Finite Group Databasebeta

← #25968101

Subgroups — #25968101

Order 11008.

2196 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583450C211yesmaximal, characteristic, complemented
2#529×D43C211yesmaximal, characteristic, complemented
3#19145635C212yesmaximal, complemented
4#19145629C212yesmaximal, complemented
5#19145622C211yesmaximal, characteristic, complemented
6#19145615C211yesmaximal, characteristic, complemented
7#19145610C211yesmaximal, characteristic, complemented
8#19145576C212yesmaximal, complemented
9#19145570C212yesmaximal, complemented
10#19145565C212yesmaximal, complemented
11#19145559C212yesmaximal, complemented
12#19145058C212yesmaximal, complemented
13#19144997C212yesmaximal, complemented
14#19144068C212yesmaximal, complemented
15#19144060C212yesmaximal, complemented
16#19143854C212yesmaximal, complemented
17#19143846C212yesmaximal, complemented
18#19143225C211yesmaximal, characteristic, complemented
19C43×#3218C211yesmaximal, characteristic, complemented
20C22×#10621902C2212yes—
21C2×#13063357C2214yescomplemented
22C2×#13063352C2214yescomplemented
23#14583450—21no—
24#14583450—21no—
25#14583450—21no—
26#14583450—21no—
27#14583450C2212yes—
28#14583450C2212yes—
29#14583450C2212yescomplemented
30#14583450C2212yescomplemented
31C2×#13063322C2211yescharacteristic, complemented
32#14583436C2211yescharacteristic, complemented
33#14583435C2211yescharacteristic
34#14583434C2211yescharacteristic, complemented
35#14583433C2211yescharacteristic
36#14583432—21no—
37#14583431C2211yescharacteristic, complemented
38#14583430C2211yescharacteristic
39#14583429—21no—
40#14583428C2211yescharacteristic, complemented
41#14583427—21no—
42#14583426—21no—
43#126×D43—21no—
44#125×D43C2211yescharacteristic, complemented
45C2×#13063314C2212yescomplemented
46#124×D43C2211yescharacteristic, complemented
47#123×D43—21no—
48C22⋊Q8×D43C2211yescharacteristic
49C2×#13063300—21no—
50C2×#13063300—21no—
51#121×D43C2211yescharacteristic
52C4×Q8×D43C2211yescharacteristic, complemented
53C2×#13063287—21no—
54C2×#13063287—21no—
55C4×D4×D43—21no—
56C4×D4×D43C2211yescharacteristic, complemented
57#117×D43—21no—
58C2×C42×D43C2211yescharacteristic
59#14583291C2212yescomplemented
60#14583289C2212yescomplemented
61#14583288C2212yescomplemented
62#14583284C2214yescomplemented
63#14583280C2214yescomplemented
64#14583267C2212yescomplemented
65#14583265C2212yescomplemented
66#14583264C2212yescomplemented
67#14583255C2214yescomplemented
68#14583255C2214yescomplemented
69#14583124C2214yescomplemented
70#14583123C2214yescomplemented
71#14583117C2214yescomplemented
72#14583116C2214yescomplemented
73#14583106C2212yescomplemented
74#14583101C2212yescomplemented
75#14583100C2212yescomplemented
76#14583099C2212yescomplemented
77#14583095C2212yescomplemented
78#14583094C2212yescomplemented
79#14583064C2214yescomplemented
80#14583060C2214yescomplemented
81#14583055C2212yescomplemented
82#14583052C2212yescomplemented
83#14583049C2212yescomplemented
84#14583047C2214yescomplemented
85#14583043C2214yescomplemented
86#14583038C2212yes—
87#14583035C2212yes—
88#14583032C2212yes—
89#14582956C2211yescharacteristic, complemented
90#14582954C2212yescomplemented
91#14582951C2212yescomplemented
92#14582949C2212yescomplemented
93#14582921C2212yescomplemented
94#14582899C2214yescomplemented
