Finite Group Databasebeta

← #25968088

Subgroups — #25968088

Order 11008.

2164 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic, complemented
2#532×D43C211yesmaximal, characteristic
3#19145605C212yesmaximal, complemented
4#19145604C212yesmaximal, complemented
5#19145596C214yesmaximal, complemented
6#19145550C214yesmaximal, complemented
7#19145542C212yesmaximal, complemented
8#19145535C212yesmaximal, complemented
9#19145050C212yesmaximal, complemented
10#19144986C212yesmaximal, complemented
11#19144069C211yesmaximal, characteristic, complemented
12#19144067C211yesmaximal, characteristic, complemented
13#19144063C211yesmaximal, characteristic, complemented
14#19143856C212yesmaximal, complemented
15#19143851C212yesmaximal, complemented
16#19143227C211yesmaximal, characteristic, complemented
17C43×#3037C211yesmaximal, characteristic, complemented
18C2×#41×D43C2212yes—
19C2×#13063358C2212yescomplemented
20C2×#13063356C2212yescomplemented
21C2×#13063355C2212yescomplemented
22#14583453—21no—
23#14583453—21no—
24#14583453—21no—
25#14583453—21no—
26#14583453C2212yes—
27#14583453C2212yes—
28#14583453C2212yescomplemented
29#14583453C2212yescomplemented
30#14583450C2211yescharacteristic
31#14583449C2211yescharacteristic
32#14583448C2212yes—
33#14583447C2211yescharacteristic
34#14583446—21no—
35#14583446—21no—
36#14583445C2212yes—
37#14583444—21no—
38#14583444—21no—
39C2×#13063324C2211yescharacteristic, complemented
40C2×#13063323C2211yescharacteristic, complemented
41C4⋊Q8×D43C2211yescharacteristic
42#127×D43C2211yescharacteristic
43C2×#13063315—21no—
44#124×D43C2212yes—
45C2×#13063305C2211yescharacteristic
46C2×#13063303—21no—
47C2×#13063301C2211yescharacteristic
48#121×D43—21no—
49#121×D43—21no—
50C2×C4×Dic86—21no—
51C2×C4×Dic86C2211yescharacteristic, complemented
52C4×D4×D43—21no—
53C4×D4×D43—21no—
54C2×#13063282—21no—
55C2×C42×D43C2211yescharacteristic
56#14583292C2214yescomplemented
57#14583290C2214yescomplemented
58#14583277C2214yescomplemented
59#14583270C2214yescomplemented
60#14583260C2214yescomplemented
61#14583257C2214yescomplemented
62#14583248C2214yescomplemented
63#14583244C2214yescomplemented
64#14583122C2214yescomplemented
65#14583121C2214yescomplemented
66#14583118C2214yescomplemented
67#14583110C2212yescomplemented
68#14583109C2212yescomplemented
69#14583106C2212yescomplemented
70#14583100C2212yescomplemented
71#14583099C2212yescomplemented
72#14583096C2212yescomplemented
73#14583064C2214yescomplemented
74#14583062C2214yescomplemented
75#14583060C2214yescomplemented
76#14583058C2214yescomplemented
77#14583056C2214yes—
78#14583053C2214yes—
79#14583051C2214yes—
80#14583048C2214yes—
81#14582955C2212yes—
82#14582955C2212yescomplemented
83#14582951C2212yes—
84#14582951C2212yescomplemented
85#14582923C2211yescharacteristic, complemented
86#14582901C2212yescomplemented
87#14582900C2212yescomplemented
88#14582898C2212yescomplemented
89#14582862C2212yes—
90M16×Dic43C2212yescomplemented
91C2×#137×C43C2212yescomplemented
92C43×#532C2211yescharacteristic
