Finite Group Databasebeta

← #15638597

Subgroups — #15638597

Order 2816.

2514 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082378C211yesmaximal, characteristic, complemented
2C2×#10623085C211yesmaximal, characteristic, complemented
3#13080582C214yesmaximal, complemented
4#13080574C214yesmaximal, complemented
5#13080098C214yesmaximal, complemented
6#13080091C214yesmaximal, complemented
7#13079605C211yesmaximal, characteristic, complemented
8#13079599C211yesmaximal, characteristic, complemented
9#13079415C212yesmaximal, complemented
10#13079375C212yesmaximal, complemented
11#13078707C211yesmaximal, characteristic, complemented
12#13077863C212yesmaximal, complemented
13D11×#447C212yesmaximal, complemented
14#13077644C211yesmaximal, characteristic, complemented
15C11×#3109C211yesmaximal, characteristic, complemented
16C2×#67042—21no—
17C22×#4341C2211yescharacteristic, complemented
18C22×D4×D11C2211yescharacteristic, complemented
19C11×#532C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic, complemented
21#10623364—21no—
22C2×#66983—21no—
23C22×(C2×D11)⋊C4—21no—
24C2×#66964C2214yescomplemented
25C2×D8×D11C2214yescomplemented
26#10623257C2212yescomplemented
27#10623248C2212yescomplemented
28#10623207—22no—
29#10623136—21no—
30#10623136—21no—
31D11×#121C2212yes—
32D11×#121C2212yescomplemented
33#10623085—22no—
34#10623085—22no—
35#10623085C2214yescomplemented
36#10623085C2214yescomplemented
37#10623082C2212yescomplemented
38#10623081—22no—
39D4×D44C2212yescomplemented
40C2×#66950C2211yescharacteristic, complemented
41C2×#66948C2211yescharacteristic, complemented
42C2×#66939—21no—
43C2×#66935—21no—
44#10623008C2211yescharacteristic, complemented
45C2×#66928C2211yescharacteristic, complemented
46C2×C4×D44C2211yescharacteristic
47C11×#481C2212yescomplemented
48C11×#476C2212yescomplemented
49C11×#459C2212yescomplemented
50C11×#447C2212yescomplemented
51C11×#442C2214yescomplemented
52C11×#432C2211yescharacteristic, complemented
53#10622830C2212yescomplemented
54#10622771C2214yescomplemented
55#10622769C2214yescomplemented
56#10622702C2212yescomplemented
57#10622687C2212yescomplemented
58#10622653C2212yescomplemented
59#10622649C2212yescomplemented
60#10622629C2214yescomplemented
61#10622628C2212yescomplemented
62#10622627C2214yescomplemented
63#10622621C2212yescomplemented
64#10622581C2212yescomplemented
65#10622539C2211yescharacteristic, complemented
66#10622478C2214yescomplemented
67#10622477C2214yescomplemented
68#10622476C2214yescomplemented
69#10622475C2214yescomplemented
70#10622457C2214yescomplemented
71#10622449C2214yescomplemented
72#10622395C2214yescomplemented
73#10622394C2214yescomplemented
74#10622391C2214yescomplemented
75#10622389C2214yescomplemented
76#10622386C2214yescomplemented
77#10622386C2214yescomplemented
78#10622384C2214yescomplemented
79D11×#102C2214yescomplemented
80#10622351C2212yescomplemented
