Finite Group Databasebeta

← #15625196

Subgroups — #15625196

Order 2816.

2822 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081909C211yesmaximal, characteristic, complemented
2C2×D11×#127C211yesmaximal, characteristic, complemented
3#13079638C214yesmaximal, complemented
4#13079633C214yesmaximal, complemented
5#13079556C214yesmaximal, complemented
6#13079533C214yesmaximal, complemented
7#13079064C212yesmaximal, complemented
8#13078988C212yesmaximal, complemented
9#13078097C211yesmaximal, characteristic, complemented
10#13078096C211yesmaximal, characteristic, complemented
11#13078092C211yesmaximal, characteristic, complemented
12#13077845C212yesmaximal, complemented
13#13077841C212yesmaximal, complemented
14#13077248C211yesmaximal, characteristic, complemented
15C11×#3038C211yesmaximal, characteristic, complemented
16C22×D4×D11—22no—
17C22×D4×D11C2212yes—
18C2×C11×AGL(1,ℤ/8)C2212yescomplemented
19C2×C11×#127C2211yescharacteristic
20C4×C11×#41C2211yescharacteristic, complemented
21#10623363C2211yescharacteristic, complemented
22#10623359C2211yescharacteristic
23C2×#67002C2212yescomplemented
24C2×#66993—22no—
25C2×#66993C2212yes—
26C2×#66985C2212yescomplemented
27C2×#66961C2212yescomplemented
28D11×#127—22no—
29D11×#127—22no—
30D11×#127C2214yes—
31D11×#127C2214yes—
32#10623111C2212yescomplemented
33#10623109C2212yescomplemented
34#10623088C2212yescomplemented
35#10623079C2212yescomplemented
36#10623078—22no—
37#10623069—22no—
38#10623059—22no—
39#10623055C2211yescharacteristic
40#10623048C2211yescharacteristic, complemented
41C2×#66927C2211yescharacteristic
42C4×#4339—22no—
43C4×#4339C2211yescharacteristic, complemented
44C2×C42×D11C2211yescharacteristic
45C11×#460C2214yescomplemented
46C11×#459C2214yescomplemented
47C11×#423C2211yescharacteristic, complemented
48C11×#418C2212yescomplemented
49#10622828C2212yescomplemented
50#10622789C2214yescomplemented
51#10622788C2214yescomplemented
52#10622782C2218yescomplemented
53#10622769C2218yescomplemented
54#10622767C2214yescomplemented
55#10622764C2214yescomplemented
56#10622744C2212yescomplemented
57#10622739C2212yes—
58M16×Dic11C2212yescomplemented
59#10622688C2214yescomplemented
60#10622685C2214yescomplemented
61#10622640C2214yescomplemented
62#10622628C2214yescomplemented
63#10622614C2212yescomplemented
64#10622537C2211yescharacteristic, complemented
65#10622461C2214yescomplemented
66#10622456C2214yescomplemented
67#10622448C2214yescomplemented
68#10622446C2214yescomplemented
69#10622389C2218yescomplemented
70#10622386C2218yescomplemented
71#10622377C2218yescomplemented
72#10622373C2218yescomplemented
73C24×D11—22no—
74C2×C11×#41C2311yescharacteristic
75C22×D4×C11—22no—
76C22×D4×C11C2312yes—
77C22×C22⋊D11—22no—
78C22×C22⋊D11—24no—
79C2×D4×D11—24no—