93C2×C4×Q8×C43C2211yescharacteristic, complemented
94C43×#464C2214yescomplemented
95C43×#462C2212yescomplemented
96C43×#460C2212yescomplemented
97C43×#423C2211yescharacteristic, complemented
98C43×#417C2212yescomplemented
99C2×#10621902C2312yes—
100C2×#10621898—22no—
101C2×#10621898C2312yes—
102C2×#10621900—22no—
103C2×#10621900C2312yes—
104#41×D43—44no—
105#41×D43—44no—
106C22×Dic86—21no—
107C22×Dic86C2311yescharacteristic
108C2×Q8×D43C2312yes—
109C2×D4×D43—22no—
110C2×D4×D43—21no—
111C2×D4×D43—21no—
112C2×D4×D43C2312yes—
113C22×C4×D43—22no—
114C22×C4×D43D411yescharacteristic
115C22×C4×D43D411yescharacteristic
116C22×C4×D43C2311yescharacteristic
117#13063358—44no—
118#13063356—44no—
119#13063355—44no—
120C2×Dic172C2314yes—
121C2×#10621885C2314yes—
122C2×#10621885C2314yes—
123C2×#10621873C2314yes—
124C2×#10621883C2314yes—
125C2×#10621884C2314yes—
126C2×#10621877C2312yes—
127#13063325C2311yescharacteristic
128#13063324—21no—
129#13063324—21no—
130#13063324—21no—
131#13063324—21no—
132#13063324C2312yes—
133#13063324C2312yes—
134#13063323—21no—
135#13063323—21no—
136#13063323C2312yes—
137#13063323C2312yes—
138#13063323C2312yes—
139#13063322C2311yescharacteristic
140#13063321—21no—
141#13063321—21no—
142#13063321C2312yes—
143#13063315—22no—
144#13063315—22no—
145#13063315—22no—
146#13063315—22no—
147#13063314C2312yes—
148#13063313C2312yes—
149#13063312C2312yes—
150#13063311—22no—
151#13063311—22no—
152#13063305—21no—
153#13063305—21no—
154#13063305C2312yes—
155#13063305C2312yes—
156#13063303—22no—
157#13063303—22no—
158#13063303—22no—
159#13063303—22no—
160#13063301—21no—
161#13063301—21no—
162#13063301C2312yes—
163#13063301C2312yes—
164#13063300—21no—
165#13063300—21no—
166#13063299—21no—
167#13063299—21no—
168#13063298—22no—
169#13063298—22no—
170#13063297—22no—
171#13063297—22no—
172#13063296—21no—
173#13063296—21no—
174C4×Dic86—21no—
175C4×Dic86—21no—
176C4×Dic86—22no—
177C4×Dic86—22no—
178C4×Dic86—22no—
179C4×Dic86—22no—
180C4×Dic86C2312yes—
181C4×Dic86C2312yes—
182C4×D172—21no—
183C4×D172—21no—
184D4×Dic43—21no—
185D4×Dic43—21no—
186#13063287—21no—
187#13063287—21no—
188C4×C22⋊D43—22no—
189C4×C22⋊D43—22no—
190(C22⋊D43)⋊C4—22no—
191(C22⋊D43)⋊C4—22no—
192#13063282—22no—
193#13063282—22no—
194#13063282—22no—
195#13063282—22no—
196C2×C4⋊Dic43—21no—
197C2×C4⋊Dic43C2311yescharacteristic
198C2×Dic43⋊C4—21no—
199C2×Dic43⋊C4—21no—
200C2×Dic43⋊C4—21no—
201C2×Dic43⋊C4—21no—
202C2×Dic43⋊C4—21no—
203C4⋊C4×D43—21no—
204C4⋊C4×D43—21no—
205C2×(C2×D43)⋊C4—21no—
206C2×(C2×D43)⋊C4—21no—
207C22⋊C4×D43—22no—
208C22⋊C4×D43—22no—
209C2×C4×Dic43—21no—
210C2×C4×Dic43D411yescharacteristic
211C2×C4×Dic43D411yescharacteristic
212C2×C4×Dic43C2311yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43D411yescharacteristic
215C42×D43D411yescharacteristic
216C42×D43D411yescharacteristic
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219C42×D43C2311yescharacteristic
220C42×D43C2311yescharacteristic
221C4⋊(C43⋊C8)C2312yes—
222C4⋊(C43⋊C8)C2312yes—
223#13063250C2314yes—
224#13063249C2314yes—
