Finite Group Databasebeta

← #25971463

Subgroups — #25971463

Order 11008.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148489C211yesmaximal, characteristic, complemented
2#19148464C211yesmaximal, characteristic, complemented
3#19146011C212yesmaximal, complemented
4#19146003C212yesmaximal, complemented
5#19145832C211yesmaximal, characteristic, complemented
6#19145830C211yesmaximal, characteristic, complemented
7#19145795C211yesmaximal, characteristic, complemented
8#19145789C211yesmaximal, characteristic, complemented
9#19145609C211yesmaximal, characteristic, complemented
10#19145609C211yesmaximal, characteristic, complemented
11#19145582C211yesmaximal, characteristic, complemented
12#19145465C212yesmaximal, complemented
13#19145458C212yesmaximal, complemented
14#19145296C211yesmaximal, characteristic, complemented
15#19145290C211yesmaximal, characteristic, complemented
16#19145193C211yesmaximal, characteristic, complemented
17#19145187C211yesmaximal, characteristic, complemented
18#19144880C212yesmaximal, complemented
19#19144832C212yesmaximal, complemented
20#19144778C212yesmaximal, complemented
21#19144776C212yesmaximal, complemented
22#19143241C211yesmaximal, characteristic, complemented
23C43×#3213C211yesmaximal, characteristic, complemented
24#14583632—21no—
25#14583631—21no—
26#14583631—21no—
27#14583631—21no—
28#14583618—21no—
29#14583618—21no—
30#14583575—21no—
31#14583575—21no—
32#14583575—21no—
33#14583575—21no—
34#14583568—21no—
35#14583567—21no—
36#14583546—21no—
37#14583544—21no—
38#14583542—21no—
39#14583537—21no—
40#14583518C2211yescharacteristic
41#14583518C2211yescharacteristic
42#14583518C2211yescharacteristic, complemented
43#14583518C2211yescharacteristic, complemented
44#14583502C2212yes—
45#14583500C2212yescomplemented
46#14583473C2211yescharacteristic
47#14583466C2211yescharacteristic
48#14583465C2212yes—
49#14583456C2211yescharacteristic, complemented
50#14583454C2211yescharacteristic, complemented
51#14583450C2211yescharacteristic, complemented
52#14583449C2211yescharacteristic
53#14583447C2211yescharacteristic, complemented
54#127×D43C2211yescharacteristic, complemented
55#14583428C2211yescharacteristic
56#14583428C2211yescharacteristic
57#14583428C2211yescharacteristic, complemented
58#14583428C2211yescharacteristic, complemented
59#14583377C2211yescharacteristic, complemented
60#14583374C2211yescharacteristic, complemented
61#14583371C2212yescomplemented
62C4×#10621898C2211yescharacteristic
63#14583308C2211yescharacteristic, complemented
64#14583308C2211yescharacteristic, complemented
65#14583305C2211yescharacteristic, complemented
66#14583305C2211yescharacteristic, complemented
67#14583289C2211yescharacteristic
68#14583289C2211yescharacteristic
69#14583264C2211yescharacteristic, complemented
70#14583264C2211yescharacteristic, complemented
71#14583263C2211yescharacteristic, complemented
72#14583263C2211yescharacteristic, complemented
73#14583258C2211yescharacteristic, complemented
74#14583258C2211yescharacteristic, complemented
75#14583239C2212yescomplemented
76#14583238C2212yescomplemented
77#14583224C2212yescomplemented
78#14583224C2212yescomplemented
79#14583222C2212yes—
80#14583221C2212yes—
81#14583220C2212yescomplemented
82#14583220C2212yescomplemented
83#14583208C2212yescomplemented
84#14583204C2212yescomplemented
85#14583201C2212yescomplemented
86#14583197C2212yescomplemented
87#14583190C2212yescomplemented
88#14583189C2212yescomplemented
89#14583180C2212yescomplemented
90#14583179C2212yescomplemented
91#14583151C2212yescomplemented
92#14583149C2212yescomplemented
93#14583148C2212yescomplemented
94#14583142C2212yescomplemented
95#14583134C2212yescomplemented
96#14583132C2212yescomplemented
97#14583131C2212yescomplemented
98#14583125C2212yescomplemented
99#14583111C2212yescomplemented
100#14583111C2212yescomplemented
101#14583097C2212yescomplemented