80C2×D4×D11—24no—
81C2×D4×D11—24no—
82C2×D4×D11—24no—
83C2×D4×D11—24no—
84C2×D4×D11—44no—
85C2×D4×D11—44no—
86C2×D4×D11—416no—
87C2×D4×D11C2318yes—
88C2×#4339—22no—
89C2×#4339C2311yescharacteristic
90C22×D44—22no—
91C22×D44C2312yes—
92C22×C4×D11D412yes—
93C22×C4×D11C2311yescharacteristic
94C11×AGL(1,ℤ/8)—44no—
95C2×C11×SD16C2314yescomplemented
96C2×C11×D8C2314yescomplemented
97C2×C11×M16C2312yes—
98C11×#127—21no—
99C11×#127—21no—
100C11×#127C2314yes—
101C4×Q8×C11C2312yescomplemented
102C4×D4×C11—22no—
103C4×D4×C11C2312yescomplemented
104C11×#117—21no—
105C11×#117C2311yescharacteristic
106C2×C42×C11—21no—
107C2×C42×C11C2311yescharacteristic
108#67002—44no—
109#67000C2311yescharacteristic, complemented
110#66999C2312yes—
111#66997C2311yescharacteristic, complemented
112C2×#4325C2314yescomplemented
113#66993—24no—
114#66993—24no—
115#66993—24no—
116#66993—24no—
117#66993—24no—
118#66993C2314yes—
119#66993C2314yes—
120#66993C2311yescharacteristic, complemented
121#66992—22no—
122#66991C2312yes—
123#66990—21no—
124#66989C2311yescharacteristic, complemented
125#66988—21no—
126C2×#4324C2314yescomplemented
127#66985—44no—
128C2×#4323C2314yescomplemented
129C2×#4323C2314yescomplemented
130C4×C22⋊D11—22no—
131C4×C22⋊D11—22no—
132C4×C22⋊D11—22no—
133C4×C22⋊D11—22no—
134C4×C22⋊D11—22no—
135#66979—22no—
136#66979C2311yescharacteristic
137C2×C4×Dic11D412yes—
138C2×C4×Dic11C2311yescharacteristic
139C2×#4318C2312yes—
140#66961—44no—
141C2×D88C2314yescomplemented
142C2×#4314C2314yescomplemented
143#66951—22no—
144#66950C2312yes—
145#66949—22no—
146#66948C2312yes—
147#66947—22no—
148#66943C2312yescomplemented
149#66942—22no—
150#66941C2312yescomplemented
151#66939—21no—
152#66938—22no—
153#66937—22no—
154#66936—22no—
155#66935—21no—
156#66932—22no—
157#66931—22no—
158#66927—21no—
159#66927—21no—
160#66927C2314yes—
161C4×D44—22no—
162C4×D44—22no—
163C4×D44C2312yescomplemented
164#66925—22no—
165#66925—21no—
166#66925—22no—
167C42×D11—21no—
168C42×D11D412yes—
169C42×D11D412yes—
170C42×D11C2312yes—
171C42×D11C2312yes—
172C4×Dic22—22no—
173C4×Dic22—22no—
174C4×Dic22C2312yescomplemented
175C11×C4⋊C8C2314yescomplemented
176C11×#102C2318yescomplemented
177#66896C2318yescomplemented
178#66885C2318yescomplemented
179(C2×D11)⋊C8C2318yes—
180#66879C2314yescomplemented
181C8×Dic11C2314yescomplemented
182#66873C2318yescomplemented
183C4⋊(C11⋊C8)C2314yescomplemented
184#60798—111nomaximal, Sylow
185C24×C11—22no—
186C23×D11—22no—
187C23×D11—28no—
188C23×D11—48no—
189C23×D11—416no—
190C23×D11C2×D411yescharacteristic
191C11×#41—22no—
192C11×#41—22no—
193C2×Q8×C11C2411yescharacteristic
194C2×D4×C11—21no—
195C2×D4×C11—22no—
196C2×D4×C11—24no—
197C2×D4×C11—24no—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—48no—
201C2×D4×C11C2414yes—