225#13063248C2314yes—
226#13063247C2314yes—
227#13063246C2314yes—
228#13063245C2314yes—
229(C2×D43)⋊C8C2314yes—
230(C2×D43)⋊C8C2314yes—
231#13063235C2314yes—
232C8×Dic43C2314yes—
233C2×#41×C43C2312yes—
234C22×Q8×C43C2311yescharacteristic
235#137×C43—44no—
236C2×Q16×C43C2314yes—
237C2×SD16×C43C2314yes—
238C2×M16×C43C2312yes—
239C4⋊Q8×C43C2311yescharacteristic
240#127×C43C2311yescharacteristic
241#124×C43C2312yes—
242#121×C43—21no—
243#121×C43—21no—
244C4×Q8×C43—21no—
245C4×Q8×C43—21no—
246C4×Q8×C43C2312yes—
247C4×Q8×C43C2312yes—
248C4×D4×C43—21no—
249C4×D4×C43—21no—
250C2×C4⋊C4×C43—21no—
251C2×C4⋊C4×C43C2311yescharacteristic
252C2×C42×C43—21no—
253C2×C42×C43C2311yescharacteristic
254C4⋊C8×C43C2312yes—
255C4⋊C8×C43C2312yes—
256#103×C43C2314yes—
257#102×C43C2314yes—
258C23×D43—22no—
259C23×D43C2×D411yescharacteristic
260#41×C43—24no—
261#41×C43—24no—
262C2×Q8×C43—21no—
263C2×Q8×C43—22no—
264C2×Q8×C43—22no—
265C2×Q8×C43C2412yes—
266C2×Q8×C43C2412yes—
267C2×D4×C43—21no—
268C2×D4×C43—21no—
269C2×D4×C43—22no—
270C2×D4×C43C2412yes—
271C22×C4×C43—22no—
272C22×C4×C43—21no—
273C22×C4×C43—21no—
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2×D411yescharacteristic
276C22×C4×C43C2411yescharacteristic
277C2×C22⋊D43—22no—
278C2×C22⋊D43—22no—
279C2×C22⋊D43—22no—
280C2×C22⋊D43—22no—
281C2×C22⋊D43—22no—
282C22×Dic43—22no—
283C22×Dic43—21no—
284C22×Dic43—21no—
285C22×Dic43C2×D411yescharacteristic
286C22×Dic43C2×D411yescharacteristic
287C22×Dic43C2×D411yescharacteristic
288#10621902—42no—
289#10621902—42no—
290Q8×D43—42no—
291Q8×D43—42no—
292#10621900—42no—
293#10621900—42no—
294#10621900—48no—
295D4×D43—48no—
296D4×D43—42no—
297D4×D43—42no—
298D4×D43—44no—
299D4×D43—44no—
300#10621898—24no—
301#10621898—24no—
302#10621898—48no—
303C2×D172—21no—
304C2×D172—21no—
305C2×D172—22no—
306C2×D172C2412yes—
307C2×C4×D43—22no—
308C2×C4×D43—22no—
309C2×C4×D43—24no—
310C2×C4×D43—22no—
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—42no—
314C2×C4×D43—48no—
315C2×C4×D43C2×D411yescharacteristic
316C2×C4×D43C2×D411yescharacteristic
317C2×C4×D43C2×D411yescharacteristic
318C2×C4×D43C2×D411yescharacteristic
319C2×C4×D43C2×D411yescharacteristic
320C2×C4×D43C2×D411yescharacteristic
321C2×C4×D43C2×D411yescharacteristic
322C2×C4×D43C2×D411yescharacteristic
323C2×C4×D43C2×D411yescharacteristic
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2411yescharacteristic
326C2×C4×D43C2411yescharacteristic
327C2×Dic86—22no—
328C2×Dic86—22no—
329C2×Dic86—21no—
330C2×Dic86—22no—
331C2×Dic86—22no—
332C2×Dic86—22no—
333C2×Dic86—44no—
334C2×Dic86C2412yes—
335C2×Dic86C2412yes—
336Q16×C43—44no—
337SD16×C43—44no—
338M16×C43—24no—
339C2×C8×C43C2414yes—
340C4⋊C4×C43—22no—
341C4⋊C4×C43—22no—
342C4⋊C4×C43—21no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43C2412yes—
346C22⋊C4×C43—22no—
347C22⋊C4×C43—22no—
348C42×C43—22no—
349C42×C43—22no—
350C42×C43C2×D411yescharacteristic
351C42×C43C2×D411yescharacteristic
352C42×C43C2411yescharacteristic
353C42×C43C2411yescharacteristic
354C22⋊Dic43—22no—
355C22⋊Dic43—22no—