95#14582899C2214yescomplemented
96#14582861C2212yes—
97#14582851C2212yescomplemented
98C2×C4⋊Q8×C43C2211yescharacteristic, complemented
99C43×#529C2211yescharacteristic
100C43×#497C2212yescomplemented
101C43×#491C2212yescomplemented
102C43×#462C2212yescomplemented
103C43×#461C2212yescomplemented
104C43×#451C2212yescomplemented
105C43×#448C2212yes—
106C43×#432C2211yescharacteristic, complemented
107C2×#10621902—22no—
108C2×#10621902—22no—
109C2×#10621902—48no—
110C2×#10621902C2314yes—
111C2×#10621902C2314yes—
112C2×Q8×D43C2311yescharacteristic
113C22×D172—22no—
114C22×D172—21no—
115C22×D172—21no—
116C22×D172C2312yes—
117C2×D4×D43—21no—
118C2×D4×D43C2311yescharacteristic
119C22×C4×D43—22no—
120C22×C4×D43—21no—
121C22×C4×D43D411yescharacteristic
122C22×C4×D43D411yescharacteristic
123C22×C4×D43C2311yescharacteristic
124#13063357—48no—
125#13063352—48no—
126C2×#10621885C2314yes—
127C2×#10621873C2314yes—
128C2×#10621884C2314yes—
129C2×#10621884C2314yes—
130C2×D344C2314yes—
131C2×#10621882C2314yes—
132C2×#10621872C2314yes—
133#13063322—21no—
134#13063322—21no—
135#13063322C2312yes—
136#13063322C2312yes—
137#13063320—21no—
138#13063320—21no—
139#13063320—21no—
140#13063319—21no—
141#13063318—21no—
142#13063318—21no—
143#13063318—21no—
144#13063317C2311yescharacteristic
145#13063316C2311yescharacteristic
146#13063316C2311yescharacteristic
147#13063315—21no—
148#13063315—21no—
149#13063314—22no—
150#13063314—22no—
151#13063314C2314yes—
152#13063314C2311yescharacteristic
153#13063314C2314yes—
154#13063313C2311yescharacteristic
155#13063312C2311yescharacteristic
156#13063311—21no—
157#13063311—21no—
158#13063310—21no—
159#13063310—21no—
160#13063309—21no—
161#13063308—21no—
162#13063307—21no—
163#13063307—21no—
164#13063306—21no—
165#13063305C2311yescharacteristic
166#13063304C2311yescharacteristic
167#13063303—21no—
168#13063302—21no—
169#13063301C2311yescharacteristic
170#13063300—22no—
171#13063300—22no—
172#13063300—22no—
173#13063300—22no—
174#13063300—22no—
175#13063300—22no—
176#13063300—22no—
177#13063300—22no—
178#13063300C2311yescharacteristic
179#13063299C2311yescharacteristic
180#13063298—21no—
181#13063297—21no—
182#13063296C2311yescharacteristic
183Q8×Dic43C2311yescharacteristic
184C4×Dic86—21no—
185C4×Dic86C2311yescharacteristic
186#13063290—21no—
187#13063290C2311yescharacteristic
188C4×D172—21no—
189C4×D172C2311yescharacteristic
190D4×Dic43—21no—
191D4×Dic43C2311yescharacteristic
192#13063287—21no—
193#13063287—22no—
194#13063287—22no—
195#13063287—22no—
196#13063287—22no—
197#13063287—22no—
198#13063287—22no—
199#13063287—22no—
200#13063287—22no—
201#13063287C2311yescharacteristic
202C4×C22⋊D43—21no—
203C4×C22⋊D43—21no—
204C4×C22⋊D43—21no—
205(C22⋊D43)⋊C4—21no—
206(C22⋊D43)⋊C4—21no—
207(C22⋊D43)⋊C4—21no—
208#13063284—21no—
209#13063283—21no—
210#13063283—21no—
211#13063282—21no—
212#13063282—21no—
213#13063281—21no—
214#13063281—21no—
215C4⋊C4×D43—21no—
216C4⋊C4×D43—21no—
217C4⋊C4×D43—21no—
218C4⋊C4×D43—21no—
219C4⋊C4×D43C2311yescharacteristic
220C4⋊C4×D43C2311yescharacteristic
221C2×(C2×D43)⋊C4—22no—
222C2×(C2×D43)⋊C4—22no—
223C22⋊C4×D43—21no—
224C22⋊C4×D43—21no—
225C22⋊C4×D43—21no—
226C22⋊C4×D43—21no—
227C22⋊C4×D43—21no—
228C2×C4×Dic43D411yescharacteristic
229C2×C4×Dic43D411yescharacteristic
230C2×C4×Dic43C2311yescharacteristic
231C42×D43—21no—
232C42×D43D411yescharacteristic
