D11—21no—
538C22×D11—42no—
539C22×D11—42no—
540C22×D11—42no—
541C22×D11—416no—
542C22×D11—432no—
543C22×D11—48no—
544C22×D11—44no—
545C22×D11—44no—
546C22×D11—48no—
547C22×D11—42no—
548C22×D11#12014yes—
549C22×D11C22×D411yescharacteristic
550C22×D11C22×D411yescharacteristic
551C22×D11C22×D412yes—
552Q8×C11—24no—
553Q8×C11—22no—
554Q8×C11—21no—
555Q8×C11—21no—
556Q8×C11C22×D414yes—
557D4×C11—216no—
558D4×C11—24no—
559D4×C11—22no—
560D4×C11—21no—
561D4×C11—21no—
562D4×C11—44no—
563D4×C11—42no—
564D4×C11C22×D414yes—
565C2×C4×C11—216no—
566C2×C4×C11—24no—
567C2×C4×C11—22no—
568C2×C4×C11—22no—
569C2×C4×C11—24no—
570C2×C4×C11—22no—
571C2×C4×C11—22no—
572C2×C4×C11—22no—
573C2×C4×C11—21no—
574C2×C4×C11—42no—
575C2×C4×C11C22×D412yes—
576C2×C4×C11C22×D411yescharacteristic
577C2×C4×C11C22×D412yes—
578C2×C4×C11C22×D412yes—
579C2×C4×C11C2511yescharacteristic
580C22⋊D11—216no—
581C22⋊D11—216no—
582C22⋊D11—28no—
583C22⋊D11—28no—
584C22⋊D11—44no—
585C22⋊D11—42no—
586C22⋊D11—42no—
587C22⋊D11—44no—
588C22⋊D11—42no—
589C2×Dic11—22no—
590C2×Dic11—24no—
591C2×Dic11—22no—
592C2×Dic11—24no—
593C2×Dic11—24no—
594C2×Dic11—28no—
595C2×Dic11—28no—
596C2×Dic11—22no—
597C2×Dic11—21no—
598C2×Dic11—42no—
599C2×Dic11#12014yes—
600C2×Dic11C22×D412yes—
601C2×Dic11C22×D411yescharacteristic
602C2×Dic11C22×D411yescharacteristic
603D44—28no—
604D44—28no—
605D44—24no—
606D44—22no—
607D44—21no—
608D44—21no—
609D44—42no—
610D44—44no—
611D44C22×D414yes—
612C4×D11—216no—
613C4×D11—216no—
614C4×D11—24no—
615C4×D11—24no—
616C4×D11—24no—
617C4×D11—22no—
618C4×D11—22no—
619C4×D11—24no—
620C4×D11—24no—
621C4×D11—28no—
622C4×D11—28no—
623C4×D11—44no—
624C4×D11—42no—
625C4×D11—42no—
626C4×D11—42no—
627C4×D11#12014yes—
628C4×D11#12014yes—
629C4×D11C22×D412yes—
630C4×D11C22×D412yes—
631C4×D11C22×D412yes—
632C4×D11C22×D412yes—
633Dic22—216no—
634Dic22—24no—
635Dic22—22no—
636Dic22—21no—
637Dic22—21no—
638Dic22—42no—
639Dic22C22×D414yes—
640C8×C11—22no—
641C8×C11—22no—
642C11⋊C8—22no—
643C11⋊C8—22no—
644C22×#41—114no—
645C22×#41—114no—
646C22×#41—111no—
647C22×#41—111no—
648C22×#41—111no—
649C22×#41—111no—
650C22×#41—221no—
651C22×#41—221no—
652C22×#41—222no—
653C22×#41—222no—
654C22×#41—228no—
655C22×#41—228no—
656C22×#41C2×D1111yescharacteristic, complemented
657C23×Q8—111no—
658C23×D4—111no—
659C23×D4—221no—
660C24×C4—111no—
661C24×C4—221no—
662#575—228no—
663#575—228no—
664C2×#137—111no—
665C2×#137—111no—
666C2×#137—112no—
667C2×#137—112no—
668C2×#137—111no—
669C2×#137C2×D1111yescharacteristic, complemented
670C2×AGL(1,ℤ/8)—111no—
671C2×AGL(1,ℤ/8)—111no—
672C2×AGL(1,ℤ/8)—112no—
673C2×AGL(1,ℤ/8)—112no—
674C2×AGL(1,ℤ/8)—111no—
675C2×AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
676C2×#135—112no—
677C2×#135—112no—
678C2×#135—112no—
679C2×#135—112no—
680C22×M16—111no—