356#10621885—44no—
357#10621885—44no—
358#10621884—44no—
359#10621883—44no—
360(C2×D43)⋊C4—22no—
361(C2×D43)⋊C4—22no—
362(C2×D43)⋊C4—22no—
363(C2×D43)⋊C4—22no—
364(C2×D43)⋊C4—22no—
365(C2×D43)⋊C4—22no—
366(C2×D43)⋊C4—22no—
367(C2×D43)⋊C4—22no—
368C4⋊Dic43—21no—
369C4⋊Dic43—21no—
370C4⋊Dic43—21no—
371C4⋊Dic43—22no—
372C4⋊Dic43—22no—
373C4⋊Dic43C2412yes—
374Dic43⋊C4—22no—
375Dic43⋊C4—22no—
376Dic43⋊C4—22no—
377Dic43⋊C4—22no—
378Dic43⋊C4—22no—
379Dic43⋊C4—22no—
380Dic43⋊C4—22no—
381Dic43⋊C4—22no—
382Dic43⋊C4—22no—
383Dic43⋊C4—22no—
384Dic43⋊C4—22no—
385Dic43⋊C4—22no—
386C4×Dic43—22no—
387C4×Dic43—22no—
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2×D411yescharacteristic
390C4×Dic43C2×D411yescharacteristic
391C4×Dic43C2×D411yescharacteristic
392C4×Dic43C2×D411yescharacteristic
393C4×Dic43C2×D411yescharacteristic
394C4×Dic43C2×D411yescharacteristic
395C4×Dic43C2×D411yescharacteristic
396C4×Dic43C2×D411yescharacteristic
397C4×Dic43C2×D411yescharacteristic
398C4×Dic43C2411yescharacteristic
399C4×Dic43C2411yescharacteristic
400#10621877—24no—
401C2×C43⋊C8C2414yes—
402Dic172—44no—
403#10621873—44no—
404C23×C43—22no—
405C23×C43C22×D411yescharacteristic
406C22×D43—22no—
407C22×D43—22no—
408C22×D43—22no—
409C22×D43—41no—
410C22×D43—44no—
411C22×D43—44no—
412C22×D43—44no—
413C22×D43C22×D411yescharacteristic
414C22×D43C22×D411yescharacteristic
415Q8×C43—22no—
416Q8×C43—22no—
417Q8×C43—22no—
418Q8×C43—22no—
419Q8×C43—42no—
420D4×C43—22no—
421D4×C43—22no—
422D4×C43—42no—
423D4×C43—44no—
424D4×C43—42no—
425C2×C4×C43—22no—
426C2×C4×C43—22no—
427C2×C4×C43—22no—
428C2×C4×C43—22no—
429C2×C4×C43—41no—
430C2×C4×C43—42no—
431C2×C4×C43—42no—
432C2×C4×C43—44no—
433C2×C4×C43C22×D411yescharacteristic
434C2×C4×C43C22×D411yescharacteristic
435C2×C4×C43C22×D411yescharacteristic
436C2×C4×C43C22×D411yescharacteristic
437C2×C4×C43C22×D411yescharacteristic
438C2×C4×C43H(5,𝔽2)12yes—
439C2×C4×C43H(5,𝔽2)12yes—
440C2×C4×C43C2511yescharacteristic
441C22⋊D43—44no—
442C22⋊D43—44no—
443C22⋊D43—44no—
444C22⋊D43—44no—
445C22⋊D43—44no—
446C2×Dic43—22no—
447C2×Dic43—22no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—22no—
452C2×Dic43—44no—
453C2×Dic43—42no—
454C2×Dic43—42no—
455C2×Dic43C22×D411yescharacteristic
456C2×Dic43C22×D411yescharacteristic
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459C2×Dic43C22×D411yescharacteristic
460C2×Dic43C22×D411yescharacteristic
461D172—22no—
462D172—22no—
463D172—42no—
464D172—44no—
465D172—42no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—22no—
470C4×D43—21no—
471C4×D43—21no—
472C4×D43—21no—
473C4×D43—21no—
474C4×D43—22no—
475C4×D43—22no—
476C4×D43—22no—
477C4×D43—41no—
478C4×D43—41no—
479C4×D43—44no—
480C4×D43—44no—
481C4×D43—44no—
482C4×D43#13714yescomplemented
483Dic86—22no—
484Dic86—22no—
485Dic86—22no—
486Dic86—22no—
487Dic86—44no—
488Dic86—44no—
489Dic86—42no—
490Dic86—44no—
491C8×C43—24no—
492C43⋊C8—24no—
493#60804—431nomaximal, Sylow
494C22×C43—21no—
495C22×C43—21no—
496C22×C43—42no—
497C22×C43—42no—
498C22×C43—42no—
499C22×C43#53512yes—