81#10622345C2212yescomplemented
82#10622339C2212yescomplemented
83D11×C22⋊C8C2212yescomplemented
84#10622327C2212yescomplemented
85#10622325C2212yescomplemented
86#10622319C2214yescomplemented
87C24×D11—21no—
88C2×C11×#41—21no—
89C22×D4×C11C2311yescharacteristic
90C23×C4×C11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C23×Dic11—21no—
94#67042—48no—
95C2×#4343—22no—
96C2×#4341—22no—
97C2×#4341—44no—
98C2×#4341C2314yes—
99C2×D4×D11—22no—
100C2×D4×D11—22no—
101C2×D4×D11—22no—
102C2×D4×D11—22no—
103C2×D4×D11—44no—
104C2×D4×D11C2314yes—
105C2×D4×D11C2312yes—
106C2×D4×D11C2312yescomplemented
107C2×#4339—21no—
108C2×#4339—22no—
109C22×D44—21no—
110C22×D44—22no—
111C22×D44D411yescharacteristic
112C22×D44C2311yescharacteristic
113C22×C4×D11C2311yescharacteristic
114C22×C4×D11C2311yescharacteristic
115C22×Dic22C2311yescharacteristic
116C2×C11×D8C2314yes—
117C11×C4⋊Q8C2311yescharacteristic, complemented
118C11×#127C2311yescharacteristic, complemented
119C11×#124—21no—
120C11×#121—21no—
121C11×#121C2312yes—
122C4×D4×C11—21no—
123C4×D4×C11—21no—
124C4×D4×C11—21no—
125C4×D4×C11C2312yes—
126C4×D4×C11C2312yes—
127C4×D4×C11C2312yescomplemented
128C2×C11×C4⋊C4C2311yescharacteristic
129C2×C11×C22⋊C4—21no—
130C2×C42×C11C2311yescharacteristic
131#66999—22no—
132#66992—22no—
133#66992—22no—
134#66991—22no—
135#66991C2312yes—
136#66991C2312yescomplemented
137#66990—22no—
138#66990—22no—
139C2×#4324C2314yescomplemented
140C2×#4323C2314yes—
141C2×#4323C2314yes—
142#66983—21no—
143#66983—24no—
144#66983—24no—
145#66983—22no—
146#66983C2312yes—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4—21no—
150C2×(C2×D11)⋊C4—21no—
151C2×(C2×D11)⋊C4—24no—
152C2×(C2×D11)⋊C4—24no—
153C2×(C2×D11)⋊C4D411yescharacteristic
154C2×(C2×D11)⋊C4D411yescharacteristic
155C2×C4⋊Dic11—21no—
156C2×C4⋊Dic11D411yescharacteristic
157#66977—22no—
158#66964—48no—
159D8×D11—48no—
160C2×D88C2314yes—
161C2×#4314C2314yescomplemented
162C2×#4313C2314yescomplemented
163C2×C8×D11C2314yes—
164#66950—22no—
165#66950C2314yes—
166#66948—22no—
167#66948C2314yes—
168#66948C2312yes—
169#66948C2312yescomplemented
170#66947—22no—
171#66947—22no—
172C4⋊C4×D11C2312yes—
173C4⋊C4×D11C2312yescomplemented
174#66939—24no—
175#66939—24no—
176#66937—22no—
177#66937—22no—
178#66936—22no—
179#66936—22no—
180#66935—24no—
181#66935—24no—
182#66935—22no—
183#66935—22no—
184C22⋊C4×D11—22no—
185C22⋊C4×D11—22no—
186#66928—21no—
187#66928—21no—
188#66928—21no—
189#66928C2312yes—
190#66928C2312yes—
191#66927C2311yescharacteristic, complemented
192C4×D44—21no—
193C4×D44D412yes—
194C4×D44D412yes—
195C4×D44C2312yes—
196C4×D44C2312yes—
197C4×D44C2312yescomplemented
198#66922C2311yescharacteristic, complemented
199C11×#106C2314yescomplemented
200C11×C4⋊C8C2312yescomplemented
201C11×#102C2314yes—
202C11×#102C2314yescomplemented
203C11×C22⋊C8C2312yes—
204C11×#97C2312yescomplemented
205#66896C2314yes—
206C22⋊(C11⋊C8)C2312yes—
