Finite Group Databasebeta

← #15620941

Subgroups — #15620941

Order 2816.

2918 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623353C211yesmaximal, characteristic, complemented
2C22×M16×D11C211yesmaximal, characteristic, complemented
3C2×#10623055C211yesmaximal, characteristic, complemented
4C2×#10623359C211yesmaximal, characteristic, complemented
5#13078249C214yesmaximal, complemented
6#13078244C214yesmaximal, complemented
7#13078238C214yesmaximal, complemented
8#13078233C214yesmaximal, complemented
9#13078224C214yesmaximal, complemented
10#13078196C214yesmaximal, complemented
11#13077205C211yesmaximal, characteristic, complemented
12#13077136C211yesmaximal, characteristic, complemented
13C11×#2896C211yesmaximal, characteristic, complemented
14C22×C11×#41C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19#10623359—21no—
20#10623359—21no—
21#10623359—22no—
22#10623359C2214yes—
23#10623359C2212yescomplemented
24#10623359C2212yescomplemented
25C2×#67004C2212yescomplemented
26#10623353—28no—
27C2×#67003C2214yescomplemented
28C2×#67002C2212yescomplemented
29C2×#66999C2212yescomplemented
30C2×#66995C2212yescomplemented
31C2×#66991C2212yescomplemented
32C2×#66990—21no—
33C2×#66988—21no—
34C2×#66985C2212yescomplemented
35C2×C4×C22⋊D11—22no—
36C2×#66979C2211yescharacteristic
37C22×#4318C2211yescharacteristic
38C2×M16×D11—28no—
39C2×M16×D11C2214yescomplemented
40C2×M16×D11C2214yescomplemented
41C22×#4313C2212yescomplemented
42C22×C8×D11C2212yescomplemented
43#10623055—21no—
44#10623055—21no—
45#10623055—22no—
46#10623055C2214yes—
47#10623055C2212yescomplemented
48#10623055C2212yescomplemented
49C2×#66950C2212yescomplemented
50C2×#66948C2212yescomplemented
51C2×#66939—21no—
52C2×#66935—21no—
53C2×C4×D44—22no—
54C11×#419C2212yescomplemented
55C11×#418C2212yescomplemented
56C11×#417C2214yescomplemented
57C11×#416C2214yescomplemented
58#10622746C2214yescomplemented
59#10622744C2212yescomplemented
60#10622733C2212yescomplemented
61#10622726C2214yescomplemented
62#10622611C2214yescomplemented
63#10622608C2214yescomplemented
64#10622577C2214yescomplemented
65#10622429C2218yescomplemented
66#10622426C2218yescomplemented
67#10622425C2218yescomplemented
68#10622420C2218yescomplemented
69#10622395C2218yescomplemented
70#10622393C2218yescomplemented
71#10622391C2218yescomplemented
72#10622388C2218yescomplemented
73C24×D11D411yescharacteristic
74C2×C11×#41—21no—
75C2×C11×#41—21no—
76C2×C11×#41—24no—
77C2×C11×#41—24no—
78C2×C11×#41C2312yes—
79C2×C11×#41C2312yes—
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11—21no—
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C23×C4×C11C2311yescharacteristic
85C22×C22⋊D11—21no—
86C22×C22⋊D11—22no—
87C23×Dic11D411yescharacteristic
88C2×#4339—21no—
89C2×#4339—21no—
90C2×#4339—24no—
91C2×#4339—24no—
92C2×#4339C2312yes—
93C2×#4339C2312yes—
94C22×D44—22no—
95C22×D44C2311yescharacteristic
96C22×C4×D11—24no—
