Finite Group Databasebeta

← #15634347

Subgroups — #15634347

Order 2816.

2010 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082194C211yesmaximal, characteristic, complemented
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13081542C212yesmaximal, complemented
4#13081534C214yesmaximal, complemented
5#13081520C212yesmaximal, complemented
6#13081512C214yesmaximal, complemented
7#13081473C212yesmaximal, complemented
8#13081468C212yesmaximal, complemented
9#13079160C212yesmaximal, complemented
10#13078429C212yesmaximal, complemented
11#13078425C211yesmaximal, characteristic, complemented
12#13078412C212yesmaximal, complemented
13#13078409C211yesmaximal, characteristic, complemented
14M16×Dic22C211yesmaximal, characteristic, complemented
15C4×#66961C211yesmaximal, characteristic
16#13077423C212yesmaximal
17C11×#3165C211yesmaximal, characteristic, complemented
18C22×Q8×D11—21no—
19C11×#533C2211yescharacteristic
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×#66999—21no—
22C2×#66961C2211yescharacteristic
23#10623261C2211yescharacteristic, complemented
24#10623258—21no—
25#10623258—22no—
26#10623258—21no—
27#10623258C2212yes—
28#10623258C2214yes—
29#10623258C2212yes—
30#10623258C2211yescharacteristic, complemented
31#10623253C2211yescharacteristic, complemented
32#10623252C2211yescharacteristic, complemented
33#10623221C2212yescomplemented
34#10623216C2212yescomplemented
35#10623167—22no—
36#10623166—21no—
37#10623163—21no—
38#10623109—22no—
39#10623109—21no—
40C4×Q8×D11—21no—
41#10623053C2212yes—
42#10623048C2212yes—
43C2×#66949—22no—
44C2×#66946C2212yes—
45C2×#66941C2212yes—
46C4×#4339C2211yescharacteristic
47C2×C4×D44C2211yescharacteristic
48C2×C4×Dic22C2211yescharacteristic
49C11×#501C2214yescomplemented
50C11×#500C2212yescomplemented
51C11×#498C2212yescomplemented
52C11×#428C2212yes—
53C11×#428C2212yes—
54C4×C11×M16C2211yescharacteristic
55#10622746C2211yescharacteristic
56#10622744C2211yescharacteristic
57#10622734C2211yescharacteristic
58#10622731C2212yes—
59M16×Dic11C2212yes—
60#10622707C2212yescomplemented
61#10622704C2212yescomplemented
62#10622700C2212yes—
63#10622700C2212yescomplemented
64#10622697C2212yes—
65#10622697C2212yescomplemented
66#10622679C2214yes—
67#10622614C2212yes—
68#10622608C2212yes—
69#10622579C2212yes—
70#10622577C2212yes—
71#10622537C2211yescharacteristic
72#10622504C2214yes—
73#10622503C2214yes—
74#10622503C2214yescomplemented
75#10622502C2214yes—
76#10622489C2214yescomplemented
77#10622488C2214yescomplemented
78#10622487C2214yescomplemented
79#10622485C2214yes—
80#10622484C2214yes—
81#10622483C2214yes—
82#10622483C2214yescomplemented
83#10622482C2214yes—
84#10622469C2214yescomplemented
85#10622468C2214yescomplemented
86#10622467C2214yescomplemented
87#10622465C2214yes—
88#10622324C2212yes—
89#10622323C2212yes—
90#10622314C2214yescomplemented