207#66885C2314yes—
208(C2×D11)⋊C8C2314yes—
209(C2×D11)⋊C8C2314yescomplemented
210#66880C2314yescomplemented
211#66874C2314yescomplemented
212#66873C2314yes—
213#66873C2314yescomplemented
214#66872C2314yescomplemented
215C4⋊(C11⋊C8)C2312yescomplemented
216#66867C2312yescomplemented
217#61569—111nomaximal, Sylow
218C24×C11—21no—
219C23×D11—21no—
220C23×D11—24no—
221C23×D11—22no—
222C23×D11—22no—
223C23×D11—44no—
224C23×D11—44no—
225C23×D11—82no—
226C23×D11C2×D411yescharacteristic
227C23×D11C2×D411yescharacteristic
228C11×#41—44no—
229C2×Q8×C11—21no—
230C2×D4×C11—24no—
231C2×D4×C11—22no—
232C2×D4×C11—21no—
233C2×D4×C11—21no—
234C2×D4×C11—21no—
235C2×D4×C11C2412yes—
236C2×D4×C11C2412yes—
237C22×C4×C11—21no—
238C22×C4×C11—22no—
239C22×C4×C11—22no—
240C22×C4×C11—22no—
241C22×C4×C11—82no—
242C22×C4×C11C2×D411yescharacteristic
243C22×C4×C11C2×D411yescharacteristic
244C22×C4×C11C2411yescharacteristic
245C2×C22⋊D11—24no—
246C2×C22⋊D11—22no—
247C2×C22⋊D11—22no—
248C2×C22⋊D11—22no—
249C2×C22⋊D11—24no—
250C2×C22⋊D11—22no—
251C2×C22⋊D11—22no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C22×Dic11—24no—
255C22×Dic11—21no—
256C22×Dic11—44no—
257C22×Dic11C2×D411yescharacteristic
258C22×Dic11C2×D411yescharacteristic
259#4343—48no—
260#4341—28no—
261#4341—44no—
262#4341—48no—
263D4×D11—28no—
264D4×D11—44no—
265D4×D11—48no—
266D4×D11—44no—
267D4×D11—44no—
268D4×D11—48no—
269D4×D11—48no—
270D4×D11—48no—
271#4339—44no—
272#4339—48no—
273C2×D44—24no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—24no—
277C2×D44—21no—
278C2×D44—21no—
279C2×D44—21no—
280C2×D44—42no—
281C2×D44—48no—
282C2×D44—82no—
283C2×D44C2×D412yes—
284C2×D44C2×D412yes—
285C2×D44C2412yes—
286C2×D44C2412yes—
287C2×C4×D11—22no—
288C2×C4×D11—22no—
289C2×C4×D11—22no—
290C2×C4×D11—42no—
291C2×C4×D11—42no—
292C2×C4×D11C2×D412yes—
293C2×C4×D11C2×D412yes—
294C2×C4×D11C2412yes—
295C2×C4×D11C2412yes—
296C2×Dic22—21no—
297C2×Dic22—21no—
298C2×Dic22—42no—
299C2×Dic22C2412yes—
300C11×D8—28no—
301C2×C8×C11C2414yes—
302C11×C4⋊C4—21no—
303C11×C4⋊C4—21no—
304C11×C4⋊C4C2412yes—
305C11×C4⋊C4C2412yes—
306C11×C22⋊C4—22no—
307C11×C22⋊C4—22no—
308C11×C22⋊C4—22no—
309C11×C22⋊C4—22no—
310C42×C11C2×D411yescharacteristic
311C42×C11C2×D411yescharacteristic
312C42×C11C2411yescharacteristic
313C42×C11C2411yescharacteristic
314C22⋊Dic11—22no—
315C22⋊Dic11—22no—
316#4324—44no—
317#4323—28no—
318#4323—44no—
319(C2×D11)⋊C4—22no—
320(C2×D11)⋊C4—22no—
321(C2×D11)⋊C4—24no—
322(C2×D11)⋊C4—24no—
323(C2×D11)⋊C4—22no—
324(C2×D11)⋊C4—22no—
325(C2×D11)⋊C4—22no—
326(C2×D11)⋊C4—22no—
327(C2×D11)⋊C4—22no—
328(C2×D11)⋊C4—22no—
329(C2×D11)⋊C4C2×D412yes—
330(C2×D11)⋊C4C2×D412yes—
331(C2×D11)⋊C4C2×D412yes—
332(C2×D11)⋊C4C2×D412yes—
333C4⋊Dic11—24no—
334C4⋊Dic11—21no—
335C4⋊Dic11C2×D412yes—
336C4⋊Dic11C2×D412yes—
337C4⋊Dic11C2412yes—
338Dic11⋊C4—22no—
339Dic11⋊C4—22no—
340C2×C11⋊C8C2414yes—
341D88—44no—
342#4314—44no—
343#4313—44no—
