Finite Group Databasebeta

← #15622155

Subgroups — #15622155

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081908C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3#13078757C212yesmaximal, complemented
4#13078751C212yesmaximal, complemented
5#13078712C212yesmaximal, complemented
6#13078704C212yesmaximal, complemented
7#13078666C212yesmaximal, complemented
8#13078660C212yesmaximal, complemented
9#13078621C212yesmaximal, complemented
10#13078613C212yesmaximal, complemented
11#13078539C211yesmaximal, characteristic, complemented
12#13078412C212yesmaximal, complemented
13#13078079C212yesmaximal, complemented
14#13077846C211yesmaximal, characteristic, complemented
15#13077842C211yesmaximal, characteristic, complemented
16#13077429C212yesmaximal, complemented
17#13077423C212yesmaximal, complemented
18#13077245C211yesmaximal, characteristic, complemented
19C11×#3092C211yesmaximal, characteristic, complemented
20C23×D44C2211yescharacteristic
21C23×C4×D11—21no—
22C11×#525C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24#10623363C2211yescharacteristic, complemented
25#41×Dic11C2211yescharacteristic, complemented
26C2×#67002C2212yes—
27#10623322C2211yescharacteristic
28C22×(C2×D11)⋊C4—21no—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66961C2212yes—
31#10623180—21no—
32#10623180—21no—
33#10623155C2211yescharacteristic, complemented
34#10623155C2211yescharacteristic, complemented
35#10623153C2211yescharacteristic, complemented
36#10623153C2211yescharacteristic, complemented
37#10623131C2211yescharacteristic, complemented
38#10623131C2211yescharacteristic, complemented
39#10623127C2211yescharacteristic, complemented
40#10623127C2211yescharacteristic, complemented
41#10623117—21no—
42#10623117—21no—
43#10623069—21no—
44#10623069—21no—
45C4×#4341—21no—
46C4×#4341—21no—
47#10623053C2211yescharacteristic, complemented
48#10623048C2211yescharacteristic, complemented
49C2×#66946—21no—
50C2×#66946—21no—
51C2×#66946—21no—
52C2×#66946—21no—
53C2×#66946—21no—
54C2×#66946—21no—
55C2×#66946C2212yes—
56C2×#66946C2212yes—
57C2×#66946C2212yes—
58C2×#66946C2212yes—
59C2×#66946C2212yes—
60C2×#66946C2212yes—
61C11×#484C2212yescomplemented
62C11×#483C2212yescomplemented
63C11×#481C2212yescomplemented
64C11×#480C2212yescomplemented
65C11×#428C2212yescomplemented
66C11×#417C2212yescomplemented
67C11×#407C2211yescharacteristic
68#10622820C2211yescharacteristic
69#10622744C2212yes—
70#10622731C2212yescomplemented
71M16×Dic11C2212yescomplemented
72#10622659C2212yes—
73#10622659C2212yes—
74#10622649C2212yes—
75#10622649C2212yes—
76#10622614C2212yes—
77#10622584C2212yescomplemented
78#10622583C2212yescomplemented
79#10622581C2212yescomplemented
80#10622580C2212yescomplemented
81#10622579C2212yescomplemented
82#10622577C2212yescomplemented
83#10622504C2214yescomplemented
84#10622503C2214yescomplemented
85#10622502C2214yescomplemented
86#10622485C2214yescomplemented
87#10622484C2214yescomplemented
88#10622483C2214yescomplemented
89#10622482C2214yescomplemented
90#10622465C2214yescomplemented
91#10622432C2214yescomplemented
92#10622431C2214yescomplemented
93#10622430C2214yescomplemented
94#10622401C2214yescomplemented
95#10622400C2214yescomplemented
96#10622399C2214yescomplemented
97#10622398C2214yescomplemented
98#10622369C2214yescomplemented
99#10622345C2212yes—
100#10622345C2212yes—
101#10622344C2212yes—
102#10622344C2212yes—
