Finite Group Databasebeta

← #15632593

Subgroups — #15632593

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082174C211yesmaximal, characteristic
2#13081242C212yesmaximal, complemented
3#13081231C212yesmaximal, complemented
4#13081095C214yesmaximal, complemented
5#13081065C214yesmaximal, complemented
6#13081004C212yesmaximal, complemented
7#13080967C212yesmaximal, complemented
8#13079158C211yesmaximal, characteristic, complemented
9#13078560C212yesmaximal, complemented
10#13078539C212yesmaximal, complemented
11#13078425C211yesmaximal, characteristic, complemented
12#13078421C211yesmaximal, characteristic, complemented
13#13078242C212yesmaximal, complemented
14C4×#66995C211yesmaximal, characteristic, complemented
15D4×#4318C211yesmaximal, characteristic, complemented
16C2×#10622577C212yesmaximal, complemented
17C2×C11×#554C211yesmaximal, characteristic, complemented
18C11×#554—21no—
19C11×#554—22no—
20C11×#554—21no—
21C11×#554C2214yes—
22C11×#554C2212yes—
23C11×#554C2212yes—
24C2×C11×C4⋊Q8C2211yescharacteristic
25C2×C11×#125—21no—
26C2×C11×C22⋊Q8—22no—
27C2×C11×C22⋊Q8C2212yes—
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×D4×C11—21no—
30C2×C4×D4×C11C2211yescharacteristic
31C22×C11×C4⋊C4C2212yes—
32C2×#66995C2211yescharacteristic
33#10623337—21no—
34#10623322C2212yes—
35C2×#66979C2212yes—
36C22×#4318C2212yes—
37#10623096C2212yes—
38#10623094C2211yescharacteristic
39#10623088—21no—
40#10623086C2211yescharacteristic
41#10623074C2211yescharacteristic
42#10623073C2211yescharacteristic
43#10623072C2212yes—
44#10623069—22no—
45C4×#4341—21no—
46#10623044—21no—
47#10623026—22no—
48C4×#4339C2211yescharacteristic
49#10623001C2211yescharacteristic
50#10622838C2211yescharacteristic
51#10622838C2212yes—
52#10622820C2212yes—
53#10622707C2212yescomplemented
54#10622704C2212yescomplemented
55#10622700C2212yescomplemented
56#10622697C2212yescomplemented
57#10622693C2214yescomplemented
58#10622692C2212yescomplemented
59#10622691C2212yescomplemented
60#10622665C2214yescomplemented
61#10622664C2214yescomplemented
62#10622662C2214yescomplemented
63#10622661C2214yescomplemented
64#10622658C2214yescomplemented
65#10622658C2214yescomplemented
66#10622657C2214yescomplemented
67#10622656C2214yescomplemented
68#10622643C2212yescomplemented
69C4×#4326C2212yescomplemented
70#10622639C2212yescomplemented
71C4×#4325C2212yescomplemented
72#10622635C2214yescomplemented
73#10622634C2212yescomplemented
74#10622633C2212yescomplemented
75#10622625C2212yes—
76#10622624C2214yes—
77D4×C11⋊C8C2212yes—
78#10622584C2214yescomplemented
79#10622583C2214yescomplemented
80#10622581C2214yescomplemented
81#10622580C2214yescomplemented
82#10622579C2211yescharacteristic
83#10622579C2212yes—
84#10622577C2212yes—
85#10622577C2212yes—
86#10622577C2212yes—
87#10622577C2212yes—
88#10622577C2211yescharacteristic