500C22×C43C23×D411yescharacteristic
501C2×D43—21no—
502C2×D43—21no—
503C2×D43—21no—
504C2×D43—21no—
505C2×D43—21no—
506C2×D43—44no—
507C2×D43—42no—
508C2×D43—42no—
509C2×D43—42no—
510C2×D43—88no—
511C2×D43C2×#13712yes—
512C4×C43—21no—
513C4×C43—21no—
514C4×C43—21no—
515C4×C43—42no—
516C4×C43—42no—
517C4×C43—42no—
518C4×C43#53512yes—
519C4×C43C2×#13712yes—
520C4×C43C2×H(5,𝔽2)11yescharacteristic
521C4×C43C2×H(5,𝔽2)11yescharacteristic
522Dic43—21no—
523Dic43—21no—
524Dic43—21no—
525Dic43—21no—
526Dic43—42no—
527Dic43—42no—
528Dic43—42no—
529Dic43C2×#13712yes—
530Dic43#57512yes—
531C2×#533—431no—
532C2×#532—431no—
533#3216—432no—
534#3216—432no—
535#3215—434no—
536#3210—434no—
537#3209—432no—
538#3208—432no—
539#3152—432no—
540#3141—432no—
541#3037—431no—
542#3037—431no—
543#3037—431no—
544#3037D4311yescharacteristic, complemented
545#3007—432no—
546#3007—432no—
547#2920—431no—
548C2×C43—22no—
549C2×C43—82no—
550C2×C43C2×#53511yescharacteristic
551C2×C43C22×#13711yescharacteristic
552C2×C43C2×#57511yescharacteristic
553D43—22no—
554D43—41no—
555D43—82no—
556C22×#41—432no—
557C2×#137—432no—
558C2×#137—432no—
559C2×#137—432no—
560C2×#137C2×D4312yescomplemented
561#533—432no—
562#533—432no—
563#533—432no—
564#533—432no—
565#533—861no—
566#533—861no—
567#533—861no—
568#533—861no—
569#532—432no—
570#532—431no—
571#532—431no—
572#532—432no—
573#532—431no—
574#532—861no—
575#532—861no—
576#532—861no—
577#532—861no—
578#532C2×D4311yescharacteristic
579C2×C4⋊Q8—431no—
580C2×C4⋊Q8—431no—
581C2×C4⋊Q8—431no—
582C2×#127—431no—
583C2×#125—861no—
584C2×#124—432no—
585C2×C22⋊Q8—431no—
586C2×C22⋊Q8—431no—
587C2×C22⋊Q8—861no—
588C2×#121—861no—
589C2×#121—861no—
590C2×C4×Q8—431no—
591C2×C4×Q8—861no—
592C2×C4×Q8C2×D4311yescharacteristic, complemented
593C2×C4×D4—861no—
594C2×C4×D4—861no—
595C2×#117—861no—
596C22×C42—431no—
597#497—434no—
598#497—434no—
599#494—434no—
600#492—434no—
601#489—434no—
602#489—434no—
603#487—434no—
604#486—434no—
605#464—434no—
606#464—434no—
607#464—434no—
608#464C2×D4314yescomplemented
609#462—432no—
610#462—432no—
611#462—432no—
612#462C2×D4312yescomplemented
613#460—432no—
614#460—432no—
615#460—432no—
616#460C2×D4312yescomplemented
617#452—434no—
618#452—434no—
619#452—434no—
620#452—434no—
621#451—434no—
622#451—434no—
623#450—434no—
624#450—434no—
625#432—432no—
626#432—432no—
627#431—432no—
628#431—432no—
629#423—431no—
630#423C2×D4311yescharacteristic, complemented
631#417—432no—
632#417—432no—
633#417—432no—
634#417C2×D4312yescomplemented
635#407—432no—
636C4×M16—432no—
637C43#6080411yescharacteristic, complemented, Sylow
638C2×#41—432no—
639C2×#41—432no—
640C2×#41—432no—
641C2×#41—862no—
642C2×#41—862no—
643C2×#41—1724no—
644C2×#41—1724no—
645C2×#41C22×D4312yes—
646C22×Q8—432no—
647C22×Q8—431no—
648C22×Q8—861no—
649C22×Q8C22×D4311yescharacteristic
650C22×D4—432no—
651C22×D4—861no—
652C22×D4—861no—
653C22×D4—862no—
654C23×C4—431no—
655C23×C4—431no—
656C23×C4—431no—
657C23×C4—862no—
658#137—44no—
659#137—1724no—
660#137—1724no—
661#137—1724no—
