Finite Group Databasebeta

← #15649500

Subgroups — #15649500

Order 2816.

1958 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic, complemented
2#13081511C212yesmaximal, complemented
3#13081334C212yesmaximal, complemented
4#13081211C212yesmaximal, complemented
5#13081050C214yesmaximal, complemented
6#13080915C212yesmaximal, complemented
7#13080571C214yesmaximal, complemented
8#13079972C212yesmaximal, complemented
9#13079932C211yesmaximal, characteristic, complemented
10#13079846C212yesmaximal, complemented
11#13079760C211yesmaximal, characteristic, complemented
12#13078761C212yesmaximal, complemented
13#13078612C211yesmaximal, characteristic, complemented
14#13078425C212yesmaximal, complemented
15C2×#10622700C211yesmaximal, characteristic, complemented
16#13077733C211yesmaximal, characteristic, complemented
17C11×#3499C211yesmaximal, characteristic, complemented
18C2×C11×2−1+4—21no—
19D4×Q8×C11—21no—
20D4×Q8×C11C2212yescomplemented
21C11×#547—22no—
22C11×#547—21no—
23C11×#547C2214yes—
24C11×#547C2212yescomplemented
25C11×#536—21no—
26C11×#536—22no—
27C11×#532C2211yescharacteristic
28C11×#532C2212yescomplemented
29C2×C11×C4⋊Q8C2211yescharacteristic
30C2×C11×C4⋊Q8C2212yescomplemented
31C4×C11×#41C2211yescharacteristic
32#10623359—21no—
33#10623115C2211yescharacteristic
34#10623112—21no—
35#10623110C2211yescharacteristic
36#10623094C2211yescharacteristic
37#10623089—21no—
38#10623087—22no—
39#10623082C2211yescharacteristic
40#10623081C2212yes—
41#10623072C2212yes—
42#10623059—22no—
43D11×#117—21no—
44#10623010C2212yes—
45C4×#4339C2212yes—
46C2×C4×D44C2211yescharacteristic
47#10623001C2211yescharacteristic
48#10622707C2212yescomplemented
49#10622707C2212yescomplemented
50#10622707C2212yescomplemented
51#10622706C2212yescomplemented
52#10622704C2214yescomplemented
53#10622702C2214yes—
54#10622700C2211yescharacteristic
55#10622700C2212yes—
56#10622700C2212yes—
57#10622700C2211yescharacteristic
58#10622700C2212yes—
59#10622700C2212yes—
60#10622697C2214yes—
61#10622693C2214yescomplemented
62#10622692C2212yescomplemented
63#10622688C2212yescomplemented
64#10622685C2211yescharacteristic
65#10622685C2211yescharacteristic
66#10622655C2214yescomplemented
67#10622654C2214yes—
68#10622652C2214yes—
69#10622650C2214yes—
70#10622649C2212yes—
71#10622648C2214yescomplemented
72#10622646C2212yes—
73#10622637C2212yescomplemented
74#10622632C2212yescomplemented
75#10622631C2214yescomplemented
76#10622629C2214yes—
77#10622627C2214yes—
78C4×#4323C2212yes—
79C4×#4323C2212yes—
80#10622625C2212yescomplemented
81#10622624C2214yes—
82#10622622C2214yescomplemented
83#10622621C2212yescomplemented
84#10622584C2214yes—
85#10622583C2214yescomplemented
86#10622581C2214yes—
87#10622579C2214yes—
88C2×#66873C2212yes—
89#10622577C2214yescomplemented
90C2×#66871C2212yes—
91#10622539C2212yescomplemented
92#10622538C2211yescharacteristic
