Finite Group Databasebeta

← #15626775

Subgroups — #15626775

Order 2816.

2168 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081912C211yesmaximal, characteristic, complemented
2C2×#10623008C211yesmaximal, characteristic, complemented
3#13080004C212yesmaximal, complemented
4#13079997C212yesmaximal, complemented
5#13079979C214yesmaximal, complemented
6#13079943C214yesmaximal, complemented
7#13079933C212yesmaximal, complemented
8#13079926C212yesmaximal, complemented
9#13078432C212yesmaximal, complemented
10#13078415C212yesmaximal, complemented
11#13078235C214yesmaximal, complemented
12#13078097C212yesmaximal, complemented
13#13078082C212yesmaximal, complemented
14C2×C11×#423C211yesmaximal, characteristic, complemented
15C22×#4339—21no—
16C22×C11×M16C2212yes—
17C22×C42×C11C2211yescharacteristic
18#10623322—21no—
19#10623322—21no—
20#10623322C2212yes—
21C2×#66983—21no—
22C2×#66983C2212yes—
23C2×#66961C2214yes—
24#10623010—21no—
25#10623010—21no—
26#10623010—21no—
27#10623010—21no—
28#10623010C2212yescomplemented
29#10623010C2212yescomplemented
30#10623008—21no—
31#10623008—21no—
32#10623008—21no—
33#10623008—21no—
34#10623008C2211yescharacteristic
35#10623008C2212yes—
36#10623008C2212yes—
37#10623008C2212yes—
38#10623008C2212yes—
39#10623008C2211yescharacteristic, complemented
40#10623008C2211yescharacteristic, complemented
41C2×#66928—21no—
42C2×#66927C2211yescharacteristic
43C4×#4339—21no—
44C4×#4339—21no—
45C4×#4339C2212yes—
46C2×C4×D44—21no—
47C2×C4×D44C2212yes—
48#10623001C2211yescharacteristic
49#10623001C2211yescharacteristic, complemented
50#10623001C2211yescharacteristic, complemented
51C2×#66922C2211yescharacteristic
52C11×#423C2212yes—
53C11×#423C2212yes—
54C11×#423C2212yescomplemented
55C11×#423C2212yescomplemented
56C2×C11×C4⋊C8C2212yescomplemented
57C2×C11×C4⋊C8C2212yescomplemented
58#10622748C2218yescomplemented
59#10622747C2218yescomplemented
60#10622746C2214yes—
61#10622744C2214yes—
62#10622734C2214yes—
63#10622728C2218yescomplemented
64#10622727C2218yescomplemented
65#10622464C2214yescomplemented
66#10622463C2214yescomplemented
67#10622461C2214yescomplemented
68#10622461C2214yescomplemented
69#10622460C2218yescomplemented
70#10622459C2214yescomplemented
71#10622459C2214yescomplemented
72#10622457C2218yescomplemented
73#10622456C2214yescomplemented
74#10622456C2214yescomplemented
75#10622456C2214yescomplemented
76#10622455C2214yescomplemented
77#10622455C2214yescomplemented
78#10622454C2214yescomplemented
79C23×C4×C11D411yescharacteristic
80C23×C4×C11D411yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—22no—
83C2×#4339—21no—
84C2×#4339—21no—
85C2×#4339—22no—
86C2×#4339—22no—
87C2×#4339—22no—
88C2×#4339—22no—
89C2×#4339—48no—
90C2×#4339C2312yes—
91C22×D44—21no—
92C22×D44—21no—
93C22×D44C2312yes—
94C22×C4×D11—22no—
95C22×Dic22—21no—
96C2×C11×M16—44no—
97C2×C11×M16C2314yes—
98C2×C11×M16C2314yes—
99C22×C8×C11C2314yes—
100C2×C42×C11D411yescharacteristic
101C2×C42×C11D411yescharacteristic
102C2×C42×C11D411yescharacteristic
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D411yescharacteristic
105C2×C42×C11D411yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2311yescharacteristic
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2311yescharacteristic
110C2×C42×C11C2311yescharacteristic