103#10622332C2212yescomplemented
104#10622332C2212yescomplemented
105#10622331C2212yescomplemented
106#10622331C2212yescomplemented
107C24×D11—21no—
108C2×C11×#41C2311yescharacteristic
109C23×C4×C11—21no—
110C23×C4×C11C2311yescharacteristic
111C23×Dic11D411yescharacteristic
112C23×Dic11D411yescharacteristic
113C2×#4341—21no—
114C2×#4341—21no—
115C2×#4339C2311yescharacteristic
116C22×D44—21no—
117C22×D44—21no—
118C22×D44—21no—
119C22×D44—28no—
120C22×D44C2312yes—
121C22×D44C2312yes—
122C22×D44C2312yes—
123C22×C4×D11—22no—
124C22×C4×D11—22no—
125C22×C4×D11—22no—
126C22×C4×D11—22no—
127C22×C4×D11—22no—
128C22×C4×D11—22no—
129C22×C4×D11—48no—
130C2×C11×M16C2312yes—
131C11×#123—21no—
132C11×C22⋊Q8C2311yescharacteristic
133C11×C22⋊Q8C2311yescharacteristic
134C11×#121C2311yescharacteristic
135C11×#121C2311yescharacteristic
136C11×#120—21no—
137C4×D4×C11—21no—
138C4×D4×C11—21no—
139C11×#117C2311yescharacteristic
140C2×C11×C4⋊C4—21no—
141C2×C11×C4⋊C4—21no—
142C2×C11×C4⋊C4—21no—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2312yes—
146#67006—21no—
147#67002—28no—
148#67000C2311yescharacteristic, complemented
149Q8×Dic11C2311yescharacteristic, complemented
150Q8×Dic11C2311yescharacteristic, complemented
151#66997C2311yescharacteristic, complemented
152C2×#4325C2314yes—
153#66993C2311yescharacteristic, complemented
154#66992—21no—
155#66992—21no—
156#66992—21no—
157#66992—21no—
158#66989C2311yescharacteristic, complemented
159#66988—21no—
160#66988—21no—
161D4×Dic11—21no—
162D4×Dic11—21no—
163D4×Dic11—21no—
164D4×Dic11—21no—
165D4×Dic11C2311yescharacteristic, complemented
166D4×Dic11C2311yescharacteristic, complemented
167C2×#4323C2314yes—
168#66983C2311yescharacteristic
169#66983C2311yescharacteristic
170#66982—21no—
171C4×C22⋊D11—21no—
172C4×C22⋊D11—21no—
173C4×C22⋊D11—21no—
174C4×C22⋊D11—21no—
175C2×(C2×D11)⋊C4—22no—
176C2×(C2×D11)⋊C4—22no—
177C2×(C2×D11)⋊C4—22no—
178C2×(C2×D11)⋊C4—22no—
179C2×(C2×D11)⋊C4—22no—
180C2×(C2×D11)⋊C4—22no—
181#66979—21no—
182#66979C2311yescharacteristic
183#66977C2311yescharacteristic
184#66977C2311yescharacteristic
185C2×C4×Dic11—21no—
186C2×C4×Dic11D411yescharacteristic
187C2×C4×Dic11D411yescharacteristic
188C2×C4×Dic11D411yescharacteristic
189C2×C4×Dic11D411yescharacteristic
190C2×C4×Dic11D411yescharacteristic
191C2×C4×Dic11D411yescharacteristic
192C2×C4×Dic11C2311yescharacteristic
193C2×C4×Dic11C2311yescharacteristic
194C2×C4×Dic11C2311yescharacteristic
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×C4×Dic11C2311yescharacteristic
198C2×#4318C2312yes—
199#66961—28no—
200C2×D88C2314yes—
201C2×#4314C2314yes—
202#66951—21no—
203#66951—21no—
204#66946—22no—
205#66946—22no—
206#66946—22no—
207#66946—22no—
208#66946—22no—
209#66946—22no—
210#66946—22no—
211#66946—22no—
212#66946—22no—
213#66946—22no—
214#66946—22no—
215#66946—22no—
216#66946C2314yes—
217#66946C2314yes—
218#66946C2314yes—
219#66946C2314yes—
220#66946C2311yescharacteristic, complemented
221#66946C2311yescharacteristic, complemented
222#66945—21no—
223#66945—21no—
224#66943C2311yescharacteristic, complemented
225#66943C2311yescharacteristic, complemented
226#66942—21no—
227#66942—21no—
228#66941C2311yescharacteristic, complemented
229#66941C2311yescharacteristic, complemented
230#66940—21no—
231#66940—21no—
232#66940C2311yescharacteristic, complemented
233#66940C2311yescharacteristic, complemented
234#66939—21no—