93#10622537C2212yescomplemented
94C2×C4⋊(C11⋊C8)C2211yescharacteristic
95C11×2−1+4—48no—
96C2×C11×#41—24no—
97C2×C11×#41—22no—
98C2×C11×#41—21no—
99C2×C11×#41—22no—
100C2×C11×#41D411yescharacteristic
101C22×Q8×C11—22no—
102C22×Q8×C11—21no—
103C22×Q8×C11—22no—
104C2×#4339C2312yes—
105C22×D44C2311yescharacteristic
106C22×C4×D11—21no—
107C11×C4⋊Q8—21no—
108C11×C4⋊Q8—21no—
109C11×C4⋊Q8—22no—
110C11×C4⋊Q8—22no—
111C11×C4⋊Q8C2312yes—
112C11×C4⋊Q8C2312yes—
113C11×C4⋊Q8C2311yescharacteristic
114C11×C4⋊Q8C2314yes—
115C11×#127C2311yescharacteristic
116C11×#124—21no—
117C11×#124—22no—
118C11×#123—24no—
119C11×#123—24no—
120C11×#123—24no—
121C11×C22⋊Q8—22no—
122C11×C22⋊Q8—24no—
123C11×C22⋊Q8—24no—
124C11×C22⋊Q8—22no—
125C11×#121—21no—
126C11×#121—22no—
127C11×#121C2312yes—
128C11×#121C2314yes—
129C4×Q8×C11D411yescharacteristic
130C4×Q8×C11C2311yescharacteristic
131C4×D4×C11—21no—
132C4×D4×C11—22no—
133C4×D4×C11D412yes—
134C4×D4×C11D411yescharacteristic
135C4×D4×C11C2312yes—
136C4×D4×C11C2314yes—
137C4×D4×C11C2312yes—
138C4×D4×C11C2311yescharacteristic
139C11×#117D411yescharacteristic
140C11×#117D412yes—
141C2×C11×C4⋊C4—21no—
142C2×C11×C4⋊C4—22no—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2314yes—
145C2×C42×C11C2311yescharacteristic
146C2×C42×C11C2312yes—
147#66999—21no—
148#66999—21no—
149#66991—21no—
150#66991—21no—
151#66990—22no—
152#66988—22no—
153C2×#4324C2314yes—
154C2×#4323C2312yes—
155C2×#4323C2312yes—
156#66983C2312yes—
157#66982—22no—
158C4×C22⋊D11—22no—
159C4×C22⋊D11—22no—
160C4×C22⋊D11—22no—
161C2×(C2×D11)⋊C4—21no—
162#66979—21no—
163#66979C2312yes—
164C2×C4⋊Dic11C2311yescharacteristic
165#66977—21no—
166#66977C2312yes—
167#66977C2312yes—
168C2×#4318C2314yes—
169C22×C11⋊C8C2312yes—
170#66951—22no—
171#66949—22no—
172#66947—22no—
173#66945—21no—
174#66945—21no—
175C4⋊C4×D11—21no—
176C4⋊C4×D11—21no—
177#66942—22no—
178#66938—22no—
179#66937—22no—
180#66936—22no—
181C22⋊C4×D11—22no—
182#66932—22no—
183#66930—22no—
184#66929—22no—
185#66928C2312yes—
186C4×D44—21no—
187C4×D44—21no—
188C4×D44C2311yescharacteristic
189C4×D44C2311yescharacteristic
190C4×D44C2311yescharacteristic
191C4×D44C2311yescharacteristic
192C4×D44C2312yes—
193#66925—22no—
194#66925—22no—
195C42×D11—22no—
196#66923—21no—
197#66923C2312yes—
198#66922C2311yescharacteristic
199#66922C2311yescharacteristic
200C4×Dic22—21no—
201C4×Dic22C2312yes—
202C4×Dic22C2312yes—
203#66896C2314yes—
204#66896C2312yes—
205#66896C2312yes—
206C22⋊(C11⋊C8)C2312yes—
207C22⋊(C11⋊C8)C2314yes—
208#66874C2314yes—
209#66874C2314yes—
210#66874C2314yes—
211#66873C2314yes—
212#66873C2314yes—
213#66873C2312yes—
214#66873C2312yes—
215#66872C2314yes—
216#66872C2314yes—
217#66872C2314yes—
218#66871C2314yes—
219#66871C2314yes—
220#66871C2312yes—
221#66871C2312yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2312yes—
224C4⋊(C11⋊C8)C2311yescharacteristic
