Finite Group Databasebeta

← #25982683

Subgroups — #25982683

Order 11008.

2350 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148830C211yesmaximal, characteristic, complemented
2#19148228C211yesmaximal, characteristic, complemented
3#19146742C212yesmaximal, complemented
4#19146734C212yesmaximal, complemented
5#19146451C212yesmaximal, complemented
6#19146443C212yesmaximal, complemented
7#19146269C212yesmaximal, complemented
8#19146265C212yesmaximal, complemented
9#19146079C212yesmaximal, complemented
10#19146072C212yesmaximal, complemented
11#19145643C212yesmaximal, complemented
12#19145459C212yesmaximal, complemented
13#19145356C211yesmaximal, characteristic, complemented
14#19144834C212yesmaximal, complemented
15#19143860C212yesmaximal, complemented
16C2×#14583035C211yesmaximal, characteristic, complemented
17C2×#14583032C211yesmaximal, characteristic, complemented
18#19143649C211yesmaximal, characteristic, complemented
19C43×#3188C211yesmaximal, characteristic, complemented
20C2×#13063371C2211yescharacteristic, complemented
21C23×D172C2211yescharacteristic, complemented
22C2×#13063352C2212yescomplemented
23C22×D344C2212yescomplemented
24C22×#10621882C2212yescomplemented
25C2×D8×D43C2212yescomplemented
26#14583637—22no—
27#14583601C2212yescomplemented
28#14583597C2212yescomplemented
29#14583545—21no—
30#14583545—21no—
31#14583540C2212yescomplemented
32#14583540C2212yescomplemented
33D4×D172—21no—
34D4×D172—21no—
35#14583533C2212yescomplemented
36#14583533C2212yescomplemented
37#14583533C2212yescomplemented
38D4×C22⋊D43—22no—
39D4×C22⋊D43C2212yescomplemented
40#14583502C2212yescomplemented
41#14583487—21no—
42#14583486—21no—
43#14583468C2211yescharacteristic, complemented
44#14583465C2212yescomplemented
45#14583463C2211yescharacteristic, complemented
46#14583461—21no—
47#14583460—22no—
48#14583457—21no—
49#14583410C2211yescharacteristic
50C2×#13063299C2211yescharacteristic, complemented
51#120×D43—22no—
52#14583373C2211yescharacteristic, complemented
53#14583285C2212yescomplemented
54#14583274C2212yescomplemented
55#14583262C2212yescomplemented
56#14583255C2212yescomplemented
57#14583232C2211yescharacteristic, complemented
58#14583226C2212yescomplemented
59#14583225C2212yescomplemented
60#14583223C2212yescomplemented
61#14583215C2211yescharacteristic, complemented
62#14583202C2212yescomplemented
63#14583198C2212yescomplemented
64#14583153C2212yescomplemented
65#14583151C2212yescomplemented
66#14583136C2212yescomplemented
67#14583134C2212yescomplemented
68#14583133C2212yescomplemented
69#14583130C2212yescomplemented
70#14583117C2212yescomplemented
71#14583116C2212yescomplemented
72#14583093C2212yescomplemented
73#14583093C2212yescomplemented
74#14583093C2212yescomplemented
75#14583092C2212yescomplemented
76#14583049C2211yescharacteristic, complemented
77#14583047C2212yescomplemented
78#14583044C2212yescomplemented
79#14583043C2212yescomplemented
80#14583035C2212yescomplemented
81#14583035C2212yescomplemented
82#14583035C2212yescomplemented
83#14583035C2212yescomplemented
84#14583034C2212yescomplemented
85#14583034C2212yescomplemented
86#14583034C2212yescomplemented
87#14583032C2212yescomplemented
88#14583032C2212yescomplemented
89#14583032C2212yescomplemented
90#14583032C2212yescomplemented
91#14583032C2211yescharacteristic, complemented
92#14583031C2212yescomplemented
93#14583010C2212yescomplemented
94#14583008C2212yescomplemented
95#14582981C2212yescomplemented
96#14582979C2212yescomplemented
97#14582970C2212yescomplemented
98#14582967C2212yescomplemented
99C8×C22⋊D43C2212yescomplemented
100(C22⋊D43)⋊C8C2212yescomplemented
101#14582957C2212yescomplemented
102#14582902C2212yescomplemented
103#14582894C2212yescomplemented
104C2×#13063247C2212yescomplemented
105C2×#13063245C2212yescomplemented