102#14583097C2212yescomplemented
103#14583092C2212yes—
104#14583092C2212yes—
105#14583048C2212yescomplemented
106#14583048C2212yescomplemented
107#14583038C2212yescomplemented
108#14583033C2212yescomplemented
109#14583031C2212yes—
110#14583031C2212yes—
111#14583011C2212yescomplemented
112#14583008C2212yescomplemented
113#14583002C2212yescomplemented
114#14583000C2212yescomplemented
115SD16×Dic43C2212yescomplemented
116#14582984C2212yescomplemented
117D8×Dic43C2212yescomplemented
118#14582979C2212yescomplemented
119#14582959C2212yescomplemented
120#14582957C2212yescomplemented
121#14582956C2211yescharacteristic, complemented
122#14582954C2211yescharacteristic, complemented
123#14582954C2211yescharacteristic, complemented
124#14582924C2212yescomplemented
125#14582864C2212yes—
126#14582851C2211yescharacteristic, complemented
127#97×D43C2211yescharacteristic, complemented
128C43×#532C2211yescharacteristic
129C2×#124×C43C2211yescharacteristic, complemented
130C43×#496C2211yescharacteristic
131C43×#496C2211yescharacteristic
132C43×#489C2211yescharacteristic, complemented
133C43×#489C2211yescharacteristic, complemented
134C43×#463C2212yescomplemented
135C43×#463C2212yescomplemented
136C43×#448C2212yescomplemented
137C43×#447C2212yescomplemented
138C43×#432C2211yescharacteristic, complemented
139C2×#10621902—21no—
140C2×#10621898—21no—
141C2×#10621898C2311yescharacteristic
142C2×#10621900—21no—
143C2×D4×D43—21no—
144C2×D4×D43—21no—
145C2×D4×D43C2312yes—
146C2×#10621884C2312yes—
147C2×#10621884C2312yes—
148C2×#10621882C2312yes—
149C2×#10621882C2312yes—
150C2×#10621872C2312yes—
151C2×C8×D43C2312yes—
152#13063325C2311yescharacteristic
153#13063325C2311yescharacteristic
154#13063325C2311yescharacteristic
155#13063323—21no—
156#13063322C2311yescharacteristic
157#13063321—22no—
158#13063321—21no—
159#13063321—21no—
160#13063321—21no—
161#13063321C2312yes—
162#13063318—21no—
163#13063318—21no—
164#13063318—21no—
165#13063318—21no—
166#13063318—21no—
167#13063318—21no—
168#13063318—21no—
169#13063318—21no—
170#13063317C2311yescharacteristic
171#13063317C2311yescharacteristic
172#13063316C2312yes—
173#13063314—21no—
174#13063314—21no—
175#13063313—21no—
176#13063312—21no—
177#13063312—21no—
178#13063311—22no—
179#13063311—21no—
180#13063311—21no—
181#13063311—21no—
182#13063311—21no—
183#13063309—21no—
184#13063309—21no—
185#13063309—21no—
186#13063309—21no—
187#13063309—22no—
188#13063308—21no—
189#13063308—21no—
190#13063308—22no—
191#13063307—21no—
192#13063307—21no—
193#13063307—21no—
194#13063307—21no—
195#13063307—22no—
196#13063307—22no—
197#13063305—21no—
198#13063304—21no—
199#13063304—21no—
200#13063302—21no—
201#13063302—21no—
202#13063302—21no—
203#13063302—21no—
204#13063301—21no—
205#13063301C2311yescharacteristic
206#13063301C2311yescharacteristic
207#13063301C2311yescharacteristic
208#13063301C2311yescharacteristic
209#13063300—21no—
210#13063300C2312yes—
211#13063299—21no—
212#13063299—22no—
213#13063299C2312yes—
214#13063298—22no—
215#13063297—22no—
216#13063296—21no—
217#13063296—22no—
218#13063296C2312yes—
219#13063296C2311yescharacteristic
220#13063296C2311yescharacteristic
221#13063296C2311yescharacteristic
222#13063296C2311yescharacteristic
223#13063295—22no—
224#13063294—21no—
225#13063294—21no—
226#13063293—22no—
227Q8×Dic43—21no—
228Q8×Dic43—21no—
229Q8×Dic43—21no—
230Q8×Dic43C2311yescharacteristic
231Q8×Dic43C2311yescharacteristic
232Q8×Dic43C2311yescharacteristic
233Q8×Dic43C2311yescharacteristic
234C4×Dic86—21no—
235C4×Dic86—21no—
236C4×Dic86D411yescharacteristic
237C4×Dic86D411yescharacteristic
238#13063290—21no—
239C4×D172—21no—
240C4×D172D411yescharacteristic
241C4×D172D411yescharacteristic
242C4×D172C2312yes—
243D4×Dic43—21no—
244D4×Dic43—21no—
245D4×Dic43—21no—
246D4×Dic43C2311yescharacteristic
247D4×Dic43C2311yescharacteristic
248D4×Dic43C2312yes—
249D4×Dic43C2311yescharacteristic
250D4×Dic43C2311yescharacteristic