681C22×M16—111no—
682#525—111no—
683#525—111no—
684#525—112no—
685#525—112no—
686#525—111no—
687#525—222no—
688#525—221no—
689#525—221no—
690#525C2×D1111yescharacteristic, complemented
691C2×#123—221no—
692C2×C22⋊Q8—112no—
693C2×#121—112no—
694C2×#120—221no—
695C2×C4×D4—222no—
696C2×#117—111no—
697#452—114no—
698#452—114no—
699#452—114no—
700#452C2×D1114yescomplemented
701#451—114no—
702#451—114no—
703#450—114no—
704#450—114no—
705#449—114no—
706#449—114no—
707#449—114no—
708#449C2×D1114yescomplemented
709#448—114no—
710#448—114no—
711#447—114no—
712#447—114no—
713#419—111no—
714#419—111no—
715#419—111no—
716#419C2×D1111yescharacteristic, complemented
717#418—111no—
718#418—111no—
719#418—111no—
720#418C2×D1111yescharacteristic, complemented
721#417—114no—
722#417—114no—
723#416—114no—
724#416—114no—
725#407—111no—
726#407—111no—
727#407—111no—
728#407—114no—
729#407C2×D1111yescharacteristic, complemented
730C2×C22⋊C8—114no—
731C22×C11—22no—
732C22×C11—22no—
733C22×C11—24no—
734C22×C11—22no—
735C22×C11—22no—
736C22×C11—44no—
737C22×C11—48no—
738C22×C11—44no—
739C22×C11—41no—
740C22×C11—42no—
741C22×C11C2×#12012yes—
742C22×C11C23×D411yescharacteristic
743C2×D11—28no—
744C2×D11—22no—
745C2×D11—22no—
746C2×D11—22no—
747C2×D11—22no—
748C2×D11—24no—
749C2×D11—44no—
750C2×D11—48no—
751C2×D11—48no—
752C2×D11—432no—
753C2×D11—48no—
754C2×D11—44no—
755C2×D11—41no—
756C2×D11—42no—
757C2×D11—84no—
758C2×D11C2×#12012yes—
759C2×D11C2×#12012yes—
760C2×D11#57514yescomplemented
761C4×C11—22no—
762C4×C11—24no—
763C4×C11—41no—
764C4×C11—42no—
765C4×C11C2×#12012yes—
766C4×C11C23×D411yescharacteristic
767C4×C11C23×D411yescharacteristic
768Dic11—22no—
769Dic11—24no—
770Dic11—41no—
771Dic11—42no—
772Dic11C2×#12012yes—
773Dic11C2×#12012yes—
774C25—111no—
775C25—221no—
776C2×#41—24no—
777C2×#41—24no—
778C2×#41—22no—
779C2×#41—118no—
780C2×#41—112no—
781C2×#41—112no—
782C2×#41—111no—
783C2×#41—118no—
784C2×#41—112no—
785C2×#41—112no—
786C2×#41—111no—
787C2×#41—111no—
788C2×#41—114no—
789C2×#41—224no—
790C2×#41—224no—
791C2×#41—221no—
792C2×#41—224no—
793C2×#41—224no—
794C2×#41—2216no—
795C2×#41—221no—
796C2×#41—221no—
797C2×#41—224no—
798C2×#41—224no—
799C2×#41—224no—
800C2×#41—221no—
801C2×#41—221no—
802C2×#41—221no—
803C2×#41—224no—
804C2×#41—224no—
805C2×#41—224no—
806C2×#41—2216no—
807C2×#41—2216no—
808C2×#41—2216no—
809C2×#41—2216no—
810C2×#41—2216no—
811C2×#41—2232no—
812C2×#41—2232no—
813C2×#41—222no—
814C2×#41C22×D1111yescharacteristic
815C2×#41C22×D1114yes—
816C22×Q8—111no—
817C22×Q8—114no—
818C22×Q8—111no—
819C22×Q8—221no—
820C22×Q8—222no—
821C22×Q8—224no—
822C22×Q8—224no—
823C22×Q8C22×D1111yescharacteristic
824C22×D4—21no—
825C22×D4—111no—
826C22×D4—114no—
827C22×D4—111no—
828C22×D4—221no—
829C22×D4—222no—
830C22×D4—221no—