97C22×C4×D11—24no—
98C22×C4×D11—21no—
99C22×C4×D11D412yes—
100C22×C4×D11D412yes—
101C22×C4×D11D411yescharacteristic
102C22×C4×D11D411yescharacteristic
103C22×C4×D11C2311yescharacteristic
104C22×C4×D11C2311yescharacteristic
105C22×C4×D11C2312yes—
106C22×C4×D11C2312yes—
107C22×Dic22C2311yescharacteristic
108C2×C11×M16—24no—
109C2×C11×M16C2312yes—
110C2×C11×M16C2312yes—
111C22×C8×C11C2312yes—
112C11×#117—21no—
113C11×#117—21no—
114C11×#117C2312yes—
115C11×#117C2312yes—
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C22⋊C4—21no—
118C2×C42×C11—21no—
119C2×C22⋊Dic11—21no—
120C2×C22⋊Dic11—22no—
121#67004—28no—
122#67003—216no—
123#67002—28no—
124#66999—22no—
125#66999—22no—
126#66999C2314yes—
127#66999C2314yes—
128C2×#4326C2314yescomplemented
129#66995—28no—
130C2×#4325C2314yescomplemented
131#66991—22no—
132#66991—22no—
133#66991C2314yes—
134#66991C2314yes—
135#66990—24no—
136#66990—22no—
137#66990—22no—
138#66988—24no—
139#66988—22no—
140#66988—22no—
141C2×#4324C2314yescomplemented
142#66985—28no—
143C2×#4323C2314yescomplemented
144C4×C22⋊D11—24no—
145C4×C22⋊D11—24no—
146C4×C22⋊D11—24no—
147C4×C22⋊D11—24no—
148C2×(C2×D11)⋊C4—22no—
149C2×(C2×D11)⋊C4—22no—
150C2×(C2×D11)⋊C4—22no—
151#66979—21no—
152#66979—21no—
153#66979C2312yes—
154#66979C2312yes—
155C2×C4⋊Dic11—22no—
156C2×C4⋊Dic11C2312yes—
157C2×Dic11⋊C4—22no—
158C2×C4×Dic11—21no—
159C2×#4318D418yescomplemented
160C2×#4318C2312yes—
161C2×#4318C2312yes—
162C22×C11⋊C8C2312yes—
163M16×D11—216no—
164M16×D11—216no—
165C2×#4313—28no—
166C2×#4313C2318yes—
167C2×C8×D11—28no—
168C2×C8×D11C2318yes—
169#66950—22no—
170#66950—22no—
171#66950C2314yes—
172#66950C2314yes—
173#66948—22no—
174#66948—22no—
175#66948C2314yes—
176#66948C2314yes—
177#66939—24no—
178#66939—22no—
179#66939—22no—
180#66935—24no—
181#66935—22no—
182#66935—22no—
183C4×D44—24no—
184C4×D44—24no—
185C4×D44—24no—
186C4×D44—24no—
187C11×#103C2318yescomplemented
188C11×#102C2318yescomplemented
189#66885C2318yescomplemented
190#66880C2318yescomplemented
191#66872C2318yescomplemented
192#66871C2318yescomplemented
193#60444—111nomaximal, Sylow
194C24×C11—21no—
195C24×C11C2×D411yescharacteristic
196C23×D11—24no—
197C23×D11—21no—
198C23×D11—44no—
199C23×D11C2×D411yescharacteristic
200C23×D11C2×D412yes—
201C23×D11C2×D412yes—
202C23×D11C2×D411yescharacteristic
203C11×#41—24no—
204C11×#41—24no—
205C11×#41—24no—
206C11×#41—24no—
207C11×#41—44no—
208C11×#41—44no—
209C2×Q8×C11—21no—
210C2×Q8×C11—22no—
211C2×Q8×C11—22no—
212C2×Q8×C11C2412yes—
213C2×D4×C11—22no—
214C2×D4×C11—22no—
215C2×D4×C11—22no—
216C2×D4×C11—21no—
217C2×D4×C11—22no—
218C2×D4×C11—44no—
219C2×D4×C11C2412yes—
220C22×C4×C11—21no—
221C22×C4×C11—22no—
222C22×C4×C11—22no—
223C22×C4×C11—22no—
224C22×C4×C11—44no—
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D414yes—
229C22×C4×C11#4114yes—
230C22×C4×C11C2411yescharacteristic
231C22×C4×C11C2411yescharacteristic