251#13063287—21no—
252#13063287C2312yes—
253C4×C22⋊D43—22no—
254C4×C22⋊D43D411yescharacteristic
255C4×C22⋊D43D411yescharacteristic
256C4×C22⋊D43D411yescharacteristic
257C4×C22⋊D43D411yescharacteristic
258(C22⋊D43)⋊C4—21no—
259(C22⋊D43)⋊C4—21no—
260(C22⋊D43)⋊C4—21no—
261(C22⋊D43)⋊C4—21no—
262(C22⋊D43)⋊C4—22no—
263#13063284—21no—
264#13063284—21no—
265#13063284C2311yescharacteristic
266#13063284C2311yescharacteristic
267#13063284C2311yescharacteristic
268#13063283C2312yes—
269#13063282C2311yescharacteristic
270#13063282C2311yescharacteristic
271#13063281—21no—
272#13063281—21no—
273#13063281—21no—
274#13063281—21no—
275C2×C22⋊Dic43—21no—
276C2×C22⋊Dic43—21no—
277C2×(C2×D43)⋊C4—22no—
278C22⋊C4×D43—22no—
279C42×D43C2311yescharacteristic
280C42×D43C2311yescharacteristic
281#13063259C2312yes—
282#13063259C2312yes—
283#13063258C2312yes—
284#13063258C2312yes—
285#13063257C2312yes—
286#13063257C2312yes—
287#13063256C2312yes—
288#13063256C2312yes—
289C4⋊(C43⋊C8)C2312yes—
290Dic43⋊C8C2312yes—
291Dic43⋊C8C2312yes—
292#13063249C2312yes—
293#13063249C2312yes—
294#13063247C2312yes—
295#13063247C2312yes—
296#13063247C2312yes—
297#13063247C2312yes—
298#13063246C2312yes—
299#13063246C2312yes—
300#13063246C2312yes—
301#13063246C2312yes—
302#13063246C2312yes—
303#13063246C2312yes—
304C22⋊(C43⋊C8)C2312yes—
305(C2×D43)⋊C8C2312yes—
306(C2×D43)⋊C8C2312yes—
307#13063236C2311yescharacteristic
308#13063236C2311yescharacteristic
309#13063235C2312yes—
310C8×Dic43C2312yes—
311C2×#41×C43—21no—
312C22×Q8×C43C2311yescharacteristic
313C22×D4×C43C2311yescharacteristic
314C2×SD16×C43C2312yes—
315C2×SD16×C43C2312yes—
316C2×D8×C43C2312yes—
317C2×D8×C43C2312yes—
318C4⋊Q8×C43C2311yescharacteristic
319#127×C43C2311yescharacteristic
320#124×C43—21no—
321#124×C43—21no—
322#124×C43—21no—
323#124×C43C2311yescharacteristic
324#124×C43C2311yescharacteristic
325#124×C43C2311yescharacteristic
326#124×C43C2311yescharacteristic
327#121×C43—21no—
328#121×C43C2312yes—
329C4×D4×C43—21no—
330C4×D4×C43C2312yes—
331C2×C22⋊C4×C43—21no—
332C2×C22⋊C4×C43—21no—
333C2×C42×C43C2311yescharacteristic
334C4⋊C8×C43C2312yes—
335#103×C43C2312yes—
336#103×C43C2312yes—
337#102×C43C2312yes—
338#102×C43C2312yes—
339C22⋊C8×C43C2312yes—
340#97×C43C2311yescharacteristic
341#97×C43C2311yescharacteristic
342C24×C43—21no—
343C23×D43—22no—
344#41×C43—82no—
345C2×Q8×C43—21no—
346C2×Q8×C43—21no—
347C2×Q8×C43—42no—
348C2×Q8×C43C2411yescharacteristic
349C2×Q8×C43C2411yescharacteristic
350C2×D4×C43—21no—
351C2×D4×C43—21no—
352C2×D4×C43—21no—
353C2×D4×C43—22no—
354C2×D4×C43—42no—
355C2×D4×C43C2411yescharacteristic
356C2×D4×C43C2411yescharacteristic
357C2×D4×C43C2412yes—
358C22×C4×C43—22no—
359C22×C4×C43—21no—
360C22×C4×C43C2×D411yescharacteristic
361C22×C4×C43C2×D411yescharacteristic
362C22×C4×C43C2411yescharacteristic
363C2×C22⋊D43—22no—
364C2×C22⋊D43—22no—
365C2×C22⋊D43—22no—
366C2×C22⋊D43—22no—
367C2×C22⋊D43—21no—
368C2×C22⋊D43—21no—
369C2×C22⋊D43—21no—
370C2×C22⋊D43—21no—
371C2×C22⋊D43—22no—
372C2×C22⋊D43C2×D411yescharacteristic
373C2×C22⋊D43C2×D411yescharacteristic
374C22×Dic43—22no—
375C22×Dic43—21no—
376C22×Dic43—21no—
377C22×Dic43—21no—
378C22×Dic43—21no—
379#10621902—82no—
380#10621900—82no—
381D4×D43—42no—
382D4×D43—42no—
383D4×D43—82no—
384D4×D43—82no—
385#10621898—42no—
386#10621898—82no—
387C2×D172—21no—
388C2×D172—21no—
389C2×D172—22no—
390C2×D172C2×D411yescharacteristic
391C2×D172C2412yes—
392C2×C4×D43—22no—
393C2×C4×D43—22no—
394C2×C4×D43C2×D411yescharacteristic
395C2×C4×D43C2×D411yescharacteristic
396C2×C4×D43C2×D411yescharacteristic
397C2×C4×D43C2×D411yescharacteristic
398C2×C4×D43C2411yescharacteristic
399C2×C4×D43C2411yescharacteristic
400C2×Dic86—21no—
401C2×Dic86—21no—
402C2×Dic86—21no—
403C2×Dic86C2×D411yescharacteristic
404SD16×C43—42no—
405SD16×C43—42no—
406D8×C43—42no—
407D8×C43—42no—
408C2×C8×C43C2412yes—
409C2×C8×C43C2412yes—
410C4⋊C4×C43—21no—