831C22×D4—224no—
832C22×D4—224no—
833C22×D4—224no—
834C22×D4—2216no—
835C22×D4—222no—
836C22×D4—221no—
837C22×D4—221no—
838C22×D4—221no—
839C22×D4—224no—
840C22×D4C22×D1111yescharacteristic
841C23×C4—21no—
842C23×C4—111no—
843C23×C4—111no—
844C23×C4—112no—
845C23×C4—111no—
846C23×C4—111no—
847C23×C4—112no—
848C23×C4—112no—
849C23×C4—111no—
850C23×C4—112no—
851C23×C4—224no—
852C23×C4—224no—
853C23×C4—221no—
854C23×C4—224no—
855C23×C4—224no—
856C23×C4—221no—
857C23×C4—221no—
858C23×C4—2216no—
859C23×C4—221no—
860C23×C4—221no—
861C23×C4C22×D1111yescharacteristic
862#137—24no—
863#137—224no—
864#137—228no—
865#137—228no—
866#137—224no—
867#137—224no—
868AGL(1,ℤ/8)—24no—
869AGL(1,ℤ/8)—224no—
870AGL(1,ℤ/8)—228no—
871AGL(1,ℤ/8)—228no—
872AGL(1,ℤ/8)—224no—
873AGL(1,ℤ/8)—224no—
874#135—228no—
875#135—228no—
876#135—228no—
877#135—228no—
878C2×Q16—112no—
879C2×Q16—112no—
880C2×Q16—112no—
881C2×Q16C22×D1112yescomplemented
882C2×SD16—112no—
883C2×SD16—112no—
884C2×SD16—112no—
885C2×SD16—112no—
886C2×SD16—112no—
887C2×SD16—112no—
888C2×SD16C22×D1112yescomplemented
889C2×SD16C22×D1112yescomplemented
890C2×D8—112no—
891C2×D8—112no—
892C2×D8—112no—
893C2×D8C22×D1112yescomplemented
894C2×M16—111no—
895C2×M16—111no—
896C2×M16—112no—
897C2×M16—112no—
898C2×M16—224no—
899C2×M16—224no—
900C2×M16C22×D1111yescharacteristic
901C2×M16C22×D1111yescharacteristic
902C22×C8—112no—
903C22×C8—112no—
904#123—21no—
905#123—222no—
906#123—221no—
907#123—222no—
908#123—221no—
909#123—221no—
910C22⋊Q8—112no—
911C22⋊Q8—112no—
912C22⋊Q8—112no—
913C22⋊Q8—222no—
914C22⋊Q8—222no—
915C22⋊Q8C22×D1112yescomplemented
916#121—112no—
917#121—112no—
918#121—112no—
919#121—222no—
920#121—222no—
921#121C22×D1112yescomplemented
922#120—21no—
923#120—221no—
924#120—222no—
925#120—222no—
926#120—221no—
927#120—221no—
928C4×D4—22no—
929C4×D4—222no—
930C4×D4—222no—
931C4×D4—222no—
932C4×D4—222no—
933C4×D4—222no—
934C4×D4—222no—
935C4×D4—222no—
936#117—111no—
937#117—112no—
938#117—221no—
939#117—221no—
940#117C22×D1111yescharacteristic
941C2×C4⋊C4—112no—
942C2×C4⋊C4—222no—
943C2×C22⋊C4—222no—
944C2×C22⋊C4—221no—
945C2×C22⋊C4—222no—
946C2×C42—221no—
947#103—114no—
948#103—114no—
949#103—114no—
950#103C22×D1114yescomplemented
951#102—114no—
952#102—114no—
953#102—114no—
954#102C22×D1114yescomplemented
955C22⋊C8—114no—
956C22⋊C8—114no—
957C22⋊C8—114no—
958C22⋊C8C22×D1114yescomplemented
959C2×C11—22no—
960C2×C11—42no—
961C2×C11—44no—
962C2×C11—81no—
963C2×C11C22×#12011yescharacteristic
964C2×C11C2×#57512yes—
965D11—24no—
966D11—22no—
967D11—22no—
968D11—44no—
969D11—81no—
970C24—21no—
971C24—111no—
972C24—111no—
973C24—112no—
974C24—112no—
975C24—224no—
976C24—224no—
977C24—221no—
978C24—228no—
979C24—221no—
980C24—444no—
981C24—448no—
982C24D4×D1111yescharacteristic
983#41—216no—