202C2×D4×C11C2411yescharacteristic
203C22×C4×C11—22no—
204C22×C4×C11—21no—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2411yescharacteristic
207C2×C22⋊D11—22no—
208C2×C22⋊D11—28no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—21no—
212C2×C22⋊D11—22no—
213C2×C22⋊D11—416no—
214C2×C22⋊D11—48no—
215C22×Dic11C2×D412yes—
216C22×Dic11C2×D411yescharacteristic
217D4×D11—48no—
218D4×D11—48no—
219D4×D11—416no—
220D4×D11—416no—
221D4×D11—416no—
222D4×D11—416no—
223D4×D11—416no—
224#4339—22no—
225#4339—22no—
226#4339—48no—
227C2×D44—22no—
228C2×D44—22no—
229C2×D44—24no—
230C2×D44—24no—
231C2×D44—24no—
232C2×D44—24no—
233C2×D44—48no—
234C2×D44C2414yes—
235C2×D44C2411yescharacteristic
236C2×C4×D11—28no—
237C2×C4×D11—21no—
238C2×C4×D11—22no—
239C2×C4×D11—22no—
240C2×C4×D11—22no—
241C2×C4×D11C2×D412yes—
242C2×C4×D11C2×D412yes—
243C2×C4×D11C2×D412yes—
244C2×C4×D11C2×D412yes—
245C2×C4×D11C2×D412yes—
246C2×C4×D11C2412yes—
247C2×Dic22—22no—
248C2×Dic22C2411yescharacteristic
249C11×SD16—44no—
250C11×D8—44no—
251C11×M16—24no—
252C2×C8×C11C2414yes—
253C11×C4⋊C4—22no—
254C11×C4⋊C4C2412yes—
255C11×C22⋊C4—21no—
256C11×C22⋊C4—22no—
257C42×C11—21no—
258C42×C11—22no—
259C42×C11C2×D411yescharacteristic
260C42×C11C2×D411yescharacteristic
261C42×C11C2412yes—
262C22⋊Dic11—22no—
263C22⋊Dic11—22no—
264C22⋊Dic11—21no—
265#4325—44no—
266#4324—44no—
267#4323—44no—
268#4323—44no—
269(C2×D11)⋊C4—22no—
270(C2×D11)⋊C4—22no—
271(C2×D11)⋊C4—22no—
272(C2×D11)⋊C4—22no—
273(C2×D11)⋊C4—22no—
274C4⋊Dic11—22no—
275C4⋊Dic11—22no—
276C4⋊Dic11C2412yes—
277Dic11⋊C4—22no—
278Dic11⋊C4—22no—
279Dic11⋊C4—22no—
280Dic11⋊C4—22no—
281Dic11⋊C4—22no—
282C4×Dic11—21no—
283C4×Dic11—22no—
284C4×Dic11C2×D412yes—
285C4×Dic11C2×D412yes—
286C4×Dic11C2×D412yes—
287C4×Dic11C2×D412yes—
288C4×Dic11C2×D412yes—
289C4×Dic11C2411yescharacteristic
290C4×Dic11C2411yescharacteristic
291#4318—24no—
292C2×C11⋊C8C2414yes—
293D88—44no—
294#4314—44no—
295#3444—111no—
296C22×#127—111no—
297#3217—114no—
298#3217—114no—
299#3208—114no—
300#3205—114no—
301#3151—112no—
302#3138—112no—
303#3038—111no—
304#3038—111no—
305#3038—111no—
306#3038D1111yescharacteristic, complemented
307#3003—112no—
308#3003—112no—
309#2920—111no—
310C23×C11—21no—
311C23×C11—24no—
312C23×C11—48no—
313C23×C11—44no—
314C23×C11C22×D411yescharacteristic
315C22×D11—22no—
316C22×D11—24no—
317C22×D11—21no—
318C22×D11—24no—
319C22×D11—416no—
320C22×D11—416no—
321C22×D11—48no—
322C22×D11—44no—
323C22×D11—416no—
324C22×D11—832no—
325C22×D11C22×D412yes—
326Q8×C11—21no—
327Q8×C11—21no—
328D4×C11—21no—
329D4×C11—24no—
330D4×C11—21no—
331D4×C11—24no—
332D4×C11—48no—
333D4×C11—42no—
334D4×C11—44no—
335D4×C11—48no—
336C2×C4×C11—24no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—42no—
340C2×C4×C11—44no—
341C2×C4×C11C22×D412yes—