411C4⋊C4×C43C2412yes—
412C22⋊C4×C43—21no—
413C22⋊C4×C43—21no—
414C22⋊C4×C43—21no—
415C22⋊C4×C43—21no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43—21no—
419C22⋊C4×C43—21no—
420C22⋊C4×C43—22no—
421C22⋊C4×C43—22no—
422C42×C43C2×D411yescharacteristic
423C42×C43C2×D411yescharacteristic
424C42×C43C2411yescharacteristic
425C42×C43C2411yescharacteristic
426C22⋊Dic43—22no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—21no—
430C22⋊Dic43—21no—
431C22⋊Dic43—21no—
432C22⋊Dic43—21no—
433C22⋊Dic43—21no—
434C22⋊Dic43—21no—
435C22⋊Dic43—22no—
436C22⋊Dic43—21no—
437C22⋊Dic43—21no—
438C22⋊Dic43C2×D411yescharacteristic
439C22⋊Dic43C2×D411yescharacteristic
440#10621884—42no—
441#10621884—42no—
442#10621882—42no—
443#10621882—42no—
444(C2×D43)⋊C4—22no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4C2×D411yescharacteristic
454(C2×D43)⋊C4C2×D411yescharacteristic
455(C2×D43)⋊C4C2×D411yescharacteristic
456(C2×D43)⋊C4C2×D411yescharacteristic
457C4⋊Dic43—21no—
458C4⋊Dic43—21no—
459C4⋊Dic43—21no—
460C4⋊Dic43—21no—
461C4⋊Dic43—21no—
462C4⋊Dic43—21no—
463C4⋊Dic43—21no—
464C4⋊Dic43—22no—
465C4⋊Dic43C2×D411yescharacteristic
466C4⋊Dic43C2×D411yescharacteristic
467C4⋊Dic43C2411yescharacteristic
468C4⋊Dic43C2411yescharacteristic
469C4⋊Dic43C2411yescharacteristic
470C4⋊Dic43C2411yescharacteristic
471C4⋊Dic43C2412yes—
472Dic43⋊C4—21no—
473Dic43⋊C4—21no—
474Dic43⋊C4—21no—
475Dic43⋊C4—21no—
476Dic43⋊C4—21no—
477Dic43⋊C4—21no—
478Dic43⋊C4—21no—
479Dic43⋊C4—21no—
480Dic43⋊C4—22no—
481Dic43⋊C4C2×D411yescharacteristic
482Dic43⋊C4C2×D411yescharacteristic
483Dic43⋊C4C2×D411yescharacteristic
484Dic43⋊C4C2×D411yescharacteristic
485C4×Dic43—21no—
486C4×Dic43—21no—
487C4×Dic43—21no—
488C4×Dic43—21no—
489C4×Dic43—21no—
490C4×Dic43—21no—
491C4×Dic43—22no—
492C4×Dic43C2×D411yescharacteristic
493C4×Dic43C2×D411yescharacteristic
494C4×Dic43C2×D411yescharacteristic
495C4×Dic43C2×D411yescharacteristic
496C4×Dic43C2411yescharacteristic
497C4×Dic43C2411yescharacteristic
498C2×C43⋊C8C2412yes—
499C2×C43⋊C8C2412yes—
500#10621872—42no—
501C8×D43—42no—
502C23×C43—21no—
503C23×C43—21no—
504C23×C43—22no—
505C23×C43—42no—
506C23×C43—81no—
507C23×C43—81no—
508C23×C43C22×D411yescharacteristic
509C22×D43—22no—
510C22×D43—44no—
511C22×D43—82no—
512C22×D43—82no—
513C22×D43C22×D411yescharacteristic
514C22×D43C22×D411yescharacteristic
515Q8×C43—22no—
516Q8×C43—22no—
517Q8×C43—42no—
518Q8×C43—42no—
519D4×C43—22no—
520D4×C43—22no—
521D4×C43—22no—
522D4×C43—22no—
523D4×C43—42no—
524D4×C43—42no—
525D4×C43—42no—
526D4×C43—82no—
527C2×C4×C43—22no—
528C2×C4×C43—21no—
529C2×C4×C43—21no—
530C2×C4×C43—22no—
531C2×C4×C43—41no—
532C2×C4×C43—41no—
533C2×C4×C43—42no—
534C2×C4×C43—82no—
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43C22×D411yescharacteristic
537C2×C4×C43C22×D411yescharacteristic
538C2×C4×C43C22×D411yescharacteristic
539C2×C4×C43C22×D411yescharacteristic
540C2×C4×C43C2511yescharacteristic
541C22⋊D43—41no—
542C22⋊D43—41no—
543C22⋊D43—44no—
544C22⋊D43—82no—
545C22⋊D43—82no—
546C22⋊D43—82no—
547C22⋊D43—81no—
548C22⋊D43—81no—
549C22⋊D43—81no—
550C22⋊D43—81no—
551C22⋊D43—82no—
552C2×Dic43—21no—
553C2×Dic43—21no—
554C2×Dic43—21no—
555C2×Dic43—21no—
556C2×Dic43—22no—
557C2×Dic43—82no—
558C2×Dic43—81no—
559C2×Dic43—81no—
560C2×Dic43—81no—
561C2×Dic43—81no—
562C2×Dic43C22×D411yescharacteristic
563C2×Dic43C22×D411yescharacteristic
564C2×Dic43C22×D411yescharacteristic
565C2×Dic43C22×D411yescharacteristic
566C2×Dic43C22×D411yescharacteristic
567C2×Dic43C22×D411yescharacteristic
568D172—22no—
569D172—22no—
570D172—41no—
571D172—42no—
572D172—42no—
573D172—82no—
574C4×D43—22no—
575C4×D43—22no—
576C4×D43—41no—
577C4×D43—41no—
578C4×D43—41no—
579C4×D43—41no—
580C4×D43—82no—
581C4×D43—82no—
582Dic86—41no—
583Dic86—42no—
584Dic86—81no—
585Dic86—81no—
586C8×C43—22no—
587C8×C43—22no—
588C43⋊C8—22no—
589C43⋊C8—22no—
590#61017—431nomaximal, Sylow
591C22×C43—21no—
592C22×C43—21no—