106#14582864C2212yescomplemented
107C2×C22⋊(C43⋊C8)C2211yescharacteristic, complemented
108C43×#525C2211yescharacteristic, complemented
109C2×#121×C43C2211yescharacteristic, complemented
110C43×#484C2211yescharacteristic, complemented
111C43×#482C2212yescomplemented
112C43×#481C2211yescharacteristic, complemented
113C43×#466C2212yescomplemented
114C43×#465C2212yescomplemented
115C43×#450C2211yescharacteristic, complemented
116C43×#449C2212yescomplemented
117C43×#447C2211yescharacteristic, complemented
118C2×C22⋊C8×C43C2211yescharacteristic, complemented
119C24×D43—21no—
120#13063371—44no—
121C2×#10621902C2312yes—
122C2×#10621898—21no—
123C2×#10621898C2311yescharacteristic
124C22×D172—21no—
125C22×D172—21no—
126C22×D172—21no—
127C22×D172—21no—
128C22×D172—44no—
129C22×D172C2311yescharacteristic
130C22×D172C2312yes—
131C22×D172C2312yes—
132C22×D172C2311yescharacteristic
133C22×D172C2311yescharacteristic
134C22×C22⋊D43—21no—
135C22×C22⋊D43—22no—
136C2×D4×D43—22no—
137C2×D4×D43—22no—
138C2×D4×D43—22no—
139C2×D4×D43—22no—
140C2×D4×D43C2312yes—
141C2×D4×D43C2312yescomplemented
142#13063352—44no—
143C2×#10621884C2312yescomplemented
144C2×D344—44no—
145C2×D344C2312yes—
146C2×D344C2312yes—
147C2×D344C2312yes—
148C2×D344C2312yes—
149C2×#10621882—44no—
150C2×#10621882C2312yes—
151C2×#10621882C2312yes—
152C2×#10621882C2312yes—
153C2×#10621882C2312yes—
154C2×#10621882C2312yescomplemented
155D8×D43—44no—
156C2×#10621872C2312yescomplemented
157C22×C43⋊C8C2312yes—
158C2×C8×D43C2312yescomplemented
159#13063322—21no—
160#13063321—22no—
161#13063321C2312yes—
162#13063321C2312yescomplemented
163#13063320—22no—
164#13063318—22no—
165#13063316C2312yescomplemented
166#13063314C2312yes—
167#13063313—21no—
168#13063311—22no—
169#13063310—22no—
170#13063310—22no—
171#13063310—22no—
172#13063309—22no—
173#13063309—22no—
174#13063308D412yes—
175#13063307—22no—
176#13063304D411yescharacteristic
177#13063304D411yescharacteristic
178#13063300—22no—
179#13063300—22no—
180#13063300C2312yes—
181#13063300C2312yes—
182#13063300C2312yescomplemented
183#13063299—21no—
184#13063299—21no—
185#13063299—22no—
186#13063299—21no—
187#13063299—21no—
188#13063299D411yescharacteristic
189#13063299D411yescharacteristic
190#13063299C2312yes—
191#13063299C2312yes—
192#13063298—22no—
193#13063298—22no—
194#13063298—22no—
195#13063297—22no—
196#13063297—22no—
197#13063297—22no—
198#13063296—22no—
199#13063296C2312yescomplemented
200#13063295—22no—
201#13063295—22no—
202#13063295—22no—
203#13063295—22no—
204#13063295—22no—
205#13063295—22no—
206#13063295—22no—
207#13063294—22no—
208#13063294D412yes—
209#13063293—22no—
210#13063293—22no—
211#13063293—22no—
212#13063293—22no—
213#13063293—22no—
214#13063293—22no—
215C4×D172—21no—
216C4×D172—21no—
217D4×Dic43—22no—
218D4×Dic43C2312yescomplemented
219#13063287C2312yes—
220#13063287C2312yes—
221#13063287C2312yescomplemented
222C4×C22⋊D43—22no—
223C4×C22⋊D43C2312yes—
224C4×C22⋊D43C2312yes—
225#13063284C2311yescharacteristic
226#13063283C2312yescomplemented
227C2×C4⋊Dic43C2311yescharacteristic
228C2×(C2×D43)⋊C4—21no—
229C22⋊C4×D43—22no—
230C22⋊C4×D43—22no—
231C22⋊C4×D43—22no—
232#13063258C2312yescomplemented
233#13063256C2312yescomplemented
234Dic43⋊C8C2312yescomplemented
235Dic43⋊C8C2312yescomplemented
236#13063249C2312yescomplemented
237#13063247C2312yes—
238#13063247C2312yes—
239#13063247C2312yes—
240#13063247C2312yes—
241#13063246C2312yescomplemented
242#13063245C2312yes—
243#13063245C2312yes—
244#13063245C2312yes—
245#13063245C2312yes—
246#13063245C2312yescomplemented
247#13063245C2312yescomplemented
248C22⋊(C43⋊C8)C2312yes—
249C22⋊(C43⋊C8)C2311yescharacteristic
250C22⋊(C43⋊C8)C2311yescharacteristic
251(C2×D43)⋊C8C2312yescomplemented
252(C2×D43)⋊C8C2312yescomplemented
253#13063235C2312yescomplemented
254C8×Dic43C2312yescomplemented