225C4⋊(C11⋊C8)C2314yes—
226C4⋊(C11⋊C8)C2311yescharacteristic
227#66867C2314yes—
228C4×C11⋊C8C2312yes—
229#62107—111nomaximal, Sylow
230C23×D11—21no—
231C11×#41—24no—
232C11×#41—48no—
233C11×#41—416no—
234C11×#41—48no—
235C11×#41—44no—
236C2×Q8×C11—24no—
237C2×Q8×C11—22no—
238C2×Q8×C11—21no—
239C2×Q8×C11—22no—
240C2×Q8×C11—48no—
241C2×Q8×C11—48no—
242C2×Q8×C11—44no—
243C2×Q8×C11C2×D411yescharacteristic
244C2×D4×C11—24no—
245C2×D4×C11—22no—
246C2×D4×C11—21no—
247C2×D4×C11—21no—
248C2×D4×C11C2×D412yes—
249C2×D4×C11C2×D411yescharacteristic
250C2×D4×C11C2412yes—
251C22×C4×C11—24no—
252C22×C4×C11—22no—
253C22×C4×C11—24no—
254C22×C4×C11—22no—
255C22×C4×C11C2×D412yes—
256C22×C4×C11C2×D411yescharacteristic
257C22×C4×C11C2×D412yes—
258C22×C4×C11C2×D411yescharacteristic
259C22×C4×C11C2411yescharacteristic
260C22×C4×C11C2412yes—
261C2×C22⋊D11—22no—
262C2×C22⋊D11—22no—
263C22×Dic11—21no—
264#4339—24no—
265#4339—42no—
266C2×D44—22no—
267C2×D44—21no—
268C2×D44—41no—
269C2×D44C2411yescharacteristic
270C2×D44C2411yescharacteristic
271C2×C4×D11—21no—
272C2×C4×D11—22no—
273C2×C4×D11—21no—
274C2×C4×D11—21no—
275C2×C4×D11—21no—
276C2×C4×D11—22no—
277C2×C4×D11—44no—
278C2×Dic22—21no—
279C2×Dic22C2412yes—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—24no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—24no—
285C11×C4⋊C4—22no—
286C11×C4⋊C4C2×D412yes—
287C11×C4⋊C4C2×D411yescharacteristic
288C11×C4⋊C4C2×D411yescharacteristic
289C11×C4⋊C4C2×D412yes—
290C11×C4⋊C4C2414yes—
291C11×C4⋊C4C2412yes—
292C11×C22⋊C4—24no—
293C11×C22⋊C4—22no—
294C11×C22⋊C4—24no—
295C11×C22⋊C4—22no—
296C11×C22⋊C4C2×D412yes—
297C11×C22⋊C4C2×D412yes—
298C11×C22⋊C4C2×D412yes—
299C42×C11C2×D411yescharacteristic
300C42×C11C2×D411yescharacteristic
301C42×C11C2×D412yes—
302C42×C11C2×D412yes—
303C42×C11C2411yescharacteristic
304C42×C11C2412yes—
305C42×C11C2411yescharacteristic
306C22⋊Dic11—22no—
307C22⋊Dic11—22no—
308C22⋊Dic11—22no—
309#4324—44no—
310#4323—24no—
311#4323—42no—
312(C2×D11)⋊C4—21no—
313(C2×D11)⋊C4—22no—
314(C2×D11)⋊C4—22no—
315(C2×D11)⋊C4—22no—
316(C2×D11)⋊C4—21no—
317(C2×D11)⋊C4—21no—
318(C2×D11)⋊C4—21no—
319(C2×D11)⋊C4—22no—
320C4⋊Dic11—21no—
321C4⋊Dic11—21no—
322C4⋊Dic11—21no—
323C4⋊Dic11—21no—
324C4⋊Dic11C2411yescharacteristic
325C4⋊Dic11C2411yescharacteristic
326C4⋊Dic11C2412yes—
327Dic11⋊C4—22no—
328Dic11⋊C4—22no—
329Dic11⋊C4—22no—
330Dic11⋊C4—22no—
331Dic11⋊C4—22no—
332Dic11⋊C4—22no—
333C4×Dic11—22no—
334C4×Dic11—22no—
335C4×Dic11—22no—
336#4318—44no—
337C2×C11⋊C8—42no—
338C2×C11⋊C8C2412yes—
339C2×C11⋊C8C2412yes—
340C2×C11⋊C8C2414yes—
341#3499D1111yescharacteristic, complemented
342#3475—111no—
343#3384—112no—
344#3367—112no—
345#3354—112no—
346#3343—114no—
347#3330—112no—
348#3306—114no—
349#3251—112no—
350#3246—111no—
351#3239—112no—
352#3229—111no—
353#3115—112no—
354#3100—111no—
355#3079—112no—
356C2×#474—111no—
357#2989—111no—