593C22×C43—21no—
594C22×C43—42no—
595C22×C43—42no—
596C22×C43—41no—
597C22×C43—41no—
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—42no—
601C22×C43—41no—
602C22×C43—41no—
603C22×C43—162no—
604C22×C43C23×D411yescharacteristic
605C2×D43—21no—
606C2×D43—21no—
607C2×D43—21no—
608C2×D43—21no—
609C2×D43—21no—
610C2×D43—21no—
611C2×D43—42no—
612C2×D43—42no—
613C2×D43—42no—
614C2×D43—164no—
615C4×C43—21no—
616C4×C43—21no—
617C4×C43—21no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—42no—
621C4×C43—41no—
622C4×C43—41no—
623C4×C43#58512yes—
624Dic43—21no—
625Dic43—21no—
626Dic43—21no—
627Dic43—21no—
628Dic43—21no—
629Dic43—21no—
630Dic43—42no—
631Dic43—41no—
632Dic43—41no—
633Dic43—41no—
634Dic43—41no—
635#3510—431no—
636#3508—431no—
637#3257—432no—
638#3257—432no—
639#3240—431no—
640#3240—431no—
641#3235—431no—
642#3235—431no—
643#3217—431no—
644#3217—431no—
645#3213—431no—
646#3213D4311yescharacteristic, complemented
647#3200—432no—
648#3199—432no—
649#3180—431no—
650#3180—431no—
651#3171—431no—
652#3171—431no—
653#3126—432no—
654#3122—432no—
655#3118—432no—
656#3118—432no—
657#2923—431no—
658C2×C43—41no—
659C2×C43—82no—
660C2×C43—81no—
661C2×C43—81no—
662C2×C43#344911yescharacteristic
663C2×C43#358511yescharacteristic
664C2×C43#358511yescharacteristic
665D43—41no—
666D43—41no—
667D43—82no—
668#559—861no—
669#559—861no—
670#559—861no—
671#559—861no—
672#556—861no—
673#556—861no—
674#551—861no—
675#551—861no—
676#551—861no—
677#551—861no—
678#550—861no—
679#550—861no—
680#546—861no—
681#546—861no—
682#546—861no—
683#546—861no—
684#542—431no—
685#542—431no—
686#542—431no—
687#542—431no—
688#540—432no—
689#540—432no—
690#536—431no—
691#535—431no—
692#535—432no—
693#533—431no—
694#533—431no—
695#532—431no—
696#532—431no—
697#532—431no—
698#532C2×D4311yescharacteristic
699C2×#127—431no—
700#529—431no—
701#529—431no—
702#529—431no—
703#529—431no—
704C2×#124C2×D4311yescharacteristic, complemented
705#519—431no—
706#518—431no—
707#518—432no—
708C4×#41—431no—
709#501—431no—
710#501—431no—
711#501—431no—
712#501—431no—
713#496—431no—
714#496—431no—
715#496C2×D4311yescharacteristic
716#496C2×D4311yescharacteristic
717#490—431no—
718#490—431no—
719#490—431no—
720#490—431no—
721#489—431no—
722#489—431no—
723#489C2×D4311yescharacteristic, complemented
724#489C2×D4311yescharacteristic, complemented
725#485—432no—
726#485—432no—
727#482—432no—
728#482—432no—
729#482—432no—
730#482—432no—
731#482—432no—
732#482—432no—
733#479—432no—
734#479—432no—
735#478—432no—
736#478—432no—
737#476—432no—
738#476—432no—
739#474—432no—
740#474—432no—
741#469—432no—
742#469—432no—
743#468—432no—
744#468—432no—
745#466—432no—
746#466—432no—
747#465—432no—
748#465—432no—
749#463—432no—
750#463—432no—
751#463C2×D4312yescomplemented
752#463C2×D4312yescomplemented
753#460—432no—
754#460—432no—
755#459—432no—
756#459—432no—
757#450—432no—
758#450—432no—
759#448—432no—
760#448C2×D4312yescomplemented
761#447—432no—
762#447—432no—
763#447—432no—
764#447C2×D4312yescomplemented
765#442—432no—
766#442—432no—
767#440—432no—
768#440—432no—
769C4×SD16—432no—
770C4×SD16—432no—
771C4×D8—432no—
772C4×D8—432no—
773#433—432no—
774#433—432no—
775#432—431no—
776#432—431no—
777#432—431no—
778#432C2×D4311yescharacteristic, complemented
779#424—432no—
780#408—432no—
781C4×M16—431no—
782C2×#97—431no—
783C43#6101711yescharacteristic, complemented, Sylow
784C2×#41—21no—
785C2×#41—431no—
786C2×#41—861no—
787C2×#41—861no—
788C2×#41—861no—
789C22×Q8C22×D4311yescharacteristic
790C22×D4—432no—
791C22×D4—861no—
792C22×D4—861no—
793C22×D4C22×D4311yescharacteristic
794C2×SD16—432no—
795C2×SD16—432no—
796C2×SD16C22×D4312yes—
797C2×SD16C22×D4312yes—
798C2×D8—432no—
799C2×D8—432no—
800C2×D8C22×D4312yes—
801C2×D8C22×D4312yes—
802C2×M16—432no—
803C22×C8—432no—
804C4⋊Q8—431no—
805C4⋊Q8—431no—
806C4⋊Q8—431no—
807C4⋊Q8—861no—
808C4⋊Q8C22×D4311yescharacteristic