255C2×#41×C43C2311yescharacteristic
256C22×D4×C43—21no—
257C22×D4×C43C2311yescharacteristic
258C23×C4×C43C2311yescharacteristic
259C2×SD16×C43C2312yescomplemented
260C2×D8×C43C2312yescomplemented
261C22×C8×C43C2312yes—
262#123×C43—21no—
263C22⋊Q8×C43C2311yescharacteristic
264C22⋊Q8×C43C2311yescharacteristic
265#121×C43—21no—
266#121×C43—21no—
267#121×C43C2312yes—
268#121×C43C2312yes—
269#121×C43C2311yescharacteristic
270#121×C43C2311yescharacteristic
271#120×C43—21no—
272C4×D4×C43—21no—
273C4×D4×C43—21no—
274#117×C43C2311yescharacteristic
275C2×C4⋊C4×C43C2311yescharacteristic
276C2×C22⋊C4×C43—21no—
277#107×C43C2312yescomplemented
278#106×C43C2312yescomplemented
279#103×C43C2312yescomplemented
280#102×C43C2312yescomplemented
281#102×C43C2312yescomplemented
282#102×C43C2312yescomplemented
283C22⋊C8×C43C2312yes—
284C22⋊C8×C43C2311yescharacteristic
285C22⋊C8×C43C2311yescharacteristic
286C24×C43—21no—
287C24×C43C2×D411yescharacteristic
288C23×D43—21no—
289C23×D43—22no—
290C23×D43—22no—
291C23×D43—21no—
292C23×D43—21no—
293C23×D43—22no—
294C23×D43—22no—
295C23×D43—44no—
296C23×D43—82no—
297C23×D43—82no—
298#41×C43—42no—
299C2×Q8×C43C2411yescharacteristic
300C2×D4×C43—21no—
301C2×D4×C43—21no—
302C2×D4×C43—21no—
303C2×D4×C43—21no—
304C2×D4×C43—22no—
305C2×D4×C43—22no—
306C2×D4×C43—42no—
307C2×D4×C43—82no—
308C2×D4×C43C2411yescharacteristic
309C2×D4×C43C2412yes—
310C22×C4×C43—21no—
311C22×C4×C43—21no—
312C22×C4×C43—42no—
313C22×C4×C43C2×D411yescharacteristic
314C22×C4×C43C2×D411yescharacteristic
315C22×C4×C43C2×D411yescharacteristic
316C22×C4×C43C2411yescharacteristic
317C22×C4×C43C2411yescharacteristic
318C22×C4×C43C2411yescharacteristic
319C2×C22⋊D43—22no—
320C2×C22⋊D43—22no—
321C2×C22⋊D43—22no—
322C2×C22⋊D43—22no—
323C2×C22⋊D43—22no—
324C2×C22⋊D43—22no—
325C2×C22⋊D43—22no—
326C2×C22⋊D43—22no—
327C2×C22⋊D43—22no—
328C2×C22⋊D43—82no—
329C2×C22⋊D43—84no—
330C2×C22⋊D43C2×D412yes—
331C2×C22⋊D43C2×D412yes—
332C2×C22⋊D43C2×D412yes—
333C22×Dic43—22no—
334C22×Dic43—21no—
335#10621902—24no—
336#10621902—42no—
337D4×D43—24no—
338D4×D43—48no—
339D4×D43—42no—
340D4×D43—42no—
341D4×D43—42no—
342D4×D43—84no—
343D4×D43—84no—
344D4×D43—84no—
345#10621898—42no—
346#10621898—44no—
347C2×D172—21no—
348C2×D172—24no—
349C2×D172—22no—
350C2×D172—22no—
351C2×D172—21no—
352C2×D172—21no—
353C2×D172—22no—
354C2×D172—22no—
355C2×D172—22no—
356C2×D172—22no—
357C2×D172—24no—
358C2×D172—24no—
359C2×D172—44no—
360C2×D172—42no—
361C2×D172—42no—
362C2×D172—42no—
363C2×D172—44no—
364C2×D172—44no—
365C2×D172—44no—
366C2×D172—42no—
367C2×D172C2×D411yescharacteristic
368C2×D172C2412yes—
369C2×D172C2412yes—
370C2×D172C2412yes—
371C2×C4×D43—22no—
372C2×C4×D43—22no—
373C2×C4×D43—22no—
374C2×C4×D43—22no—
375C2×C4×D43C2412yes—
376C2×Dic86C2×D411yescharacteristic
377SD16×C43—42no—
378D8×C43—42no—
379C2×C8×C43—42no—
380C2×C8×C43C2412yes—
381C2×C8×C43C2412yes—
382C4⋊C4×C43—21no—
383C4⋊C4×C43—21no—
384C4⋊C4×C43—21no—
385C4⋊C4×C43C2411yescharacteristic
386C4⋊C4×C43C2411yescharacteristic
387C4⋊C4×C43C2412yes—
388C22⋊C4×C43—22no—
389C22⋊C4×C43—22no—
390C22⋊C4×C43—21no—
391C22⋊C4×C43—21no—
392C22⋊C4×C43—21no—
393C22⋊C4×C43—21no—
394C22⋊C4×C43—21no—
395C42×C43—21no—
396C22⋊Dic43—22no—
397C22⋊Dic43—22no—
398C22⋊Dic43C2×D412yes—
399C22⋊Dic43C2×D412yes—
400C22⋊Dic43C2×D412yes—
401#10621884—42no—
402#10621882—24no—
403#10621882—24no—
404#10621882—42no—
405#10621882—42no—
406#10621882—42no—
407(C2×D43)⋊C4—22no—
408(C2×D43)⋊C4—22no—
409(C2×D43)⋊C4—22no—
410(C2×D43)⋊C4—22no—
411(C2×D43)⋊C4—22no—
412(C2×D43)⋊C4—22no—
413(C2×D43)⋊C4—22no—
414(C2×D43)⋊C4—22no—
415(C2×D43)⋊C4—22no—
416(C2×D43)⋊C4—22no—
417(C2×D43)⋊C4—22no—
418(C2×D43)⋊C4C2×D412yes—
419(C2×D43)⋊C4C2×D412yes—
420C4⋊Dic43—21no—
421C4⋊Dic43—22no—
422C4⋊Dic43C2×D411yescharacteristic
423C4⋊Dic43C2×D411yescharacteristic