89#10622577C2214yescomplemented
90#10622577C2214yescomplemented
91C2×#66872C2214yescomplemented
92C2×#66871C2214yescomplemented
93#10622537C2211yescharacteristic
94C4×#4318C2211yescharacteristic
95C22×Q8×C11—21no—
96C22×Q8×C11C2311yescharacteristic
97C22×D4×C11D411yescharacteristic
98C23×C4×C11—22no—
99C23×C4×C11C2312yes—
100C2×#4341—21no—
101C2×#4339C2311yescharacteristic
102C11×C4⋊Q8—21no—
103C11×C4⋊Q8—21no—
104C11×C4⋊Q8C2312yes—
105C11×C4⋊Q8C2312yes—
106C11×#125—22no—
107C11×#125—24no—
108C11×#125—22no—
109C11×C22⋊Q8—22no—
110C11×C22⋊Q8—22no—
111C11×C22⋊Q8—24no—
112C11×C22⋊Q8—24no—
113C11×C22⋊Q8—24no—
114C11×C22⋊Q8—24no—
115C11×C22⋊Q8C2314yes—
116C11×C22⋊Q8C2314yes—
117C4×Q8×C11—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11C2312yes—
120C4×Q8×C11C2312yes—
121C4×D4×C11—24no—
122C4×D4×C11—22no—
123C4×D4×C11—22no—
124C4×D4×C11D411yescharacteristic
125C4×D4×C11D412yes—
126C4×D4×C11D411yescharacteristic
127C4×D4×C11C2312yes—
128C4×D4×C11C2311yescharacteristic
129C4×D4×C11C2311yescharacteristic
130C2×C11×C4⋊C4—22no—
131C2×C11×C4⋊C4—22no—
132C2×C11×C4⋊C4—22no—
133C2×C11×C4⋊C4—21no—
134C2×C11×C4⋊C4—21no—
135C2×C11×C4⋊C4—22no—
136C2×C11×C4⋊C4D411yescharacteristic
137C2×C11×C4⋊C4C2314yes—
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2312yes—
140C2×C11×C4⋊C4C2314yes—
141C2×C11×C22⋊C4—22no—
142C2×C11×C22⋊C4D412yes—
143C2×C42×C11—21no—
144C2×C42×C11C2311yescharacteristic
145#67006—22no—
146C2×C22⋊Dic11—22no—
147C2×#4326C2312yes—
148#66995—24no—
149C2×#4325C2312yes—
150#66992—22no—
151#66991—21no—
152#66989—21no—
153#66988—22no—
154D4×Dic11—21no—
155#66983C2312yes—
156#66983C2312yes—
157#66982—22no—
158C4×C22⋊D11—21no—
159C4×C22⋊D11—21no—
160C4×C22⋊D11—22no—
161C4×C22⋊D11—22no—
162#66979—22no—
163#66979—22no—
164#66979C2312yes—
165#66979C2311yescharacteristic
166#66979C2312yes—
167#66979C2312yes—
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170#66977—21no—
171#66977—21no—
172#66977C2312yes—
173#66977C2312yes—
174C2×C4×Dic11—22no—
175C2×#4318—28no—
176C2×#4318C2311yescharacteristic
177C2×#4318C2312yes—
178C2×#4318C2314yes—
179C2×#4318C2311yescharacteristic
180C22×C11⋊C8C2314yes—
181#66951—22no—
182#66950—21no—
183#66945—21no—
184#66943—21no—
185#66942—22no—
186#66940—21no—
187#66939—22no—
188#66938—22no—
189#66936—22no—
190(C22⋊D11)⋊C4—22no—
191#66932—22no—
192#66932—22no—
193#66931—22no—
194#66930—22no—
195C4×D44C2311yescharacteristic
196C4×D44C2311yescharacteristic
197#66925—21no—
198C42×D11—21no—
199#66923C2312yes—
200#66922C2311yescharacteristic
201#66922C2311yescharacteristic
202C4×Dic22—21no—
203C4×Dic22—21no—
204C4×Dic22C2311yescharacteristic
205C4×Dic22C2311yescharacteristic
206#66899C2314yes—
207#66899C2314yes—
208#66899C2312yes—
209#66899C2312yes—
210C22⋊(C11⋊C8)C2314yes—
211C22⋊(C11⋊C8)C2314yes—
212#66874C2312yes—
213#66874C2314yes—
214#66873C2312yes—
215#66873C2314yes—