235#66939—21no—
236#66938—21no—
237#66938—21no—
238(C22⋊D11)⋊C4—21no—
239(C22⋊D11)⋊C4—21no—
240(C22⋊D11)⋊C4—21no—
241(C22⋊D11)⋊C4—21no—
242(C22⋊D11)⋊C4—21no—
243(C22⋊D11)⋊C4—21no—
244#66932—21no—
245#66932—21no—
246#66931—21no—
247#66931—21no—
248#66931—21no—
249#66931—21no—
250#66930—21no—
251#66930—21no—
252#66930—21no—
253#66930—21no—
254#66925—21no—
255C42×D11—21no—
256C4×Dic22—21no—
257C4×Dic22—21no—
258C11×#107C2314yescomplemented
259C11×#106C2314yescomplemented
260C11×#103C2314yescomplemented
261C11×#102C2314yescomplemented
262C11×C22⋊C8C2312yes—
263C11×C22⋊C8C2312yes—
264C22⋊(C11⋊C8)C2312yes—
265C22⋊(C11⋊C8)C2312yes—
266#66885C2314yes—
267#66885C2314yes—
268#66879C2314yescomplemented
269Dic11⋊C8C2314yescomplemented
270Dic11⋊C8C2314yescomplemented
271C8×Dic11C2314yescomplemented
272#66874C2314yescomplemented
273#66873C2314yes—
274#66873C2314yes—
275#66873C2314yescomplemented
276#66872C2314yescomplemented
277#66871C2314yescomplemented
278#60558—111nomaximal, Sylow
279C24×C11C2×D411yescharacteristic
280C23×D11—28no—
281C23×D11—22no—
282C23×D11—22no—
283C23×D11—22no—
284C23×D11—44no—
285C23×D11—44no—
286C11×#41—24no—
287C2×Q8×C11C2411yescharacteristic
288C2×D4×C11—21no—
289C2×D4×C11—21no—
290C2×D4×C11—21no—
291C2×D4×C11C2411yescharacteristic
292C22×C4×C11—24no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11—22no—
296C22×C4×C11—21no—
297C22×C4×C11—44no—
298C22×C4×C11C2×D411yescharacteristic
299C22×C4×C11C2×D411yescharacteristic
300C22×C4×C11C2×D411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C22×C4×C11C2411yescharacteristic
304C2×C22⋊D11—21no—
305C2×C22⋊D11—21no—
306C2×C22⋊D11—21no—
307C2×C22⋊D11—21no—
308C2×C22⋊D11—21no—
309C22×Dic11—24no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—42no—
313C22×Dic11C2×D411yescharacteristic
314C22×Dic11C2×D411yescharacteristic
315C22×Dic11C2×D411yescharacteristic
316C22×Dic11C2×D411yescharacteristic
317C22×Dic11C2×D411yescharacteristic
318C22×Dic11C2×D411yescharacteristic
319C22×Dic11C2×D411yescharacteristic
320C22×Dic11C2×D411yescharacteristic
321C22×Dic11C2×D411yescharacteristic
322C22×Dic11C2×D411yescharacteristic
323C22×Dic11C2×D411yescharacteristic
324C22×Dic11C2×D411yescharacteristic
325#4341—44no—
326#4341—44no—
327#4339—24no—
328C2×D44—28no—
329C2×D44—28no—
330C2×D44—28no—
331C2×D44—28no—
332C2×D44—28no—
333C2×D44—22no—
334C2×D44—22no—
335C2×D44—22no—
336C2×D44—24no—
337C2×D44#4118yescomplemented
338C2×D44C2411yescharacteristic
339C2×D44C2414yes—
340C2×C4×D11—21no—
341C2×C4×D11—21no—
342C2×C4×D11—24no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—24no—
346C2×C4×D11—21no—
347C2×C4×D11—48no—
348C2×C4×D11—48no—
349C2×C4×D11—48no—
350C2×C4×D11—48no—
351C2×C4×D11—48no—
352C2×C4×D11—48no—
353C2×Dic22—21no—
354C2×Dic22—21no—
355C2×Dic22C2411yescharacteristic
356C11×M16—24no—
357C2×C8×C11C2414yes—
358C11×C4⋊C4—21no—
359C11×C4⋊C4—21no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—22no—
363C11×C4⋊C4C2414yes—
364C11×C4⋊C4C2411yescharacteristic
365C11×C4⋊C4C2411yescharacteristic
366C11×C22⋊C4—21no—
367C11×C22⋊C4—21no—
368C11×C22⋊C4—21no—
369C11×C22⋊C4—21no—
370C11×C22⋊C4—21no—
371C42×C11—21no—
372C22⋊Dic11—21no—
373C22⋊Dic11—21no—
374C22⋊Dic11—21no—
375C22⋊Dic11—21no—
376C22⋊Dic11—21no—
377C22⋊Dic11—21no—
378C22⋊Dic11—21no—
379#4325—28no—
380#4323—28no—
381(C2×D11)⋊C4—21no—
382(C2×D11)⋊C4—21no—
383(C2×D11)⋊C4—21no—