424C4⋊Dic43C2412yes—
425Dic43⋊C4—22no—
426Dic43⋊C4C2×D412yes—
427Dic43⋊C4C2×D412yes—
428C4×Dic43—22no—
429C4×Dic43C2412yes—
430C2×C43⋊C8—42no—
431C2×C43⋊C8C2412yes—
432C2×C43⋊C8C2412yes—
433D344—24no—
434D344—24no—
435D344—42no—
436D344—42no—
437#10621872—42no—
438C8×D43—42no—
439C23×C43—22no—
440C23×C43—22no—
441C23×C43—22no—
442C23×C43—21no—
443C23×C43—41no—
444C23×C43—42no—
445C23×C43—81no—
446C23×C43—81no—
447C23×C43C22×D411yescharacteristic
448C23×C43C22×D411yescharacteristic
449C23×C43C22×D411yescharacteristic
450C22×D43—22no—
451C22×D43—24no—
452C22×D43—22no—
453C22×D43—22no—
454C22×D43—44no—
455C22×D43—44no—
456C22×D43—44no—
457C22×D43—42no—
458C22×D43—44no—
459C22×D43—44no—
460C22×D43—42no—
461C22×D43—82no—
462C22×D43—82no—
463C22×D43—82no—
464C22×D43—82no—
465C22×D43—82no—
466C22×D43—81no—
467C22×D43—81no—
468C22×D43—82no—
469C22×D43—82no—
470C22×D43—81no—
471C22×D43—81no—
472C22×D43—81no—
473C22×D43—81no—
474C22×D43—816no—
475C22×D43C22×D412yes—
476Q8×C43—22no—
477D4×C43—22no—
478D4×C43—22no—
479D4×C43—22no—
480D4×C43—42no—
481D4×C43—42no—
482D4×C43—42no—
483D4×C43—44no—
484D4×C43—81no—
485D4×C43—82no—
486C2×C4×C43—22no—
487C2×C4×C43—22no—
488C2×C4×C43—22no—
489C2×C4×C43—22no—
490C2×C4×C43—21no—
491C2×C4×C43—21no—
492C2×C4×C43—21no—
493C2×C4×C43—41no—
494C2×C4×C43—41no—
495C2×C4×C43—41no—
496C2×C4×C43—42no—
497C2×C4×C43—81no—
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D411yescharacteristic
500C2×C4×C43C22×D411yescharacteristic
501C2×C4×C43C2511yescharacteristic
502C22⋊D43—24no—
503C22⋊D43—24no—
504C22⋊D43—42no—
505C22⋊D43—44no—
506C22⋊D43—44no—
507C22⋊D43—82no—
508C22⋊D43—82no—
509C22⋊D43—82no—
510C22⋊D43—82no—
511C22⋊D43—82no—
512C22⋊D43—82no—
513C22⋊D43—82no—
514C2×Dic43—22no—
515C2×Dic43—82no—
516C2×Dic43—81no—
517C2×Dic43C22×D412yes—
518C2×Dic43C22×D412yes—
519C2×Dic43C22×D412yes—
520D172—24no—
521D172—22no—
522D172—22no—
523D172—22no—
524D172—22no—
525D172—22no—
526D172—41no—
527D172—44no—
528D172—44no—
529D172—42no—
530D172—44no—
531D172—81no—
532D172—82no—
533D172—82no—
534D172—82no—
535D172H(5,𝔽2)14yes—
536C4×D43—22no—
537C4×D43—22no—
538C4×D43—44no—
539C4×D43—82no—
540C4×D43—82no—
541C4×D43—82no—
542Dic86—41no—
543C8×C43—22no—
544C8×C43—22no—
545C43⋊C8—22no—
546C43⋊C8—22no—
547#61630—431nomaximal, Sylow
548C22×C43—21no—
549C22×C43—21no—
550C22×C43—21no—
551C22×C43—21no—
552C22×C43—21no—
553C22×C43—21no—
554C22×C43—21no—
555C22×C43—44no—
556C22×C43—41no—
557C22×C43—42no—
558C22×C43—41no—
559C22×C43—41no—
560C22×C43—42no—
561C22×C43—42no—
562C22×C43—162no—
563C22×C43#57612yes—
564C22×C43#57612yes—
565C22×C43C23×D411yescharacteristic
566C2×D43—24no—
567C2×D43—22no—
568C2×D43—22no—
569C2×D43—22no—
570C2×D43—42no—
571C2×D43—42no—
572C2×D43—42no—
573C2×D43—42no—
574C2×D43—42no—
575C2×D43—42no—
576C2×D43—42no—
577C2×D43—42no—
578C2×D43—84no—
579C2×D43—88no—
580C2×D43—88no—
581C2×D43—84no—
582C2×D43—164no—
583C2×D43—164no—
584C2×D43—162no—
585C4×C43—21no—
586C4×C43—21no—
587C4×C43—21no—
588C4×C43—41no—
589C4×C43—41no—
590C4×C43—41no—
591C4×C43—42no—
592C4×C43C2×H(5,𝔽2)12yes—
593Dic43—22no—
594Dic43—22no—
595Dic43—22no—
596Dic43—42no—
597#3537—431no—
598#3484—431no—
599#3318—432no—
600#3318—432no—
601#3297—432no—
602#3297—432no—
603D4×D8—432no—
604D4×D8—432no—
605#3264—432no—
606#3264—432no—
607#3220—432no—
608#3199—432no—
609#3188—431no—
610#3188D4311yescharacteristic, complemented
611#3122—432no—
612#3008—432no—
613C2×#447—431no—
614C2×#447—431no—
615#2977—431no—
616C2×C43—22no—
617C2×C43—22no—
618C2×C43—41no—
619C2×C43—81no—
620C2×C43—82no—
621C2×C43#348411yescharacteristic
622C2×C43C2×#57611yescharacteristic
623C2×C43C2×#57611yescharacteristic
624D43—42no—
625D43—44no—
626D43—82no—
627D43—82no—
628C2×H(5,𝔽2)—431no—
629C23×D4—431no—
630C2×AGL(1,ℤ/8)—432no—
631C22×D8—432no—
632C22×D8—432no—