344C8×D11—44no—
345#3496—111no—
346C2×#546—111no—
347#3306—114no—
348#3306—114no—
349#3264—114no—
350#3264—114no—
351#3213—111no—
352#3213—111no—
353#3192—112no—
354#3187—112no—
355#3109—111no—
356#3109D1111yescharacteristic, complemented
357#3006—112no—
358C2×#447—112no—
359#2973—111no—
360C23×C11—24no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—42no—
364C23×C11—42no—
365C23×C11C22×D411yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—41no—
370C22×D11—41no—
371C22×D11—41no—
372C22×D11—41no—
373C22×D11—48no—
374C22×D11—44no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—42no—
378C22×D11—48no—
379C22×D11—44no—
380C22×D11—84no—
381C22×D11—82no—
382C22×D11—82no—
383C22×D11—82no—
384C22×D11—82no—
385C22×D11—816no—
386C22×D11AGL(1,ℤ/8)14yescomplemented
387C22×D11C22×D412yes—
388C22×D11C22×D412yes—
389Q8×C11—42no—
390D4×C11—24no—
391D4×C11—22no—
392D4×C11—24no—
393D4×C11—42no—
394D4×C11—44no—
395D4×C11—81no—
396D4×C11H(5,𝔽2)14yescomplemented
397C2×C4×C11—22no—
398C2×C4×C11—22no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—41no—
402C2×C4×C11—44no—
403C2×C4×C11—42no—
404C2×C4×C11—82no—
405C2×C4×C11—82no—
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D411yescharacteristic
408C2×C4×C11C22×D411yescharacteristic
409C2×C4×C11C22×D411yescharacteristic
410C2×C4×C11C22×D411yescharacteristic
411C2×C4×C11C2511yescharacteristic
412C22⋊D11—48no—
413C22⋊D11—48no—
414C22⋊D11—44no—
415C22⋊D11—44no—
416C22⋊D11—44no—
417C22⋊D11—82no—
418C22⋊D11—82no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—48no—
424C2×Dic11—42no—
425C2×Dic11C22×D412yes—
426C2×Dic11C22×D412yes—
427D44—24no—
428D44—24no—
429D44—24no—
430D44—24no—
431D44—42no—
432D44—42no—
433D44—44no—
434D44—44no—
435D44—81no—
436D44—84no—
437C4×D11—24no—
438C4×D11—24no—
439C4×D11—42no—
440C4×D11—42no—
441C4×D11—44no—
442C4×D11—44no—
443C4×D11—44no—
444Dic22—24no—
445Dic22—42no—
446Dic22—42no—
447C8×C11—24no—
448C11⋊C8—24no—
449C2×H(5,𝔽2)—221no—
450C22×#41—111no—
451C23×D4—111no—
452C2×AGL(1,ℤ/8)—114no—
453C22×D8—114no—
454#547—112no—
455#547—112no—
456#546—114no—
457#546—114no—
458#546—222no—
459#546—222no—
460#546—222no—
461#546—222no—
462D42—112no—
463D42—112no—
464#537—221no—
465#534—221no—
466#534—221no—
467#532—111no—
468#532C2×D1111yescharacteristic, complemented
469C2×#124—111no—
470C2×#123—221no—
471C2×C22⋊Q8—111no—
472C2×#121—112no—
473C2×#121—112no—
474C2×#121—111no—
475C2×#121—221no—
476C2×#120—221no—
477C2×C4×D4—111no—
478C2×C4×D4C2×D1111yescharacteristic, complemented
479C22×C22⋊C4—221no—
480#496—112no—
481#496—112no—
482#489—112no—
483#489—112no—
484#483—114no—
485#481—112no—
486#481—114no—
487#481C2×D1112yescomplemented
488#476—112no—
489#476C2×D1112yescomplemented
490#469—114no—
491#469—114no—
492#465—114no—
493#465—114no—
494#463—114no—
495#463—114no—
496#459—112no—
497#459C2×D1112yescomplemented
498#450—114no—
499#449—114no—
500#449—114no—
501#448—112no—