91C4×D88C2212yes—
92C4×#4314C2212yes—
93#10622292C2212yescomplemented
94C8×Dic22C2212yescomplemented
95C22×Q8×C11—21no—
96C2×Q8×D11—24no—
97C2×Q8×D11—22no—
98C2×Q8×D11—22no—
99C2×Q8×D11—21no—
100C2×Q8×D11—48no—
101C2×#4339C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—22no—
105C22×Dic22—22no—
106C22×Dic22D411yescharacteristic
107C2×C11×M16C2311yescharacteristic
108C2×C11×M16C2311yescharacteristic
109C11×C4⋊Q8—21no—
110C11×C4⋊Q8—21no—
111C11×C4⋊Q8C2311yescharacteristic
112C11×C4⋊Q8C2312yes—
113C11×C4⋊Q8C2311yescharacteristic
114C11×C4⋊Q8C2312yes—
115C11×#125C2312yes—
116C11×C22⋊Q8—21no—
117C11×C22⋊Q8—21no—
118C4×Q8×C11—21no—
119C4×Q8×C11—21no—
120C11×#117C2312yes—
121C2×C11×C4⋊C4—21no—
122C2×C11×C4⋊C4C2312yes—
123C2×C42×C11C2311yescharacteristic
124#66999—22no—
125#66999—24no—
126#66999—22no—
127#66999—21no—
128#66999—22no—
129Q8×Dic11—21no—
130#66997—21no—
131#66997—22no—
132C4×C22⋊D11—21no—
133C4×C22⋊D11—21no—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—22no—
136#66979C2311yescharacteristic
137C2×C4⋊Dic11D411yescharacteristic
138C2×C4⋊Dic11C2311yescharacteristic
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4D412yes—
141C2×C4×Dic11C2312yes—
142C2×#4318C2312yes—
143#66961Q818yescomplemented
144C2×D88C2312yes—
145C2×#4314C2312yes—
146#66950—21no—
147#66950—22no—
148#66949—22no—
149#66949—24no—
150#66949—24no—
151#66949—24no—
152#66949—24no—
153#66949—22no—
154#66949—22no—
155#66946—22no—
156#66946—22no—
157#66946C2314yes—
158#66946C2312yes—
159#66946C2314yes—
160#66946C2312yes—
161C4⋊C4×D11—21no—
162C4⋊C4×D11—22no—
163#66943C2312yes—
164#66943C2312yes—
165#66942—22no—
166#66942—22no—
167#66942—22no—
168#66941—22no—
169#66941—21no—
170#66941—22no—
171#66941—22no—
172#66941C2314yes—
173#66941C2312yes—
174#66941C2314yes—
175#66941C2312yes—
176#66940—21no—
177#66940—22no—
178#66940C2312yes—
179#66940C2312yes—
180(C22⋊D11)⋊C4—22no—
181(C22⋊D11)⋊C4—22no—
182#66931—22no—
183#66931—22no—
184C4×D44—21no—
185C4×D44—21no—
186C4×D44C2312yes—
187C4×D44C2312yes—
188C4×D44C2311yescharacteristic
189C4×D44C2311yescharacteristic
190#66925—21no—
191#66925—22no—
192C42×D11—21no—
193C42×D11—22no—
194C4×Dic22—22no—
195C4×Dic22—22no—
196C4×Dic22D411yescharacteristic
197C4×Dic22D412yes—
198C4×Dic22D411yescharacteristic
199C4×Dic22C2311yescharacteristic
200C4×Dic22C2311yescharacteristic
201C4×Dic22C2311yescharacteristic
202C4×Dic22C2311yescharacteristic
203C4×Dic22C2312yes—
204C11×#107C2314yes—
205C11×#107C2314yes—
206C11×#106C2314yes—
207C11×#106C2314yes—
208C11×#97C2312yes—
209C4×C8×C11C2312yes—
210#66885C2312yes—
211#66885C2312yes—
212#66885C2312yes—
213#66882C2312yes—
214#66881C2312yes—
215#66880C2312yes—
216#66879C2314yes—
217Dic11⋊C8C2314yes—
218Dic11⋊C8C2314yes—
219C8×Dic11C2314yes—
220#66874C2314yes—
221#66873C2314yes—
222#66873C2314yes—
223#66873C2314yes—
224#66872C2314yes—
225#66872C2314yes—