633C22×D8—432no—
634#560—862no—
635#553—432no—
636#553—432no—
637#546—432no—
638#546—432no—
639#546—861no—
640#546—861no—
641D42—432no—
642D42—432no—
643D42—432no—
644D42—432no—
645D42—861no—
646D42—861no—
647D42—862no—
648#540—432no—
649#538—861no—
650#538—861no—
651#535—432no—
652#535—431no—
653#535—431no—
654#534—861no—
655#534—861no—
656#534—862no—
657#525—431no—
658#525C2×D4311yescharacteristic, complemented
659C2×#121—431no—
660C2×#121C2×D4311yescharacteristic, complemented
661C2×#120—862no—
662#518—431no—
663#496—432no—
664#493—432no—
665#490—432no—
666#488—432no—
667#484—431no—
668#484C2×D4311yescharacteristic, complemented
669#482—432no—
670#482—432no—
671#482—432no—
672#482C2×D4312yescomplemented
673#481—431no—
674#481C2×D4311yescharacteristic, complemented
675#478—432no—
676#478—432no—
677#469—432no—
678#469—432no—
679#466—432no—
680#466—432no—
681#466—432no—
682#466C2×D4312yescomplemented
683#465—432no—
684#465C2×D4312yescomplemented
685#463—432no—
686#463—432no—
687#459—432no—
688#459—432no—
689#459—432no—
690#459—432no—
691#450—431no—
692#450C2×D4311yescharacteristic, complemented
693#449—432no—
694#449—432no—
695#449—432no—
696#449C2×D4312yescomplemented
697#447—432no—
698#447—432no—
699#447—431no—
700#447—432no—
701#447—432no—
702#447—432no—
703#447—432no—
704#447—432no—
705#447—432no—
706#447—432no—
707#447—432no—
708#447—432no—
709#447—432no—
710#447C2×D4311yescharacteristic, complemented
711#442—432no—
712#442—432no—
713C4×D8—432no—
714C4×D8—432no—
715#435—432no—
716#435—432no—
717C8×D4—432no—
718C8×D4—432no—
719#433—432no—
720#418—432no—
721#416—432no—
722C2×#102—432no—
723C2×#102—432no—
724#408—432no—
725C2×C22⋊C8—431no—
726C2×C22⋊C8C2×D4311yescharacteristic, complemented
727C43#6163011yescharacteristic, complemented, Sylow
728C25—861no—
729H(5,𝔽2)—1724no—
730C2×#41—431no—
731C2×#41—432no—
732C2×#41—861no—
733C2×#41C22×D4311yescharacteristic
734C22×D4—21no—
735C22×D4—432no—
736C22×D4—432no—
737C22×D4—431no—
738C22×D4—432no—
739C22×D4—432no—
740C22×D4—431no—
741C22×D4—431no—
742C22×D4—861no—
743C22×D4—862no—
744C22×D4—862no—
745C22×D4—862no—
746C22×D4—862no—
747C22×D4—862no—
748C22×D4—861no—
749C22×D4—861no—
750C22×D4—861no—
751C22×D4—861no—
752C22×D4—1724no—
753C22×D4C22×D4311yescharacteristic
754C23×C4C22×D4311yescharacteristic
755AGL(1,ℤ/8)—1724no—
756C2×SD16—432no—
757C2×SD16C22×D4312yescomplemented
758C2×D8—432no—
759C2×D8—432no—
760C2×D8—432no—
761C2×D8—432no—
762C2×D8—432no—
763C2×D8—432no—
764C2×D8—432no—
765C2×D8—432no—
766C2×D8—432no—
767C2×D8—1724no—
768C2×D8—1724no—
769C2×D8—1724no—
770C2×D8C22×D4312yescomplemented
771C2×M16—432no—
772C22×C8—432no—
773C22×C8—432no—
774C22×C8C22×D4312yes—
775#127—432no—
776#127—432no—
777#127—861no—
778#127—862no—
779#126—862no—
780#126—862no—
781#125—432no—
782#124—432no—
783#124—861no—
784#124—862no—
785#123—21no—
786#123—432no—
787#123—862no—
788#123—862no—
789#123—862no—
790#123—862no—
791#123—862no—
792#123—862no—
793C22⋊Q8—431no—
794C22⋊Q8—431no—
795C22⋊Q8C22×D4311yescharacteristic
796C22⋊Q8C22×D4311yescharacteristic
797#121—21no—
798#121—21no—
799#121—431no—
800#121—431no—
801#121—432no—
802#121—432no—
803#121—432no—
804#121—432no—
805#121—432no—
806#121—432no—
807#121—862no—
808#121—862no—
809#121—862no—
810#121—862no—
811#121—862no—
812#121—862no—
813#121—862no—
814#121—861no—
815#121—861no—
816#121—862no—
817#121—862no—
818#121—862no—
819#121—861no—
820#121—861no—
821#121C22×D4312yes—
822#121C22×D4312yes—
823#121C22×D4311yescharacteristic
824#121C22×D4311yescharacteristic
825#120—21no—
826#120—432no—
827#120—862no—
828#120—862no—
829#120—862no—
830#120—862no—
831#120—862no—
832#120—862no—
833#120—862no—
834#120—862no—
835#120—862no—
836#120—862no—
837#120—862no—
838#120—862no—
839#120—862no—
840#120—862no—
841C4×D4—21no—
842C4×D4—21no—