111C2×C42×C11C2311yescharacteristic
112#67006—22no—
113#66983—22no—
114#66983—22no—
115#66983—22no—
116#66983—22no—
117#66983—22no—
118#66983—22no—
119#66983—21no—
120#66983—21no—
121#66983—21no—
122#66983—21no—
123#66983C2314yes—
124#66983C2312yes—
125#66983C2314yes—
126#66983C2312yes—
127#66982—22no—
128#66982—22no—
129#66982—22no—
130C4×C22⋊D11—22no—
131C4×C22⋊D11—22no—
132C4×C22⋊D11—22no—
133C4×C22⋊D11—22no—
134C4×C22⋊D11—22no—
135C4×C22⋊D11—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4—22no—
138#66979—21no—
139#66979—21no—
140#66979C2312yes—
141C2×C4⋊Dic11—21no—
142C2×C4⋊Dic11C2312yes—
143#66977—21no—
144#66977—21no—
145#66977—21no—
146#66977—21no—
147#66977C2312yes—
148#66977C2312yes—
149#66961—48no—
150C2×D88C2318yes—
151C2×#4314C2318yes—
152#66929—22no—
153#66929—22no—
154#66928—22no—
155#66928—22no—
156#66928—22no—
157#66928—22no—
158#66928—21no—
159#66928—21no—
160#66928C2312yes—
161#66927—21no—
162#66927—21no—
163#66927C2312yes—
164#66927C2312yes—
165#66927C2311yescharacteristic
166C4×D44—22no—
167C4×D44—22no—
168C4×D44—22no—
169C4×D44—22no—
170C4×D44—22no—
171C4×D44—22no—
172C4×D44—21no—
173C4×D44—21no—
174C4×D44—21no—
175C4×D44—21no—
176C4×D44C2314yes—
177C4×D44C2314yes—
178C4×D44C2312yes—
179C4×D44C2312yes—
180#66925—22no—
181#66925—22no—
182#66925—22no—
183C42×D11—22no—
184#66923—21no—
185#66923—21no—
186#66923C2312yes—
187#66922—21no—
188#66922—21no—
189#66922C2311yescharacteristic
190#66922C2312yes—
191#66922C2312yes—
192#66922C2311yescharacteristic
193#66922C2311yescharacteristic
194C4×Dic22—21no—
195C4×Dic22—21no—
196C4×Dic22—21no—
197C4×Dic22—21no—
198C4×Dic22C2312yes—
199C4×Dic22C2312yes—
200C11×C4⋊C8C2314yes—
201C11×C4⋊C8C2314yes—
202C11×C4⋊C8C2314yes—
203C11×C4⋊C8C2314yes—
204#66885C2318yes—
205#66885C2318yes—
206#66885C2318yes—
207#66882C2318yes—
208#66881C2318yes—
209#66880C2318yes—
210#60916—111nomaximal, Sylow
211C24×C11C2×D411yescharacteristic
212C23×D11—22no—
213C22×C4×C11—24no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11—42no—
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D411yescharacteristic
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2×D411yescharacteristic
223C22×C4×C11C2×D411yescharacteristic
224C22×C4×C11C2×D411yescharacteristic
225C22×C4×C11C2×D411yescharacteristic
226C22×C4×C11C2×D411yescharacteristic
227C22×C4×C11C2×D411yescharacteristic
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2×D411yescharacteristic
231C22×C4×C11C2×D411yescharacteristic
232C22×C4×C11C2411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C22×C4×C11C2411yescharacteristic
235C2×C22⋊D11—22no—
236C2×C22⋊D11—22no—
237C2×C22⋊D11—22no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—48no—
241C22×Dic11—22no—
242#4339—24no—
243#4339—24no—
244#4339—44no—
245#4339—48no—
246#4339—48no—
247#4339—48no—
248#4339—44no—
249#4339—48no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—22no—
253C2×D44—21no—
254C2×D44—21no—
255C2×D44—22no—
256C2×D44—22no—
257C2×D44—24no—
258C2×D44—24no—
259C2×D44—44no—
260C2×D44—44no—
261C2×D44C2414yes—
262C2×D44C2412yes—
263C2×C4×D11—22no—
264C2×C4×D11—22no—
265C2×C4×D11—22no—
266C2×C4×D11—24no—
267C2×C4×D11—24no—
268C2×C4×D11—48no—
269C2×Dic22—21no—
270C2×Dic22—21no—
271C2×Dic22—22no—
272C2×Dic22—22no—
273C2×Dic22—44no—
274C2×Dic22C2412yes—
275C11×M16—28no—