232C22×C4×C11C2411yescharacteristic
233C2×C22⋊D11—22no—
234C2×C22⋊D11—22no—
235C2×C22⋊D11—24no—
236C2×C22⋊D11—24no—
237C2×C22⋊D11—48no—
238C2×C22⋊D11—44no—
239C22×Dic11—24no—
240C22×Dic11—22no—
241C22×Dic11—21no—
242C22×Dic11C2×D412yes—
243C22×Dic11C2×D411yescharacteristic
244C22×Dic11C2×D411yescharacteristic
245C22×Dic11C2×D412yes—
246#4339—24no—
247#4339—24no—
248#4339—24no—
249#4339—24no—
250#4339—44no—
251#4339—44no—
252C2×D44—24no—
253C2×D44—24no—
254C2×D44—21no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—48no—
258C2×D44C2412yes—
259C2×C4×D11—28no—
260C2×C4×D11—28no—
261C2×C4×D11—24no—
262C2×C4×D11—24no—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—24no—
266C2×C4×D11—24no—
267C2×C4×D11—22no—
268C2×C4×D11—22no—
269C2×C4×D11—24no—
270C2×C4×D11—24no—
271C2×C4×D11—22no—
272C2×C4×D11—22no—
273C2×C4×D11—44no—
274C2×C4×D11C2×D412yes—
275C2×C4×D11C2×D412yes—
276C2×C4×D11C2×D412yes—
277C2×C4×D11C2×D412yes—
278C2×C4×D11C2×D412yes—
279C2×C4×D11C2×D412yes—
280C2×C4×D11C2412yes—
281C2×C4×D11C2412yes—
282C2×Dic22—22no—
283C2×Dic22—21no—
284C2×Dic22—22no—
285C2×Dic22C2412yes—
286C11×M16—24no—
287C11×M16—24no—
288C2×C8×C11—24no—
289C2×C8×C11C2414yes—
290C11×C4⋊C4—22no—
291C11×C4⋊C4C2414yes—
292C11×C22⋊C4—22no—
293C11×C22⋊C4—22no—
294C42×C11—22no—
295C42×C11—22no—
296C22⋊Dic11—24no—
297C22⋊Dic11—24no—
298C22⋊Dic11—22no—
299C22⋊Dic11—22no—
300#4326—28no—
301#4325—28no—
302#4324—28no—
303#4323—28no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4—24no—
309(C2×D11)⋊C4—24no—
310C4⋊Dic11—24no—
311C4⋊Dic11—24no—
312C4⋊Dic11—22no—
313C4⋊Dic11C2414yes—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316C4×Dic11—22no—
317C4×Dic11—22no—
318#4318C2×D418yescomplemented
319#4318C2×D418yescomplemented
320C2×C11⋊C8C2×D418yescomplemented
321C2×C11⋊C8C2414yes—
322#4313—216no—
323C8×D11—216no—
324C2×#575—111no—
325C23×M16—111no—
326C2×#525—111no—
327C2×#525—111no—
328#3056—114no—
329#3056—114no—
330#3055—114no—
331#3055—114no—
332#3054—114no—
333#3050—114no—
334#2911—111no—
335#2896—111no—
336#2896D1111yescharacteristic, complemented
337C23×C11—22no—
338C23×C11—42no—
339C23×C11—44no—
340C23×C11—42no—
341C23×C11#12114yes—
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×D411yescharacteristic
345C22×D11—22no—
346C22×D11—24no—
347C22×D11—24no—
348C22×D11—24no—
349C22×D11—22no—
350C22×D11—24no—
351C22×D11—24no—
352C22×D11—22no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—416no—
357C22×D11—44no—
358C22×D11—42no—
359C22×D11C22×D412yes—
360C22×D11C22×D412yes—
361Q8×C11—22no—
362Q8×C11—22no—
363Q8×C11—42no—
364D4×C11—22no—
365D4×C11—22no—
366D4×C11—44no—
367D4×C11—44no—
368D4×C11—42no—
369C2×C4×C11—22no—
370C2×C4×C11—24no—
371C2×C4×C11—44no—
372C2×C4×C11—42no—
373C2×C4×C11—44no—
374C2×C4×C11—44no—
375C2×C4×C11#12114yes—
376C2×C4×C11#12114yes—
377C2×C4×C11#12114yes—
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D412yes—
381C2×C4×C11C22×D412yes—