358C23×C11—22no—
359C23×C11C22×D412yes—
360C23×C11C22×D411yescharacteristic
361C22×D11—21no—
362C22×D11—21no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—81no—
366Q8×C11—22no—
367Q8×C11—48no—
368Q8×C11—42no—
369Q8×C11—44no—
370Q8×C11—44no—
371D4×C11—24no—
372D4×C11—22no—
373D4×C11—22no—
374D4×C11—22no—
375D4×C11—42no—
376D4×C11—48no—
377D4×C11—44no—
378D4×C11—42no—
379C2×C4×C11—24no—
380C2×C4×C11—21no—
381C2×C4×C11—22no—
382C2×C4×C11—21no—
383C2×C4×C11—22no—
384C2×C4×C11—24no—
385C2×C4×C11—22no—
386C2×C4×C11—41no—
387C2×C4×C11—42no—
388C2×C4×C11—48no—
389C2×C4×C11—48no—
390C2×C4×C11—44no—
391C2×C4×C11—44no—
392C2×C4×C11AGL(1,ℤ/8)14yes—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D412yes—
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D411yescharacteristic
399C2×C4×C11C22×D411yescharacteristic
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11C2511yescharacteristic
402C22⋊D11—44no—
403C22⋊D11—82no—
404C2×Dic11—21no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—21no—
408C2×Dic11—42no—
409D44—21no—
410D44—21no—
411D44—21no—
412D44—42no—
413D442−1+412yescomplemented
414C4×D11—44no—
415C4×D11—42no—
416C4×D11—42no—
417C4×D11—42no—
418C4×D11—42no—
419C4×D11—82no—
420Dic22—22no—
421Dic22—22no—
422Dic22—81no—
423C11⋊C8—22no—
424C11⋊C8—24no—
425C11⋊C8—22no—
426C2×2−1+4—21no—
427#556—111no—
428#555—111no—
429#554—111no—
430#553—221no—
431#552—112no—
432#552—221no—
433#551—222no—
434D4×Q8—21no—
435D4×Q8C2×D1112yescomplemented
436#547—22no—
437#547—21no—
438#547—111no—
439#547C2×D1114yes—
440#547C2×D1112yescomplemented
441#546—112no—
442#536—21no—
443#536—22no—
444#533—111no—
445#532C2×D1111yescharacteristic
446#532C2×D1112yescomplemented
447C2×C4⋊Q8C2×D1111yescharacteristic
448C2×C4⋊Q8C2×D1112yescomplemented
449#529—112no—
450#529—222no—
451#525—221no—
452C4×#41—112no—
453C4×#41C2×D1111yescharacteristic
454C2×C4×D4—111no—
455C2×#117—221no—
456#501—114no—
457#498—112no—
458#489—114no—
459#487—112no—
460#484—114no—
461#483—114no—
462#482—114no—
463#481—114no—
464#480—112no—
465#478—114no—
466#477—114no—
467#476—114no—
468#476—112no—
469#475—112no—
470#475—112no—
471#475—112no—
472#474—112no—
473#474—111no—
474#474—112no—
475#474—112no—
476#474—111no—
477#474—112no—
478#469—114no—
479#468—114no—
480#465—114no—
481#463—114no—
482#461—112no—
483#460—112no—
484#459—111no—
485#459—111no—
486#449—114no—
487#447—112no—
488#446—112no—
489#442—114no—
490#440—114no—
491C4×D8—112no—
492C4×D8—112no—
493#436—112no—
494#435—114no—
495#432—112no—
496#431—111no—
497#428—114no—
498C2×#107—112no—
499#423—112no—
500C2×C4⋊C8—111no—
501#417—114no—
502C2×#102—112no—
503C22×C11—21no—
504C22×C11—21no—
505C22×C11—22no—
506C22×C11—22no—
507C22×C11—22no—
508C22×C11—42no—
509C22×C11—42no—
510C22×C11—42no—
511C22×C11C2×AGL(1,ℤ/8)12yes—
512C22×C11C23×D411yescharacteristic
513C2×D11—22no—
514C2×D11—41no—