216#66872C2312yes—
217#66872C2314yes—
218#66872C2314yes—
219#66872C2314yes—
220#66872C2314yes—
221#66871C2312yes—
222#66871C2314yes—
223#66871C2314yes—
224#66871C2314yes—
225#66871C2314yes—
226C4⋊(C11⋊C8)C2312yes—
227C4⋊(C11⋊C8)C2312yes—
228#66867C2312yes—
229C4×C11⋊C8C2312yes—
230#61254—111nomaximal, Sylow
231C24×C11C2×D412yes—
232C2×Q8×C11—21no—
233C2×Q8×C11—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—22no—
236C2×Q8×C11—22no—
237C2×Q8×C11—82no—
238C2×Q8×C11C2412yes—
239C2×D4×C11—24no—
240C2×D4×C11C2×D412yes—
241C2×D4×C11C2×D411yescharacteristic
242C2×D4×C11C2×D411yescharacteristic
243C22×C4×C11—24no—
244C22×C4×C11—24no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—22no—
248C22×C4×C11—24no—
249C22×C4×C11—24no—
250C22×C4×C11—84no—
251C22×C4×C11C2×D412yes—
252C22×C4×C11C2×D411yescharacteristic
253C22×C4×C11C2×D412yes—
254C22×C4×C11C2×D412yes—
255C22×C4×C11C2×D411yescharacteristic
256C22×C4×C11C2412yes—
257C22×C4×C11C2412yes—
258C22×C4×C11C2411yescharacteristic
259C2×C22⋊D11—22no—
260C2×C22⋊D11—21no—
261C2×C22⋊D11—22no—
262C22×Dic11—22no—
263C22×Dic11—22no—
264#4341—44no—
265#4339—22no—
266#4339—22no—
267C2×D44C2411yescharacteristic
268C2×C4×D11—21no—
269C2×C4×D11—21no—
270C2×C4×D11—21no—
271C2×Dic22—21no—
272C2×Dic22—21no—
273C2×Dic22C2411yescharacteristic
274C11×C4⋊C4—21no—
275C11×C4⋊C4—24no—
276C11×C4⋊C4—24no—
277C11×C4⋊C4—22no—
278C11×C4⋊C4—22no—
279C11×C4⋊C4—22no—
280C11×C4⋊C4—22no—
281C11×C4⋊C4—22no—
282C11×C4⋊C4—24no—
283C11×C4⋊C4—24no—
284C11×C4⋊C4C2×D411yescharacteristic
285C11×C4⋊C4C2×D412yes—
286C11×C4⋊C4C2×D411yescharacteristic
287C11×C4⋊C4C2412yes—
288C11×C4⋊C4C2414yes—
289C11×C22⋊C4—24no—
290C11×C22⋊C4—24no—
291C11×C22⋊C4C2×D412yes—
292C11×C22⋊C4C2×D412yes—
293C11×C22⋊C4C2×D412yes—
294C11×C22⋊C4C2×D412yes—
295C42×C11—22no—
296C42×C11—22no—
297C42×C11C2×D411yescharacteristic
298C42×C11C2×D411yescharacteristic
299C42×C11C2411yescharacteristic
300C42×C11C2411yescharacteristic
301C22⋊Dic11—22no—
302C22⋊Dic11—22no—
303C22⋊Dic11—22no—
304C22⋊Dic11—22no—
305C22⋊Dic11—22no—
306C22⋊Dic11—21no—
307#4326—24no—
308#4325—24no—
309(C2×D11)⋊C4—21no—
310(C2×D11)⋊C4—21no—
311(C2×D11)⋊C4—22no—
312(C2×D11)⋊C4—22no—
313C4⋊Dic11—21no—
314C4⋊Dic11—21no—
315C4⋊Dic11—22no—
316C4⋊Dic11—22no—
317C4⋊Dic11C2411yescharacteristic
318C4⋊Dic11C2412yes—
319C4⋊Dic11C2411yescharacteristic
320C4⋊Dic11C2412yes—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325Dic11⋊C4—22no—
326Dic11⋊C4—22no—
327C4×Dic11—22no—
328C4×Dic11—21no—
329C4×Dic11—21no—
330C4×Dic11—21no—
331C4×Dic11—22no—
332C4×Dic11—22no—
333#4318—28no—
334#4318—24no—
335#4318—22no—
336#4318#4114yescomplemented
337C2×C11⋊C8—28no—
338C2×C11⋊C8C2412yes—
339C2×C11⋊C8C2414yes—
340C2×C11⋊C8C2412yes—
341#3475—111no—
342C2×#554D1111yescharacteristic, complemented
343#3357—112no—
344#3356—112no—
345#3346—114no—
346#3344—114no—