382C2×C4×C11C22×D412yes—
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4112yes—
385C2×C4×C11C2×#4112yes—
386C2×C4×C11C2×#4112yes—
387C2×C4×C11C2511yescharacteristic
388C22⋊D11—48no—
389C22⋊D11—44no—
390C22⋊D11—44no—
391C22⋊D11—48no—
392C2×Dic11—24no—
393C2×Dic11—24no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—24no—
397C2×Dic11—22no—
398C2×Dic11—44no—
399C2×Dic11—42no—
400C2×Dic11C22×D412yes—
401C2×Dic11C22×D412yes—
402D44—22no—
403D44—22no—
404D44—48no—
405D44—48no—
406D44—42no—
407C4×D11—24no—
408C4×D11—24no—
409C4×D11—24no—
410C4×D11—24no—
411C4×D11—24no—
412C4×D11—24no—
413C4×D11—22no—
414C4×D11—22no—
415C4×D11—22no—
416C4×D11—22no—
417C4×D11—44no—
418C4×D11—44no—
419Dic22—22no—
420Dic22—22no—
421Dic22—42no—
422C8×C11—24no—
423C11⋊C8C22×D418yes—
424C22×#41—111no—
425C22×#41C2×D1111yescharacteristic
426C24×C4—111no—
427#575—228no—
428C2×#137—112no—
429C2×#137—112no—
430C2×AGL(1,ℤ/8)—112no—
431C2×AGL(1,ℤ/8)—112no—
432C2×#135—114no—
433C22×M16—111no—
434C22×M16—114no—
435C22×M16—114no—
436C22×M16—112no—
437C22×M16—228no—
438C22×M16C2×D1111yescharacteristic
439C23×C8—112no—
440#525—114no—
441#525—112no—
442#525—112no—
443#525—114no—
444#525—112no—
445#525—112no—
446#525—222no—
447#525—221no—
448#525—221no—
449#525—222no—
450#525—221no—
451#525—221no—
452C2×#123—221no—
453C2×#123—221no—
454C2×C22⋊Q8—112no—
455C2×C22⋊Q8—112no—
456C2×#121—112no—
457C2×#121—112no—
458C2×#120—221no—
459C2×#120—221no—
460C2×C4×D4—222no—
461C2×C4×D4—222no—
462C2×#117—111no—
463C2×#117C2×D1111yescharacteristic
464#470—118no—
465#469—118no—
466#468—118no—
467#468—118no—
468#467—118no—
469#466—118no—
470#465—118no—
471#465—118no—
472#428—114no—
473#428—114no—
474#427—114no—
475#419—112no—
476#419C2×D1112yescomplemented
477#418—112no—
478#418C2×D1112yescomplemented
479#417—114no—
480#417C2×D1114yescomplemented
481#416—114no—
482#416C2×D1114yescomplemented
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—44no—
487C22×C11—42no—
488C22×C11—44no—
489C22×C11—84no—
490C22×C11C2×#12112yes—
491C22×C11C2×#12112yes—
492C22×C11C2×#12112yes—
493C22×C11C23×D411yescharacteristic
494C2×D11—28no—
495C2×D11—22no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—22no—
500C2×D11—48no—
501C2×D11—48no—
502C2×D11—44no—
503C2×D11—42no—
504C2×D11—44no—
505C2×D11—84no—
506C2×D11#57514yescomplemented
507C4×C11—42no—
508C4×C11—44no—
509C4×C11C2×#12112yes—
510C4×C11C2×#12112yes—
511C4×C11C2×#12112yes—
512C4×C11C23×D411yescharacteristic
513C4×C11C22×#4111yescharacteristic
514Dic11—22no—
515Dic11—22no—
516Dic11—42no—
517Dic11—44no—
518C25—111no—
519C2×#41—21no—
520C2×#41—21no—
521C2×#41—24no—
522C2×#41—24no—
523C2×#41—112no—
524C2×#41—112no—
525C2×#41—221no—
526C2×#41—221no—
527C2×#41—224no—
528C2×#41—224no—
529C2×#41C22×D1112yes—
530C2×#41C22×D1112yes—
531C22×Q8—111no—
532C22×Q8C22×D1111yescharacteristic
533C22×D4—21no—
534C22×D4—111no—
535C22×D4—222no—
536C22×D4—222no—