226#66871C2314yes—
227#66871C2314yes—
228C4⋊(C11⋊C8)C2312yes—
229C4⋊(C11⋊C8)C2312yes—
230Q8×AGL(1,ℤ/8)—111nomaximal, Sylow
231C23×D11—21no—
232C2×Q8×C11—21no—
233C2×Q8×C11—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—21no—
236C2×Q8×C11—44no—
237C22×C4×C11—22no—
238C22×C4×C11C2×D411yescharacteristic
239C22×C4×C11C2×D411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C2×C22⋊D11—21no—
242C22×Dic11—21no—
243C22×Dic11C2×D412yes—
244C22×Dic11C2×D412yes—
245Q8×D11—416no—
246Q8×D11—48no—
247Q8×D11—44no—
248Q8×D11—48no—
249#4339—22no—
250#4339C2×Q814yescomplemented
251C2×D44—21no—
252C2×D44—22no—
253C2×D44C2×Q814yescomplemented
254C2×D44C2412yes—
255C2×D44C2411yescharacteristic
256C2×C4×D11—22no—
257C2×C4×D11—24no—
258C2×C4×D11—24no—
259C2×C4×D11—22no—
260C2×C4×D11—21no—
261C2×C4×D11—21no—
262C2×C4×D11—22no—
263C2×C4×D11—22no—
264C2×C4×D11—21no—
265C2×C4×D11—44no—
266C2×C4×D11—48no—
267C2×Dic22—24no—
268C2×Dic22—22no—
269C2×Dic22—24no—
270C2×Dic22—24no—
271C2×Dic22—22no—
272C2×Dic22—48no—
273C2×Dic22C2×D412yes—
274C2×Dic22C2×D411yescharacteristic
275C2×Dic22C2×D411yescharacteristic
276C2×Dic22C2411yescharacteristic
277C11×M16—22no—
278C11×M16C2×Q814yescomplemented
279C2×C8×C11C2412yes—
280C2×C8×C11C2412yes—
281C11×C4⋊C4—21no—
282C11×C4⋊C4—22no—
283C11×C4⋊C4—22no—
284C11×C4⋊C4—22no—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—22no—
287C11×C4⋊C4—22no—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2414yes—
290C11×C4⋊C4C2412yes—
291C11×C22⋊C4—22no—
292C42×C11—22no—
293C42×C11C2×D411yescharacteristic
294C42×C11C2×D411yescharacteristic
295C42×C11C2411yescharacteristic
296C42×C11C2411yescharacteristic
297C22⋊Dic11—21no—
298(C2×D11)⋊C4—22no—
299(C2×D11)⋊C4—22no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—21no—
303(C2×D11)⋊C4—21no—
304(C2×D11)⋊C4—22no—
305(C2×D11)⋊C4—22no—
306C4⋊Dic11—22no—
307C4⋊Dic11—22no—
308C4⋊Dic11—21no—
309C4⋊Dic11C2×D411yescharacteristic
310C4⋊Dic11C2×D412yes—
311C4⋊Dic11C2×D411yescharacteristic
312C4⋊Dic11C2411yescharacteristic
313C4⋊Dic11C2412yes—
314C4⋊Dic11C2411yescharacteristic
315Dic11⋊C4—22no—
316Dic11⋊C4—22no—
317Dic11⋊C4—22no—
318Dic11⋊C4—22no—
319Dic11⋊C4—22no—
320Dic11⋊C4—22no—
321Dic11⋊C4—24no—
322Dic11⋊C4—24no—
323Dic11⋊C4—21no—
324Dic11⋊C4—21no—
325Dic11⋊C4C2×D412yes—
326Dic11⋊C4C2×D412yes—
327Dic11⋊C4C2×D412yes—
328Dic11⋊C4C2×D412yes—
329C4×Dic11—22no—
330C4×Dic11—22no—
331C4×Dic11—21no—
332C4×Dic11—21no—
333C4×Dic11—21no—
334C4×Dic11C2×D412yes—
335C4×Dic11C2×D412yes—
336C4×Dic11C2412yes—
337C4×Dic11C2412yes—
338#4318—24no—
339C2×C11⋊C8C2414yes—
340D88C2×Q818yescomplemented
341#4314C2×Q818yescomplemented
342Q8×#41—111no—
343C2×D4×Q8—111no—
344#3386—114no—
345#3386—112no—
346#3384—114no—
347#3384—112no—
348Q8×SD16—112no—
349Q8×D8—112no—
350#3165—112no—
351#3165D1111yescharacteristic, complemented
352#3079—112no—
353#3079—111no—