843C4×D4—432no—
844C4×D4—432no—
845C4×D4—432no—
846C4×D4—432no—
847C4×D4—432no—
848C4×D4—432no—
849C4×D4—861no—
850C4×D4—861no—
851C4×D4—862no—
852C4×D4—862no—
853#117—431no—
854#117—432no—
855#117C22×D4311yescharacteristic
856C2×C4⋊C4—431no—
857C2×C4⋊C4C22×D4311yescharacteristic
858C2×C22⋊C4—21no—
859C2×C22⋊C4—862no—
860C2×C22⋊C4—862no—
861C2×C22⋊C4—862no—
862C2×C22⋊C4—861no—
863#107—432no—
864#107C22×D4312yescomplemented
865#106—432no—
866#106C22×D4312yescomplemented
867C4⋊C8—432no—
868C4⋊C8—432no—
869#103—432no—
870#103C22×D4312yescomplemented
871#102—432no—
872#102—432no—
873#102—432no—
874#102—432no—
875#102—432no—
876#102—432no—
877#102—432no—
878#102—432no—
879#102—432no—
880#102—432no—
881#102—432no—
882#102C22×D4312yescomplemented
883#102C22×D4312yescomplemented
884#102C22×D4312yescomplemented
885C22⋊C8—432no—
886C22⋊C8—431no—
887C22⋊C8—431no—
888C22⋊C8—432no—
889C22⋊C8—432no—
890C22⋊C8C22×D4312yes—
891C22⋊C8C22×D4311yescharacteristic
892C22⋊C8C22×D4311yescharacteristic
893#97—432no—
894C4×C8—432no—
895C24—21no—
896C24—862no—
897C24—862no—
898C24—861no—
899C24—861no—
900C24—861no—
901C24—862no—
902C24—862no—
903C24—3442no—
904C24—3442no—
905C24—1724no—
906C24D4×D4311yescharacteristic
907#41—42no—
908#41—864no—
909#41—1722no—
910#41—1724no—
911#41—1722no—
912C2×Q8—431no—
913C2×Q8C23×D4311yescharacteristic
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—22no—
917C2×D4—21no—
918C2×D4—22no—
919C2×D4—21no—
920C2×D4—42no—
921C2×D4—82no—
922C2×D4—432no—
923C2×D4—432no—
924C2×D4—432no—
925C2×D4—431no—
926C2×D4—432no—
927C2×D4—432no—
928C2×D4—432no—
929C2×D4—864no—
930C2×D4—864no—
931C2×D4—864no—
932C2×D4—862no—
933C2×D4—862no—
934C2×D4—862no—
935C2×D4—862no—
936C2×D4—862no—
937C2×D4—862no—
938C2×D4—862no—
939C2×D4—862no—
940C2×D4—862no—
941C2×D4—862no—
942C2×D4—864no—
943C2×D4—862no—
944C2×D4—862no—
945C2×D4—862no—
946C2×D4—861no—
947C2×D4—861no—
948C2×D4—862no—
949C2×D4—862no—
950C2×D4—861no—
951C2×D4—3444no—
952C2×D4—3444no—
953C2×D4—3444no—
954C2×D4—3444no—
955C2×D4—3442no—
956C2×D4—1722no—
957C2×D4—1722no—
958C2×D4—1722no—
959C2×D4—1722no—
960C2×D4—1724no—
961C2×D4—1724no—
962C2×D4—1724no—
963C2×D4—1724no—
964C2×D4—1722no—
965C2×D4—1722no—
966C2×D4—1722no—
967C2×D4—1728no—
968C2×D4C23×D4311yescharacteristic
969C2×D4C23×D4312yes—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—42no—
973C22×C4—432no—
974C22×C4—862no—
975C22×C4—862no—
976C22×C4—862no—
977C22×C4—862no—
978C22×C4—862no—
979C22×C4—861no—
980C22×C4D4×D4311yescharacteristic
981C22×C4D4×D4311yescharacteristic
982C22×C4D4×D4311yescharacteristic
983C22×C4C23×D4311yescharacteristic
984C22×C4C23×D4311yescharacteristic
985C22×C4C23×D4311yescharacteristic
986SD16—42no—
987SD16—1722no—
988D8—42no—
989D8—864no—
990D8—864no—
991D8—864no—
992D8—864no—
993D8—1722no—
994D8—1722no—
995D8—1722no—
996D8—1722no—
997D8—1722no—
998M16—1722no—
999C2×C8—42no—
1000C2×C8—432no—
1001C2×C8—432no—
1002C2×C8—1722no—
1003C2×C8—1722no—
1004C2×C8C23×D4312yes—
1005C2×C8C23×D4312yes—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—431no—
1010C4⋊C4—431no—
1011C4⋊C4—432no—
1012C4⋊C4—432no—
1013C4⋊C4—432no—
1014C4⋊C4—862no—
1015C4⋊C4—862no—
1016C4⋊C4—861no—
1017C4⋊C4C23×D4312yes—
1018C4⋊C4C23×D4311yescharacteristic
1019C4⋊C4C23×D4311yescharacteristic
1020C22⋊C4—21no—
1021C22⋊C4—21no—
1022C22⋊C4—21no—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—21no—
1026C22⋊C4—21no—
1027C22⋊C4—432no—
1028C22⋊C4—432no—
1029C22⋊C4—432no—
1030C22⋊C4—432no—
1031C22⋊C4—432no—
1032C22⋊C4—862no—
1033C22⋊C4—862no—
1034C22⋊C4—862no—
1035C22⋊C4—862no—
1036C22⋊C4—862no—
1037C22⋊C4—862no—
1038C22⋊C4—862no—
1039C22⋊C4—862no—
1040C22⋊C4—862no—
1041C22⋊C4—862no—
1042C22⋊C4—862no—
1043C22⋊C4—862no—
1044C22⋊C4—862no—
1045C42—21no—
1046C42—432no—
1047C42—862no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—21no—