384(C2×D11)⋊C4—21no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—21no—
390(C2×D11)⋊C4—21no—
391C4⋊Dic11—21no—
392C4⋊Dic11—21no—
393C4⋊Dic11—21no—
394C4⋊Dic11—21no—
395C4⋊Dic11C2411yescharacteristic
396C4⋊Dic11C2411yescharacteristic
397Dic11⋊C4—21no—
398Dic11⋊C4—21no—
399Dic11⋊C4—21no—
400Dic11⋊C4—21no—
401Dic11⋊C4—21no—
402Dic11⋊C4—21no—
403Dic11⋊C4—21no—
404Dic11⋊C4—21no—
405Dic11⋊C4—21no—
406Dic11⋊C4—21no—
407C4×Dic11—21no—
408C4×Dic11—21no—
409C4×Dic11—21no—
410C4×Dic11—21no—
411C4×Dic11—21no—
412C4×Dic11C2×D411yescharacteristic
413C4×Dic11C2×D411yescharacteristic
414C4×Dic11C2×D411yescharacteristic
415C4×Dic11C2×D411yescharacteristic
416C4×Dic11C2×D411yescharacteristic
417C4×Dic11C2×D411yescharacteristic
418C4×Dic11C2×D411yescharacteristic
419C4×Dic11C2×D411yescharacteristic
420C4×Dic11C2×D411yescharacteristic
421C4×Dic11C2×D411yescharacteristic
422C4×Dic11C2×D411yescharacteristic
423C4×Dic11C2×D411yescharacteristic
424C4×Dic11C2411yescharacteristic
425C4×Dic11C2411yescharacteristic
426C4×Dic11C2411yescharacteristic
427C4×Dic11C2411yescharacteristic
428#4318—24no—
429C2×C11⋊C8C2414yes—
430D88—28no—
431#4314—28no—
432#3444—111no—
433C22×C4×D4—111no—
434#3114—112no—
435#3114—112no—
436#3110—112no—
437#3109—112no—
438#3105—112no—
439#3105—112no—
440#3101—112no—
441#3100—112no—
442#3092—111no—
443#3092D1111yescharacteristic, complemented
444#3077—112no—
445#3036—112no—
446#3003—111no—
447#3003—111no—
448C4×AGL(1,ℤ/8)—112no—
449C4×AGL(1,ℤ/8)—112no—
450#2920—111no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—21no—
455C23×C11C22×D411yescharacteristic
456C23×C11C22×D411yescharacteristic
457C23×C11C22×D411yescharacteristic
458C22×D11—28no—
459C22×D11—28no—
460C22×D11—28no—
461C22×D11—24no—
462C22×D11—21no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11—432no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470Q8×C11—22no—
471D4×C11—22no—
472D4×C11—42no—
473D4×C11—42no—
474D4×C11—42no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—21no—
481C2×C4×C11—21no—
482C2×C4×C11—21no—
483C2×C4×C11—24no—
484C2×C4×C11—44no—
485C2×C4×C11—44no—
486C2×C4×C11—44no—
487C2×C4×C11—42no—
488C2×C4×C11C22×D411yescharacteristic
489C2×C4×C11C22×D411yescharacteristic
490C2×C4×C11C22×D411yescharacteristic
491C2×C4×C11C2×#4114yes—
492C2×C4×C11C2511yescharacteristic
493C22⋊D11—42no—
494C22⋊D11—42no—
495C22⋊D11—42no—
496C22⋊D11—42no—
497C22⋊D11—42no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—21no—
506C2×Dic11—21no—
507C2×Dic11—21no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—42no—
513C2×Dic11—42no—
514C2×Dic11AGL(1,ℤ/8)14yescomplemented
515C2×Dic11C22×D411yescharacteristic
516C2×Dic11C22×D411yescharacteristic
517C2×Dic11C22×D411yescharacteristic
518C2×Dic11C22×D411yescharacteristic
519C2×Dic11C22×D411yescharacteristic
520C2×Dic11C22×D411yescharacteristic
521C2×Dic11C22×D411yescharacteristic
522C2×Dic11C22×D411yescharacteristic
523D44—28no—
524D44—28no—
525D44—28no—
526D44—24no—
527D44—22no—
528D44C2×#4118yes—
529C4×D11—48no—
530C4×D11—48no—
531C4×D11—42no—
532C4×D11—42no—
533C4×D11—48no—
534C4×D11—48no—
535C4×D11—42no—
536Dic22—22no—
537Dic22—42no—
538Dic22—42no—
539C8×C11—24no—
540C11⋊C8—24no—
541C23×D4—111no—
542C24×C4—221no—
543C2×AGL(1,ℤ/8)—112no—
544C2×AGL(1,ℤ/8)—112no—
545#533—111no—
546#533—111no—
547#533—111no—
548#532—111no—
549#532—111no—
550#532—111no—
551#529—111no—
552#529—111no—
553#529—111no—