809#127—432no—
810#127—431no—
811#127—861no—
812#127—861no—
813#127—862no—
814#127—861no—
815#127C22×D4311yescharacteristic
816#126—861no—
817#126—861no—
818#126—861no—
819#126—861no—
820#126—861no—
821#126—861no—
822#126—861no—
823#126—861no—
824#125—432no—
825#125—431no—
826#125—431no—
827#124—21no—
828#124—21no—
829#124—21no—
830#124—861no—
831#124—861no—
832#124—861no—
833#124—861no—
834#124—861no—
835#124—861no—
836#124—862no—
837#124—861no—
838#124—861no—
839#124—861no—
840#124C22×D4311yescharacteristic
841#124C22×D4311yescharacteristic
842#124C22×D4311yescharacteristic
843#124C22×D4311yescharacteristic
844#123—861no—
845#123—861no—
846#123—861no—
847#123—861no—
848#123—862no—
849#123—862no—
850#123—862no—
851#123—861no—
852#123—861no—
853#123—861no—
854#123—861no—
855#123—862no—
856#123—861no—
857#123—861no—
858C22⋊Q8—431no—
859C22⋊Q8—431no—
860C22⋊Q8—431no—
861C22⋊Q8—431no—
862C22⋊Q8—861no—
863C22⋊Q8—861no—
864C22⋊Q8—861no—
865C22⋊Q8—861no—
866C22⋊Q8—861no—
867C22⋊Q8—861no—
868C22⋊Q8—861no—
869C22⋊Q8—861no—
870#121—21no—
871#121—431no—
872#121—431no—
873#121—431no—
874#121—431no—
875#121—432no—
876#121—432no—
877#121—432no—
878#121—862no—
879#121—862no—
880#121—862no—
881#121—862no—
882#121—861no—
883#121—861no—
884#121—861no—
885#121C22×D4312yes—
886#120—862no—
887#120—862no—
888#120—861no—
889#120—861no—
890C4×Q8—431no—
891C4×Q8—431no—
892C4×Q8—431no—
893C4×Q8—431no—
894C4×Q8—431no—
895C4×Q8—431no—
896C4×Q8—861no—
897C4×Q8—861no—
898C4×Q8—861no—
899C4×Q8—861no—
900C4×Q8—861no—
901C4×Q8—861no—
902C4×D4—21no—
903C4×D4—431no—
904C4×D4—431no—
905C4×D4—431no—
906C4×D4—431no—
907C4×D4—431no—
908C4×D4—431no—
909C4×D4—431no—
910C4×D4—431no—
911C4×D4—432no—
912C4×D4—432no—
913C4×D4—431no—
914C4×D4—431no—
915C4×D4—432no—
916C4×D4—861no—
917C4×D4—861no—
918C4×D4—862no—
919C4×D4—861no—
920C4×D4—861no—
921C4×D4—861no—
922C4×D4—861no—
923C4×D4—862no—
924C4×D4—861no—
925C4×D4—861no—
926C4×D4—861no—
927C4×D4C22×D4312yes—
928#117—431no—
929#117—431no—
930#117—431no—
931#117—431no—
932#117—431no—
933#117—432no—
934#117—861no—
935#117—861no—
936#117—861no—
937#117—861no—
938#117—861no—
939#117—861no—
940C2×C22⋊C4—21no—
941C2×C22⋊C4—21no—
942C2×C22⋊C4—862no—
943C2×C22⋊C4—862no—
944C2×C22⋊C4—861no—
945C2×C22⋊C4—861no—
946C2×C42—431no—
947C2×C42—431no—
948C2×C42C22×D4311yescharacteristic
949#107—432no—
950#107—432no—
951#107—432no—
952#107—432no—
953#106—432no—
954#106—432no—
955#106—432no—
956#106—432no—
957C4⋊C8—432no—
958C4⋊C8—432no—
959C4⋊C8—432no—
960C4⋊C8C22×D4312yes—
961#103—432no—
962#103—432no—
963#103C22×D4312yes—
964#103C22×D4312yes—
965#102—432no—
966#102—432no—
967#102—432no—
968#102—432no—
969#102—432no—
970#102—432no—
971#102—432no—
972#102—432no—
973#102—432no—
974#102—432no—
975#102C22×D4312yes—
976#102C22×D4312yes—
977C22⋊C8—432no—
978C22⋊C8—432no—
979C22⋊C8—432no—
980C22⋊C8C22×D4312yes—
981#97—432no—
982#97—431no—
983#97—431no—
984#97C22×D4311yescharacteristic
985#97C22×D4311yescharacteristic
986C4×C8—432no—
987C24—21no—
988C24—862no—
989#41—82no—
990#41—3442no—
991#41—3442no—
992#41—3442no—
993#41—1722no—
994C2×Q8—21no—
995C2×Q8—21no—
996C2×Q8—42no—
997C2×Q8—431no—
998C2×Q8—861no—
999C2×Q8—861no—
1000C2×Q8—861no—
1001C2×Q8C23×D4311yescharacteristic
1002C2×Q8C23×D4311yescharacteristic
1003C2×D4—22no—
1004C2×D4—21no—
1005C2×D4—21no—
1006C2×D4—21no—
1007C2×D4—42no—
1008C2×D4—431no—
1009C2×D4—431no—
1010C2×D4—431no—
1011C2×D4—432no—
1012C2×D4—862no—
1013C2×D4—862no—
1014C2×D4—862no—
1015C2×D4—862no—
1016C2×D4—861no—
1017C2×D4—861no—
1018C2×D4—861no—
1019C2×D4—861no—
1020C2×D4—862no—
1021C2×D4—862no—
1022C2×D4—861no—
1023C2×D4—861no—
1024C2×D4—3442no—
1025C2×D4—3442no—
1026C2×D4—1722no—
1027C2×D4—1722no—
1028C2×D4C23×D4312yes—
1029C2×D4C23×D4311yescharacteristic
1030C2×D4C23×D4311yescharacteristic
1031C22×C4—21no—
1032C22×C4—22no—
1033C22×C4—431no—
1034C22×C4—431no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—431no—