1052C23—41no—
1053C23—42no—
1054C23—81no—
1055C23—81no—
1056C23—432no—
1057C23—864no—
1058C23—862no—
1059C23—862no—
1060C23—862no—
1061C23—3442no—
1062C23—3442no—
1063C23—3441no—
1064C23—3441no—
1065C23—3441no—
1066C23—3441no—
1067C23—3441no—
1068C23—3441no—
1069C23—3442no—
1070C23—3442no—
1071C23—3442no—
1072C23—3442no—
1073C23—3442no—
1074C23—34416no—
1075C23—1724no—
1076C23—1724no—
1077C23—1722no—
1078C23—1724no—
1079C23—1724no—
1080C23—1724no—
1081C23—1722no—
1082C23C2×D4×D4311yescharacteristic
1083C23C2×D4×D4311yescharacteristic
1084C23C2×D4×D4311yescharacteristic
1085Q8—22no—
1086Q8—1721no—
1087D4—22no—
1088D4—22no—
1089D4—22no—
1090D4—42no—
1091D4—42no—
1092D4—44no—
1093D4—42no—
1094D4—81no—
1095D4—82no—
1096D4—434no—
1097D4—864no—
1098D4—864no—
1099D4—864no—
1100D4—862no—
1101D4—862no—
1102D4—862no—
1103D4—862no—
1104D4—862no—
1105D4—3441no—
1106D4—3442no—
1107D4—3442no—
1108D4—3442no—
1109D4—3442no—
1110D4—3442no—
1111D4—3442no—
1112D4—3442no—
1113D4—3442no—
1114D4—3442no—
1115D4—3442no—
1116D4—1721no—
1117D4—1724no—
1118D4—1724no—
1119D4—1722no—
1120D4—1724no—
1121D4—1722no—
1122D4—1724no—
1123D4—1724no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
1130C2×C4—21no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—42no—
1135C2×C4—81no—
1136C2×C4—432no—
1137C2×C4—432no—
1138C2×C4—432no—
1139C2×C4—862no—
1140C2×C4—862no—
1141C2×C4—862no—
1142C2×C4—3442no—
1143C2×C4—3442no—
1144C2×C4—3442no—
1145C2×C4—3442no—
1146C2×C4—3441no—
1147C2×C4—1724no—
1148C2×C4C2×D4×D4311yescharacteristic
1149C2×C4C2×D4×D4311yescharacteristic
1150C2×C4C2×D4×D4311yescharacteristic
1151C2×C4C24×D4311yescharacteristic
1152C8—22no—
1153C8—22no—
1154C8—862no—
1155C8—862no—
1156C22—21no—
1157C22—21no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—44no—
1164C22—42no—
1165C22—41no—
1166C22—42no—
1167C22—41no—
1168C22—41no—
1169C22—42no—
1170C22—162no—
1171C22—862no—
1172C22—862no—
1173C22—862no—
1174C22—864no—
1175C22—3448no—
1176C22—3448no—
1177C22—3444no—
1178C22—3444no—
1179C22—1722no—
1180C22—1722no—
1181C22—1722no—
1182C22—1722no—
1183C22—1722no—
1184C22—1722no—
1185C22—1722no—
1186C22—1722no—
1187C22—6882no—
1188C22—6884no—
1189C22—6884no—
1190C22#1458370112yes—
1191C22#1458370312yes—
1192C22C22×D4×D4311yescharacteristic
1193C4—21no—
1194C4—21no—
1195C4—21no—
1196C4—41no—
1197C4—42no—
1198C4—41no—
1199C4—41no—
1200C4—862no—
1201C4—862no—
1202C4—862no—
1203C4—1722no—
1204C4H(5,𝔽2)×D4312yes—
1205C2—22no—
1206C2—22no—
1207C2—41no—
1208C2—82no—
1209C2—81no—
1210C2—3442no—
1211C2—3442no—
1212C2—1722no—
1213C2—1724no—
1214C2#1914822711yescharacteristic
1215C2C2×#1458370111yescharacteristic
1216C2C2×#1458370311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3188C2
socleC22×C43C23×D4
hypercenter#3188D43
hypocenterC43#61630
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3188

Complements

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

NH ≅ G/Ntype
1. #19148830C2semidirect
2. #19148228C2semidirect
3. #19146742C2semidirect
4. #19146734C2semidirect
5. #19146451C2semidirect
6. #19146443C2semidirect
7. #19146269C2semidirect
8. #19146265C2semidirect
9. #19146079C2semidirect
10. #19146072C2semidirect
11. #19145643C2semidirect
12. #19145459C2semidirect
13. #19145356C2semidirect
14. #19144834C2semidirect
15. #19143860C2semidirect
16. C2×#14583035C2semidirect
17. C2×#14583032C2semidirect
18. #19143649C2semidirect
19. C43×#3188C2semidirect
20. C2×#13063371C22semidirect
21. C23×D172C22semidirect
22. C2×#13063352C22semidirect
23. C22×D344C22semidirect
24. C22×#10621882C22semidirect
25. C2×D8×D43C22semidirect
27. #14583601C22semidirect
28. #14583597C22semidirect
31. #14583540C22semidirect
32. #14583540C22semidirect
35. #14583533C22semidirect
36. #14583533C22semidirect
37. #14583533C22semidirect