515C2×D11—41no—
516C2×D11—41no—
517C2×D11—41no—
518C2×D11—41no—
519C2×D11—84no—
520C4×C11—21no—
521C4×C11—21no—
522C4×C11—22no—
523C4×C11—22no—
524C4×C11—21no—
525C4×C11—22no—
526C4×C11—44no—
527C4×C11—42no—
528C4×C11C2×AGL(1,ℤ/8)12yes—
529C4×C11C2×AGL(1,ℤ/8)12yes—
530C4×C11C2×2−1+411yescharacteristic
531C4×C11#58511yescharacteristic
532Dic11—42no—
533Dic11—42no—
534Dic11—41no—
535Dic11—41no—
5362−1+4—48no—
537C2×#41—24no—
538C2×#41—22no—
539C2×#41—21no—
540C2×#41—22no—
541C2×#41—112no—
542C2×#41C22⋊D1111yescharacteristic
543C22×Q8—22no—
544C22×Q8—21no—
545C22×Q8—22no—
546C22×D4—111no—
547C23×C4—221no—
548C2×SD16—114no—
549C2×D8—112no—
550C2×D8—112no—
551C2×M16—114no—
552C22×C8—112no—
553C4⋊Q8—21no—
554C4⋊Q8—21no—
555C4⋊Q8—22no—
556C4⋊Q8—22no—
557C4⋊Q8—111no—
558C4⋊Q8—111no—
559C4⋊Q8C22×D1112yes—
560C4⋊Q8C22×D1112yes—
561C4⋊Q8C22×D1111yescharacteristic
562C4⋊Q8C22×D1114yes—
563#127C22×D1111yescharacteristic
564#126—222no—
565#126—222no—
566#126—222no—
567#125—112no—
568#125—222no—
569#125—221no—
570#124—21no—
571#124—22no—
572#124—112no—
573#124—222no—
574#123—24no—
575#123—24no—
576#123—24no—
577#123—222no—
578#123—222no—
579#123—222no—
580#123—222no—
581C22⋊Q8—22no—
582C22⋊Q8—24no—
583C22⋊Q8—24no—
584C22⋊Q8—22no—
585C22⋊Q8—112no—
586C22⋊Q8—112no—
587C22⋊Q8—221no—
588C22⋊Q8—221no—
589C22⋊Q8—221no—
590C22⋊Q8—222no—
591#121—21no—
592#121—22no—
593#121—112no—
594#121—221no—
595#121—221no—
596#121—222no—
597#121C22×D1112yes—
598#121C22×D1114yes—
599#120—222no—
600C4×Q8—112no—
601C4×Q8—112no—
602C4×Q8—221no—
603C4×Q8C22⋊D1111yescharacteristic
604C4×Q8C22×D1111yescharacteristic
605C4×D4—21no—
606C4×D4—22no—
607C4×D4—111no—
608C4×D4—111no—
609C4×D4—111no—
610C4×D4—111no—
611C4×D4—112no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4—222no—
615C4×D4—221no—
616C4×D4—221no—
617C4×D4C22⋊D1112yes—
618C4×D4C22⋊D1111yescharacteristic
619C4×D4C22×D1112yes—
620C4×D4C22×D1114yes—
621C4×D4C22×D1112yes—
622C4×D4C22×D1111yescharacteristic
623#117—112no—
624#117—221no—
625#117—221no—
626#117—221no—
627#117—222no—
628#117—222no—
629#117—222no—
630#117C22⋊D1111yescharacteristic
631#117C22⋊D1112yes—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—111no—
635C2×C4⋊C4—221no—
636C2×C4⋊C4—221no—
637C2×C4⋊C4C22×D1112yes—
638C2×C4⋊C4C22×D1114yes—
639C2×C22⋊C4—221no—
640C2×C22⋊C4—222no—
641C2×C42—222no—
642C2×C42C22×D1111yescharacteristic
643C2×C42C22×D1112yes—
644#107—114no—
645#107—114no—
646#107—112no—
647#107—112no—
648#106—114no—
649#106—114no—
650#106—114no—
651C4⋊C8—112no—
652C4⋊C8—112no—
653C4⋊C8—111no—
654C4⋊C8—114no—
655C4⋊C8—111no—
656#103—114no—
657#103—114no—
658#103—114no—
659#102—112no—
660#102—112no—
661#102—114no—
662#102—114no—
663#102—114no—
664#102—112no—
665#102—112no—
666C22⋊C8—112no—
667C22⋊C8—114no—
668#97—114no—
669C4×C8—112no—
670C2×C11—22no—
671C2×C11—42no—
672C2×C11—82no—
673C2×C11#348911yescharacteristic