347#3338—112no—
348#3335—112no—
349#3165—111no—
350#3095—112no—
351#3092—112no—
352#3079—111no—
353#3078—111no—
354#3056—112no—
355C4×#137—111no—
356D4×M16—111no—
357C2×#428—112no—
358C23×C11—24no—
359C23×C11—24no—
360C23×C11—42no—
361C23×C11C22×D412yes—
362C23×C11C22×D411yescharacteristic
363C23×C11C22×D412yes—
364C22×D11—21no—
365Q8×C11—22no—
366Q8×C11—22no—
367Q8×C11—42no—
368Q8×C11—82no—
369Q8×C11—82no—
370D4×C11—24no—
371D4×C11—22no—
372D4×C11#13714yescomplemented
373C2×C4×C11—24no—
374C2×C4×C11—24no—
375C2×C4×C11—24no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—24no—
384C2×C4×C11—41no—
385C2×C4×C11—42no—
386C2×C4×C11—44no—
387C2×C4×C11—42no—
388C2×C4×C11—84no—
389C2×C4×C11—84no—
390C2×C4×C11C22×D412yes—
391C2×C4×C11C22×D411yescharacteristic
392C2×C4×C11C22×D411yescharacteristic
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D411yescharacteristic
396C2×C4×C11C22×D411yescharacteristic
397C2×C4×C11C2×#4112yes—
398C2×C4×C112−1+412yes—
399C2×C4×C11C2511yescharacteristic
400C22⋊D11—42no—
401C22⋊D11—44no—
402C22⋊D11—82no—
403C2×Dic11—21no—
404C2×Dic11—21no—
405C2×Dic11—21no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—44no—
409C2×Dic11—82no—
410D44—21no—
411D44—21no—
412C4×D11—42no—
413C4×D11—42no—
414C4×D11—81no—
415Dic22—21no—
416Dic22—21no—
417Dic22—42no—
418Dic22—81no—
419C11⋊C8—24no—
420C11⋊C8—22no—
421C11⋊C8C2×#4114yes—
422C2×#137—111no—
423C22×M16—112no—
424#556—111no—
425#555—111no—
426#554—21no—
427#554—22no—
428#554—21no—
429#554—111no—
430#554C2×D1112yes—
431#554C2×D1114yes—
432#554C2×D1112yes—
433#553—112no—
434#552—112no—
435#552—221no—
436#551—222no—
437#547—111no—
438#546—221no—
439#533—111no—
440C2×C4⋊Q8C2×D1111yescharacteristic
441#529—222no—
442#529—221no—
443C2×#125—21no—
444#525—112no—
445C2×C22⋊Q8—22no—
446C2×C22⋊Q8C2×D1112yes—
447C4×#41—111no—
448C4×#41—221no—
449C2×C4×Q8C2×D1111yescharacteristic
450C2×C4×D4—21no—
451C2×C4×D4C2×D1111yescharacteristic
452C2×#117—112no—
453C22×C4⋊C4C2×D1112yes—
454#501—114no—
455#500—112no—
456#498—112no—
457#485—114no—
458#485—114no—
459#484—114no—
460#484—114no—
461#483—114no—
462#483—114no—
463#481—114no—
464#480—114no—
465#479—114no—
466#477—112no—
467#477—112no—
468#476—112no—
469#475—112no—
470#475—112no—
471#474—112no—
472#470—114no—
473#468—114no—
474#467—114no—
475#465—114no—
476#441—112no—
477#440—112no—
478C4×Q16—112no—
479C4×SD16—112no—
480#436—112no—
481#435—114no—
482C8×D4—112no—
483#428—112no—
484#428—112no—
485#428—114no—
486#428—114no—
487#428—112no—
488#428—112no—
489#428—111no—
490C2×#107—114no—
491C2×#106—114no—
492#423—111no—
493#419—112no—
494#419—111no—
495#417—112no—
496#417—111no—
497#407—112no—
498C4×M16—111no—
499C22×C11—21no—
500C22×C11—22no—
501C22×C11—22no—
502C22×C11—21no—
503C22×C11—22no—
504C22×C11—22no—
505C22×C11—22no—
506C22×C11—48no—
507C22×C11#54712yes—