502#448—112no—
503#447—112no—
504#447—114no—
505#447—112no—
506#447—114no—
507#447—114no—
508#447—112no—
509#447C2×D1112yescomplemented
510#442—114no—
511#442C2×D1114yescomplemented
512#435—114no—
513#435—114no—
514#432—111no—
515#432C2×D1111yescharacteristic, complemented
516#417—114no—
517C2×#102—114no—
518#407—112no—
519C2×C22⋊C8—112no—
520C22×C11—21no—
521C22×C11—21no—
522C22×C11—24no—
523C22×C11—48no—
524C22×C11—42no—
525C22×C11—42no—
526C22×C11—42no—
527C22×C11—42no—
528C22×C11—42no—
529C22×C11C2×AGL(1,ℤ/8)12yes—
530C22×C11C23×D411yescharacteristic
531C2×D11—22no—
532C2×D11—22no—
533C2×D11—22no—
534C2×D11—22no—
535C2×D11—22no—
536C2×D11—44no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—816no—
544C2×D11—82no—
545C2×D11—84no—
546C2×D11—164no—
547C2×D11—164no—
548C2×D11C2×AGL(1,ℤ/8)14yes—
549C4×C11—21no—
550C4×C11—21no—
551C4×C11—21no—
552C4×C11—21no—
553C4×C11—21no—
554C4×C11—42no—
555C4×C11—42no—
556C4×C11C2×H(5,𝔽2)12yes—
557Dic11—22no—
558Dic11—22no—
559Dic11—42no—
560Dic11—42no—
561C25—221no—
562H(5,𝔽2)—448no—
563C2×#41—21no—
564C2×#41—114no—
565C2×#41—222no—
566C2×#41—222no—
567C2×#41—222no—
568C2×#41—221no—
569C2×#41—444no—
570C22×Q8—111no—
571C22×D4—114no—
572C22×D4—112no—
573C22×D4—112no—
574C22×D4—111no—
575C22×D4—111no—
576C22×D4—222no—
577C22×D4—221no—
578C22×D4—222no—
579C22×D4—221no—
580C22×D4—222no—
581C22×D4—222no—
582C22×D4—222no—
583C22×D4—221no—
584C22×D4—444no—
585C22×D4C22×D1111yescharacteristic
586C23×C4—21no—
587C23×C4—111no—
588C23×C4—111no—
589C23×C4—221no—
590AGL(1,ℤ/8)—448no—
591C2×SD16—114no—
592C2×SD16—114no—
593C2×D8—114no—
594C2×D8—114no—
595C2×D8—114no—
596C2×D8—448no—
597C2×D8C22×D1114yes—
598C2×M16—114no—
599C22×C8—114no—
600C4⋊Q8—111no—
601C4⋊Q8C22×D1111yescharacteristic, complemented
602#127—111no—
603#127C22×D1111yescharacteristic, complemented
604#124—21no—
605#124—112no—
606#124—112no—
607#124—221no—
608#124—221no—
609#124—221no—
610#123—222no—
611#123—222no—
612#123—224no—
613#123—224no—
614#123—222no—
615#123—222no—
616C22⋊Q8—114no—
617C22⋊Q8—222no—
618C22⋊Q8—222no—
619C22⋊Q8—222no—
620#121—21no—
621#121—112no—
622#121—112no—
623#121—112no—
624#121—112no—
625#121—112no—
626#121—114no—
627#121—222no—
628#121—222no—
629#121—224no—
630#121—224no—
631#121—222no—
632#121—222no—
633#121—222no—
634#121—222no—
635#121—222no—
636#121—221no—
637#121C22×D1112yes—
638#120—222no—
639#120—222no—
640#120—224no—
641#120—224no—
642#120—222no—
643#120—222no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647C4×D4—112no—
648C4×D4—112no—
649C4×D4—112no—
650C4×D4—112no—
651C4×D4—112no—
652C4×D4—221no—
653C4×D4C22×D1112yes—
654C4×D4C22×D1112yes—
655C4×D4C22×D1112yescomplemented
656C2×C4⋊C4—111no—
657C2×C4⋊C4—112no—
658C2×C4⋊C4—112no—
659C2×C4⋊C4—221no—
660C2×C4⋊C4C22×D1111yescharacteristic
661C2×C22⋊C4—21no—
662C2×C22⋊C4—111no—
663C2×C22⋊C4—111no—
664C2×C22⋊C4—222no—
665C2×C22⋊C4—222no—
666C2×C22⋊C4—224no—