342C2×C4×C11C22×D411yescharacteristic
343C2×C4×C11C22×D412yes—
344C2×C4×C11H(5,𝔽2)12yes—
345C2×C4×C11H(5,𝔽2)12yes—
346C2×C4×C11C2511yescharacteristic
347C22⋊D11—416no—
348C22⋊D11—416no—
349C22⋊D11—42no—
350C22⋊D11—44no—
351C22⋊D11—44no—
352C22⋊D11—416no—
353C2×Dic11—22no—
354C2×Dic11—24no—
355C2×Dic11—21no—
356C2×Dic11—22no—
357C2×Dic11C22×D412yes—
358C2×Dic11C22×D412yes—
359C2×Dic11C22×D412yes—
360D44—24no—
361D44—21no—
362D44—21no—
363D44—24no—
364D44—48no—
365D44—44no—
366D44—44no—
367D44—48no—
368C4×D11—24no—
369C4×D11—24no—
370C4×D11—24no—
371C4×D11—22no—
372C4×D11—22no—
373C4×D11—24no—
374C4×D11—42no—
375C4×D11—44no—
376C4×D11AGL(1,ℤ/8)18yescomplemented
377Dic22—21no—
378Dic22—21no—
379Dic22—44no—
380C8×C11—24no—
381C11⋊C8—24no—
382C23×D4—112no—
383C23×D4—222no—
384C2×AGL(1,ℤ/8)—112no—
385C2×AGL(1,ℤ/8)—112no—
386C2×AGL(1,ℤ/8)—112no—
387C2×AGL(1,ℤ/8)C2×D1112yescomplemented
388#533—111no—
389#533—112no—
390#532—112no—
391#532—111no—
392C2×#127—112no—
393C2×#127—114no—
394C2×#127—114no—
395C2×#127—111no—
396C2×#127—222no—
397C2×#127—222no—
398C2×#127—222no—
399C2×#127C2×D1111yescharacteristic
400#529—112no—
401#529—112no—
402#529—222no—
403#529—222no—
404#525—111no—
405#525—111no—
406#525—222no—
407C4×#41—111no—
408C4×#41—222no—
409C4×#41C2×D1111yescharacteristic, complemented
410C22×C42—111no—
411#496—114no—
412#496—114no—
413#493—114no—
414#492—114no—
415#490—118no—
416#486—118no—
417#460—114no—
418#460—114no—
419#460—114no—
420#460C2×D1114yescomplemented
421#459—114no—
422#459—114no—
423#459—114no—
424#459C2×D1114yescomplemented
425#450—118no—
426#450—118no—
427#447—118no—
428#447—118no—
429#432—114no—
430#431—114no—
431#423—111no—
432#423C2×D1111yescharacteristic, complemented
433#418—112no—
434#418—112no—
435#418—112no—
436#418C2×D1112yescomplemented
437#407—112no—
438C4×M16—112no—
439C22×C11—22no—
440C22×C11—41no—
441C22×C11—44no—
442C22×C11—42no—
443C22×C11—48no—
444C22×C11—88no—
445C22×C11#53512yes—
446C22×C11C23×D411yescharacteristic
447C2×D11—28no—
448C2×D11—22no—
449C2×D11—22no—
450C2×D11—44no—
451C2×D11—41no—
452C2×D11—48no—
453C2×D11—42no—
454C2×D11—832no—
455C2×D11—88no—
456C2×D11C2×AGL(1,ℤ/8)14yes—
457C4×C11—22no—
458C4×C11—41no—
459C4×C11—42no—
460C4×C11#53512yes—
461C4×C11C2×AGL(1,ℤ/8)14yes—
462C4×C11C2×H(5,𝔽2)11yescharacteristic
463C4×C11C2×H(5,𝔽2)11yescharacteristic
464Dic11—22no—
465Dic11—22no—
466Dic11—41no—
467Dic11—42no—
468Dic11C2×AGL(1,ℤ/8)14yes—
469C25—222no—
470C2×#41—111no—
471C2×#41—222no—
472C2×#41C22×D1111yescharacteristic
473C22×D4—22no—
474C22×D4—118no—
475C22×D4—112no—
476C22×D4—224no—
477C22×D4—224no—
478C22×D4—224no—
479C22×D4—224no—
480C22×D4—224no—
481C22×D4—224no—
482C22×D4—222no—
483C22×D4—222no—
484C22×D4—444no—
485C22×D4—444no—
486C22×D4—4416no—
487C22×D4C22×D1112yes—