554#529—111no—
555#529—221no—
556#529—221no—
557#529—221no—
558#529—221no—
559#525—111no—
560#525—221no—
561#525—221no—
562#525C2×D1111yescharacteristic
563C4×#41—111no—
564C4×#41—111no—
565C4×#41—221no—
566C4×#41—221no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—112no—
570C2×C4×D4—112no—
571C2×C4×D4—112no—
572C2×C4×D4—112no—
573C2×C4×D4—221no—
574C2×C4×D4—221no—
575C2×C4×D4—221no—
576C2×C4×D4—221no—
577C2×C4×D4—221no—
578C2×C4×D4—221no—
579C22×C4⋊C4C2×D1111yescharacteristic
580C22×C22⋊C4—221no—
581C22×C42—111no—
582#484—112no—
583#484C2×D1112yescomplemented
584#483—112no—
585#483C2×D1112yescomplemented
586#481—112no—
587#481C2×D1112yescomplemented
588#480—112no—
589#480C2×D1112yescomplemented
590#478—114no—
591#478—114no—
592#476—114no—
593#474—114no—
594#463—114no—
595#463—114no—
596#461—114no—
597#459—114no—
598#450—112no—
599#450—112no—
600#450—112no—
601#450—112no—
602#447—112no—
603#447—112no—
604#447—112no—
605#447—112no—
606#442—114no—
607#442—114no—
608#440—114no—
609#440—114no—
610C4×SD16—114no—
611C4×SD16—114no—
612C4×D8—114no—
613C4×D8—114no—
614#432—112no—
615#432—112no—
616#431—112no—
617#431—112no—
618#428—112no—
619#428C2×D1112yescomplemented
620#423—112no—
621#418—112no—
622#418—112no—
623#417—112no—
624#417C2×D1112yescomplemented
625#407—111no—
626#407C2×D1111yescharacteristic
627C4×M16—112no—
628C22×C11—28no—
629C22×C11—21no—
630C22×C11—21no—
631C22×C11—21no—
632C22×C11—21no—
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—41no—
636C22×C11—41no—
637C22×C11—41no—
638C22×C11#52512yes—
639C22×C11C2×AGL(1,ℤ/8)12yes—
640C22×C11#57512yes—
641C22×C11C23×D411yescharacteristic
642C2×D11—28no—
643C2×D11—416no—
644C2×D11—416no—
645C2×D11—416no—
646C2×D11—44no—
647C2×D11—44no—
648C2×D11—41no—
649C2×D11—41no—
650C2×D11—41no—
651C4×C11—21no—
652C4×C11—21no—
653C4×C11—41no—
654C4×C11—44no—
655C4×C11—41no—
656C4×C11—41no—
657C4×C11#52512yes—
658C4×C11C22×#4112yes—
659Dic11—21no—
660Dic11—21no—
661Dic11—21no—
662Dic11—21no—
663Dic11—21no—
664Dic11—21no—
665Dic11—41no—
666Dic11—41no—
667Dic11—41no—
668Dic11C2×AGL(1,ℤ/8)12yes—
669Dic11C2×AGL(1,ℤ/8)12yes—
670C25—221no—
671C2×#41—111no—
672C2×#41—221no—
673C2×#41—221no—
674C2×#41C22×D1111yescharacteristic
675C22×D4—112no—
676C22×D4—112no—
677C22×D4—112no—
678C22×D4—228no—
679C22×D4—221no—
680C22×D4—221no—
681C22×D4—221no—
682C23×C4—21no—
683C23×C4—111no—
684C23×C4—111no—
685C23×C4—222no—
686C23×C4—222no—
687C23×C4—222no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—448no—
692C23×C4C22×D1111yescharacteristic
693AGL(1,ℤ/8)—228no—
694AGL(1,ℤ/8)—228no—
695C2×SD16—114no—
696C2×SD16—114no—
697C2×D8—114no—
698C2×D8—114no—
699C2×M16—112no—
700C2×M16C22×D1112yes—
701C4⋊Q8—111no—
702C4⋊Q8—111no—
703C4⋊Q8—111no—
704#127—111no—
705#126—221no—
706#126—221no—
707#126—221no—
708#126—221no—
709#125—111no—
710#125—111no—
711#125—221no—
712#125—221no—
713#124—111no—
714#124—111no—
715#124—221no—
716#124—221no—
717#123—21no—
718#123—221no—
719#123—221no—
720#123—221no—
721#123—221no—
722#123—221no—
723C22⋊Q8—111no—
724C22⋊Q8—111no—
725C22⋊Q8—221no—
726C22⋊Q8—221no—
727C22⋊Q8—221no—
728C22⋊Q8—221no—
729C22⋊Q8C22×D1111yescharacteristic
730C22⋊Q8C22×D1111yescharacteristic
731#121—111no—
732#121—111no—
733#121—221no—
734#121—221no—
735#121—221no—
736#121—221no—
737#121C22×D1111yescharacteristic
738#121C22×D1111yescharacteristic
739#120—21no—
740#120—221no—