667C2×C22⋊C4—224no—
668C2×C22⋊C4—221no—
669C2×C22⋊C4—221no—
670C2×C22⋊C4—221no—
671C2×C22⋊C4—221no—
672C2×C42C22×D1111yescharacteristic
673#106—114no—
674#106C22×D1114yescomplemented
675C4⋊C8—112no—
676C4⋊C8C22×D1112yescomplemented
677#103—114no—
678#103—114no—
679#102—114no—
680#102—114no—
681#102—114no—
682#102—114no—
683#102C22×D1114yes—
684#102C22×D1114yescomplemented
685C22⋊C8—112no—
686C22⋊C8—114no—
687C22⋊C8—114no—
688C22⋊C8C22×D1112yes—
689#97—112no—
690#97C22×D1112yescomplemented
691C2×C11—22no—
692C2×C11—44no—
693C2×C11—82no—
694C2×C11#348411yescharacteristic
695C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
696C2×C11#358511yescharacteristic
697D11—24no—
698D11—42no—
699D11—82no—
700D11—82no—
701C24—21no—
702C24—111no—
703C24—111no—
704C24—224no—
705C24—222no—
706C24—222no—
707C24—221no—
708C24—444no—
709C24—444no—
710C24—882no—
711#41—44no—
712#41—228no—
713#41—444no—
714#41—448no—
715#41—444no—
716#41—448no—
717#41—448no—
718C2×Q8—21no—
719C2×Q8—112no—
720C2×Q8—221no—
721C2×Q8—221no—
722C2×Q8—442no—
723C2×D4—24no—
724C2×D4—22no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—112no—
729C2×D4—112no—
730C2×D4—112no—
731C2×D4—112no—
732C2×D4—224no—
733C2×D4—222no—
734C2×D4—222no—
735C2×D4—224no—
736C2×D4—224no—
737C2×D4—222no—
738C2×D4—222no—
739C2×D4—228no—
740C2×D4—224no—
741C2×D4—222no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—221no—
745C2×D4—221no—
746C2×D4—221no—
747C2×D4—442no—
748C2×D4—448no—
749C2×D4—444no—
750C2×D4—444no—
751C2×D4—444no—
752C2×D4—448no—
753C2×D4—448no—
754C2×D4—448no—
755C2×D4—448no—
756C2×D4—444no—
757C2×D4—444no—
758C2×D4—882no—
759C2×D4C23×D1112yes—
760C2×D4C23×D1112yes—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—82no—
766C22×C4—111no—
767C22×C4—111no—
768C22×C4—112no—
769C22×C4—112no—
770C22×C4—112no—
771C22×C4—112no—
772C22×C4—222no—
773C22×C4—222no—
774C22×C4—224no—
775C22×C4—221no—
776C22×C4—222no—
777C22×C4—442no—
778C22×C4—442no—
779C22×C4—444no—
780C22×C4D4×D1111yescharacteristic
781C22×C4D4×D1111yescharacteristic
782C22×C4C23×D1111yescharacteristic
783SD16—444no—
784SD16—444no—
785D8—28no—
786D8—228no—
787D8—444no—
788D8—444no—
789M16—444no—
790C2×C8—114no—
791C2×C8—444no—
792C2×C8C23×D1114yes—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—112no—
796C4⋊C4—112no—
797C4⋊C4—112no—
798C4⋊C4—222no—
799C4⋊C4—222no—
800C4⋊C4—224no—
801C4⋊C4—221no—
802C4⋊C4C23×D1112yes—
803C4⋊C4C23×D1112yes—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—112no—
809C22⋊C4—112no—
810C22⋊C4—112no—
811C22⋊C4—112no—
812C22⋊C4—224no—
813C22⋊C4—222no—
814C22⋊C4—222no—
815C22⋊C4—224no—
816C22⋊C4—222no—
817C22⋊C4—222no—
818C22⋊C4—222no—
819C22⋊C4—222no—
820C22⋊C4—222no—
821C22⋊C4—222no—
822C22⋊C4—222no—
823C22⋊C4—222no—
824C42D4×D1111yescharacteristic
825C42D4×D1111yescharacteristic
826C42C23×D1111yescharacteristic
827C42C23×D1111yescharacteristic
828C11#6156911yescharacteristic, complemented, Sylow