354#3077—112no—
355#3077—111no—
356Q8×M16—111no—
357C4×AGL(1,ℤ/8)—112no—
358C4×AGL(1,ℤ/8)—111no—
359C23×C11C22×D411yescharacteristic
360C22×D11—24no—
361C22×D11—21no—
362C22×D11—22no—
363C22×D11—42no—
364C22×D11—42no—
365Q8×C11—44no—
366Q8×C11—44no—
367Q8×C11—42no—
368Q8×C11—81no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—24no—
373C2×C4×C11—41no—
374C2×C4×C11—44no—
375C2×C4×C11C22×D411yescharacteristic
376C2×C4×C11C22×D411yescharacteristic
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×Q812yes—
381C2×C4×C112−1+412yes—
382C2×C4×C11C2511yescharacteristic
383C22⋊D11—24no—
384C2×Dic11—21no—
385C2×Dic11—24no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—22no—
389C2×Dic11—42no—
390C2×Dic11—42no—
391C2×Dic11C22×D412yes—
392C2×Dic11C22×D412yes—
393C2×Dic11C22×D412yes—
394C2×Dic11C22×D412yes—
395D44—24no—
396D44—22no—
397D44—21no—
398D44C22×Q814yes—
399D44C22×Q812yescomplemented
400C4×D11—24no—
401C4×D11—48no—
402C4×D11—44no—
403C4×D11—44no—
404C4×D11—42no—
405C4×D11—48no—
406C4×D11—44no—
407C4×D11—82no—
408C4×D11—81no—
409Dic22—22no—
410Dic22—21no—
411Dic22—24no—
412Dic22—48no—
413Dic22—48no—
414Dic22—44no—
415Dic22—82no—
416Dic22AGL(1,ℤ/8)14yescomplemented
417Dic22C22×Q812yescomplemented
418C8×C11—22no—
419C8×C11C22×Q814yescomplemented
420C11⋊C8—24no—
421C23×Q8—221no—
422C2×AGL(1,ℤ/8)—111no—
423Q82—111no—
424#557—111no—
425#557—112no—
426#554—111no—
427#554—112no—
428#554—221no—
429#554—222no—
430D4×Q8—112no—
431D4×Q8—114no—
432D4×Q8—112no—
433D4×Q8—111no—
434D4×Q8—221no—
435D4×Q8—222no—
436D4×Q8—221no—
437D4×Q8—221no—
438#533—112no—
439#533—222no—
440#533—221no—
441#533C2×D1111yescharacteristic
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8C2×D1111yescharacteristic
444C2×C22⋊Q8—222no—
445C2×C22⋊Q8—221no—
446C4×#41—112no—
447C4×#41—111no—
448C2×C4×Q8—111no—
449C2×C4×Q8—221no—
450C2×C4×D4—112no—
451C2×C4×D4—111no—
452#501—114no—
453#501—114no—
454#501C2×D1114yescomplemented
455#500—114no—
456#500C2×D1112yescomplemented
457#498—114no—
458#498C2×D1112yescomplemented
459#478—114no—
460#478—114no—
461#478—114no—
462#477—112no—
463#477—114no—
464#476—112no—
465#476—112no—
466#476—114no—
467#476—114no—
468#475—112no—
469#475—114no—
470#474—112no—
471#474—112no—
472#474—114no—
473#474—114no—
474#446—114no—
475#446—112no—
476C8×Q8—112no—
477#442—114no—
478#442—112no—
479#440—114no—
480#440—112no—
481C4×SD16—114no—
482C4×SD16—112no—
483C4×D8—114no—
484C4×D8—112no—
485#428—111no—
486#428—112no—
487#428—112no—
488#428C2×D1112yes—
489#428C2×D1112yes—
490#423—112no—
491#423—111no—
492#418—111no—
493#418—112no—
494#417—111no—
495#417—112no—
496C4×M16—112no—
497C4×M16C2×D1111yescharacteristic
498C22×C11—21no—
499C22×C11—21no—
500C22×C11D4×Q812yes—
501C22×C11C23×D411yescharacteristic
502C2×D11—24no—
503C2×D11—22no—
504C2×D11—48no—
505C2×D11—42no—
506C2×D11—41no—
507C2×D11—42no—