537C22×D4—221no—
538C22×D4C22×D1111yescharacteristic
539C23×C4—21no—
540C23×C4—111no—
541C23×C4—112no—
542C23×C4—112no—
543C23×C4—111no—
544C23×C4—111no—
545C23×C4—112no—
546C23×C4—112no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—224no—
550C23×C4—224no—
551C23×C4—221no—
552C23×C4C22×D1111yescharacteristic
553#137—228no—
554#137—228no—
555AGL(1,ℤ/8)—228no—
556AGL(1,ℤ/8)—228no—
557#135—2216no—
558C2×Q16—114no—
559C2×SD16—114no—
560C2×SD16—114no—
561C2×D8—114no—
562C2×M16—24no—
563C2×M16—118no—
564C2×M16—112no—
565C2×M16—112no—
566C2×M16—118no—
567C2×M16—228no—
568C2×M16—2216no—
569C2×M16—2216no—
570C2×M16C22×D1112yes—
571C2×M16C22×D1112yes—
572C22×C8—112no—
573C22×C8—118no—
574C22×C8—228no—
575C22×C8C22×D1112yes—
576#123—224no—
577#123—222no—
578#123—222no—
579#123—224no—
580#123—222no—
581#123—222no—
582C22⋊Q8—114no—
583C22⋊Q8—114no—
584C22⋊Q8—114no—
585C22⋊Q8—114no—
586C22⋊Q8—222no—
587C22⋊Q8—222no—
588C22⋊Q8—222no—
589C22⋊Q8—222no—
590#121—114no—
591#121—114no—
592#121—114no—
593#121—114no—
594#121—222no—
595#121—222no—
596#121—222no—
597#121—222no—
598#120—222no—
599#120—224no—
600#120—222no—
601#120—222no—
602#120—224no—
603#120—222no—
604C4×D4—224no—
605C4×D4—224no—
606C4×D4—224no—
607C4×D4—224no—
608C4×D4—224no—
609C4×D4—224no—
610C4×D4—224no—
611C4×D4—224no—
612#117—21no—
613#117—21no—
614#117—112no—
615#117—112no—
616#117—221no—
617#117—221no—
618#117C22×D1112yes—
619#117C22×D1112yes—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—222no—
622C2×C4⋊C4—222no—
623C2×C4⋊C4C22×D1112yes—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—221no—
630C2×C42—21no—
631C2×C42—221no—
632#107—118no—
633#106—118no—
634#103—118no—
635#103C22×D1118yescomplemented
636#102—118no—
637#102C22×D1118yescomplemented
638C2×C11—22no—
639C2×C11—22no—
640C2×C11—22no—
641C2×C11—82no—
642C2×C11C22×#12111yescharacteristic
643C2×C11C2×#57512yes—
644D11—24no—
645D11—42no—
646D11—82no—
647C24—21no—
648C24—111no—
649C24—112no—
650C24—112no—
651C24—111no—
652C24—224no—
653C24—221no—
654C24—444no—
655C24D4×D1111yescharacteristic
656#41—24no—
657#41—24no—
658#41—24no—
659#41—24no—
660#41—44no—
661#41—44no—
662#41—224no—
663#41—224no—
664#41—224no—
665#41—224no—
666#41—444no—
667#41—444no—
668C2×Q8—21no—
669C2×Q8—22no—
670C2×Q8—22no—
671C2×Q8—112no—
672C2×Q8—221no—
673C2×Q8—222no—
674C2×Q8—222no—
675C2×Q8C23×D1112yes—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—22no—
679C2×D4—22no—
680C2×D4—21no—
681C2×D4—44no—
682C2×D4—112no—
683C2×D4—224no—
684C2×D4—224no—
685C2×D4—224no—
686C2×D4—224no—
687C2×D4—222no—
688C2×D4—222no—
689C2×D4—222no—
690C2×D4—222no—
691C2×D4—221no—
692C2×D4—448no—
693C2×D4—448no—
694C2×D4—444no—
695C2×D4C23×D1112yes—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—44no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—111no—
704C22×C4—111no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—224no—
714C22×C4—228no—