829C23—24no—
830C23—22no—
831C23—22no—
832C23—42no—
833C23—42no—
834C23—112no—
835C23—114no—
836C23—112no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—441no—
841C23—441no—
842C23—441no—
843C23—441no—
844C23—448no—
845C23—442no—
846C23—442no—
847C23—448no—
848C23—444no—
849C23—444no—
850C23—442no—
851C23—884no—
852C23—882no—
853C23—882no—
854C23—882no—
855C23—882no—
856C23—8816no—
857C23C2×D4×D1111yescharacteristic
858Q8—42no—
859Q8—224no—
860Q8—442no—
861Q8—442no—
862D4—24no—
863D4—22no—
864D4—24no—
865D4—42no—
866D4—44no—
867D4—81no—
868D4—224no—
869D4—224no—
870D4—224no—
871D4—224no—
872D4—442no—
873D4—442no—
874D4—444no—
875D4—444no—
876D4—448no—
877D4—448no—
878D4—444no—
879D4—444no—
880D4—444no—
881D4—881no—
882D4—884no—
883D4—882no—
884D4—882no—
885D4#6704214yescomplemented
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—41no—
891C2×C4—44no—
892C2×C4—42no—
893C2×C4—82no—
894C2×C4—82no—
895C2×C4—112no—
896C2×C4—112no—
897C2×C4—224no—
898C2×C4—224no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—442no—
902C2×C4—442no—
903C2×C4—444no—
904C2×C4—444no—
905C2×C4—444no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—448no—
909C2×C4—442no—
910C2×C4C2×D4×D1111yescharacteristic
911C2×C4C2×D4×D1111yescharacteristic
912C2×C4C2×D4×D1111yescharacteristic
913C2×C4C2×D4×D1111yescharacteristic
914C2×C4C2×D4×D1111yescharacteristic
915C2×C4C24×D1111yescharacteristic
916C8—24no—
917C8—224no—
918C22—21no—
919C22—21no—
920C22—24no—
921C22—48no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—114no—
928C22—222no—
929C22—222no—
930C22—222no—
931C22—222no—
932C22—222no—
933C22—444no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—882no—
941C22—884no—
942C22—8816no—
943C22—1764no—
944C22—1764no—
945C22D11×AGL(1,ℤ/8)12yes—
946C22C22×D4×D1111yescharacteristic
947C4—21no—
948C4—21no—
949C4—21no—
950C4—21no—
951C4—21no—
952C4—42no—
953C4—42no—
954C4—222no—
955C4—222no—
956C4—442no—
957C4—442no—
958C4C2×#6704212yes—
959C2—22no—
960C2—44no—
961C2—82no—
962C2—224no—
963C2—442no—
964C2—882no—
965C2—882no—
966C2#1308224911yescharacteristic
967C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
968C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3109C2
socleC22×C11C23×D4
hypercenter#3109D11
hypocenterC11#61569
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3109

Complements

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

NH ≅ G/Ntype
1. #13082378C2semidirect
2. C2×#10623085C2semidirect
3. #13080582C2semidirect
4. #13080574C2semidirect
5. #13080098C2semidirect
6. #13080091C2semidirect
7. #13079605C2semidirect
8. #13079599C2semidirect
9. #13079415C2semidirect
10. #13079375C2semidirect
11. #13078707C2semidirect
12. #13077863C2semidirect
13. D11×#447C2semidirect
14. #13077644C2semidirect
15. C11×#3109C2semidirect
17. C22×#4341C22semidirect
18. C22×D4×D11C22semidirect
19. C11×#532C22semidirect