984#41—28no—
985#41—28no—
986#41—22no—
987#41—22no—
988#41—118no—
989#41—118no—
990#41—118no—
991#41—118no—
992#41—228no—
993#41—228no—
994#41—2232no—
995#41—2232no—
996#41—2216no—
997#41—228no—
998#41—228no—
999#41—224no—
1000#41—224no—
1001#41—228no—
1002#41—228no—
1003#41—224no—
1004#41—224no—
1005#41—222no—
1006#41—222no—
1007#41—222no—
1008#41—222no—
1009#41—2232no—
1010#41—2232no—
1011#41—222no—
1012#41—222no—
1013#41—444no—
1014#41—444no—
1015C2×Q8—22no—
1016C2×Q8—21no—
1017C2×Q8—114no—
1018C2×Q8—112no—
1019C2×Q8—111no—
1020C2×Q8—224no—
1021C2×Q8—221no—
1022C2×Q8—228no—
1023C2×Q8—222no—
1024C2×Q8—222no—
1025C2×Q8—228no—
1026C2×Q8—2216no—
1027C2×Q8—228no—
1028C2×Q8—222no—
1029C2×Q8—221no—
1030C2×Q8D4×D1114yescomplemented
1031C2×Q8C23×D1111yescharacteristic
1032C2×Q8C23×D1112yes—
1033C2×D4—28no—
1034C2×D4—24no—
1035C2×D4—22no—
1036C2×D4—21no—
1037C2×D4—21no—
1038C2×D4—22no—
1039C2×D4—114no—
1040C2×D4—112no—
1041C2×D4—111no—
1042C2×D4—228no—
1043C2×D4—222no—
1044C2×D4—222no—
1045C2×D4—222no—
1046C2×D4—221no—
1047C2×D4—222no—
1048C2×D4—222no—
1049C2×D4—224no—
1050C2×D4—221no—
1051C2×D4—228no—
1052C2×D4—2232no—
1053C2×D4—2232no—
1054C2×D4—2216no—
1055C2×D4—228no—
1056C2×D4—222no—
1057C2×D4—222no—
1058C2×D4—228no—
1059C2×D4—228no—
1060C2×D4—224no—
1061C2×D4—228no—
1062C2×D4—222no—
1063C2×D4—221no—
1064C2×D4—222no—
1065C2×D4—221no—
1066C2×D4—221no—
1067C2×D4—222no—
1068C2×D4—444no—
1069C2×D4—448no—
1070C2×D4D4×D1114yescomplemented
1071C2×D4C23×D1111yescharacteristic
1072C2×D4C23×D1112yes—
1073C22×C4—28no—
1074C22×C4—21no—
1075C22×C4—24no—
1076C22×C4—22no—
1077C22×C4—22no—
1078C22×C4—21no—
1079C22×C4—111no—
1080C22×C4—111no—
1081C22×C4—111no—
1082C22×C4—114no—
1083C22×C4—114no—
1084C22×C4—111no—
1085C22×C4—111no—
1086C22×C4—112no—
1087C22×C4—112no—
1088C22×C4—111no—
1089C22×C4—112no—
1090C22×C4—112no—
1091C22×C4—112no—
1092C22×C4—112no—
1093C22×C4—112no—
1094C22×C4—112no—
1095C22×C4—224no—
1096C22×C4—228no—
1097C22×C4—228no—
1098C22×C4—224no—
1099C22×C4—224no—
1100C22×C4—224no—
1101C22×C4—224no—
1102C22×C4—228no—
1103C22×C4—222no—
1104C22×C4—222no—
1105C22×C4—221no—
1106C22×C4—224no—
1107C22×C4—224no—
1108C22×C4—228no—
1109C22×C4—2232no—
1110C22×C4—2232no—
1111C22×C4—228no—
1112C22×C4—222no—
1113C22×C4—221no—
1114C22×C4—224no—
1115C22×C4—228no—
1116C22×C4—222no—
1117C22×C4—222no—
1118C22×C4—221no—
1119C22×C4—221no—
1120C22×C4—222no—
1121C22×C4—222no—
1122C22×C4—224no—
1123C22×C4—221no—
1124C22×C4—444no—
1125C22×C4D4×D1112yes—
1126C22×C4D4×D1111yescharacteristic
1127C22×C4C23×D1112yes—
1128C22×C4C23×D1111yescharacteristic
1129Q16—24no—
1130Q16—224no—
1131Q16—224no—
1132Q16—224no—
1133SD16—24no—
1134SD16—24no—
1135SD16—224no—
1136SD16—224no—
1137SD16—224no—
1138SD16—224no—
1139SD16—224no—
1140SD16—224no—
1141D8—24no—