715C22×C4—228no—
716C22×C4—224no—
717C22×C4—224no—
718C22×C4—224no—
719C22×C4—224no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—224no—
724C22×C4—224no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—221no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—444no—
731C22×C4#433914yes—
732C22×C4D4×D1111yescharacteristic
733C22×C4D4×D1111yescharacteristic
734C22×C4D4×D1111yescharacteristic
735C22×C4D4×D1114yes—
736C22×C4C23×D1111yescharacteristic
737C22×C4C23×D1111yescharacteristic
738C22×C4C23×D1111yescharacteristic
739Q16—228no—
740SD16—228no—
741SD16—228no—
742D8—228no—
743M16—24no—
744M16—24no—
745M16—118no—
746M16—118no—
747M16—2216no—
748C2×C8—24no—
749C2×C8—118no—
750C2×C8—114no—
751C2×C8—2216no—
752C2×C8C23×D1114yes—
753C4⋊C4—22no—
754C4⋊C4—114no—
755C4⋊C4—224no—
756C4⋊C4—224no—
757C4⋊C4—224no—
758C4⋊C4—224no—
759C4⋊C4—222no—
760C4⋊C4C23×D1114yes—
761C22⋊C4—22no—
762C22⋊C4—22no—
763C22⋊C4—224no—
764C22⋊C4—224no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4—224no—
768C22⋊C4—224no—
769C22⋊C4—224no—
770C22⋊C4—224no—
771C22⋊C4—222no—
772C22⋊C4—222no—
773C42—22no—
774C42—22no—
775C42—222no—
776C42—222no—
777C11#6044411yescharacteristic, complemented, Sylow
778C23—22no—
779C23—42no—
780C23—44no—
781C23—42no—
782C23—112no—
783C23—112no—
784C23—224no—
785C23—224no—
786C23—224no—
787C23—222no—
788C23—224no—
789C23—224no—
790C23—222no—
791C23—222no—
792C23—442no—
793C23—442no—
794C23—442no—
795C23—444no—
796C23—4416no—
797C23—442no—
798C23#6693714yes—
799C23C2×D4×D1111yescharacteristic
800C23C2×D4×D1111yescharacteristic
801C23C2×D4×D1111yescharacteristic
802Q8—22no—
803Q8—22no—
804Q8—42no—
805Q8—222no—
806Q8—222no—
807Q8—442no—
808D4—22no—
809D4—22no—
810D4—44no—
811D4—44no—
812D4—42no—
813D4—222no—
814D4—222no—
815D4—448no—
816D4—448no—
817D4—448no—
818D4—448no—
819D4—444no—
820D4—444no—
821D4—442no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—44no—
825C2×C4—42no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—112no—
829C2×C4—112no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—222no—
833C2×C4—222no—
834C2×C4—224no—
835C2×C4—224no—
836C2×C4—224no—
837C2×C4—224no—
838C2×C4—224no—
839C2×C4—224no—
840C2×C4—222no—
841C2×C4—222no—
842C2×C4—222no—
843C2×C4—222no—
844C2×C4—224no—
845C2×C4—222no—
846C2×C4—444no—
847C2×C4—442no—
848C2×C4—444no—
849C2×C4—444no—
850C2×C4#6693714yes—
851C2×C4#6693714yes—
852C2×C4#6693714yes—
853C2×C4C2×#433912yes—
854C2×C4C2×#433912yes—
855C2×C4C2×#433912yes—
856C2×C4C2×D4×D1111yescharacteristic
857C2×C4C2×D4×D1111yescharacteristic
858C2×C4C2×D4×D1112yes—
859C2×C4C2×D4×D1112yes—
860C2×C4C2×D4×D1112yes—
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4C24×D1111yescharacteristic
863C8—24no—
864C8—118no—
865C22—22no—
866C22—22no—
867C22—22no—
868C22—44no—
869C22—44no—
870C22—42no—
871C22—84no—
872C22—114no—
873C22—228no—
874C22—222no—
875C22—222no—
876C22—222no—
877C22—222no—
