Finite Group Databasebeta

← #25971461

Subgroups — #25971461

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#19148484C211yesmaximal, characteristic, complemented
2#19148469C211yesmaximal, characteristic, complemented
3#19146004C212yesmaximal, complemented
4#19146002C212yesmaximal, complemented
5#19145837C211yesmaximal, characteristic, complemented
6#19145831C211yesmaximal, characteristic, complemented
7#19145788C211yesmaximal, characteristic, complemented
8#19145788C211yesmaximal, characteristic, complemented
9#19145613C211yesmaximal, characteristic, complemented
10#19145577C211yesmaximal, characteristic, complemented
11#19145577C211yesmaximal, characteristic, complemented
12#19145464C212yesmaximal, complemented
13#19145458C212yesmaximal, complemented
14#19145292C211yesmaximal, characteristic, complemented
15#19145290C211yesmaximal, characteristic, complemented
16#19145189C211yesmaximal, characteristic, complemented
17#19145187C211yesmaximal, characteristic, complemented
18#19144884C212yesmaximal, complemented
19#19144836C212yesmaximal, complemented
20#19144780C212yesmaximal, complemented
21#19144772C212yesmaximal, complemented
22#19143241C211yesmaximal, characteristic, complemented
23C43×#3217C211yesmaximal, characteristic, complemented
24#14583635—21no—
25#14583635—21no—
26#14583633—21no—
27#14583632—21no—
28#14583617—21no—
29#14583616—21no—
30#14583578—21no—
31#14583577—21no—
32#14583574—21no—
33#14583573—21no—
34#14583569—21no—
35#14583569—21no—
36#14583543—21no—
37#14583543—21no—
38#14583543—21no—
39#14583543—21no—
40#14583522C2211yescharacteristic
41#14583521C2211yescharacteristic, complemented
42#14583516C2211yescharacteristic
43#14583514C2211yescharacteristic, complemented
44#14583503C2212yes—
45#14583503C2212yescomplemented
46#14583472C2211yescharacteristic
47#14583466C2212yes—
48#14583465C2211yescharacteristic
49#14583456C2211yescharacteristic, complemented
50#14583455C2211yescharacteristic, complemented
51#14583447C2211yescharacteristic
52#14583447C2211yescharacteristic
53#14583447C2211yescharacteristic, complemented
54#14583447C2211yescharacteristic, complemented
55#14583434C2211yescharacteristic, complemented
56#14583433C2211yescharacteristic
57#14583428C2211yescharacteristic, complemented
58#124×D43C2211yescharacteristic, complemented
59#14583375C2211yescharacteristic, complemented
60#14583374C2212yescomplemented
61#14583371C2211yescharacteristic, complemented
62C4×#10621898C2211yescharacteristic
63#14583309C2211yescharacteristic, complemented
64#14583309C2211yescharacteristic, complemented
65#14583308C2211yescharacteristic, complemented
66#14583308C2211yescharacteristic, complemented
67#14583286C2211yescharacteristic
68#14583286C2211yescharacteristic
69#14583263C2211yescharacteristic, complemented
70#14583263C2211yescharacteristic, complemented
71#14583259C2211yescharacteristic, complemented
72#14583259C2211yescharacteristic, complemented
73#14583258C2211yescharacteristic, complemented
74#14583258C2211yescharacteristic, complemented
75#14583241C2212yescomplemented
76#14583237C2212yescomplemented
77#14583224C2212yes—
78#14583222C2212yescomplemented
79#14583222C2212yescomplemented
80#14583221C2212yescomplemented
81#14583221C2212yescomplemented
82#14583220C2212yes—
83#14583207C2212yescomplemented
84#14583206C2212yescomplemented
85#14583200C2212yescomplemented