741C4×Q8—111no—
742C4×Q8—111no—
743C4×Q8—111no—
744C4×Q8—111no—
745C4×Q8—221no—
746C4×Q8—221no—
747C4×Q8—221no—
748C4×Q8—221no—
749C4×D4—21no—
750C4×D4—21no—
751C4×D4—111no—
752C4×D4—111no—
753C4×D4—114no—
754C4×D4—114no—
755C4×D4—114no—
756C4×D4—114no—
757C4×D4—111no—
758C4×D4—111no—
759C4×D4—221no—
760C4×D4—221no—
761C4×D4—222no—
762C4×D4—222no—
763C4×D4—222no—
764C4×D4—222no—
765C4×D4—222no—
766C4×D4—222no—
767C4×D4—222no—
768C4×D4—222no—
769C4×D4—222no—
770C4×D4—222no—
771C4×D4—222no—
772C4×D4—222no—
773C4×D4—221no—
774C4×D4—221no—
775C4×D4—221no—
776C4×D4—221no—
777C4×D4—221no—
778C4×D4—221no—
779C4×D4—221no—
780C4×D4—221no—
781C4×D4—221no—
782C4×D4—221no—
783C4×D4—221no—
784C4×D4—221no—
785#117—111no—
786#117—221no—
787#117—221no—
788#117—221no—
789#117—221no—
790#117—221no—
791#117—221no—
792#117—221no—
793#117—221no—
794#117C22×D1111yescharacteristic
795C2×C4⋊C4—21no—
796C2×C4⋊C4—21no—
797C2×C4⋊C4—21no—
798C2×C4⋊C4C22×D1112yes—
799C2×C4⋊C4C22×D1112yes—
800C2×C4⋊C4C22×D1112yes—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—222no—
804C2×C22⋊C4—222no—
805C2×C22⋊C4—222no—
806C2×C22⋊C4—222no—
807C2×C42—111no—
808C2×C42—111no—
809C2×C42—111no—
810C2×C42—111no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—221no—
820C2×C42—221no—
821#107—114no—
822#107C22×D1114yescomplemented
823#106—114no—
824#106C22×D1114yescomplemented
825C4⋊C8—114no—
826C4⋊C8—114no—
827#103—114no—
828#103C22×D1114yescomplemented
829#102—114no—
830#102—114no—
831#102—114no—
832#102—114no—
833#102—114no—
834#102C22×D1114yescomplemented
835C22⋊C8—112no—
836C22⋊C8—112no—
837C22⋊C8C22×D1112yes—
838C22⋊C8C22×D1112yes—
839#97—114no—
840C4×C8—114no—
841C2×C11—22no—
842C2×C11—22no—
843C2×C11—22no—
844C2×C11—81no—
845C2×C11C2×#52511yescharacteristic
846C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
847C2×C11C2×#57511yescharacteristic
848D11—48no—
849D11—81no—
850C24—228no—
851C24—222no—
852C24—222no—
853C24—222no—
854C24—444no—
855C24—444no—
856C24D4×D1111yescharacteristic
857#41—24no—
858#41—224no—
859#41—444no—
860#41—444no—
861C2×Q8—111no—
862C2×Q8—221no—
863C2×Q8—221no—
864C2×Q8C23×D1111yescharacteristic
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—118no—
869C2×D4—114no—
870C2×D4—111no—
871C2×D4—228no—
872C2×D4—228no—
873C2×D4—228no—
874C2×D4—228no—
875C2×D4—228no—
876C2×D4—221no—
877C2×D4—221no—
878C2×D4—221no—
879C2×D4—221no—
880C2×D4—221no—
881C2×D4—222no—
882C2×D4—222no—
883C2×D4—222no—
884C2×D4—224no—
885C2×D4C23×D1111yescharacteristic
886C22×C4—24no—
887C22×C4—22no—
888C22×C4—22no—
889C22×C4—22no—
890C22×C4—21no—
891C22×C4—44no—
892C22×C4—111no—
893C22×C4—111no—
894C22×C4—111no—
895C22×C4—111no—
896C22×C4—111no—
897C22×C4—111no—
898C22×C4—111no—
899C22×C4—111no—
900C22×C4—111no—
901C22×C4—111no—
902C22×C4—111no—
903C22×C4—111no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—224no—
907C22×C4—224no—
908C22×C4—224no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—448no—
915C22×C4—448no—
916C22×C4—448no—
917C22×C4—448no—
918C22×C4—448no—
919C22×C4—448no—
920C22×C4—442no—
921C22×C4D4×D1111yescharacteristic
922C22×C4D4×D1111yescharacteristic
923C22×C4D4×D1111yescharacteristic
924C22×C4C23×D1111yescharacteristic
925C22×C4C23×D1111yescharacteristic
926C22×C4C23×D1111yescharacteristic
927SD16—228no—
928SD16—228no—
929D8—228no—
930D8—228no—
931M16—24no—
932M16—224no—
933C2×C8—114no—