662C2×Q16—434no—
663C2×Q16—434no—
664C2×Q16—434no—
665C2×Q16C22×D4314yes—
666C2×SD16—434no—
667C2×SD16—434no—
668C2×SD16—434no—
669C2×SD16C22×D4314yes—
670C2×M16—432no—
671C2×M16C22×D4312yes—
672C4⋊Q8—432no—
673C4⋊Q8—432no—
674C4⋊Q8—432no—
675C4⋊Q8—432no—
676C4⋊Q8—432no—
677C4⋊Q8—431no—
678C4⋊Q8—861no—
679C4⋊Q8—861no—
680C4⋊Q8—861no—
681C4⋊Q8—861no—
682C4⋊Q8—861no—
683C4⋊Q8—861no—
684C4⋊Q8C22×D4311yescharacteristic
685#127—432no—
686#127—431no—
687#127—861no—
688#127—861no—
689#127C22×D4311yescharacteristic
690#125—862no—
691#125—862no—
692#125—862no—
693#125—862no—
694#124—432no—
695#124—432no—
696#124—432no—
697#124—862no—
698#124—862no—
699#124C22×D4312yes—
700C22⋊Q8—432no—
701C22⋊Q8—432no—
702C22⋊Q8—432no—
703C22⋊Q8—432no—
704C22⋊Q8—861no—
705C22⋊Q8—861no—
706C22⋊Q8—862no—
707C22⋊Q8—862no—
708C22⋊Q8—862no—
709C22⋊Q8—862no—
710C22⋊Q8—861no—
711C22⋊Q8—861no—
712#121—21no—
713#121—21no—
714#121—862no—
715#121—862no—
716#121—861no—
717#121—861no—
718#121—861no—
719#121—861no—
720#121—862no—
721#121—862no—
722#121—861no—
723#121—861no—
724C4×Q8—21no—
725C4×Q8—21no—
726C4×Q8—432no—
727C4×Q8—432no—
728C4×Q8—862no—
729C4×Q8—862no—
730C4×Q8—862no—
731C4×Q8—862no—
732C4×Q8—861no—
733C4×Q8—861no—
734C4×Q8C22×D4312yes—
735C4×Q8C22×D4312yes—
736C4×D4—21no—
737C4×D4—21no—
738C4×D4—862no—
739C4×D4—862no—
740C4×D4—861no—
741C4×D4—861no—
742C4×D4—862no—
743C4×D4—862no—
744C4×D4—861no—
745C4×D4—861no—
746C4×D4—861no—
747C4×D4—861no—
748#117—862no—
749#117—862no—
750#117—862no—
751#117—862no—
752C2×C4⋊C4—21no—
753C2×C4⋊C4—431no—
754C2×C4⋊C4—861no—
755C2×C4⋊C4—861no—
756C2×C4⋊C4—861no—
757C2×C4⋊C4—861no—
758C2×C4⋊C4—861no—
759C2×C4⋊C4—861no—
760C2×C4⋊C4—861no—
761C2×C4⋊C4—861no—
762C2×C4⋊C4C22×D4311yescharacteristic
763C2×C22⋊C4—862no—
764C2×C22⋊C4—862no—
765C2×C22⋊C4—861no—
766C2×C22⋊C4—861no—
767C2×C42—21no—
768C2×C42—431no—
769C2×C42—431no—
770C2×C42—431no—
771C2×C42—431no—
772C2×C42—431no—
773C2×C42—431no—
774C2×C42—431no—
775C2×C42—431no—
776C2×C42—431no—
777C2×C42—431no—
778C2×C42—431no—
779C2×C42—861no—
780C2×C42C22×D4311yescharacteristic
781C4⋊C8—432no—
782C4⋊C8—432no—
783C4⋊C8C22×D4312yes—
784C4⋊C8C22×D4312yes—
785#103—434no—
786#103—434no—
787#103—434no—
788#103C22×D4314yes—
789#102—434no—
790#102—434no—
791#102—434no—
792#102C22×D4314yes—
793C22⋊C8—434no—
794C22⋊C8—434no—
795#97—434no—
796C4×C8—434no—
797C24—431no—
798C24—862no—
799#41—24no—
800#41—24no—
801#41—864no—
802#41—864no—
803#41—1728no—
804#41—1722no—
805#41—1722no—
806#41—1728no—
807#41—1722no—
808#41—1722no—
809C2×Q8—21no—
810C2×Q8—22no—
811C2×Q8—22no—
812C2×Q8—432no—
813C2×Q8—432no—
814C2×Q8—862no—
815C2×Q8—862no—
816C2×Q8—862no—
817C2×Q8—861no—
818C2×Q8—862no—
819C2×Q8—862no—
820C2×Q8—1724no—
821C2×Q8—1722no—
822C2×Q8—1722no—
823C2×Q8C23×D4312yes—
824C2×Q8C23×D4312yes—
825C2×D4—22no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—432no—
829C2×D4—862no—
830C2×D4—862no—
831C2×D4—862no—
832C2×D4—862no—
833C2×D4—862no—
834C2×D4—862no—
835C2×D4—861no—
836C2×D4—861no—
837C2×D4—1724no—
838C2×D4—1722no—