233C42×D43D411yescharacteristic
234C42×D43D411yescharacteristic
235C42×D43D411yescharacteristic
236C42×D43C2311yescharacteristic
237C42×D43C2311yescharacteristic
238C42×D43C2311yescharacteristic
239C42×D43C2311yescharacteristic
240C4⋊(C43⋊C8)C2312yes—
241Dic43⋊C8C2314yes—
242#13063249C2314yes—
243#13063249C2314yes—
244#13063247C2314yes—
245#13063247C2314yes—
246#13063245C2314yes—
247#13063245C2314yes—
248C22⋊(C43⋊C8)C2312yes—
249(C2×D43)⋊C8C2314yes—
250#13063236C2312yes—
251C8×Dic43C2314yes—
252C22×Q8×C43C2312yes—
253C2×Q16×C43C2314yes—
254C2×SD16×C43C2314yes—
255C4⋊Q8×C43—21no—
256C4⋊Q8×C43—21no—
257C4⋊Q8×C43C2312yes—
258C4⋊Q8×C43C2312yes—
259#126×C43—21no—
260#125×C43C2311yescharacteristic
261#124×C43C2311yescharacteristic
262#123×C43—21no—
263C22⋊Q8×C43C2311yescharacteristic
264#121×C43C2311yescharacteristic
265C4×Q8×C43C2311yescharacteristic
266C4×D4×C43—21no—
267C4×D4×C43C2311yescharacteristic
268#117×C43—21no—
269C2×C4⋊C4×C43—21no—
270C2×C4⋊C4×C43—21no—
271C2×C42×C43C2311yescharacteristic
272C4⋊C8×C43C2312yes—
273#103×C43C2314yes—
274#103×C43C2314yes—
275C22⋊C8×C43C2312yes—
276#97×C43C2312yes—
277C23×D43—22no—
278C23×D43—21no—
279C23×D43C2×D411yescharacteristic
280C2×Q8×C43—22no—
281C2×Q8×C43—44no—
282C2×Q8×C43C2414yes—
283C2×Q8×C43C2411yescharacteristic
284C2×D4×C43—21no—
285C2×D4×C43C2411yescharacteristic
286C22×C4×C43—21no—
287C22×C4×C43—22no—
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C2×C22⋊D43—21no—
292C2×C22⋊D43—21no—
293C2×C22⋊D43—21no—
294C22×Dic43—21no—
295C22×Dic43C2×D411yescharacteristic
296C22×Dic43C2×D411yescharacteristic
297C22×Dic43C2×D411yescharacteristic
298#10621902—28no—
299#10621902—28no—
300#10621902—44no—
301#10621902—44no—
302#10621902—48no—
303#10621902—48no—
304Q8×D43—24no—
305D4×D43—24no—
306D4×D43—44no—
307C2×D172—22no—
308C2×D172—22no—
309C2×D172—22no—
310C2×D172—22no—
311C2×D172—22no—
312C2×D172—21no—
313C2×D172—24no—
314C2×D172—24no—
315C2×D172—48no—
316C2×D172—44no—
317C2×D172—44no—
318C2×D172—44no—
319C2×D172C2414yes—
320C2×D172C2411yescharacteristic
321C2×C4×D43—24no—
322C2×C4×D43—21no—
323C2×C4×D43—21no—
324C2×C4×D43—24no—
325C2×C4×D43—24no—
326C2×C4×D43—21no—
327C2×C4×D43—21no—
328C2×C4×D43—21no—
329C2×C4×D43—42no—
330C2×C4×D43—42no—
331C2×C4×D43—44no—
332C2×C4×D43—48no—
333C2×C4×D43C2×D411yescharacteristic
334C2×C4×D43C2×D411yescharacteristic
335C2×C4×D43C2×D411yescharacteristic
336C2×C4×D43C2×D411yescharacteristic
337C2×C4×D43C2×D411yescharacteristic
338C2×C4×D43C2×D411yescharacteristic
339C2×C4×D43C2×D411yescharacteristic
340C2×C4×D43C2×D411yescharacteristic
341C2×C4×D43C2×D411yescharacteristic
342C2×C4×D43C2×D411yescharacteristic
343C2×C4×D43C2411yescharacteristic
344C2×C4×D43C2411yescharacteristic
345C2×Dic86—21no—
346C2×Dic86C2411yescharacteristic
347Q16×C43—44no—
348SD16×C43—44no—
349C2×C8×C43C2414yes—
350C4⋊C4×C43—22no—
351C4⋊C4×C43—22no—
352C4⋊C4×C43—22no—
353C4⋊C4×C43—22no—
354C4⋊C4×C43—21no—
355C4⋊C4×C43—21no—
356C4⋊C4×C43—21no—
357C4⋊C4×C43—21no—
358C4⋊C4×C43C2411yescharacteristic
359C4⋊C4×C43C2411yescharacteristic
360C22⋊C4×C43—21no—
361C22⋊C4×C43—21no—
362C22⋊C4×C43—21no—
363C22⋊C4×C43—21no—
364C22⋊C4×C43—21no—
365C42×C43—21no—
366C42×C43C2×D411yescharacteristic
367C42×C43C2×D411yescharacteristic
368C42×C43C2411yescharacteristic
369C42×C43C2411yescharacteristic
370C22⋊Dic43—21no—