934C2×C8C23×D1114yes—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—111no—
941C4⋊C4—111no—
942C4⋊C4—221no—
943C4⋊C4—221no—
944C4⋊C4—221no—
945C4⋊C4—221no—
946C4⋊C4—221no—
947C4⋊C4—221no—
948C4⋊C4—221no—
949C4⋊C4—221no—
950C4⋊C4—221no—
951C4⋊C4—221no—
952C4⋊C4—221no—
953C4⋊C4—221no—
954C4⋊C4—221no—
955C4⋊C4—221no—
956C4⋊C4C23×D1111yescharacteristic
957C4⋊C4C23×D1111yescharacteristic
958C4⋊C4C23×D1114yes—
959C22⋊C4—21no—
960C22⋊C4—21no—
961C22⋊C4—21no—
962C22⋊C4—21no—
963C22⋊C4—21no—
964C22⋊C4—224no—
965C22⋊C4—224no—
966C22⋊C4—224no—
967C22⋊C4—224no—
968C22⋊C4—221no—
969C22⋊C4—221no—
970C22⋊C4—221no—
971C22⋊C4—221no—
972C22⋊C4—221no—
973C22⋊C4—221no—
974C22⋊C4—221no—
975C22⋊C4—221no—
976C22⋊C4—221no—
977C22⋊C4—221no—
978C22⋊C4—221no—
979C22⋊C4—221no—
980C22⋊C4—221no—
981C42—21no—
982C42—111no—
983C42—111no—
984C42—111no—
985C42—111no—
986C42—111no—
987C42—111no—
988C42—111no—
989C42—111no—
990C42—111no—
991C42—111no—
992C42—111no—
993C42—111no—
994C42—111no—
995C42—111no—
996C42—111no—
997C42—111no—
998C42—221no—
999C42—221no—
1000C42—221no—
1001C42—221no—
1002C42—221no—
1003C11#6055811yescharacteristic, complemented, Sylow
1004C23—22no—
1005C23—22no—
1006C23—22no—
1007C23—21no—
1008C23—228no—
1009C23—228no—
1010C23—228no—
1011C23—224no—
1012C23—221no—
1013C23—444no—
1014C23—444no—
1015C23—4432no—
1016C23—444no—
1017C23—444no—
1018C23—444no—
1019C23—444no—
1020C23C2×D4×D1111yescharacteristic
1021C23C2×D4×D1111yescharacteristic
1022C23C2×D4×D1111yescharacteristic
1023Q8—22no—
1024Q8—222no—
1025Q8—442no—
1026Q8—442no—
1027D4—22no—
1028D4—42no—
1029D4—42no—
1030D4—42no—
1031D4—118no—
1032D4—228no—
1033D4—228no—
1034D4—228no—
1035D4—224no—
1036D4—222no—
1037D4—442no—
1038D4—442no—
1039D4—442no—
1040D4—442no—
1041D4—442no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—24no—
1051C2×C4—44no—
1052C2×C4—44no—
1053C2×C4—44no—
1054C2×C4—42no—
1055C2×C4—114no—
1056C2×C4—111no—
1057C2×C4—111no—
1058C2×C4—111no—
1059C2×C4—111no—
1060C2×C4—111no—
1061C2×C4—111no—
1062C2×C4—111no—
1063C2×C4—111no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—221no—
1072C2×C4—221no—
1073C2×C4—221no—
1074C2×C4—448no—
1075C2×C4—448no—
1076C2×C4—442no—
1077C2×C4—448no—
1078C2×C4—448no—
1079C2×C4—442no—
1080C2×C4—442no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—442no—
1086C2×C4—442no—
1087C2×C4C2×D4×D1111yescharacteristic
1088C2×C4C2×D4×D1111yescharacteristic
1089C2×C4C2×D4×D1111yescharacteristic
1090C2×C4#41×D1114yes—
1091C2×C4C24×D1111yescharacteristic
1092C8—24no—
1093C8—224no—
1094C22—28no—
1095C22—21no—
1096C22—21no—
1097C22—21no—
1098C22—21no—
1099C22—21no—
1100C22—21no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—228no—
1105C22—4416no—
1106C22—4416no—
1107C22—4416no—
1108C22—444no—
1109C22—444no—
1110C22—441no—
1111C22—441no—
1112C22—441no—
1113C22#1062318712yes—
1114C22D11×AGL(1,ℤ/8)12yes—
1115C22#1062330812yes—
1116C22C22×D4×D1111yescharacteristic
1117C4—21no—
1118C4—21no—
1119C4—44no—
1120C4—41no—
1121C4—41no—
1122C4—41no—
1123C4—112no—
1124C4—112no—
1125C4—221no—
1126C4—221no—
1127C4—221no—
1128C4—221no—
1129C4—221no—
1130C4—221no—
1131C4—441no—
1132C4—441no—
1133C4—441no—
1134C4#1062318712yes—
1135C4C2×#41×D1112yes—
1136C2—22no—
1137C2—22no—
1138C2—22no—
1139C2—81no—
1140C2—448no—
1141C2—881no—
1142C2C2×#1062318711yescharacteristic
1143C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1144C2C2×#1062330811yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3092C2