276C11×M16—44no—
277C2×C8×C11—44no—
278C2×C8×C11C2418yes—
279C42×C11C2×D411yescharacteristic
280C42×C11C2×D411yescharacteristic
281C42×C11C2×D411yescharacteristic
282C42×C11C2×D411yescharacteristic
283C42×C11C2×D411yescharacteristic
284C42×C11C2×D411yescharacteristic
285C42×C11C2×D411yescharacteristic
286C42×C11C2×D411yescharacteristic
287C42×C11C2×D411yescharacteristic
288C42×C11C2×D411yescharacteristic
289C42×C11C2×D411yescharacteristic
290C42×C11C2×D411yescharacteristic
291C42×C11C2411yescharacteristic
292C42×C11C2411yescharacteristic
293C42×C11C2411yescharacteristic
294C42×C11C2411yescharacteristic
295C22⋊Dic11—22no—
296C22⋊Dic11—22no—
297C22⋊Dic11—22no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—22no—
301(C2×D11)⋊C4—22no—
302(C2×D11)⋊C4—22no—
303(C2×D11)⋊C4—22no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308C4⋊Dic11—21no—
309C4⋊Dic11—21no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11—22no—
313C4⋊Dic11—22no—
314C4⋊Dic11—22no—
315C4⋊Dic11C2414yes—
316C4⋊Dic11C2412yes—
317C4⋊Dic11C2412yes—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—22no—
322Dic11⋊C4—22no—
323Dic11⋊C4—22no—
324C4×Dic11—22no—
325C4×Dic11—22no—
326C4×Dic11—22no—
327D88—48no—
328#4314—48no—
329#3444—111no—
330C2×#532—111no—
331#3254—112no—
332#3253—112no—
333#3251—114no—
334#3247—114no—
335#3246—112no—
336#3245—112no—
337#3079—112no—
338#3077—112no—
339#3055—114no—
340#3038—112no—
341#3036—112no—
342C2×#423D1111yescharacteristic, complemented
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—41no—
346C23×C11C22×D411yescharacteristic
347C23×C11C22×D411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C22×D11—22no—
350C22×D11—24no—
351C22×D11—44no—
352C22×D11—44no—
353C22×D11—44no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11AGL(1,ℤ/8)14yescomplemented
373C2×C4×C11C22×D411yescharacteristic
374C2×C4×C11C22×D411yescharacteristic
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11H(5,𝔽2)12yes—
385C2×C4×C112−1+412yes—
386C2×C4×C11C2511yescharacteristic
387C22⋊D11—48no—
388C22⋊D11—44no—
389C22⋊D11—44no—
390C22⋊D11—48no—
391C22⋊D11—44no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—24no—
396C2×Dic11—44no—
397D44—24no—
398D44—22no—
399D44—24no—
400D44—22no—
401D44—44no—
402D44—44no—
403D44—42no—
404D44—44no—
405D44—44no—
406D44—42no—
407D44—44no—
408C4×D11—48no—
409C4×D11—44no—
410C4×D11—48no—
411C4×D11—44no—
412C4×D11—44no—
413Dic22—22no—
414Dic22—22no—
415Dic22—44no—
416Dic22—42no—
417Dic22—44no—
418Dic22—42no—
419C8×C11—28no—
420C22×#41—221no—
421C2×AGL(1,ℤ/8)—114no—
422C22×M16C2×D1112yes—
423#533—111no—
424#533—111no—
425#533—111no—
426#532—112no—
427#532—112no—
428#532—112no—
429#532—112no—
430#532—111no—
431#532—111no—
432#532—111no—
433#532—221no—
434#532—221no—
435#532—221no—
436#532—221no—
437C2×C4⋊Q8—111no—
438C2×#127—111no—
439#529—112no—
440#529—112no—
441#529—221no—
442#529—221no—
443#529—221no—
444#529—221no—
445C2×#124—221no—
446#525—112no—
447#525—221no—
448#525—221no—
449C2×#121—112no—
450C2×#121—221no—
451C4×#41—112no—
452C4×#41—221no—
453C4×#41—221no—
454C2×C4×D4—112no—
455C2×C4×D4—221no—
456C22×C42C2×D1111yescharacteristic
457#478—118no—
458#477—114no—
459#476—114no—
460#476—114no—
461#475—114no—
462#474—114no—
463#474—114no—
464#469—118no—
465#468—118no—
466#466—118no—
467#465—118no—
468#463—118no—