371C22⋊Dic43—21no—
372C22⋊Dic43—21no—
373C22⋊Dic43—21no—
374C22⋊Dic43—21no—
375#10621885—44no—
376#10621884—44no—
377#10621884—44no—
378#10621882—44no—
379(C2×D43)⋊C4—21no—
380(C2×D43)⋊C4—21no—
381(C2×D43)⋊C4—21no—
382(C2×D43)⋊C4—21no—
383(C2×D43)⋊C4—21no—
384(C2×D43)⋊C4—21no—
385(C2×D43)⋊C4—21no—
386(C2×D43)⋊C4—21no—
387(C2×D43)⋊C4—24no—
388(C2×D43)⋊C4—24no—
389(C2×D43)⋊C4—24no—
390(C2×D43)⋊C4—24no—
391(C2×D43)⋊C4—21no—
392(C2×D43)⋊C4—21no—
393C4⋊Dic43—21no—
394C4⋊Dic43—21no—
395C4⋊Dic43—21no—
396C4⋊Dic43—21no—
397C4⋊Dic43C2411yescharacteristic
398C4⋊Dic43C2411yescharacteristic
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401Dic43⋊C4—21no—
402Dic43⋊C4—21no—
403Dic43⋊C4—21no—
404Dic43⋊C4—21no—
405Dic43⋊C4—21no—
406Dic43⋊C4—21no—
407Dic43⋊C4—21no—
408Dic43⋊C4—21no—
409C4×Dic43—21no—
410C4×Dic43—21no—
411C4×Dic43—21no—
412C4×Dic43C2×D411yescharacteristic
413C4×Dic43C2×D411yescharacteristic
414C4×Dic43C2×D411yescharacteristic
415C4×Dic43C2×D411yescharacteristic
416C4×Dic43C2×D411yescharacteristic
417C4×Dic43C2×D411yescharacteristic
418C4×Dic43C2×D411yescharacteristic
419C4×Dic43C2×D411yescharacteristic
420C4×Dic43C2×D411yescharacteristic
421C4×Dic43C2×D411yescharacteristic
422C4×Dic43C2411yescharacteristic
423C4×Dic43C2411yescharacteristic
424C2×C43⋊C8C2414yes—
425D344—44no—
426#10621873—44no—
427#10621872—28no—
428C23×C43—21no—
429C23×C43C22×D411yescharacteristic
430C22×D43—22no—
431C22×D43—22no—
432C22×D43—21no—
433C22×D43—24no—
434C22×D43—41no—
435C22×D43—42no—
436C22×D43—42no—
437C22×D43—44no—
438C22×D43—44no—
439C22×D43—44no—
440C22×D43—42no—
441C22×D43C22×D411yescharacteristic
442C22×D43C22×D411yescharacteristic
443Q8×C43—22no—
444Q8×C43—24no—
445Q8×C43—24no—
446Q8×C43—44no—
447D4×C43—22no—
448D4×C43—42no—
449C2×C4×C43—22no—
450C2×C4×C43—22no—
451C2×C4×C43—22no—
452C2×C4×C43—21no—
453C2×C4×C43—21no—
454C2×C4×C43—21no—
455C2×C4×C43—24no—
456C2×C4×C43—44no—
457C2×C4×C43—42no—
458C2×C4×C43C22×D411yescharacteristic
459C2×C4×C43C22×D411yescharacteristic
460C2×C4×C43C22×D411yescharacteristic
461C2×C4×C43C22×D411yescharacteristic
462C2×C4×C43C22×D411yescharacteristic
463C2×C4×C43C2511yescharacteristic
464C22⋊D43—42no—
465C22⋊D43—42no—
466C22⋊D43—42no—
467C2×Dic43—22no—
468C2×Dic43—22no—
469C2×Dic43—21no—
470C2×Dic43—21no—
471C2×Dic43—21no—
472C2×Dic43—41no—
473C2×Dic43—42no—
474C2×Dic43C22×D411yescharacteristic
475C2×Dic43C22×D411yescharacteristic
476C2×Dic43C22×D411yescharacteristic
477C2×Dic43C22×D411yescharacteristic
478C2×Dic43C22×D411yescharacteristic
479C2×Dic43C22×D411yescharacteristic
480D172—24no—
481D172—22no—
482D172—24no—
483D172—44no—
484D172—44no—
485D172—44no—
486D172—44no—
487D172—48no—
488D172—42no—
489D172—48no—
490D172—44no—
491C4×D43—22no—
492C4×D43—22no—
493C4×D43—22no—
494C4×D43—22no—
495C4×D43—22no—
496C4×D43—41no—
497C4×D43—41no—
498C4×D43—41no—
499C4×D43—41no—
500C4×D43—41no—
501C4×D43—41no—
502C4×D43—42no—
503C4×D43—48no—
504C4×D43—42no—
505C4×D43—42no—
506C4×D43—42no—
507C4×D43—42no—
508C4×D43—48no—
509C4×D43H(5,𝔽2)14yes—
510Dic86—22no—
511Dic86—42no—
512C8×C43—24no—
513C43⋊C8—24no—
514#60805—431nomaximal, Sylow
515C22×C43—21no—
516C22×C43—21no—
517C22×C43—41no—
518C22×C43—41no—
519C22×C43—41no—
520C22×C43#57512yes—
521C22×C43C23×D411yescharacteristic
522C2×D43—21no—
523C2×D43—21no—
524C2×D43—21no—
525C2×D43—21no—