508C2×D11—41no—
509C4×C11—21no—
510C4×C11—21no—
511C4×C11—21no—
512C4×C11—42no—
513C4×C11—44no—
514C4×C11—42no—
515C4×C11D4×Q812yes—
516C4×C11C2×AGL(1,ℤ/8)12yes—
517C4×C11C23×Q811yescharacteristic
518C4×C11C2×2−1+411yescharacteristic
519Dic11—22no—
520Dic11—22no—
521Dic11—22no—
522Dic11—22no—
523Dic11—41no—
524Dic11—42no—
525Dic11—41no—
526Dic11C2×AGL(1,ℤ/8)14yes—
527C2×#41—111no—
528C22×Q8—21no—
529C22×Q8—111no—
530C22×Q8—222no—
531C22×Q8—221no—
532C22×Q8—222no—
533C22×Q8—224no—
534C22×Q8—222no—
535C22×Q8—448no—
536C22×D4—111no—
537C23×C4—222no—
538C23×C4—221no—
539AGL(1,ℤ/8)—118no—
540C2×SD16—112no—
541C2×D8—112no—
542C2×M16—112no—
543C2×M16C22×D1111yescharacteristic
544C2×M16C22×D1111yescharacteristic
545C4⋊Q8—21no—
546C4⋊Q8—21no—
547C4⋊Q8—114no—
548C4⋊Q8—114no—
549C4⋊Q8—112no—
550C4⋊Q8—112no—
551C4⋊Q8—222no—
552C4⋊Q8—222no—
553C4⋊Q8—221no—
554C4⋊Q8—222no—
555C4⋊Q8—222no—
556C4⋊Q8—221no—
557C4⋊Q8C22×D1112yes—
558C4⋊Q8C22×D1112yes—
559C4⋊Q8C22×D1111yescharacteristic
560C4⋊Q8C22×D1111yescharacteristic
561#125—112no—
562#125—112no—
563#125—222no—
564#125—222no—
565#125—222no—
566#125C22×D1112yes—
567C22⋊Q8—21no—
568C22⋊Q8—21no—
569C22⋊Q8—222no—
570C22⋊Q8—222no—
571C22⋊Q8—224no—
572C22⋊Q8—224no—
573C22⋊Q8—224no—
574C22⋊Q8—224no—
575C22⋊Q8—222no—
576C22⋊Q8—222no—
577C22⋊Q8—222no—
578C22⋊Q8—222no—
579C22⋊Q8—221no—
580C22⋊Q8—222no—
581C22⋊Q8—224no—
582C22⋊Q8—222no—
583C22⋊Q8—221no—
584C22⋊Q8—222no—
585C4×Q8—21no—
586C4×Q8—21no—
587C4×Q8—111no—
588C4×Q8—112no—
589C4×Q8—111no—
590C4×Q8—111no—
591C4×Q8—112no—
592C4×Q8—111no—
593C4×Q8—112no—
594C4×Q8—112no—
595C4×Q8—111no—
596C4×Q8—111no—
597C4×Q8—222no—
598C4×Q8—222no—
599C4×Q8—222no—
600C4×Q8—221no—
601C4×Q8—221no—
602C4×D4—114no—
603C4×D4—114no—
604C4×D4—112no—
605C4×D4—112no—
606C4×D4—112no—
607C4×D4—112no—
608C4×D4—111no—
609C4×D4—111no—
610C4×D4—222no—
611C4×D4—222no—
612C4×D4—222no—
613C4×D4—222no—
614C4×D4—221no—
615C4×D4—221no—
616C4×D4—221no—
617C4×D4—221no—
618#117—111no—
619#117—222no—
620#117—221no—
621#117C22×D1112yes—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—222no—
627C2×C4⋊C4—221no—
628C2×C4⋊C4—222no—
629C2×C4⋊C4C22×D1112yes—
630C2×C22⋊C4—222no—
631C2×C22⋊C4—221no—
632C2×C42—112no—
633C2×C42—222no—
634C2×C42—221no—
635C2×C42C22×D1111yescharacteristic
636#107—112no—
637#107—114no—
638#107—114no—
639#107C22×D1114yes—
640#107C22×D1114yes—
641#106—112no—
642#106—114no—
643#106—114no—
644#106C22×D1114yes—
645#106C22×D1114yes—
646C4⋊C8—114no—
647C4⋊C8—114no—
648C4⋊C8—112no—
649C4⋊C8—112no—
650#103—112no—
651#103—114no—
652#102—112no—
653#102—112no—
654#102—112no—
655#102—114no—
656#102—114no—
657#102—114no—
658#97—114no—
659#97C22×D1112yes—
660C4×C8—114no—
661C4×C8C22×D1112yes—
662C2×C11—22no—
663C2×C11C2×D4×Q811yescharacteristic
664C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
665C2×C11#358611yescharacteristic