469#461—114no—
470#460—114no—
471#460—114no—
472#459—114no—
473#459—114no—
474#459—114no—
475#428—114no—
476#423C2×D1112yes—
477#423C2×D1112yes—
478#423C2×D1112yescomplemented
479#423C2×D1112yescomplemented
480C2×C4⋊C8C2×D1112yescomplemented
481C2×C4⋊C8C2×D1112yescomplemented
482#418—114no—
483#417—114no—
484C22×C11—21no—
485C22×C11—21no—
486C22×C11—21no—
487C22×C11—21no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—21no—
491C22×C11—44no—
492C22×C11#53712yes—
493C22×C11C2×AGL(1,ℤ/8)12yes—
494C22×C11C23×D411yescharacteristic
495C2×D11—44no—
496C2×D11—42no—
497C2×D11—44no—
498C2×D11—42no—
499C2×D11—44no—
500C2×D11—42no—
501C2×D11—88no—
502C4×C11—21no—
503C4×C11—21no—
504C4×C11—21no—
505C4×C11—21no—
506C4×C11—21no—
507C4×C11—21no—
508C4×C11—21no—
509C4×C11#53712yes—
510C4×C11C2×AGL(1,ℤ/8)12yes—
511C4×C11C2×AGL(1,ℤ/8)12yes—
512C4×C11#57512yes—
513C4×C11C2×H(5,𝔽2)11yescharacteristic
514C4×C11C2×2−1+411yescharacteristic
515Dic11—42no—
516Dic11—44no—
517Dic11—42no—
518Dic11—42no—
519C2×#41—112no—
520C2×#41—221no—
521C2×#41—221no—
522C2×#41—222no—
523C2×#41—222no—
524C2×#41—222no—
525C2×#41—222no—
526C2×#41—448no—
527C22×Q8—221no—
528C22×D4—112no—
529C22×D4—222no—
530C22×D4—221no—
531C22×D4—221no—
532C23×C4—222no—
533C23×C4D4411yescharacteristic
534C23×C4D4411yescharacteristic
535C23×C4C22×D1111yescharacteristic
536AGL(1,ℤ/8)—448no—
537C2×SD16—118no—
538C2×D8—118no—
539C2×M16—44no—
540C2×M16C22×D1114yes—
541C2×M16C22×D1114yes—
542C22×C8C22×D1114yes—
543C4⋊Q8—112no—
544C4⋊Q8—112no—
545C4⋊Q8—111no—
546C4⋊Q8—111no—
547C4⋊Q8—111no—
548C4⋊Q8—221no—
549C4⋊Q8—221no—
550#127—112no—
551#127—112no—
552#127—111no—
553#127—221no—
554#127—221no—
555#126—222no—
556#126—222no—
557#125—112no—
558#125—221no—
559#125—221no—
560#124—112no—
561#124—222no—
562#124—222no—
563#124—222no—
564#124—222no—
565#124—221no—
566#124—221no—
567#123—222no—
568#123—222no—
569#123—222no—
570C22⋊Q8—112no—
571C22⋊Q8—112no—
572C22⋊Q8—221no—
573C22⋊Q8—221no—
574C22⋊Q8—221no—
575C22⋊Q8—221no—
576#121—114no—
577#121—114no—
578#121—112no—
579#121—112no—
580#121—222no—
581#121—222no—
582#121—222no—
583#121—222no—
584#121—222no—
585#121—222no—
586#121—221no—
587#121—221no—
588#121—221no—
589#121—221no—
590#120—222no—
591C4×Q8—112no—
592C4×Q8—112no—
593C4×Q8—221no—
594C4×Q8—221no—
595C4×Q8—221no—
596C4×Q8—221no—
597C4×D4—114no—
598C4×D4—114no—
599C4×D4—112no—
600C4×D4—112no—
601C4×D4—222no—
602C4×D4—222no—
603C4×D4—222no—
604C4×D4—222no—
605C4×D4—222no—
606C4×D4—222no—
607C4×D4—222no—
608C4×D4—222no—
609C4×D4—222no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—221no—
614C4×D4—221no—
615C4×D4—221no—
616C4×D4—221no—
617#117—112no—
618#117—221no—
619#117—221no—
620#117—222no—
621#117—222no—
622#117—222no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—221no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C42—222no—
628C2×C42D4411yescharacteristic
629C2×C42D4411yescharacteristic
630C2×C42D4411yescharacteristic
631C2×C42D4411yescharacteristic
632C2×C42D4411yescharacteristic
633C2×C42D4411yescharacteristic
634C2×C42C22×D1111yescharacteristic
635C2×C42C22×D1111yescharacteristic
636C2×C42C22×D1111yescharacteristic
637C2×C42C22×D1111yescharacteristic
638C2×C42C22×D1111yescharacteristic
639C2×C42C22×D1111yescharacteristic
640#107—118no—
641#106—118no—
642C4⋊C8C22×D1114yes—