1142D8—224no—
1143D8—224no—
1144D8—224no—
1145M16—22no—
1146M16—22no—
1147M16—224no—
1148M16—224no—
1149M16—222no—
1150M16—222no—
1151C2×C8—112no—
1152C2×C8—112no—
1153C2×C8—224no—
1154C2×C8—224no—
1155C2×C8C23×D1112yes—
1156C2×C8C23×D1112yes—
1157C4⋊C4—22no—
1158C4⋊C4—112no—
1159C4⋊C4—222no—
1160C4⋊C4—222no—
1161C4⋊C4—222no—
1162C4⋊C4—222no—
1163C4⋊C4C23×D1112yes—
1164C22⋊C4—21no—
1165C22⋊C4—22no—
1166C22⋊C4—22no—
1167C22⋊C4—222no—
1168C22⋊C4—222no—
1169C22⋊C4—222no—
1170C22⋊C4—222no—
1171C22⋊C4—222no—
1172C22⋊C4—221no—
1173C22⋊C4—222no—
1174C22⋊C4—222no—
1175C42—21no—
1176C42—222no—
1177C42—221no—
1178C11#6035911yescharacteristic, complemented, Sylow
1179C23—22no—
1180C23—24no—
1181C23—22no—
1182C23—21no—
1183C23—42no—
1184C23—44no—
1185C23—112no—
1186C23—111no—
1187C23—111no—
1188C23—114no—
1189C23—224no—
1190C23—224no—
1191C23—224no—
1192C23—224no—
1193C23—224no—
1194C23—2216no—
1195C23—222no—
1196C23—224no—
1197C23—222no—
1198C23—221no—
1199C23—442no—
1200C23—442no—
1201C23—442no—
1202C23—444no—
1203C23—448no—
1204C23—442no—
1205C23—4416no—
1206C23—4432no—
1207C23—448no—
1208C23—444no—
1209C23C2×D4×D1112yes—
1210C23C2×D4×D1111yescharacteristic
1211Q8—24no—
1212Q8—22no—
1213Q8—21no—
1214Q8—21no—
1215Q8—114no—
1216Q8—2216no—
1217Q8—224no—
1218Q8—222no—
1219Q8—221no—
1220Q8—221no—
1221Q8—442no—
1222Q8C2×D4×D1114yes—
1223D4—216no—
1224D4—24no—
1225D4—22no—
1226D4—21no—
1227D4—21no—
1228D4—44no—
1229D4—42no—
1230D4—114no—
1231D4—228no—
1232D4—228no—
1233D4—228no—
1234D4—228no—
1235D4—2216no—
1236D4—2216no—
1237D4—224no—
1238D4—222no—
1239D4—221no—
1240D4—221no—
1241D4—442no—
1242D4—444no—
1243D4—442no—
1244D4—444no—
1245D4—442no—
1246D4—444no—
1247D4—442no—
1248D4C2×D4×D1114yes—
1249C2×C4—216no—
1250C2×C4—22no—
1251C2×C4—24no—
1252C2×C4—22no—
1253C2×C4—24no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—21no—
1258C2×C4—42no—
1259C2×C4—114no—
1260C2×C4—111no—
1261C2×C4—111no—
1262C2×C4—114no—
1263C2×C4—114no—
1264C2×C4—112no—
1265C2×C4—112no—
1266C2×C4—112no—
1267C2×C4—112no—
1268C2×C4—112no—
1269C2×C4—224no—
1270C2×C4—224no—
1271C2×C4—228no—
1272C2×C4—228no—
1273C2×C4—224no—
1274C2×C4—224no—
1275C2×C4—2216no—
1276C2×C4—2216no—
1277C2×C4—224no—
1278C2×C4—224no—
1279C2×C4—228no—
1280C2×C4—228no—
1281C2×C4—222no—
1282C2×C4—224no—
1283C2×C4—222no—
1284C2×C4—224no—
1285C2×C4—222no—
1286C2×C4—222no—
1287C2×C4—222no—
1288C2×C4—221no—
1289C2×C4—442no—
1290C2×C4—442no—
1291C2×C4—444no—
1292C2×C4—442no—
1293C2×C4—442no—
1294C2×C4C2×D4×D1112yes—
1295C2×C4C2×D4×D1111yescharacteristic
1296C2×C4C2×D4×D1112yes—
1297C2×C4C2×D4×D1112yes—
1298C2×C4C24×D1111yescharacteristic
1299C8—22no—
1300C8—22no—
1301C8—222no—
1302C8—222no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—24no—
1308C22—44no—
1309C22—48no—
1310C22—44no—