488C23×C4—112no—
489C23×C4—111no—
490AGL(1,ℤ/8)—44no—
491AGL(1,ℤ/8)—444no—
492AGL(1,ℤ/8)—444no—
493AGL(1,ℤ/8)—444no—
494C2×SD16—114no—
495C2×SD16—114no—
496C2×SD16—114no—
497C2×SD16C22×D1114yescomplemented
498C2×D8—114no—
499C2×D8—114no—
500C2×D8—114no—
501C2×D8C22×D1114yescomplemented
502C2×M16—112no—
503C2×M16C22×D1112yes—
504C4⋊Q8—112no—
505C4⋊Q8—111no—
506#127—21no—
507#127—21no—
508#127—114no—
509#127—114no—
510#127—111no—
511#127—114no—
512#127—224no—
513#127—224no—
514#127—224no—
515#127—224no—
516#127—224no—
517#127—221no—
518#127—221no—
519#127C22×D1114yes—
520#126—222no—
521#126—222no—
522#125—112no—
523#125—222no—
524#124—111no—
525#124—111no—
526#124—222no—
527#123—221no—
528#123—222no—
529#123—222no—
530#123—221no—
531C22⋊Q8—112no—
532C22⋊Q8—112no—
533C22⋊Q8—222no—
534C22⋊Q8—222no—
535#121—112no—
536#121—112no—
537#121—222no—
538#121—222no—
539#120—221no—
540#120—221no—
541C4×Q8—112no—
542C4×Q8—222no—
543C4×Q8—222no—
544C4×Q8C22×D1112yescomplemented
545C4×D4—22no—
546C4×D4—112no—
547C4×D4—222no—
548C4×D4—222no—
549C4×D4—222no—
550C4×D4—222no—
551C4×D4—222no—
552C4×D4—222no—
553C4×D4—222no—
554C4×D4C22×D1112yescomplemented
555#117—21no—
556#117—111no—
557#117—222no—
558#117—222no—
559#117—222no—
560#117—221no—
561#117C22×D1111yescharacteristic
562C2×C42—21no—
563C2×C42—112no—
564C2×C42—111no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—112no—
568C2×C42—112no—
569C2×C42—221no—
570C2×C42C22×D1111yescharacteristic
571C4⋊C8—114no—
572C4⋊C8C22×D1114yescomplemented
573#102—118no—
574#102—118no—
575#102—118no—
576#102C22×D1118yescomplemented
577C22⋊C8—118no—
578#97—114no—
579C4×C8—114no—
580C2×C11—22no—
581C2×C11—84no—
582C2×C11—81no—
583C2×C11C2×#53511yescharacteristic
584C2×C11C22×AGL(1,ℤ/8)12yes—
585D11—24no—
586D11—81no—
587D11—84no—
588C24—22no—
589C24—111no—
590C24—228no—
591C24—222no—
592C24—4416no—
593C24—448no—
594#41—22no—
595#41—22no—
596#41—222no—
597#41—222no—
598#41—448no—
599C2×Q8—111no—
600C2×Q8—222no—
601C2×Q8C23×D1111yescharacteristic
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—48no—
609C2×D4—114no—
610C2×D4—111no—
611C2×D4—222no—
612C2×D4—222no—
613C2×D4—228no—
614C2×D4—228no—
615C2×D4—228no—
616C2×D4—222no—
617C2×D4—221no—
618C2×D4—224no—
619C2×D4—224no—
620C2×D4—222no—
621C2×D4—224no—
622C2×D4—224no—
623C2×D4—448no—
624C2×D4—4416no—
625C2×D4—448no—
626C2×D4—448no—
627C2×D4—4416no—
628C2×D4—4416no—
629C2×D4—4416no—
630C2×D4—4416no—
631C2×D4—4416no—
632C2×D4—448no—
633C2×D4C23×D1114yes—
634C2×D4C23×D1111yescharacteristic
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—111no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—112no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—228no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—221no—
650C22×C4D4×D1112yes—