526C2×D43—21no—
527C2×D43—44no—
528C2×D43—44no—
529C2×D43—41no—
530C2×D43—41no—
531C2×D43—44no—
532C2×D43—44no—
533C2×D43—41no—
534C2×D43—84no—
535C2×D43—88no—
536C2×D43#53512yes—
537C4×C43—21no—
538C4×C43—21no—
539C4×C43—21no—
540C4×C43—21no—
541C4×C43—41no—
542C4×C43—44no—
543C4×C43—41no—
544C4×C43—41no—
545C4×C43#57512yes—
546C4×C43C2×H(5,𝔽2)12yes—
547Dic43—21no—
548Dic43—21no—
549Dic43—21no—
550Dic43—21no—
551Dic43—21no—
552Dic43—41no—
553Dic43—41no—
554Dic43—41no—
555Dic43#53512yes—
556C2×#532—431no—
557C2×#529—431no—
558#3219—432no—
559#3219—432no—
560#3218—431no—
561#3218D4311yescharacteristic, complemented
562#3217—431no—
563#3217—431no—
564#3212—432no—
565#3212—432no—
566#3211—432no—
567#3211—432no—
568#3153—432no—
569#3142—432no—
570#3037—432no—
571#3036—432no—
572#3007—432no—
573#3006—432no—
574#2920—431no—
575C2×C43—22no—
576C2×C43—81no—
577C2×C43C2×#53511yescharacteristic
578C2×C43C2×#57511yescharacteristic
579C2×C43C2×#57511yescharacteristic
580D43—22no—
581D43—41no—
582D43—84no—
583D43—81no—
584C22×#41—432no—
585C2×#137—434no—
586C2×AGL(1,ℤ/8)—434no—
587#532—432no—
588#532—432no—
589#532—432no—
590#532—432no—
591#532—861no—
592#532—861no—
593#532—861no—
594#532—861no—
595C2×C4⋊Q8C2×D4311yescharacteristic, complemented
596C2×#127—431no—
597#529—431no—
598#529—431no—
599#529—431no—
600#529—431no—
601#529—431no—
602#529—431no—
603#529—431no—
604#529—861no—
605#529—861no—
606#529—861no—
607#529—861no—
608#529C2×D4311yescharacteristic
609C2×#126—861no—
610C2×#125—431no—
611C2×#124—432no—
612C2×#124—431no—
613C2×#123—861no—
614C2×C22⋊Q8—431no—
615C2×#121—431no—
616C2×#121—861no—
617C2×#121—861no—
618C2×C4×Q8—431no—
619C2×C4×D4—431no—
620C2×C4×D4—861no—
621C2×C4×D4—861no—
622C2×C4×D4—861no—
623C2×#117—861no—
624C22×C42—431no—
625#497—432no—
626#497C2×D4312yescomplemented
627#496—432no—
628#496—432no—
629#495—434no—
630#495—434no—
631#491—432no—
632#491C2×D4312yescomplemented
633#490—432no—
634#490—432no—
635#488—434no—
636#488—434no—
637#464—434no—
638#464—434no—
639#463—434no—
640#463—434no—
641#462—432no—
642#462C2×D4312yescomplemented
643#461—432no—
644#461C2×D4312yescomplemented
645#460—432no—
646#460—432no—
647#459—432no—
648#459—432no—
649#452—434no—
650#452—434no—
651#451—432no—
652#451C2×D4312yescomplemented
653#450—432no—
654#450—432no—
655#449—434no—
656#449—434no—
657#448—432no—
658#448C2×D4312yes—
659#447—432no—
660#447—432no—
661#432—431no—
662#432—432no—
663#432C2×D4311yescharacteristic, complemented
664#431—432no—
665#431—432no—
666#423—432no—
667#417—434no—
668#417—434no—
669#407—432no—
670C4×M16—432no—
671C43#6080511yescharacteristic, complemented, Sylow
672C2×#41—434no—
673C2×#41—434no—
674C2×#41—862no—
675C2×#41—862no—
676C2×#41—1728no—
677C22×Q8—431no—
678C22×Q8C22×D4312yes—
679C22×D4—431no—
680C22×D4—432no—
681C22×D4—862no—
682C22×D4—861no—
683C22×D4—861no—
684C22×D4—861no—
685C23×C4—431no—
686C23×C4—431no—
687C23×C4—431no—
688C23×C4—861no—
689C23×C4—862no—
690#137—1728no—
691AGL(1,ℤ/8)—1728no—
692C2×Q16—434no—
693C2×Q16C22×D4314yes—
694C2×SD16—434no—
695C2×SD16—434no—
696C2×SD16—434no—
697C2×SD16C22×D4314yes—
698C2×D8—434no—
699C2×D8—434no—
700C2×M16—434no—
701C4⋊Q8—21no—
702C4⋊Q8—21no—
703C4⋊Q8C22×D4312yes—
704C4⋊Q8C22×D4312yes—
705#127—432no—
706#127—432no—
707#127—861no—
708#127—861no—
709#126—21no—
710#126—861no—
711#126—861no—