1311C22—42no—
1312C22—41no—
1313C22—114no—
1314C22—112no—
1315C22—112no—
1316C22—228no—
1317C22—222no—
1318C22—222no—
1319C22—222no—
1320C22—222no—
1321C22—224no—
1322C22—444no—
1323C22—448no—
1324C22—448no—
1325C22—448no—
1326C22—4432no—
1327C22—444no—
1328C22—442no—
1329C22—441no—
1330C22—884no—
1331C22D11×#12012yes—
1332C22C22×D4×D1111yescharacteristic
1333C4—22no—
1334C4—24no—
1335C4—42no—
1336C4—41no—
1337C4—112no—
1338C4—112no—
1339C4—222no—
1340C4—224no—
1341C4—442no—
1342C4—441no—
1343C4D11×#12012yes—
1344C4C22×D4×D1111yescharacteristic
1345C4C22×D4×D1111yescharacteristic
1346C2—22no—
1347C2—42no—
1348C2—44no—
1349C2—81no—
1350C2—224no—
1351C2—222no—
1352C2—222no—
1353C2—444no—
1354C2—881no—
1355C2C2×D11×#12011yescharacteristic
1356C2D11×#57512yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3005C2
socleC22×C11C23×D4
hypercenter#3005D11
hypocenterC11#60359
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3005

Complements

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

NH ≅ G/Ntype
1. C22×#41×D11C2semidirect
2. C2×#10623308C2semidirect
3. C2×#10623304C2semidirect
4. D11×#525C2semidirect
5. #13077873C2semidirect
6. #13077865C2semidirect
7. #13077861C2semidirect
8. #13077858C2semidirect
9. #13077856C2semidirect
10. #13077852C2semidirect
11. #13077848C2semidirect
12. #13077845C2semidirect
13. #13077841C2semidirect
14. #13077837C2semidirect
15. #13077831C2semidirect
16. #13077134C2semidirect
17. #13077130C2semidirect
18. D11×#407C2semidirect
19. C11×#3005C2semidirect
20. C22×C11×#41C22semidirect
26. C2×#41×D11C22semidirect
27. C2×#41×D11C22semidirect
29. C22×Q8×D11C22semidirect
33. C22×D4×D11C22semidirect
35. C22×#4339C22semidirect
38. C2×C11×#137C22semidirect
39. C2×C11×AGL(1,ℤ/8)C22semidirect
40. C11×#525C22semidirect
42. C2×#67004C22semidirect
43. C2×#67002C22semidirect
44. C2×#66995C22semidirect
45. C2×#66985C22semidirect
46. #10623322C22semidirect
49. C2×#66972C22semidirect
50. C2×#66971C22semidirect
51. C2×#66969C22semidirect
52. C2×#66969C22semidirect
53. C2×#66968C22semidirect
54. C2×#66967C22semidirect
55. C2×#66965C22semidirect
56. C2×#66964C22semidirect
57. C2×#66962C22semidirect
58. C2×#66961C22semidirect
59. C2×M16×D11C22semidirect
60. C2×M16×D11C22semidirect
63. #10623158C22semidirect
64. D11×C22⋊Q8C22semidirect
65. #10623137C22semidirect
66. D11×#121C22semidirect
72. D11×#117C22semidirect
73. C11×#452C22semidirect
74. C11×#449C22semidirect
75. C11×#419C22semidirect
76. C11×#418C22semidirect
77. C11×#407C22semidirect
78. #10622852C22semidirect
79. #10622851C22semidirect
80. #10622838C22semidirect
81. #10622828C22semidirect
82. #10622820C22semidirect
83. #10622799C22semidirect
84. #10622783C22semidirect
85. #10622782C22semidirect
86. #10622769C22semidirect
87. #10622744C22semidirect