643C4⋊C8C22×D1114yes—
644C4⋊C8C22×D1114yes—
645C4⋊C8C22×D1114yes—
646#103—118no—
647#102—118no—
648#102—118no—
649#102—118no—
650C2×C11—22no—
651C2×C11—22no—
652C2×C11—41no—
653C2×C11C2×#53711yescharacteristic
654C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
655C2×C11C2×#57511yescharacteristic
656D11—82no—
657D11—84no—
658C24—222no—
659C24C2×D4411yescharacteristic
660#41—224no—
661#41—224no—
662#41—448no—
663#41—448no—
664#41—448no—
665#41—444no—
666#41—448no—
667#41—444no—
668C2×Q8—112no—
669C2×Q8—221no—
670C2×Q8—221no—
671C2×Q8—222no—
672C2×Q8—222no—
673C2×Q8—444no—
674C2×D4—112no—
675C2×D4—114no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—222no—
679C2×D4—224no—
680C2×D4—224no—
681C2×D4—221no—
682C2×D4—221no—
683C2×D4—222no—
684C2×D4—222no—
685C2×D4—222no—
686C2×D4—222no—
687C2×D4—222no—
688C2×D4—224no—
689C2×D4—224no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—448no—
693C22×C4—24no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—42no—
697C22×C4—222no—
698C22×C4—222no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—224no—
702C22×C4—224no—
703C22×C4—448no—
704C22×C4C2×D4411yescharacteristic
705C22×C4C2×D4411yescharacteristic
706C22×C4C2×D4411yescharacteristic
707C22×C4C2×D4411yescharacteristic
708C22×C4C2×D4411yescharacteristic
709C22×C4C2×D4411yescharacteristic
710C22×C4C2×D4411yescharacteristic
711C22×C4C2×D4411yescharacteristic
712C22×C4C2×D4411yescharacteristic
713C22×C4C2×D4411yescharacteristic
714C22×C4C2×D4411yescharacteristic
715C22×C4C2×D4411yescharacteristic
716C22×C4C2×D4411yescharacteristic
717C22×C4C2×D4411yescharacteristic
718C22×C4C2×D4411yescharacteristic
719C22×C4C23×D1111yescharacteristic
720C22×C4C23×D1111yescharacteristic
721C22×C4C23×D1111yescharacteristic
722SD16—448no—
723D8—448no—
724M16—28no—
725M16—44no—
726C2×C8—44no—
727C2×C8C23×D1118yes—
728C4⋊C4—112no—
729C4⋊C4—112no—
730C4⋊C4—114no—
731C4⋊C4—222no—
732C4⋊C4—222no—
733C4⋊C4—222no—
734C4⋊C4—222no—
735C4⋊C4—222no—
736C4⋊C4—221no—
737C4⋊C4—221no—
738C4⋊C4—221no—
739C4⋊C4—221no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—222no—
743C4⋊C4—222no—
744C22⋊C4—222no—
745C22⋊C4—222no—
746C22⋊C4—222no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—222no—
752C22⋊C4—222no—
753C22⋊C4—222no—
754C22⋊C4—222no—
755C22⋊C4—222no—
756C22⋊C4—222no—
757C42—222no—
758C42—222no—
759C42—222no—
760C42C2×D4411yescharacteristic
761C42C2×D4411yescharacteristic
762C42C2×D4411yescharacteristic
763C42C2×D4411yescharacteristic
764C42C2×D4411yescharacteristic
765C42C2×D4411yescharacteristic
766C42C2×D4411yescharacteristic
767C42C2×D4411yescharacteristic
768C42C2×D4411yescharacteristic
769C42C2×D4411yescharacteristic
770C42C2×D4411yescharacteristic
771C42C2×D4411yescharacteristic
772C42C23×D1111yescharacteristic
773C42C23×D1111yescharacteristic
774C42C23×D1111yescharacteristic
775C42C23×D1111yescharacteristic
776C11#6091611yescharacteristic, complemented, Sylow
777C23—22no—
778C23—22no—
779C23—41no—
780C23—222no—
781C23—224no—
782C23—444no—
783C23—444no—
784C23—444no—
785C23C22×D4411yescharacteristic
786C23C22×D4411yescharacteristic
787C23C22×D4411yescharacteristic
788Q8—222no—
789Q8—222no—
790Q8—444no—
791Q8—442no—
792Q8—444no—
793Q8—442no—
794D4—222no—
795D4—224no—
796D4—224no—
797D4—222no—
798D4—444no—
799D4—444no—
800D4—442no—