674C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
675C2×C11#358611yescharacteristic
676D11—42no—
677D11—81no—
678C24—221no—
679#41—24no—
680#41—48no—
681#41—416no—
682#41—48no—
683#41—44no—
684#41—224no—
685#41—442no—
686C2×Q8—24no—
687C2×Q8—22no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—48no—
691C2×Q8—48no—
692C2×Q8—44no—
693C2×Q8—112no—
694C2×Q8—221no—
695C2×Q8C2×C22⋊D1111yescharacteristic
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—111no—
701C2×D4—111no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—221no—
706C2×D4—441no—
707C2×D4C2×C22⋊D1112yes—
708C2×D4C2×C22⋊D1111yescharacteristic
709C2×D4C23×D1112yes—
710C22×C4—24no—
711C22×C4—22no—
712C22×C4—24no—
713C22×C4—22no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—222no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—222no—
721C22×C4—444no—
722C22×C4C2×C22⋊D1112yes—
723C22×C4C2×C22⋊D1111yescharacteristic
724C22×C4C2×C22⋊D1112yes—
725C22×C4C2×C22⋊D1111yescharacteristic
726C22×C4C23×D1111yescharacteristic
727C22×C4C23×D1112yes—
728SD16—444no—
729D8—224no—
730D8—442no—
731M16—444no—
732C2×C8—112no—
733C2×C8—112no—
734C2×C8—114no—
735C2×C8—442no—
736C4⋊C4—22no—
737C4⋊C4—21no—
738C4⋊C4—24no—
739C4⋊C4—22no—
740C4⋊C4—24no—
741C4⋊C4—22no—
742C4⋊C4—112no—
743C4⋊C4—111no—
744C4⋊C4—111no—
745C4⋊C4—221no—
746C4⋊C4—221no—
747C4⋊C4—221no—
748C4⋊C4—222no—
749C4⋊C4—222no—
750C4⋊C4—222no—
751C4⋊C4—222no—
752C4⋊C4—222no—
753C4⋊C4—222no—
754C4⋊C4—221no—
755C4⋊C4C2×C22⋊D1111yescharacteristic
756C4⋊C4C2×C22⋊D1111yescharacteristic
757C4⋊C4C2×C22⋊D1112yes—
758C4⋊C4C2×C22⋊D1112yes—
759C4⋊C4C23×D1114yes—
760C4⋊C4C23×D1112yes—
761C22⋊C4—24no—
762C22⋊C4—22no—
763C22⋊C4—24no—
764C22⋊C4—22no—
765C22⋊C4—222no—
766C22⋊C4—222no—
767C22⋊C4—222no—
768C22⋊C4—221no—
769C22⋊C4—222no—
770C22⋊C4—222no—
771C22⋊C4—221no—
772C22⋊C4—221no—
773C22⋊C4—221no—
774C22⋊C4—222no—
775C22⋊C4—222no—
776C22⋊C4C2×C22⋊D1112yes—
777C22⋊C4C2×C22⋊D1112yes—
778C22⋊C4C2×C22⋊D1112yes—
779C42—222no—
780C42—222no—
781C42—222no—
782C42C2×C22⋊D1112yes—
783C42C2×C22⋊D1112yes—
784C42C2×C22⋊D1111yescharacteristic
785C42C2×C22⋊D1111yescharacteristic
786C42C23×D1111yescharacteristic
787C42C23×D1112yes—
788C42C23×D1111yescharacteristic
789C11#6210711yescharacteristic, complemented, Sylow
790C23—22no—
791C23—221no—
792C23—221no—
793C23—442no—
794C23—442no—
795C23—881no—
796C23C22×C22⋊D1112yes—
797C23C22×C22⋊D1111yescharacteristic
798Q8—22no—
799Q8—48no—
800Q8—42no—
801Q8—44no—
802Q8—44no—
803Q8—222no—
804Q8—222no—
805Q8—881no—
806D4—24no—
807D4—22no—
808D4—22no—
809D4—22no—
810D4—42no—
811D4—48no—
812D4—44no—
813D4—42no—
814D4—112no—
815D4—221no—
816D4—221no—
817D4—221no—
818D4—442no—
819D4—444no—
820D4—882no—
821C2×C4—24no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—22no—
828C2×C4—42no—
829C2×C4—41no—
830C2×C4—48no—
831C2×C4—48no—
832C2×C4—44no—
833C2×C4—44no—