666D11—42no—
667D11—44no—
668C24—221no—
669#41—114no—
670#41—222no—
671C2×Q8—21no—
672C2×Q8—22no—
673C2×Q8—22no—
674C2×Q8—21no—
675C2×Q8—44no—
676C2×Q8—111no—
677C2×Q8—112no—
678C2×Q8—111no—
679C2×Q8—111no—
680C2×Q8—222no—
681C2×Q8—224no—
682C2×Q8—224no—
683C2×Q8—222no—
684C2×Q8—224no—
685C2×Q8—448no—
686C2×Q8—448no—
687C2×Q8—444no—
688C2×Q8—4416no—
689C2×Q8—448no—
690C2×D4—114no—
691C2×D4—111no—
692C2×D4—112no—
693C2×D4—221no—
694C2×D4—221no—
695C2×D4—222no—
696C22×C4—22no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—222no—
700C22×C4—224no—
701C22×C4—224no—
702C22×C4—222no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—222no—
707C22×C4—222no—
708C22×C4—221no—
709C22×C4—444no—
710C22×C4—448no—
711C22×C4D4×D1111yescharacteristic
712C22×C4D4×D1111yescharacteristic
713C22×C4C23×D1111yescharacteristic
714SD16—118no—
715D8—118no—
716M16—22no—
717M16—224no—
718M16Q8×D1114yescomplemented
719C2×C8—114no—
720C2×C8C23×D1112yes—
721C2×C8C23×D1112yes—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—21no—
726C4⋊C4—22no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—112no—
730C4⋊C4—111no—
731C4⋊C4—112no—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—112no—
735C4⋊C4—111no—
736C4⋊C4—111no—
737C4⋊C4—111no—
738C4⋊C4—112no—
739C4⋊C4—222no—
740C4⋊C4—222no—
741C4⋊C4—222no—
742C4⋊C4—224no—
743C4⋊C4—224no—
744C4⋊C4—222no—
745C4⋊C4—222no—
746C4⋊C4—222no—
747C4⋊C4—222no—
748C4⋊C4—222no—
749C4⋊C4—221no—
750C4⋊C4—221no—
751C4⋊C4—221no—
752C4⋊C4C23×D1112yes—
753C4⋊C4C23×D1112yes—
754C4⋊C4C23×D1114yes—
755C22⋊C4—22no—
756C22⋊C4—224no—
757C22⋊C4—224no—
758C22⋊C4—222no—
759C22⋊C4—222no—
760C22⋊C4—221no—
761C22⋊C4—222no—
762C22⋊C4—222no—
763C22⋊C4—221no—
764C22⋊C4—221no—
765C42—22no—
766C42—112no—
767C42—112no—
768C42—112no—
769C42—112no—
770C42—222no—
771C42—222no—
772C42—221no—
773C42—221no—
774C42—221no—
775C42D4×D1111yescharacteristic
776C42D4×D1111yescharacteristic
777C42C23×D1111yescharacteristic
778C42C23×D1111yescharacteristic
779C11Q8×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
780C23—224no—
781C23—221no—
782C23—222no—
783C23—442no—
784C23—442no—
785C23C2×D4×D1111yescharacteristic
786Q8—44no—
787Q8—44no—
788Q8—42no—
789Q8—81no—
790Q8—114no—
791Q8—112no—
792Q8—224no—
793Q8—222no—
794Q8—221no—
795Q8—448no—
796Q8—444no—
797Q8—448no—
798Q8—882no—
799D4—112no—
800D4—114no—
801D4—224no—
802D4—224no—
803D4—222no—
804D4—221no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—41no—
810C2×C4—44no—
811C2×C4—112no—
812C2×C4—112no—
813C2×C4—112no—
814C2×C4—112no—
815C2×C4—224no—
816C2×C4—221no—
817C2×C4—224no—
818C2×C4—221no—
819C2×C4—221no—
820C2×C4—222no—
821C2×C4—444no—
822C2×C4—448no—
823C2×C4—444no—
824C2×C4—448no—
825C2×C4—442no—
826C2×C4—442no—
827C2×C4—444no—
828C2×C4—442no—
829C2×C4—881no—
830C2×C4—882no—
831C2×C4C2×D4×D1111yescharacteristic
832C2×C4C2×D4×D1111yescharacteristic