88. #10622739C22semidirect
89. #10622739C22semidirect
90. #10622733C22semidirect
91. #10622660C22semidirect
92. #10622650C22semidirect
93. #10622617C22semidirect
94. #10622614C22semidirect
95. #10622421C22semidirect
96. #10622419C22semidirect
97. #10622417C22semidirect
98. #10622416C22semidirect
99. #10622389C22semidirect
100. #10622386C22semidirect
101. #10622385C22semidirect
102. #10622384C22semidirect
103. #10622347C22semidirect
104. #10622346C22semidirect
105. #10622339C22semidirect
106. D11×C22⋊C8C22semidirect
135. C2×#4343D4semidirect
138. C2×#4343C23semidirect
143. C2×Q8×D11C23semidirect
151. C2×#4341D4semidirect
154. C2×#4341C23semidirect
164. C2×D4×D11C23semidirect
197. C2×C11×Q16C23semidirect
198. C2×C11×SD16C23semidirect
199. C2×C11×SD16C23semidirect
200. C2×C11×D8C23semidirect
204. C11×C22⋊Q8C23semidirect
205. C11×#121C23semidirect
213. C2×#4326C23semidirect
214. C2×#4326C23semidirect
216. C2×#4325C23semidirect
217. C2×#4325C23semidirect
224. C2×#4324C23semidirect
225. C2×#4324C23semidirect
227. C2×#4323C23semidirect
228. C2×#4323C23semidirect
229. #66983C23semidirect
234. #66977C23semidirect
249. C2×Dic44C23semidirect
250. C2×D88C23semidirect
251. C2×#4314C23semidirect
252. C2×#4314C23semidirect
253. C2×#4313C23semidirect
254. C2×#4313C23semidirect
255. C2×C8×D11C23semidirect
256. C2×C8×D11C23semidirect
262. #66945C23semidirect
264. C4⋊C4×D11C23semidirect
280. C11×#103C23semidirect
281. C11×#102C23semidirect
282. C11×C22⋊C8C23semidirect
283. #66899C23semidirect
284. #66896C23semidirect
285. C22⋊(C11⋊C8)C23semidirect
286. #66885C23semidirect
289. #66880C23semidirect
290. #66874C23semidirect
291. #66873C23semidirect
313. C2×Q8×C11C2×D4semidirect
322. C2×D4×C11C2×D4semidirect
364. #4343C2×D4semidirect
380. #4341C2×D4semidirect
405. C2×D44C2×D4semidirect
449. C2×Dic22C2×D4semidirect
510. #3005D11semidirect
656. C22×#41C2×D11semidirect
669. C2×#137C2×D11semidirect
675. C2×AGL(1,ℤ/8)C2×D11semidirect
690. #525C2×D11semidirect
700. #452C2×D11semidirect
708. #449C2×D11semidirect
716. #419C2×D11semidirect
720. #418C2×D11semidirect
729. #407C2×D11semidirect
760. C2×D11#575semidirect
881. C2×Q16C22×D11semidirect
888. C2×SD16C22×D11semidirect
889. C2×SD16C22×D11semidirect
893. C2×D8C22×D11semidirect
915. C22⋊Q8C22×D11semidirect
921. #121C22×D11semidirect
950. #103C22×D11semidirect
954. #102C22×D11semidirect
958. C22⋊C8C22×D11semidirect
1030. C2×Q8D4×D11semidirect
1070. C2×D4D4×D11semidirect
1178. C11#60359semidirect

Maximal subgroups

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

subgroupindex
C22×#41×D112
C2×#106233082
C2×#106233042
D11×#5252
#130778732
#130778652
#130778612
#130778582
#130778562
#130778522
#130778482
#130778452
#130778412
#130778372
#130778312
#130771342
#130771302
D11×#4072
C11×#30052
#6035911