839C2×D4—1722no—
840C2×D4—1724no—
841C2×D4—1728no—
842C2×D4C23×D4312yes—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—22no—
846C22×C4—431no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—864no—
862C22×C4—862no—
863C22×C4—862no—
864C22×C4—862no—
865C22×C4—862no—
866C22×C4—862no—
867C22×C4—861no—
868C22×C4—861no—
869C22×C4—862no—
870C22×C4—1722no—
871C22×C4—1728no—
872C22×C4D4×D4311yescharacteristic
873C22×C4D4×D4311yescharacteristic
874C22×C4C23×D4311yescharacteristic
875Q16—44no—
876Q16—1724no—
877Q16—1724no—
878Q16—1724no—
879SD16—44no—
880SD16—1724no—
881SD16—1724no—
882SD16—1724no—
883M16—24no—
884M16—864no—
885C2×C8—434no—
886C2×C8C23×D4314yes—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—432no—
893C4⋊C4—862no—
894C4⋊C4—862no—
895C4⋊C4—862no—
896C4⋊C4—862no—
897C4⋊C4—862no—
898C4⋊C4—862no—
899C4⋊C4—862no—
900C4⋊C4—862no—
901C4⋊C4—862no—
902C4⋊C4—862no—
903C4⋊C4—862no—
904C4⋊C4—862no—
905C4⋊C4—861no—
906C4⋊C4—861no—
907C4⋊C4—861no—
908C4⋊C4—862no—
909C4⋊C4—862no—
910C4⋊C4C23×D4312yes—
911C22⋊C4—22no—
912C22⋊C4—22no—
913C22⋊C4—862no—
914C22⋊C4—862no—
915C22⋊C4—862no—
916C22⋊C4—862no—
917C22⋊C4—862no—
918C22⋊C4—862no—
919C22⋊C4—862no—
920C22⋊C4—862no—
921C22⋊C4—862no—
922C22⋊C4—862no—
923C42—22no—
924C42—22no—
925C42—431no—
926C42—431no—
927C42—431no—
928C42—431no—
929C42—431no—
930C42—431no—
931C42—431no—
932C42—431no—
933C42—431no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—862no—
938C42—862no—
939C42D4×D4311yescharacteristic
940C42D4×D4311yescharacteristic
941C42C23×D4311yescharacteristic
942C42C23×D4311yescharacteristic
943C23—22no—
944C23—431no—
945C23—431no—
946C23—862no—
947C23—862no—
948C23—862no—
949C23—1721no—
950C23—1724no—
951C23—1724no—
952C23—1724no—
953C23C2×D4×D4311yescharacteristic
954Q8—22no—
955Q8—22no—
956Q8—22no—
957Q8—22no—
958Q8—42no—
959Q8—862no—
960Q8—862no—
961Q8—862no—
962Q8—862no—
963Q8—1724no—
964Q8—1724no—
965Q8—1724no—
966Q8—1722no—
967D4—22no—
968D4—22no—
969D4—42no—
970D4—44no—
971D4—42no—
972D4—862no—
973D4—862no—
974D4—1722no—
975D4—1724no—
976D4—1724no—
977D4—1724no—
978D4—1724no—
979D4—1724no—
980D4—1724no—
981D4—1722no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—41no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—44no—
990C2×C4—431no—
991C2×C4—431no—
992C2×C4—434no—
993C2×C4—431no—
994C2×C4—431no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—861no—
1008C2×C4—861no—
1009C2×C4—861no—
1010C2×C4—861no—
1011C2×C4—862no—
1012C2×C4—862no—
1013C2×C4—862no—
1014C2×C4—1721no—
1015C2×C4—1721no—
1016C2×C4—1724no—
1017C2×C4—1724no—
1018C2×C4—1724no—
1019C2×C4—1722no—
1020C2×C4—1722no—
1021C2×C4—1724no—
1022C2×C4C2×D4×D4311yescharacteristic
1023C2×C4C2×D4×D4311yescharacteristic
1024C2×C4C2×D4×D4311yescharacteristic
1025C2×C4C2×D4×D4311yescharacteristic
1026C2×C4C2×D4×D4311yescharacteristic
1027C2×C4#1306337012yes—
1028C2×C4#1306337112yes—
1029C2×C4C24×D4311yescharacteristic
1030C8—24no—
1031C8—864no—
1032C22—21no—
1033C22—21no—
1034C22—42no—
1035C22—42no—
1036C22—42no—
1037C22—432no—