878C22—222no—
879C22—448no—
880C22—448no—
881C22—444no—
882C22—444no—
883C22—442no—
884C22—884no—
885C22C2×#6693712yes—
886C22C2×#6693712yes—
887C22C2×#6693712yes—
888C22C22×D4×D1111yescharacteristic
889C4—44no—
890C4—42no—
891C4—222no—
892C4—222no—
893C4—444no—
894C4—442no—
895C4C2×#6693712yes—
896C4C2×#6693712yes—
897C4C2×#6693712yes—
898C4C22×#433911yescharacteristic
899C4C22×D4×D1111yescharacteristic
900C2—22no—
901C2—22no—
902C2—22no—
903C2—82no—
904C2—224no—
905C2—442no—
906C2—882no—
907C2C22×#6693711yescharacteristic
908C2D11×#57512yes—
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#2896C2
socleC22×C11C23×D4
hypercenter#2896D11
hypocenterC11#60444
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. C2×#10623353C2semidirect
2. C22×M16×D11C2semidirect
3. C2×#10623055C2semidirect
4. C2×#10623359C2semidirect
5. #13078249C2semidirect
6. #13078244C2semidirect
7. #13078238C2semidirect
8. #13078233C2semidirect
9. #13078224C2semidirect
10. #13078196C2semidirect
11. #13077205C2semidirect
12. #13077136C2semidirect
13. C11×#2896C2semidirect
23. #10623359C22semidirect
24. #10623359C22semidirect
25. C2×#67004C22semidirect
27. C2×#67003C22semidirect
28. C2×#67002C22semidirect
29. C2×#66999C22semidirect
30. C2×#66995C22semidirect
31. C2×#66991C22semidirect
34. C2×#66985C22semidirect
39. C2×M16×D11C22semidirect
40. C2×M16×D11C22semidirect
41. C22×#4313C22semidirect
42. C22×C8×D11C22semidirect
47. #10623055C22semidirect
48. #10623055C22semidirect
49. C2×#66950C22semidirect
50. C2×#66948C22semidirect
54. C11×#419C22semidirect
55. C11×#418C22semidirect
56. C11×#417C22semidirect
57. C11×#416C22semidirect
58. #10622746C22semidirect
59. #10622744C22semidirect
60. #10622733C22semidirect
61. #10622726C22semidirect
62. #10622611C22semidirect
63. #10622608C22semidirect
64. #10622577C22semidirect
65. #10622429C22semidirect
66. #10622426C22semidirect
67. #10622425C22semidirect
68. #10622420C22semidirect
69. #10622395C22semidirect
70. #10622393C22semidirect
71. #10622391C22semidirect
72. #10622388C22semidirect
128. C2×#4326C23semidirect
130. C2×#4325C23semidirect
141. C2×#4324C23semidirect
143. C2×#4323C23semidirect
159. C2×#4318D4semidirect
187. C11×#103C23semidirect
188. C11×#102C23semidirect
189. #66885C23semidirect
190. #66880C23semidirect
191. #66872C23semidirect
192. #66871C23semidirect
318. #4318C2×D4semidirect
319. #4318C2×D4semidirect
320. C2×C11⋊C8C2×D4semidirect
336. #2896D11semidirect
476. #419C2×D11semidirect
478. #418C2×D11semidirect
480. #417C2×D11semidirect
482. #416C2×D11semidirect
506. C2×D11#575semidirect
635. #103C22×D11semidirect
637. #102C22×D11semidirect
777. C11#60444semidirect

Maximal subgroups

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

subgroupindex
C2×#106233532
C22×M16×D112
C2×#106230552
C2×#106233592
#130782492
#130782442
#130782382
#130782332
#130782242
#130781962
#130772052
#130771362
C11×#28962
#6044411