801D4—448no—
802D4—444no—
803D4—448no—
804D4—444no—
805D4—444no—
806D4—444no—
807D4—442no—
808D4—444no—
809D4—444no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—222no—
829C2×C4—222no—
830C2×C4—222no—
831C2×C4—224no—
832C2×C4—448no—
833C2×C4—444no—
834C2×C4—448no—
835C2×C4—444no—
836C2×C4—444no—
837C2×C4—444no—
838C2×C4#6696114yescomplemented
839C2×C4C22×D4411yescharacteristic
840C2×C4C22×D4411yescharacteristic
841C2×C4C22×D4411yescharacteristic
842C2×C4C22×D4411yescharacteristic
843C2×C4C22×D4411yescharacteristic
844C2×C4C22×D4411yescharacteristic
845C2×C4C22×D4411yescharacteristic
846C2×C4C22×D4411yescharacteristic
847C2×C4C22×D4411yescharacteristic
848C2×C4C22×D4411yescharacteristic
849C2×C4C22×D4411yescharacteristic
850C2×C4#6703712yes—
851C2×C4#6704012yes—
852C2×C4C24×D1111yescharacteristic
853C8—28no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—44no—
862C22—442no—
863C22—444no—
864C22—444no—
865C22—442no—
866C22—442no—
867C22—444no—
868C22—888no—
869C22#1062304112yes—
870C22C2×#6696112yes—
871C22C23×D4411yescharacteristic
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—442no—
880C4—444no—
881C4—442no—
882C4—442no—
883C4#1062304112yes—
884C4C2×#6696112yes—
885C4C2×#6696112yes—
886C4#1062327912yes—
887C4C2×#6703711yescharacteristic
888C4C2×#6704011yescharacteristic
889C2—22no—
890C2—22no—
891C2—41no—
892C2—884no—
893C2—882no—
894C2C2×#1062304111yescharacteristic
895C2C22×#6696111yescharacteristic
896C2C2×#1062327911yescharacteristic
subgroupG/H
centerC22C23×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#423C2
socleC22×C11C23×D4
hypercenterC2×#423D11
hypocenterC11#60916
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
1. #13081912C2semidirect
2. C2×#10623008C2semidirect
3. #13080004C2semidirect
4. #13079997C2semidirect
5. #13079979C2semidirect
6. #13079943C2semidirect
7. #13079933C2semidirect
8. #13079926C2semidirect
9. #13078432C2semidirect
10. #13078415C2semidirect
11. #13078235C2semidirect
12. #13078097C2semidirect
13. #13078082C2semidirect
14. C2×C11×#423C2semidirect
28. #10623010C22semidirect
29. #10623010C22semidirect
39. #10623008C22semidirect
40. #10623008C22semidirect
49. #10623001C22semidirect
50. #10623001C22semidirect
54. C11×#423C22semidirect
55. C11×#423C22semidirect
56. C2×C11×C4⋊C8C22semidirect
57. C2×C11×C4⋊C8C22semidirect
58. #10622748C22semidirect
59. #10622747C22semidirect
63. #10622728C22semidirect
64. #10622727C22semidirect
65. #10622464C22semidirect
66. #10622463C22semidirect
67. #10622461C22semidirect
68. #10622461C22semidirect
69. #10622460C22semidirect
70. #10622459C22semidirect
71. #10622459C22semidirect
72. #10622457C22semidirect
73. #10622456C22semidirect
74. #10622456C22semidirect
75. #10622456C22semidirect
76. #10622455C22semidirect
77. #10622455C22semidirect
78. #10622454C22semidirect
342. C2×#423D11semidirect
372. C2×C4×C11AGL(1,ℤ/8)semidirect
478. #423C2×D11semidirect
479. #423C2×D11semidirect
480. C2×C4⋊C8C2×D11semidirect
481. C2×C4⋊C8C2×D11semidirect
776. C11#60916semidirect
838. C2×C4#66961semidirect

Maximal subgroups

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

subgroupindex
#130819122
C2×#106230082
#130800042
#130799972
#130799792
#130799432
#130799332
#130799262
#130784322
#130784152
#130782352
#130780972
#130780822
C2×C11×#4232
#6091611