socleC22×C11C23×D4
hypercenter#3092D11
hypocenterC11#60558
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3092

Complements

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

NH ≅ G/Ntype
1. #13081908C2semidirect
2. C22×#66946C2semidirect
3. #13078757C2semidirect
4. #13078751C2semidirect
5. #13078712C2semidirect
6. #13078704C2semidirect
7. #13078666C2semidirect
8. #13078660C2semidirect
9. #13078621C2semidirect
10. #13078613C2semidirect
11. #13078539C2semidirect
12. #13078412C2semidirect
13. #13078079C2semidirect
14. #13077846C2semidirect
15. #13077842C2semidirect
16. #13077429C2semidirect
17. #13077423C2semidirect
18. #13077245C2semidirect
19. C11×#3092C2semidirect
24. #10623363C22semidirect
25. #41×Dic11C22semidirect
33. #10623155C22semidirect
34. #10623155C22semidirect
35. #10623153C22semidirect
36. #10623153C22semidirect
37. #10623131C22semidirect
38. #10623131C22semidirect
39. #10623127C22semidirect
40. #10623127C22semidirect
47. #10623053C22semidirect
48. #10623048C22semidirect
61. C11×#484C22semidirect
62. C11×#483C22semidirect
63. C11×#481C22semidirect
64. C11×#480C22semidirect
65. C11×#428C22semidirect
66. C11×#417C22semidirect
70. #10622731C22semidirect
71. M16×Dic11C22semidirect
77. #10622584C22semidirect
78. #10622583C22semidirect
79. #10622581C22semidirect
80. #10622580C22semidirect
81. #10622579C22semidirect
82. #10622577C22semidirect
83. #10622504C22semidirect
84. #10622503C22semidirect
85. #10622502C22semidirect
86. #10622485C22semidirect
87. #10622484C22semidirect
88. #10622483C22semidirect
89. #10622482C22semidirect
90. #10622465C22semidirect
91. #10622432C22semidirect
92. #10622431C22semidirect
93. #10622430C22semidirect
94. #10622401C22semidirect
95. #10622400C22semidirect
96. #10622399C22semidirect
97. #10622398C22semidirect
98. #10622369C22semidirect
103. #10622332C22semidirect
104. #10622332C22semidirect
105. #10622331C22semidirect
106. #10622331C22semidirect
148. #67000C23semidirect
149. Q8×Dic11C23semidirect
150. Q8×Dic11C23semidirect
151. #66997C23semidirect
153. #66993C23semidirect
158. #66989C23semidirect
165. D4×Dic11C23semidirect
166. D4×Dic11C23semidirect
220. #66946C23semidirect
221. #66946C23semidirect
224. #66943C23semidirect
225. #66943C23semidirect
228. #66941C23semidirect
229. #66941C23semidirect
232. #66940C23semidirect
233. #66940C23semidirect
258. C11×#107C23semidirect
259. C11×#106C23semidirect
260. C11×#103C23semidirect
261. C11×#102C23semidirect
268. #66879C23semidirect
269. Dic11⋊C8C23semidirect
270. Dic11⋊C8C23semidirect
271. C8×Dic11C23semidirect
272. #66874C23semidirect
275. #66873C23semidirect
276. #66872C23semidirect
277. #66871C23semidirect
337. C2×D44#41semidirect
443. #3092D11semidirect
514. C2×Dic11AGL(1,ℤ/8)semidirect
583. #484C2×D11semidirect
585. #483C2×D11semidirect
587. #481C2×D11semidirect
589. #480C2×D11semidirect
619. #428C2×D11semidirect
624. #417C2×D11semidirect
822. #107C22×D11semidirect
824. #106C22×D11semidirect
828. #103C22×D11semidirect
834. #102C22×D11semidirect
1003. C11#60558semidirect

Maximal subgroups

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

subgroupindex
#130819082
C22×#669462
#130787572
#130787512
#130787122
#130787042
#130786662
#130786602
#130786212
#130786132
#130785392
#130784122
#130780792
#130778462
#130778422
#130774292
#130774232
#130772452
C11×#30922
#6055811