651C22×C4C23×D1111yescharacteristic
652SD16—44no—
653SD16—444no—
654SD16—444no—
655SD16—444no—
656D8—44no—
657D8—444no—
658D8—444no—
659D8—444no—
660M16—24no—
661M16—224no—
662C2×C8—114no—
663C2×C8C23×D1114yes—
664C4⋊C4—22no—
665C4⋊C4—112no—
666C4⋊C4—222no—
667C4⋊C4—222no—
668C4⋊C4—222no—
669C4⋊C4—222no—
670C4⋊C4—222no—
671C4⋊C4—222no—
672C4⋊C4—222no—
673C4⋊C4C23×D1112yes—
674C22⋊C4—21no—
675C22⋊C4—22no—
676C22⋊C4—222no—
677C22⋊C4—222no—
678C22⋊C4—222no—
679C22⋊C4—222no—
680C22⋊C4—222no—
681C22⋊C4—222no—
682C22⋊C4—221no—
683C22⋊C4—222no—
684C42—21no—
685C42—22no—
686C42—112no—
687C42—112no—
688C42—112no—
689C42—112no—
690C42—112no—
691C42—111no—
692C42—111no—
693C42—221no—
694C42—222no—
695C42D4×D1111yescharacteristic
696C42D4×D1111yescharacteristic
697C42C23×D1112yes—
698C11#6079811yescharacteristic, complemented, Sylow
699C23—21no—
700C23—24no—
701C23—48no—
702C23—44no—
703C23—112no—
704C23—224no—
705C23—222no—
706C23—221no—
707C23—224no—
708C23—448no—
709C23—4416no—
710C23—4416no—
711C23—4416no—
712C23—444no—
713C23—8832no—
714C23C2×D4×D1111yescharacteristic
715Q8—21no—
716Q8—21no—
717Q8—221no—
718Q8—221no—
719Q8—444no—
720D4—21no—
721D4—24no—
722D4—21no—
723D4—24no—
724D4—48no—
725D4—42no—
726D4—48no—
727D4—44no—
728D4—221no—
729D4—224no—
730D4—221no—
731D4—224no—
732D4—448no—
733D4—444no—
734D4—4416no—
735D4—444no—
736D4—4416no—
737D4—4416no—
738D4—444no—
739D4—442no—
740D4—448no—
741D4—444no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—44no—
746C2×C4—42no—
747C2×C4—112no—
748C2×C4—118no—
749C2×C4—112no—
750C2×C4—112no—
751C2×C4—224no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—222no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—221no—
761C2×C4—444no—
762C2×C4—442no—
763C2×C4C2×D4×D1112yes—
764C2×C4C2×D4×D1112yes—
765C2×C4C2×D4×D1111yescharacteristic
766C2×C4#6703712yes—
767C2×C4#6704212yes—
768C2×C4C24×D1111yescharacteristic
769C8—24no—
770C8—224no—
771C22—22no—
772C22—41no—
773C22—44no—
774C22—42no—
775C22—48no—
776C22—88no—
777C22—114no—
778C22—228no—
779C22—222no—
780C22—222no—
781C22—441no—
782C22—444no—
783C22—442no—
784C22—448no—
785C22—888no—
786C22—8832no—
787C22#1062313812yes—
788C22C22×D4×D1111yescharacteristic
789C4—22no—
790C4—41no—
791C4—42no—
792C4—114no—
793C4—222no—
794C4—222no—
795C4—441no—
796C4—442no—
797C4#1062313812yes—
798C4D11×AGL(1,ℤ/8)14yes—
799C4C2×#6703711yescharacteristic
800C4C2×#6704211yescharacteristic
801C2—22no—
802C2—84no—
803C2—81no—
804C2—224no—
805C2—884no—
806C2—881no—
807C2C2×#1062313811yescharacteristic
808C2C2×D11×AGL(1,ℤ/8)12yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3038C2
socleC22×C11C23×D4
hypercenter#3038D11
hypocenterC11#60798
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #13081909C2semidirect
2. C2×D11×#127C2semidirect