39. D4×C22⋊D43C22semidirect
40. #14583502C22semidirect
43. #14583468C22semidirect
44. #14583465C22semidirect
45. #14583463C22semidirect
50. C2×#13063299C22semidirect
52. #14583373C22semidirect
53. #14583285C22semidirect
54. #14583274C22semidirect
55. #14583262C22semidirect
56. #14583255C22semidirect
57. #14583232C22semidirect
58. #14583226C22semidirect
59. #14583225C22semidirect
60. #14583223C22semidirect
61. #14583215C22semidirect
62. #14583202C22semidirect
63. #14583198C22semidirect
64. #14583153C22semidirect
65. #14583151C22semidirect
66. #14583136C22semidirect
67. #14583134C22semidirect
68. #14583133C22semidirect
69. #14583130C22semidirect
70. #14583117C22semidirect
71. #14583116C22semidirect
72. #14583093C22semidirect
73. #14583093C22semidirect
74. #14583093C22semidirect
75. #14583092C22semidirect
76. #14583049C22semidirect
77. #14583047C22semidirect
78. #14583044C22semidirect
79. #14583043C22semidirect
80. #14583035C22semidirect
81. #14583035C22semidirect
82. #14583035C22semidirect
83. #14583035C22semidirect
84. #14583034C22semidirect
85. #14583034C22semidirect
86. #14583034C22semidirect
87. #14583032C22semidirect
88. #14583032C22semidirect
89. #14583032C22semidirect
90. #14583032C22semidirect
91. #14583032C22semidirect
92. #14583031C22semidirect
93. #14583010C22semidirect
94. #14583008C22semidirect
95. #14582981C22semidirect
96. #14582979C22semidirect
97. #14582970C22semidirect
98. #14582967C22semidirect
99. C8×C22⋊D43C22semidirect
100. (C22⋊D43)⋊C8C22semidirect
101. #14582957C22semidirect
102. #14582902C22semidirect
103. #14582894C22semidirect
104. C2×#13063247C22semidirect
105. C2×#13063245C22semidirect
106. #14582864C22semidirect
107. C2×C22⋊(C43⋊C8)C22semidirect
108. C43×#525C22semidirect
109. C2×#121×C43C22semidirect
110. C43×#484C22semidirect
111. C43×#482C22semidirect
112. C43×#481C22semidirect
113. C43×#466C22semidirect
114. C43×#465C22semidirect
115. C43×#450C22semidirect
116. C43×#449C22semidirect
117. C43×#447C22semidirect
118. C2×C22⋊C8×C43C22semidirect
141. C2×D4×D43C23semidirect
143. C2×#10621884C23semidirect
154. C2×#10621882C23semidirect
156. C2×#10621872C23semidirect
158. C2×C8×D43C23semidirect
162. #13063321C23semidirect
165. #13063316C23semidirect
182. #13063300C23semidirect
199. #13063296C23semidirect
218. D4×Dic43C23semidirect
221. #13063287C23semidirect
226. #13063283C23semidirect
232. #13063258C23semidirect
233. #13063256C23semidirect
234. Dic43⋊C8C23semidirect
235. Dic43⋊C8C23semidirect
236. #13063249C23semidirect
241. #13063246C23semidirect
246. #13063245C23semidirect
247. #13063245C23semidirect
251. (C2×D43)⋊C8C23semidirect
252. (C2×D43)⋊C8C23semidirect
253. #13063235C23semidirect
254. C8×Dic43C23semidirect
259. C2×SD16×C43C23semidirect
260. C2×D8×C43C23semidirect
277. #107×C43C23semidirect
278. #106×C43C23semidirect
279. #103×C43C23semidirect
280. #102×C43C23semidirect
281. #102×C43C23semidirect
282. #102×C43C23semidirect
610. #3188D43semidirect
658. #525C2×D43semidirect
660. C2×#121C2×D43semidirect
668. #484C2×D43semidirect
672. #482C2×D43semidirect
674. #481C2×D43semidirect
682. #466C2×D43semidirect
684. #465C2×D43semidirect
692. #450C2×D43semidirect
696. #449C2×D43semidirect
710. #447C2×D43semidirect
726. C2×C22⋊C8C2×D43semidirect
727. C43#61630semidirect
757. C2×SD16C22×D43semidirect
770. C2×D8C22×D43semidirect
864. #107C22×D43semidirect
866. #106C22×D43semidirect
870. #103C22×D43semidirect
882. #102C22×D43semidirect
883. #102C22×D43semidirect
884. #102C22×D43semidirect

Maximal subgroups

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

subgroupindex
#191488302
#191482282
#191467422
#191467342
#191464512
#191464432
#191462692
#191462652
#191460792
#191460722
#191456432
#191454592
#191453562
#191448342
#191438602
C2×#145830352
C2×#145830322
#191436492
C43×#31882
#6163043