712#126—861no—
713#126—861no—
714#126—861no—
715#126—861no—
716#126—861no—
717#125—431no—
718#125—431no—
719#125—431no—
720#125—861no—
721#125—861no—
722#125C22×D4311yescharacteristic
723#124—431no—
724#124—434no—
725#124—434no—
726#124—431no—
727#124—431no—
728#124—861no—
729#124—861no—
730#124—862no—
731#124—862no—
732#124C22×D4311yescharacteristic
733#123—21no—
734#123—861no—
735#123—861no—
736#123—861no—
737#123—861no—
738#123—861no—
739#123—861no—
740#123—861no—
741C22⋊Q8—431no—
742C22⋊Q8—431no—
743C22⋊Q8—431no—
744C22⋊Q8—861no—
745C22⋊Q8—861no—
746C22⋊Q8C22×D4311yescharacteristic
747#121—431no—
748#121—431no—
749#121—431no—
750#121—861no—
751#121—862no—
752#121—862no—
753#121—862no—
754#121—862no—
755#121—862no—
756#121—862no—
757#121—862no—
758#121—862no—
759#121—861no—
760#121C22×D4311yescharacteristic
761C4×Q8—431no—
762C4×Q8—431no—
763C4×Q8—431no—
764C4×Q8—861no—
765C4×Q8—861no—
766C4×Q8C22×D4311yescharacteristic
767C4×D4—21no—
768C4×D4—431no—
769C4×D4—431no—
770C4×D4—431no—
771C4×D4—861no—
772C4×D4—861no—
773C4×D4—862no—
774C4×D4—862no—
775C4×D4—862no—
776C4×D4—862no—
777C4×D4—862no—
778C4×D4—862no—
779C4×D4—862no—
780C4×D4—862no—
781C4×D4—861no—
782C4×D4—861no—
783C4×D4—861no—
784C4×D4—861no—
785C4×D4—861no—
786C4×D4—861no—
787C4×D4—861no—
788C4×D4C22×D4311yescharacteristic
789#117—21no—
790#117—861no—
791#117—861no—
792#117—861no—
793#117—861no—
794#117—861no—
795#117—861no—
796#117—861no—
797C2×C4⋊C4—21no—
798C2×C4⋊C4—21no—
799C2×C4⋊C4—431no—
800C2×C4⋊C4—431no—
801C2×C4⋊C4—861no—
802C2×C4⋊C4—861no—
803C2×C4⋊C4—861no—
804C2×C4⋊C4—861no—
805C2×C22⋊C4—861no—
806C2×C22⋊C4—861no—
807C2×C22⋊C4—861no—
808C2×C22⋊C4—861no—
809C2×C22⋊C4—861no—
810C2×C22⋊C4—862no—
811C2×C22⋊C4—862no—
812C2×C42—431no—
813C2×C42—431no—
814C2×C42—431no—
815C2×C42—431no—
816C2×C42—431no—
817C2×C42—431no—
818C2×C42—431no—
819C2×C42—431no—
820C2×C42—431no—
821C2×C42—431no—
822C2×C42—431no—
823C2×C42—861no—
824C2×C42C22×D4311yescharacteristic
825C4⋊C8—434no—
826C4⋊C8—432no—
827C4⋊C8C22×D4312yes—
828#103—434no—
829#103—434no—
830#103C22×D4314yes—
831#103C22×D4314yes—
832#102—434no—
833#102—434no—
834#102—434no—
835#102—434no—
836C22⋊C8—432no—
837C22⋊C8—434no—
838C22⋊C8C22×D4312yes—
839#97—432no—
840#97C22×D4312yes—
841C4×C8—434no—
842C24—431no—
843C24—861no—
844C24—862no—
845#41—868no—
846#41—868no—
847#41—1724no—
848#41—1724no—
849#41—1728no—
850#41—1728no—
851C2×Q8—22no—
852C2×Q8—44no—
853C2×Q8—431no—
854C2×Q8—861no—
855C2×Q8—864no—
856C2×Q8C23×D4314yes—
857C2×Q8C23×D4311yescharacteristic
858C2×D4—21no—
859C2×D4—434no—
860C2×D4—431no—
861C2×D4—861no—
862C2×D4—864no—
863C2×D4—864no—
864C2×D4—864no—
865C2×D4—861no—
866C2×D4—861no—
867C2×D4—861no—
868C2×D4—862no—
869C2×D4—862no—
870C2×D4—862no—
871C2×D4—862no—
872C2×D4—862no—
873C2×D4—1724no—
874C2×D4—1724no—
875C2×D4—1724no—
876C2×D4—1728no—
877C2×D4—1724no—
878C2×D4C23×D4311yescharacteristic
879C22×C4—22no—
880C22×C4—21no—
881C22×C4—431no—
882C22×C4—431no—
883C22×C4—431no—
884C22×C4—431no—
885C22×C4—431no—
886C22×C4—431no—
887C22×C4—431no—
888C22×C4—431no—
889C22×C4—431no—
890C22×C4—431no—
891C22×C4—431no—
892C22×C4—431no—
893C22×C4—431no—
894C22×C4—431no—
895C22×C4—431no—
896C22×C4—864no—
897C22×C4—861no—
898C22×C4—864no—
899C22×C4—864no—
900C22×C4—861no—
901C22×C4—861no—
902C22×C4—861no—
903C22×C4—861no—
904C22×C4—861no—