20. C2×C4×D4×C11C22semidirect
24. C2×#66964C22semidirect
25. C2×D8×D11C22semidirect
26. #10623257C22semidirect
27. #10623248C22semidirect
32. D11×#121C22semidirect
35. #10623085C22semidirect
36. #10623085C22semidirect
37. #10623082C22semidirect
39. D4×D44C22semidirect
40. C2×#66950C22semidirect
41. C2×#66948C22semidirect
44. #10623008C22semidirect
45. C2×#66928C22semidirect
47. C11×#481C22semidirect
48. C11×#476C22semidirect
49. C11×#459C22semidirect
50. C11×#447C22semidirect
51. C11×#442C22semidirect
52. C11×#432C22semidirect
53. #10622830C22semidirect
54. #10622771C22semidirect
55. #10622769C22semidirect
56. #10622702C22semidirect
57. #10622687C22semidirect
58. #10622653C22semidirect
59. #10622649C22semidirect
60. #10622629C22semidirect
61. #10622628C22semidirect
62. #10622627C22semidirect
63. #10622621C22semidirect
64. #10622581C22semidirect
65. #10622539C22semidirect
66. #10622478C22semidirect
67. #10622477C22semidirect
68. #10622476C22semidirect
69. #10622475C22semidirect
70. #10622457C22semidirect
71. #10622449C22semidirect
72. #10622395C22semidirect
73. #10622394C22semidirect
74. #10622391C22semidirect
75. #10622389C22semidirect
76. #10622386C22semidirect
77. #10622386C22semidirect
78. #10622384C22semidirect
79. D11×#102C22semidirect
80. #10622351C22semidirect
81. #10622345C22semidirect
82. #10622339C22semidirect
83. D11×C22⋊C8C22semidirect
84. #10622327C22semidirect
85. #10622325C22semidirect
86. #10622319C22semidirect
106. C2×D4×D11C23semidirect
117. C11×C4⋊Q8C23semidirect
118. C11×#127C23semidirect
127. C4×D4×C11C23semidirect
136. #66991C23semidirect
139. C2×#4324C23semidirect
161. C2×#4314C23semidirect
162. C2×#4313C23semidirect
169. #66948C23semidirect
173. C4⋊C4×D11C23semidirect
191. #66927C23semidirect
197. C4×D44C23semidirect
198. #66922C23semidirect
199. C11×#106C23semidirect
200. C11×C4⋊C8C23semidirect
202. C11×#102C23semidirect
204. C11×#97C23semidirect
209. (C2×D11)⋊C8C23semidirect
210. #66880C23semidirect
211. #66874C23semidirect
213. #66873C23semidirect
214. #66872C23semidirect
215. C4⋊(C11⋊C8)C23semidirect
216. #66867C23semidirect
356. #3109D11semidirect
386. C22×D11AGL(1,ℤ/8)semidirect
396. D4×C11H(5,𝔽2)semidirect
468. #532C2×D11semidirect
478. C2×C4×D4C2×D11semidirect
487. #481C2×D11semidirect
489. #476C2×D11semidirect
497. #459C2×D11semidirect
509. #447C2×D11semidirect
511. #442C2×D11semidirect
515. #432C2×D11semidirect
601. C4⋊Q8C22×D11semidirect
603. #127C22×D11semidirect
655. C4×D4C22×D11semidirect
674. #106C22×D11semidirect
676. C4⋊C8C22×D11semidirect
684. #102C22×D11semidirect
690. #97C22×D11semidirect
828. C11#61569semidirect
885. D4#67042semidirect

Maximal subgroups

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

subgroupindex
#130823782
C2×#106230852
#130805822
#130805742
#130800982
#130800912
#130796052
#130795992
#130794152
#130793752
#130787072
#130778632
D11×#4472
#130776442
C11×#31092
#6156911