834C2×C4—221no—
835C2×C4—222no—
836C2×C4—222no—
837C2×C4—221no—
838C2×C4—444no—
839C2×C4—442no—
840C2×C4—442no—
841C2×C4—442no—
842C2×C4—442no—
843C2×C4—442no—
844C2×C4—882no—
845C2×C4#6698514yes—
846C2×C4C22×C22⋊D1112yes—
847C2×C4C22×C22⋊D1112yes—
848C2×C4C22×C22⋊D1111yescharacteristic
849C2×C4C22×C22⋊D1111yescharacteristic
850C2×C4C22×C22⋊D1111yescharacteristic
851C2×C4C22×C22⋊D1112yes—
852C2×C4C22×C22⋊D1111yescharacteristic
853C2×C4C22×C22⋊D1111yescharacteristic
854C2×C4C24×D1111yescharacteristic
855C8—222no—
856C8—224no—
857C8—222no—
858C22—21no—
859C22—21no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—222no—
867C22—441no—
868C22—441no—
869C22—441no—
870C22—441no—
871C22—441no—
872C22—884no—
873C22C2×#6698512yes—
874C22C23×C22⋊D1111yescharacteristic
875C4—21no—
876C4—22no—
877C4—21no—
878C4—22no—
879C4—21no—
880C4—22no—
881C4—44no—
882C4—42no—
883C4—442no—
884C4—442no—
885C4—441no—
886C4—441no—
887C4C2×#6698512yes—
888C4C2×#6698512yes—
889C4D11×2−1+411yescharacteristic
890C4#1062345711yescharacteristic
891C2—22no—
892C2—42no—
893C2—82no—
894C2—442no—
895C2—881no—
896C2#1308228911yescharacteristic
897C2C22×#6698511yescharacteristic
898C2#1308340311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3499C2
socleC22×C11C23×D4
hypercenter#3499D11
hypocenterC11#62107
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #13082180C2semidirect
2. #13081511C2semidirect
3. #13081334C2semidirect
4. #13081211C2semidirect
5. #13081050C2semidirect
6. #13080915C2semidirect
7. #13080571C2semidirect
8. #13079972C2semidirect
9. #13079932C2semidirect
10. #13079846C2semidirect
11. #13079760C2semidirect
12. #13078761C2semidirect
13. #13078612C2semidirect
14. #13078425C2semidirect
15. C2×#10622700C2semidirect
16. #13077733C2semidirect
17. C11×#3499C2semidirect
20. D4×Q8×C11C22semidirect
24. C11×#547C22semidirect
28. C11×#532C22semidirect
30. C2×C11×C4⋊Q8C22semidirect
48. #10622707C22semidirect
49. #10622707C22semidirect
50. #10622707C22semidirect
51. #10622706C22semidirect
52. #10622704C22semidirect
61. #10622693C22semidirect
62. #10622692C22semidirect
63. #10622688C22semidirect
66. #10622655C22semidirect
71. #10622648C22semidirect
73. #10622637C22semidirect
74. #10622632C22semidirect
75. #10622631C22semidirect
80. #10622625C22semidirect
82. #10622622C22semidirect
83. #10622621C22semidirect
85. #10622583C22semidirect
89. #10622577C22semidirect
91. #10622539C22semidirect
93. #10622537C22semidirect
341. #3499D11semidirect
413. D442−1+4semidirect
435. D4×Q8C2×D11semidirect
440. #547C2×D11semidirect
446. #532C2×D11semidirect
448. C2×C4⋊Q8C2×D11semidirect
789. C11#62107semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130815112
#130813342
#130812112
#130810502
#130809152
#130805712
#130799722
#130799322
#130798462
#130797602
#130787612
#130786122
#130784252
C2×#106227002
#130777332
C11×#34992
#6210711