905C22×C4—1722no—
906C22×C4—1722no—
907C22×C4—1728no—
908C22×C4—1724no—
909C22×C4D4×D4311yescharacteristic
910C22×C4D4×D4311yescharacteristic
911C22×C4C23×D4311yescharacteristic
912Q16—44no—
913Q16—1724no—
914SD16—44no—
915SD16—1724no—
916SD16—1724no—
917SD16—1724no—
918D8—1724no—
919D8—1724no—
920M16—868no—
921C2×C8—434no—
922C2×C8C23×D4314yes—
923C4⋊C4—22no—
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—22no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—431no—
932C4⋊C4—431no—
933C4⋊C4—861no—
934C4⋊C4—861no—
935C4⋊C4—861no—
936C4⋊C4—861no—
937C4⋊C4—861no—
938C4⋊C4—861no—
939C4⋊C4—861no—
940C4⋊C4—861no—
941C4⋊C4—861no—
942C4⋊C4—861no—
943C4⋊C4—861no—
944C4⋊C4—861no—
945C4⋊C4—861no—
946C4⋊C4—861no—
947C4⋊C4C23×D4311yescharacteristic
948C4⋊C4C23×D4311yescharacteristic
949C22⋊C4—21no—
950C22⋊C4—21no—
951C22⋊C4—21no—
952C22⋊C4—21no—
953C22⋊C4—21no—
954C22⋊C4—861no—
955C22⋊C4—861no—
956C22⋊C4—861no—
957C22⋊C4—864no—
958C22⋊C4—864no—
959C22⋊C4—864no—
960C22⋊C4—864no—
961C22⋊C4—861no—
962C22⋊C4—861no—
963C22⋊C4—861no—
964C22⋊C4—861no—
965C22⋊C4—861no—
966C22⋊C4—861no—
967C22⋊C4—861no—
968C22⋊C4—861no—
969C22⋊C4—861no—
970C22⋊C4—861no—
971C22⋊C4—861no—
972C22⋊C4—861no—
973C42—21no—
974C42—431no—
975C42—431no—
976C42—431no—
977C42—431no—
978C42—431no—
979C42—431no—
980C42—431no—
981C42—431no—
982C42—431no—
983C42—431no—
984C42—431no—
985C42—431no—
986C42—861no—
987C42—861no—
988C42—861no—
989C42D4×D4311yescharacteristic
990C42D4×D4311yescharacteristic
991C42C23×D4311yescharacteristic
992C42C23×D4311yescharacteristic
993C23—21no—
994C23—431no—
995C23—431no—
996C23—862no—
997C23—862no—
998C23—861no—
999C23—864no—
1000C23—1721no—
1001C23—1724no—
1002C23—1724no—
1003C23—1722no—
1004C23—1722no—
1005C23—1722no—
1006C23—1724no—
1007C23C2×D4×D4311yescharacteristic
1008Q8—24no—
1009Q8—22no—
1010Q8—24no—
1011Q8—44no—
1012Q8—862no—
1013Q8—1722no—
1014D4—22no—
1015D4—42no—
1016D4—862no—
1017D4—864no—
1018D4—864no—
1019D4—1724no—
1020D4—1724no—
1021D4—1724no—
1022D4—1724no—
1023D4—1728no—
1024D4—1728no—
1025D4—1722no—
1026D4—1722no—
1027D4—1722no—
1028D4—1722no—
1029D4—1724no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—24no—
1037C2×C4—44no—
1038C2×C4—42no—
1039C2×C4—431no—
1040C2×C4—434no—
1041C2×C4—431no—
1042C2×C4—431no—
1043C2×C4—431no—
1044C2×C4—431no—
1045C2×C4—431no—
1046C2×C4—862no—
1047C2×C4—862no—
1048C2×C4—862no—
1049C2×C4—862no—
1050C2×C4—862no—
1051C2×C4—862no—
1052C2×C4—862no—
1053C2×C4—861no—
1054C2×C4—861no—
1055C2×C4—861no—
1056C2×C4—1721no—
1057C2×C4—1721no—
1058C2×C4—1721no—
1059C2×C4—1721no—
1060C2×C4—1721no—
1061C2×C4—1721no—
1062C2×C4—1728no—
1063C2×C4—1728no—
1064C2×C4—1722no—
1065C2×C4—1722no—
1066C2×C4—1722no—
1067C2×C4—1722no—
1068C2×C4—1721no—
1069C2×C4—1722no—
1070C2×C4—1722no—
1071C2×C4C2×D4×D4311yescharacteristic
1072C2×C4C2×D4×D4311yescharacteristic
1073C2×C4C2×D4×D4311yescharacteristic
1074C2×C4C2×D4×D4311yescharacteristic
1075C2×C4C2×D4×D4311yescharacteristic
1076C2×C4C24×D4311yescharacteristic
1077C8—24no—
1078C8—864no—
1079C22—21no—
1080C22—21no—
1081C22—41no—
1082C22—41no—
1083C22—41no—
1084C22—432no—
1085C22—861no—
1086C22—861no—
1087C22—861no—
1088C22—861no—
1089C22—861no—
1090C22—3448no—
1091C22—3444no—
1092C22—1724no—
1093C22—1721no—
1094C22—1724no—
1095C22—1721no—
1096C22—1724no—
1097C22—1724no—
1098C22—1721no—