1039C22×C4—862no—
1040C22×C4—861no—
1041C22×C4—861no—
1042C22×C4—861no—
1043C22×C4—861no—
1044C22×C4—862no—
1045C22×C4—862no—
1046C22×C4D4×D4311yescharacteristic
1047C22×C4D4×D4311yescharacteristic
1048C22×C4C23×D4311yescharacteristic
1049SD16—42no—
1050SD16—42no—
1051SD16—1722no—
1052SD16—1722no—
1053D8—42no—
1054D8—42no—
1055D8—1722no—
1056D8—1722no—
1057M16—1722no—
1058C2×C8—432no—
1059C2×C8—432no—
1060C2×C8—1722no—
1061C2×C8C23×D4312yes—
1062C2×C8C23×D4312yes—
1063C4⋊C4—21no—
1064C4⋊C4—431no—
1065C4⋊C4—431no—
1066C4⋊C4—431no—
1067C4⋊C4—431no—
1068C4⋊C4—431no—
1069C4⋊C4—431no—
1070C4⋊C4—431no—
1071C4⋊C4—431no—
1072C4⋊C4—431no—
1073C4⋊C4—431no—
1074C4⋊C4—432no—
1075C4⋊C4—861no—
1076C4⋊C4—861no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4—861no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—861no—
1083C4⋊C4—862no—
1084C4⋊C4—862no—
1085C4⋊C4—861no—
1086C4⋊C4—861no—
1087C4⋊C4—861no—
1088C4⋊C4—861no—
1089C4⋊C4—861no—
1090C4⋊C4—861no—
1091C4⋊C4—861no—
1092C4⋊C4C23×D4312yes—
1093C22⋊C4—21no—
1094C22⋊C4—21no—
1095C22⋊C4—21no—
1096C22⋊C4—21no—
1097C22⋊C4—21no—
1098C22⋊C4—21no—
1099C22⋊C4—21no—
1100C22⋊C4—21no—
1101C22⋊C4—22no—
1102C22⋊C4—22no—
1103C22⋊C4—431no—
1104C22⋊C4—431no—
1105C22⋊C4—431no—
1106C22⋊C4—431no—
1107C22⋊C4—431no—
1108C22⋊C4—431no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—861no—
1113C22⋊C4—861no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C22⋊C4—862no—
1117C22⋊C4—861no—
1118C22⋊C4—861no—
1119C22⋊C4—861no—
1120C22⋊C4—861no—
1121C22⋊C4—861no—
1122C22⋊C4—861no—
1123C22⋊C4—861no—
1124C22⋊C4—861no—
1125C22⋊C4—862no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—862no—
1129C22⋊C4—862no—
1130C42—431no—
1131C42—431no—
1132C42—431no—
1133C42—431no—
1134C42—431no—
1135C42—431no—
1136C42—862no—
1137C42—861no—
1138C42—861no—
1139C42—861no—
1140C42—861no—
1141C42—861no—
1142C42—861no—
1143C42D4×D4311yescharacteristic
1144C42D4×D4311yescharacteristic
1145C42C23×D4311yescharacteristic
1146C42C23×D4311yescharacteristic
1147C23—21no—
1148C23—21no—
1149C23—22no—
1150C23—42no—
1151C23—81no—
1152C23—81no—
1153C23—431no—
1154C23—431no—
1155C23—862no—
1156C23—3442no—
1157C23—3442no—
1158C23—1724no—
1159C23C2×D4×D4311yescharacteristic
1160Q8—22no—
1161Q8—22no—
1162Q8—42no—
1163Q8—42no—
1164Q8—3441no—
1165Q8—3441no—
1166Q8—1721no—
1167Q8—1722no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—42no—
1173D4—42no—
1174D4—42no—
1175D4—82no—
1176D4—862no—
1177D4—862no—
1178D4—3442no—
1179D4—3442no—
1180D4—3442no—
1181D4—3442no—
1182D4—3442no—
1183D4—3441no—
1184D4—3441no—
1185D4—3441no—
1186D4—3441no—
1187D4—1721no—
1188D4—1722no—
1189D4—1722no—
1190D4—1721no—
1191D4—1721no—
1192D4—1724no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—42no—
1200C2×C4—82no—
1201C2×C4—431no—
1202C2×C4—431no—
1203C2×C4—431no—
1204C2×C4—431no—
1205C2×C4—431no—
1206C2×C4—431no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—862no—
1214C2×C4—3442no—
1215C2×C4—3442no—
1216C2×C4—3442no—
1217C2×C4—3441no—
1218C2×C4—3441no—
1219C2×C4—3441no—
1220C2×C4—3441no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1721no—
1225C2×C4C2×D4×D4311yescharacteristic
1226C2×C4C2×D4×D4311yescharacteristic
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4C2×D4×D4311yescharacteristic
1229C2×C4C2×D4×D4311yescharacteristic
1230C2×C4C24×D4311yescharacteristic
1231C8—22no—
1232C8—22no—
1233C8—862no—
1234C8—862no—
1235C22—21no—
1236C22—21no—
1237C22—21no—
1238C22—42no—
1239C22—41no—
1240C22—41no—
1241C22—42no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—42no—
1247C22—162no—
1248C22—861no—
1249C22—861no—
1250C22—861no—
1251C22—861no—
1252C22—861no—
1253C22—861no—
1254C22—1722no—
1255C22—1722no—
1256C22—1722no—
1257C22—6884no—
1258C22C22×D4×D4311yescharacteristic
1259C4—21no—
1260C4—21no—
1261C4—21no—
1262C4—21no—
1263C4—21no—
1264C4—42no—
1265C4—41no—
1266C4—41no—
1267C4—861no—
1268C4—861no—