508C22×C11C2×#13714yes—
509C22×C11C23×D411yescharacteristic
510C2×D11—41no—
511C2×D11—41no—
512C2×D11—41no—
513C4×C11—21no—
514C4×C11—21no—
515C4×C11—22no—
516C4×C11—22no—
517C4×C11—21no—
518C4×C11—42no—
519C4×C11—44no—
520C4×C11—42no—
521C4×C11#54712yes—
522C4×C11C2×#13712yes—
523C4×C11C22×#4111yescharacteristic
524C4×C11C2×2−1+411yescharacteristic
525Dic11—42no—
526Dic11—41no—
527Dic11—41no—
528Dic11—42no—
529Dic11—41no—
530C2×#41—111no—
531C2×#41—221no—
532C22×Q8—21no—
533C22×Q8C22×D1111yescharacteristic
534C22×D4C22⋊D1111yescharacteristic
535C23×C4—22no—
536C23×C4C22×D1112yes—
537#137—224no—
538C2×Q16—112no—
539C2×SD16—112no—
540C2×M16—111no—
541C2×M16—112no—
542C2×M16—114no—
543C2×M16—111no—
544C2×M16—228no—
545C22×C8—114no—
546C4⋊Q8—21no—
547C4⋊Q8—21no—
548C4⋊Q8—111no—
549C4⋊Q8—111no—
550C4⋊Q8C22×D1112yes—
551C4⋊Q8C22×D1112yes—
552#126—222no—
553#126—222no—
554#126—222no—
555#125—22no—
556#125—22no—
557#125—24no—
558#125—112no—
559#125—222no—
560#125—221no—
561#124—221no—
562#124—222no—
563#123—222no—
564#123—222no—
565#123—222no—
566#123—222no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8—24no—
570C22⋊Q8—24no—
571C22⋊Q8—24no—
572C22⋊Q8—24no—
573C22⋊Q8—112no—
574C22⋊Q8—112no—
575C22⋊Q8—221no—
576C22⋊Q8—221no—
577C22⋊Q8—221no—
578C22⋊Q8—222no—
579C22⋊Q8C22×D1114yes—
580C22⋊Q8C22×D1114yes—
581#121—112no—
582#121—112no—
583#121—222no—
584#121—221no—
585#120—222no—
586C4×Q8—21no—
587C4×Q8—21no—
588C4×Q8—111no—
589C4×Q8—111no—
590C4×Q8—221no—
591C4×Q8—221no—
592C4×Q8—221no—
593C4×Q8C22×D1112yes—
594C4×Q8C22×D1112yes—
595C4×D4—24no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—111no—
599C4×D4—111no—
600C4×D4—221no—
601C4×D4—221no—
602C4×D4—221no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4C22⋊D1111yescharacteristic
607C4×D4C22⋊D1111yescharacteristic
608C4×D4C22⋊D1112yes—
609C4×D4C22×D1111yescharacteristic
610C4×D4C22×D1112yes—
611C4×D4C22×D1111yescharacteristic
612#117—111no—
613#117—112no—
614#117—112no—
615#117—112no—
616#117—222no—
617#117—222no—
618#117—221no—
619#117—222no—
620#117—221no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4C22⋊D1111yescharacteristic
630C2×C4⋊C4C22×D1111yescharacteristic
631C2×C4⋊C4C22×D1112yes—
632C2×C4⋊C4C22×D1114yes—
633C2×C4⋊C4C22×D1114yes—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—222no—
636C2×C22⋊C4C22⋊D1112yes—
637C2×C42—21no—
638C2×C42—222no—
639C2×C42—221no—
640C2×C42C22×D1111yescharacteristic
641#107—112no—
642#107—114no—
643#107—114no—
644#107—114no—
645#107—114no—
646#106—112no—
647#106—114no—
648#106—114no—
649#106—114no—
650#106—114no—
651C4⋊C8—112no—
652C4⋊C8—112no—
653#103—112no—
654#103—112no—
655#103—114no—
656#103—114no—
657#103—112no—
658#103—114no—
659#102—112no—
660#102—114no—
661C22⋊C8—114no—
662C22⋊C8—114no—
663#97—112no—
664C4×C8—112no—
665C2×C11—22no—
666C2×C11—24no—
667C2×C11—42no—