1099C22#1458369812yes—
1100C22C22×D4×D4311yescharacteristic
1101C4—21no—
1102C4—21no—
1103C4—21no—
1104C4—21no—
1105C4—41no—
1106C4—41no—
1107C4—44no—
1108C4—41no—
1109C4—432no—
1110C4—861no—
1111C4—861no—
1112C4—861no—
1113C4—861no—
1114C4—861no—
1115C4—1721no—
1116C4—1721no—
1117C4—1721no—
1118C4#1458369812yes—
1119C4H(5,𝔽2)×D4312yes—
1120C2—22no—
1121C2—81no—
1122C2—862no—
1123C2—3444no—
1124C2—3441no—
1125C2—1721no—
1126C2#535×D4311yescharacteristic
1127C2C2×#1458369811yescharacteristic
1128C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3218C2
socleC22×C43C23×D4
hypercenter#3218D43
hypocenterC43#60805
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3218

Complements

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

NH ≅ G/Ntype
1. C2×#14583450C2semidirect
2. #529×D43C2semidirect
3. #19145635C2semidirect
4. #19145629C2semidirect
5. #19145622C2semidirect
6. #19145615C2semidirect
7. #19145610C2semidirect
8. #19145576C2semidirect
9. #19145570C2semidirect
10. #19145565C2semidirect
11. #19145559C2semidirect
12. #19145058C2semidirect
13. #19144997C2semidirect
14. #19144068C2semidirect
15. #19144060C2semidirect
16. #19143854C2semidirect
17. #19143846C2semidirect
18. #19143225C2semidirect
19. C43×#3218C2semidirect
21. C2×#13063357C22semidirect
22. C2×#13063352C22semidirect
29. #14583450C22semidirect
30. #14583450C22semidirect
31. C2×#13063322C22semidirect
32. #14583436C22semidirect
34. #14583434C22semidirect
37. #14583431C22semidirect
40. #14583428C22semidirect
44. #125×D43C22semidirect
45. C2×#13063314C22semidirect
46. #124×D43C22semidirect
52. C4×Q8×D43C22semidirect
56. C4×D4×D43C22semidirect
59. #14583291C22semidirect
60. #14583289C22semidirect
61. #14583288C22semidirect
62. #14583284C22semidirect
63. #14583280C22semidirect
64. #14583267C22semidirect
65. #14583265C22semidirect
66. #14583264C22semidirect
67. #14583255C22semidirect
68. #14583255C22semidirect
69. #14583124C22semidirect
70. #14583123C22semidirect
71. #14583117C22semidirect
72. #14583116C22semidirect
73. #14583106C22semidirect
74. #14583101C22semidirect
75. #14583100C22semidirect
76. #14583099C22semidirect
77. #14583095C22semidirect
78. #14583094C22semidirect
79. #14583064C22semidirect
80. #14583060C22semidirect
81. #14583055C22semidirect
82. #14583052C22semidirect
83. #14583049C22semidirect
84. #14583047C22semidirect
85. #14583043C22semidirect
89. #14582956C22semidirect
90. #14582954C22semidirect
91. #14582951C22semidirect
92. #14582949C22semidirect
93. #14582921C22semidirect
94. #14582899C22semidirect
95. #14582899C22semidirect
97. #14582851C22semidirect
98. C2×C4⋊Q8×C43C22semidirect
100. C43×#497C22semidirect
101. C43×#491C22semidirect
102. C43×#462C22semidirect
103. C43×#461C22semidirect
104. C43×#451C22semidirect
106. C43×#432C22semidirect
561. #3218D43semidirect
595. C2×C4⋊Q8C2×D43semidirect
626. #497C2×D43semidirect
632. #491C2×D43semidirect
642. #462C2×D43semidirect
644. #461C2×D43semidirect
652. #451C2×D43semidirect
663. #432C2×D43semidirect
671. C43#60805semidirect

Maximal subgroups

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

subgroupindex
C2×#145834502
#529×D432
#191456352
#191456292
#191456222
#191456152
#191456102
#191455762
#191455702
#191455652
#191455592
#191450582
#191449972
#191440682
#191440602
#191438542
#191438462
#191432252
C43×#32182
#6080543