3. #13079638C2semidirect
4. #13079633C2semidirect
5. #13079556C2semidirect
6. #13079533C2semidirect
7. #13079064C2semidirect
8. #13078988C2semidirect
9. #13078097C2semidirect
10. #13078096C2semidirect
11. #13078092C2semidirect
12. #13077845C2semidirect
13. #13077841C2semidirect
14. #13077248C2semidirect
15. C11×#3038C2semidirect
18. C2×C11×AGL(1,ℤ/8)C22semidirect
20. C4×C11×#41C22semidirect
21. #10623363C22semidirect
23. C2×#67002C22semidirect
26. C2×#66985C22semidirect
27. C2×#66961C22semidirect
32. #10623111C22semidirect
33. #10623109C22semidirect
34. #10623088C22semidirect
35. #10623079C22semidirect
40. #10623048C22semidirect
43. C4×#4339C22semidirect
45. C11×#460C22semidirect
46. C11×#459C22semidirect
47. C11×#423C22semidirect
48. C11×#418C22semidirect
49. #10622828C22semidirect
50. #10622789C22semidirect
51. #10622788C22semidirect
52. #10622782C22semidirect
53. #10622769C22semidirect
54. #10622767C22semidirect
55. #10622764C22semidirect
56. #10622744C22semidirect
58. M16×Dic11C22semidirect
59. #10622688C22semidirect
60. #10622685C22semidirect
61. #10622640C22semidirect
62. #10622628C22semidirect
63. #10622614C22semidirect
64. #10622537C22semidirect
65. #10622461C22semidirect
66. #10622456C22semidirect
67. #10622448C22semidirect
68. #10622446C22semidirect
69. #10622389C22semidirect
70. #10622386C22semidirect
71. #10622377C22semidirect
72. #10622373C22semidirect
95. C2×C11×SD16C23semidirect
96. C2×C11×D8C23semidirect
101. C4×Q8×C11C23semidirect
103. C4×D4×C11C23semidirect
109. #67000C23semidirect
111. #66997C23semidirect
112. C2×#4325C23semidirect
120. #66993C23semidirect
124. #66989C23semidirect
126. C2×#4324C23semidirect
128. C2×#4323C23semidirect
129. C2×#4323C23semidirect
141. C2×D88C23semidirect
142. C2×#4314C23semidirect
148. #66943C23semidirect
150. #66941C23semidirect
163. C4×D44C23semidirect
174. C4×Dic22C23semidirect
175. C11×C4⋊C8C23semidirect
176. C11×#102C23semidirect
177. #66896C23semidirect
178. #66885C23semidirect
180. #66879C23semidirect
181. C8×Dic11C23semidirect
182. #66873C23semidirect
183. C4⋊(C11⋊C8)C23semidirect
306. #3038D11semidirect
376. C4×D11AGL(1,ℤ/8)semidirect
387. C2×AGL(1,ℤ/8)C2×D11semidirect
409. C4×#41C2×D11semidirect
420. #460C2×D11semidirect
424. #459C2×D11semidirect
432. #423C2×D11semidirect
436. #418C2×D11semidirect
497. C2×SD16C22×D11semidirect
501. C2×D8C22×D11semidirect
544. C4×Q8C22×D11semidirect
554. C4×D4C22×D11semidirect
572. C4⋊C8C22×D11semidirect
576. #102C22×D11semidirect
698. C11#60798semidirect

Maximal subgroups

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

subgroupindex
#130819092
C2×D11×#1272
#130796382
#130796332
#130795562
#130795332
#130790642
#130789882
#130780972
#130780962
#130780922
#130778452
#130778412
#130772482
C11×#30382
#6079811