668C2×C11C2×#54711yescharacteristic
669C2×C11C22×#13711yescharacteristic
670C2×C11#358511yescharacteristic
671D11—81no—
672C24C2×C22⋊D1112yes—
673#41—222no—
674#41—222no—
675#41—444no—
676C2×Q8—21no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—82no—
682C2×Q8—111no—
683C2×Q8—221no—
684C2×Q8—221no—
685C2×Q8C23×D1112yes—
686C2×D4—24no—
687C2×D4—111no—
688C2×D4—221no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4C2×C22⋊D1112yes—
692C2×D4C2×C22⋊D1111yescharacteristic
693C2×D4C2×C22⋊D1111yescharacteristic
694C22×C4—24no—
695C22×C4—24no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—84no—
702C22×C4—222no—
703C22×C4—222no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4C2×C22⋊D1111yescharacteristic
708C22×C4C2×C22⋊D1112yes—
709C22×C4C2×C22⋊D1112yes—
710C22×C4C2×C22⋊D1112yes—
711C22×C4C2×C22⋊D1111yescharacteristic
712C22×C4C23×D1112yes—
713C22×C4C23×D1112yes—
714C22×C4C23×D1111yescharacteristic
715Q16—224no—
716SD16—224no—
717M16—114no—
718M16—228no—
719M16—224no—
720M16—222no—
721C2×C8—112no—
722C2×C8—112no—
723C2×C8—114no—
724C2×C8—228no—
725C4⋊C4—21no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—22no—
731C4⋊C4—22no—
732C4⋊C4—22no—
733C4⋊C4—24no—
734C4⋊C4—24no—
735C4⋊C4—111no—
736C4⋊C4—112no—
737C4⋊C4—111no—
738C4⋊C4—112no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—221no—
742C4⋊C4—221no—
743C4⋊C4—221no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4—221no—
749C4⋊C4C2×C22⋊D1111yescharacteristic
750C4⋊C4C2×C22⋊D1111yescharacteristic
751C4⋊C4C2×C22⋊D1112yes—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1114yes—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—221no—
757C22⋊C4—222no—
758C22⋊C4—222no—
759C22⋊C4—222no—
760C22⋊C4—222no—
761C22⋊C4—222no—
762C22⋊C4—221no—
763C22⋊C4—221no—
764C22⋊C4—222no—
765C22⋊C4—222no—
766C22⋊C4C2×C22⋊D1112yes—
767C22⋊C4C2×C22⋊D1112yes—
768C22⋊C4C2×C22⋊D1112yes—
769C22⋊C4C2×C22⋊D1112yes—
770C42—22no—
771C42—22no—
772C42—221no—
773C42—222no—
774C42—222no—
775C42—222no—
776C42—221no—
777C42—221no—
778C42C2×C22⋊D1111yescharacteristic
779C42C2×C22⋊D1111yescharacteristic
780C42C23×D1111yescharacteristic
781C42C23×D1111yescharacteristic
782C11#6125411yescharacteristic, complemented, Sylow
783C23—24no—
784C23—24no—
785C23—42no—
786C23—221no—
787C23C22×C22⋊D1112yes—
788C23C22×C22⋊D1112yes—
789C23C22×C22⋊D1111yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—42no—
793Q8—82no—
794Q8—82no—
795Q8—221no—
796Q8—221no—
797Q8—442no—
798Q8—881no—
799D4—24no—
800D4—22no—
801D4—221no—
802D4—221no—
803D4—444no—
804D4—442no—
805D4—882no—
806D4#6699514yescomplemented
807C2×C4—24no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—24no—
818C2×C4—41no—
819C2×C4—42no—
820C2×C4—44no—
821C2×C4—42no—
822C2×C4—84no—
823C2×C4—84no—
824C2×C4—221no—
825C2×C4—221no—
826C2×C4—222no—
827C2×C4—222no—
828C2×C4—221no—
829C2×C4—444no—