1038C22—861no—
1039C22—861no—
1040C22—861no—
1041C22—861no—
1042C22—861no—
1043C22—3448no—
1044C22—1724no—
1045C22—1722no—
1046C22—1722no—
1047C22—1722no—
1048C22#1458346512yes—
1049C22C22×D4×D4311yescharacteristic
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—432no—
1057C4—432no—
1058C4—861no—
1059C4—861no—
1060C4—861no—
1061C4—861no—
1062C4—1722no—
1063C4—1722no—
1064C4—1722no—
1065C4#1458346512yes—
1066C4#137×D4312yes—
1067C4C2×#1306337011yescharacteristic
1068C4C2×#1306337111yescharacteristic
1069C2—22no—
1070C2—82no—
1071C2—862no—
1072C2—3442no—
1073C2—1721no—
1074C2C2×#1458346511yescharacteristic
1075C2C2×#137×D4311yescharacteristic
1076C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3037C2
socleC22×C43C23×D4
prime radical#532×D43C2
hypercenter#3037D43
hypocenterC43#60804
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3037

Complements

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

NH ≅ G/Ntype
1. C2×#14583453C2semidirect
3. #19145605C2semidirect
4. #19145604C2semidirect
5. #19145596C2semidirect
6. #19145550C2semidirect
7. #19145542C2semidirect
8. #19145535C2semidirect
9. #19145050C2semidirect
10. #19144986C2semidirect
11. #19144069C2semidirect
12. #19144067C2semidirect
13. #19144063C2semidirect
14. #19143856C2semidirect
15. #19143851C2semidirect
16. #19143227C2semidirect
17. C43×#3037C2semidirect
19. C2×#13063358C22semidirect
20. C2×#13063356C22semidirect
21. C2×#13063355C22semidirect
28. #14583453C22semidirect
29. #14583453C22semidirect
39. C2×#13063324C22semidirect
40. C2×#13063323C22semidirect
51. C2×C4×Dic86C22semidirect
56. #14583292C22semidirect
57. #14583290C22semidirect
58. #14583277C22semidirect
59. #14583270C22semidirect
60. #14583260C22semidirect
61. #14583257C22semidirect
62. #14583248C22semidirect
63. #14583244C22semidirect
64. #14583122C22semidirect
65. #14583121C22semidirect
66. #14583118C22semidirect
67. #14583110C22semidirect
68. #14583109C22semidirect
69. #14583106C22semidirect
70. #14583100C22semidirect
71. #14583099C22semidirect
72. #14583096C22semidirect
73. #14583064C22semidirect
74. #14583062C22semidirect
75. #14583060C22semidirect
76. #14583058C22semidirect
82. #14582955C22semidirect
84. #14582951C22semidirect
85. #14582923C22semidirect
86. #14582901C22semidirect
87. #14582900C22semidirect
88. #14582898C22semidirect
90. M16×Dic43C22semidirect
91. C2×#137×C43C22semidirect
93. C2×C4×Q8×C43C22semidirect
94. C43×#464C22semidirect
95. C43×#462C22semidirect
96. C43×#460C22semidirect
97. C43×#423C22semidirect
98. C43×#417C22semidirect
482. C4×D43#137semidirect
544. #3037D43semidirect
560. C2×#137C2×D43semidirect
592. C2×C4×Q8C2×D43semidirect
608. #464C2×D43semidirect
612. #462C2×D43semidirect
616. #460C2×D43semidirect
630. #423C2×D43semidirect
634. #417C2×D43semidirect
637. C43#60804semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
#532×D432
#191456052
#191456042
#191455962
#191455502
#191455422
#191455352
#191450502
#191449862
#191440692
#191440672
#191440632
#191438562
#191438512
#191432272
C43×#30372
#6080443