1269C4—861no—
1270C4—861no—
1271C4—861no—
1272C4—861no—
1273C4—1721no—
1274C4—1721no—
1275C4—1722no—
1276C4—1721no—
1277C4—1721no—
1278C4#1458373412yes—
1279C2—41no—
1280C2—81no—
1281C2—81no—
1282C2—82no—
1283C2—3442no—
1284C2—1721no—
1285C2—1721no—
1286C2#1914792611yescharacteristic
1287C2#1914937111yescharacteristic
1288C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3213C2
socleC22×C43C23×D4
hypercenter#3213D43
hypocenterC43#61017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3213

Complements

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

NH ≅ G/Ntype
1. #19148489C2semidirect
2. #19148464C2semidirect
3. #19146011C2semidirect
4. #19146003C2semidirect
5. #19145832C2semidirect
6. #19145830C2semidirect
7. #19145795C2semidirect
8. #19145789C2semidirect
9. #19145609C2semidirect
10. #19145609C2semidirect
11. #19145582C2semidirect
12. #19145465C2semidirect
13. #19145458C2semidirect
14. #19145296C2semidirect
15. #19145290C2semidirect
16. #19145193C2semidirect
17. #19145187C2semidirect
18. #19144880C2semidirect
19. #19144832C2semidirect
20. #19144778C2semidirect
21. #19144776C2semidirect
22. #19143241C2semidirect
23. C43×#3213C2semidirect
42. #14583518C22semidirect
43. #14583518C22semidirect
45. #14583500C22semidirect
49. #14583456C22semidirect
50. #14583454C22semidirect
51. #14583450C22semidirect
53. #14583447C22semidirect
54. #127×D43C22semidirect
57. #14583428C22semidirect
58. #14583428C22semidirect
59. #14583377C22semidirect
60. #14583374C22semidirect
61. #14583371C22semidirect
63. #14583308C22semidirect
64. #14583308C22semidirect
65. #14583305C22semidirect
66. #14583305C22semidirect
69. #14583264C22semidirect
70. #14583264C22semidirect
71. #14583263C22semidirect
72. #14583263C22semidirect
73. #14583258C22semidirect
74. #14583258C22semidirect
75. #14583239C22semidirect
76. #14583238C22semidirect
77. #14583224C22semidirect
78. #14583224C22semidirect
81. #14583220C22semidirect
82. #14583220C22semidirect
83. #14583208C22semidirect
84. #14583204C22semidirect
85. #14583201C22semidirect
86. #14583197C22semidirect
87. #14583190C22semidirect
88. #14583189C22semidirect
89. #14583180C22semidirect
90. #14583179C22semidirect
91. #14583151C22semidirect
92. #14583149C22semidirect
93. #14583148C22semidirect
94. #14583142C22semidirect
95. #14583134C22semidirect
96. #14583132C22semidirect
97. #14583131C22semidirect
98. #14583125C22semidirect
99. #14583111C22semidirect
100. #14583111C22semidirect
101. #14583097C22semidirect
102. #14583097C22semidirect
105. #14583048C22semidirect
106. #14583048C22semidirect
107. #14583038C22semidirect
108. #14583033C22semidirect
111. #14583011C22semidirect
112. #14583008C22semidirect
113. #14583002C22semidirect
114. #14583000C22semidirect
115. SD16×Dic43C22semidirect
116. #14582984C22semidirect
117. D8×Dic43C22semidirect
118. #14582979C22semidirect
119. #14582959C22semidirect
120. #14582957C22semidirect
121. #14582956C22semidirect
122. #14582954C22semidirect
123. #14582954C22semidirect
124. #14582924C22semidirect
126. #14582851C22semidirect
127. #97×D43C22semidirect
129. C2×#124×C43C22semidirect
132. C43×#489C22semidirect
133. C43×#489C22semidirect
134. C43×#463C22semidirect
135. C43×#463C22semidirect
136. C43×#448C22semidirect
137. C43×#447C22semidirect
138. C43×#432C22semidirect
646. #3213D43semidirect
704. C2×#124C2×D43semidirect
723. #489C2×D43semidirect
724. #489C2×D43semidirect
751. #463C2×D43semidirect
752. #463C2×D43semidirect
760. #448C2×D43semidirect
764. #447C2×D43semidirect
778. #432C2×D43semidirect
783. C43#61017semidirect

Maximal subgroups

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

subgroupindex
#191484892
#191484642
#191460112
#191460032
#191458322
#191458302
#191457952
#191457892
#191456092
#191455822
#191454652
#191454582
#191452962
#191452902
#191451932
#191451872
#191448802
#191448322
#191447782
#191447762
#191432412
C43×#32132
#6101743