830C2×C4—442no—
831C2×C4—442no—
832C2×C4—881no—
833C2×C4—882no—
834C2×C4#41×D1112yes—
835C2×C4#6704312yes—
836C2×C4C22×C22⋊D1111yescharacteristic
837C2×C4C22×C22⋊D1112yes—
838C2×C4C22×C22⋊D1111yescharacteristic
839C2×C4C22×C22⋊D1111yescharacteristic
840C2×C4C22×C22⋊D1112yes—
841C2×C4C22×C22⋊D1111yescharacteristic
842C2×C4C22×C22⋊D1111yescharacteristic
843C2×C4C24×D1111yescharacteristic
844C8—114no—
845C8—224no—
846C8—222no—
847C22—21no—
848C22—22no—
849C22—22no—
850C22—21no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—48no—
855C22—441no—
856C22—441no—
857C22—441no—
858C22C2×#6699514yes—
859C22#1062335512yes—
860C22C23×C22⋊D1111yescharacteristic
861C4—21no—
862C4—21no—
863C4—22no—
864C4—22no—
865C4—21no—
866C4—42no—
867C4—44no—
868C4—42no—
869C4—441no—
870C4—442no—
871C4—441no—
872C4—441no—
873C4—442no—
874C4C2×#6699512yes—
875C4#1062335512yes—
876C4C2×#41×D1111yescharacteristic
877C4C2×#6704311yescharacteristic
878C2—22no—
879C2—24no—
880C2—42no—
881C2—881no—
882C2C2×#1062335511yescharacteristic
883C2C22×#6699511yescharacteristic
884C2#1308339611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC22×C11C23×D4
prime radical#13082174C2
hypercenterC2×#554D11
hypocenterC11#61254
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13081242C2semidirect
3. #13081231C2semidirect
4. #13081095C2semidirect
5. #13081065C2semidirect
6. #13081004C2semidirect
7. #13080967C2semidirect
8. #13079158C2semidirect
9. #13078560C2semidirect
10. #13078539C2semidirect
11. #13078425C2semidirect
12. #13078421C2semidirect
13. #13078242C2semidirect
14. C4×#66995C2semidirect
15. D4×#4318C2semidirect
16. C2×#10622577C2semidirect
17. C2×C11×#554C2semidirect
53. #10622707C22semidirect
54. #10622704C22semidirect
55. #10622700C22semidirect
56. #10622697C22semidirect
57. #10622693C22semidirect
58. #10622692C22semidirect
59. #10622691C22semidirect
60. #10622665C22semidirect
61. #10622664C22semidirect
62. #10622662C22semidirect
63. #10622661C22semidirect
64. #10622658C22semidirect
65. #10622658C22semidirect
66. #10622657C22semidirect
67. #10622656C22semidirect
68. #10622643C22semidirect
69. C4×#4326C22semidirect
70. #10622639C22semidirect
71. C4×#4325C22semidirect
72. #10622635C22semidirect
73. #10622634C22semidirect
74. #10622633C22semidirect
78. #10622584C22semidirect
79. #10622583C22semidirect
80. #10622581C22semidirect
81. #10622580C22semidirect
89. #10622577C22semidirect
90. #10622577C22semidirect
91. C2×#66872C22semidirect
92. C2×#66871C22semidirect
336. #4318#41semidirect
342. C2×#554D11semidirect
372. D4×C11#137semidirect
782. C11#61254semidirect
806. D4#66995semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130812422
#130812312
#130810952
#130810652
#130810042
#130809672
#130791582
#130785602
#130785392
#130784252
#130784212
#130782422
C4×#669952
D4×#43182
C2×#106225772
C2×C11×#5542
#6125411