833C2×C4C2×D4×D1111yescharacteristic
834C2×C4C2×D4×D1111yescharacteristic
835C2×C4C2×D4×D1111yescharacteristic
836C2×C4C2×Q8×D1112yes—
837C2×C4#6704012yes—
838C2×C4C24×D1111yescharacteristic
839C8—22no—
840C8—224no—
841C8C2×Q8×D1114yescomplemented
842C22—21no—
843C22—21no—
844C22—222no—
845C22—224no—
846C22—448no—
847C22—441no—
848C22—442no—
849C22—442no—
850C22—441no—
851C22#1062325812yes—
852C22C22×D4×D1111yescharacteristic
853C4—21no—
854C4—21no—
855C4—21no—
856C4—42no—
857C4—44no—
858C4—42no—
859C4—114no—
860C4—222no—
861C4—222no—
862C4—222no—
863C4—222no—
864C4—441no—
865C4—442no—
866C4—441no—
867C4#1062325812yes—
868C4D11×AGL(1,ℤ/8)12yes—
869C4C22×Q8×D1111yescharacteristic
870C4C2×#6704011yescharacteristic
871C2—22no—
872C2—444no—
873C2—442no—
874C2C2×#1062325811yescharacteristic
875C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
876C2#1308339911yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3165C2
socleC22×C11C23×D4
prime radicalC2×#66961C22
hypercenter#3165D11
hypocenterC11Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
1. #13082194C2semidirect
2. C2×#10623258C2semidirect
3. #13081542C2semidirect
4. #13081534C2semidirect
5. #13081520C2semidirect
6. #13081512C2semidirect
7. #13081473C2semidirect
8. #13081468C2semidirect
9. #13079160C2semidirect
10. #13078429C2semidirect
11. #13078425C2semidirect
12. #13078412C2semidirect
13. #13078409C2semidirect
14. M16×Dic22C2semidirect
17. C11×#3165C2semidirect
23. #10623261C22semidirect
30. #10623258C22semidirect
31. #10623253C22semidirect
32. #10623252C22semidirect
33. #10623221C22semidirect
34. #10623216C22semidirect
49. C11×#501C22semidirect
50. C11×#500C22semidirect
51. C11×#498C22semidirect
60. #10622707C22semidirect
61. #10622704C22semidirect
63. #10622700C22semidirect
65. #10622697C22semidirect
74. #10622503C22semidirect
76. #10622489C22semidirect
77. #10622488C22semidirect
78. #10622487C22semidirect
82. #10622483C22semidirect
84. #10622469C22semidirect
85. #10622468C22semidirect
86. #10622467C22semidirect
90. #10622314C22semidirect
93. #10622292C22semidirect
94. C8×Dic22C22semidirect
143. #66961Q8semidirect
250. #4339C2×Q8semidirect
253. C2×D44C2×Q8semidirect
278. C11×M16C2×Q8semidirect
340. D88C2×Q8semidirect
341. #4314C2×Q8semidirect
351. #3165D11semidirect
399. D44C22×Q8semidirect
416. Dic22AGL(1,ℤ/8)semidirect
417. Dic22C22×Q8semidirect
419. C8×C11C22×Q8semidirect
454. #501C2×D11semidirect
456. #500C2×D11semidirect
458. #498C2×D11semidirect
718. M16Q8×D11semidirect
779. C11Q8×AGL(1,ℤ/8)semidirect
841. C8C2×Q8×D11semidirect

Maximal subgroups

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

subgroupindex
#130821942
C2×#106232582
#130815422
#130815342
#130815202
#130815122
#130814732
#130814682
#130791602
#130784292
#130784252
#130784122
#130784092
M16×Dic222
C4×#669612
#130774232
C11×#31652
Q8×AGL(1,ℤ/8)11