86#14583199C2212yescomplemented
87#14583187C2212yescomplemented
88#14583187C2212yescomplemented
89#14583177C2212yescomplemented
90#14583177C2212yescomplemented
91#14583151C2212yescomplemented
92#14583149C2212yescomplemented
93#14583144C2212yescomplemented
94#14583142C2212yescomplemented
95#14583134C2212yescomplemented
96#14583132C2212yescomplemented
97#14583127C2212yescomplemented
98#14583125C2212yescomplemented
99#14583116C2212yescomplemented
100#14583116C2212yescomplemented
101#14583112C2212yescomplemented
102#14583112C2212yescomplemented
103#14583096C2212yescomplemented
104#14583091C2212yes—
105#14583050C2212yescomplemented
106#14583036C2212yescomplemented
107#14583036C2212yescomplemented
108#14583033C2212yes—
109#14583031C2212yescomplemented
110#14583031C2212yescomplemented
111#14583011C2212yescomplemented
112#14583008C2212yescomplemented
113#14583000C2212yescomplemented
114#14582996C2212yescomplemented
115#14582990C2212yescomplemented
116SD16×Dic43C2212yescomplemented
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
128C2×#127×C43C2211yescharacteristic, complemented
129C43×#529C2211yescharacteristic
130C43×#496C2211yescharacteristic
131C43×#496C2211yescharacteristic
132C43×#490C2211yescharacteristic, complemented
133C43×#490C2211yescharacteristic, complemented
134C43×#460C2212yescomplemented
135C43×#459C2212yes—
136C43×#450C2212yescomplemented
137C43×#447C2212yes—
138C43×#432C2211yescharacteristic, complemented
139C2×#10621898C2311yescharacteristic
140C2×#10621900—21no—
141C2×#10621900—21no—
142C2×#10621900—21no—
143C2×#10621900—21no—
144C2×Q8×D43C2311yescharacteristic
145C2×D4×D43C2311yescharacteristic
146C2×#10621883C2312yes—
147C2×#10621883C2312yes—
148C2×#10621882C2312yes—
149C2×#10621882C2312yes—
150C2×#10621872C2312yes—
151C2×C8×D43C2312yes—
152#13063325C2311yescharacteristic
153#13063325C2311yescharacteristic
154#13063324—21no—
155#13063324C2311yescharacteristic
156#13063324C2311yescharacteristic
157#13063321—21no—
158#13063321—22no—
159#13063320—21no—
160#13063320—21no—
161#13063319—21no—
162#13063319—21no—
163#13063318—21no—
164#13063318—21no—
165#13063318—21no—
166#13063317C2311yescharacteristic
167#13063317C2312yes—
168#13063314C2311yescharacteristic
169#13063313—21no—
170#13063313C2311yescharacteristic
171#13063312—22no—
172#13063312—21no—
173#13063312—21no—
174#13063312—21no—
175#13063312—21no—
176#13063312—21no—
177#13063312C2311yescharacteristic
178#13063311—21no—
179#13063311—21no—
180#13063311—21no—
181#13063311—21no—
182#13063311—21no—
183#13063311—21no—
184#13063310—21no—
185#13063310—21no—
186#13063310—21no—
187#13063308—21no—
188#13063308—21no—
189#13063307—21no—
190#13063307—21no—
191#13063307—21no—
192#13063306—21no—
193#13063306—22no—
194#13063306—22no—
195#13063306—22no—
196#13063306—22no—
197#13063305—21no—
198#13063305C2311yescharacteristic
199#13063304—21no—
200#13063304—21no—
201#13063304—21no—
202#13063304C2311yescharacteristic
203#13063303—21no—
204#13063303—21no—
205#13063303—21no—
206#13063302—21no—
207#13063301C2311yescharacteristic
208#13063300C2311yescharacteristic
209#13063299C2311yescharacteristic
210#13063297—22no—
211#13063297—22no—
212#13063297—22no—
213#13063297—22no—
214#13063296—21no—
215#13063296—21no—
216#13063296—21no—
217#13063296—21no—
218#13063296C2312yes—
219#13063296C2312yes—
220#13063296C2311yescharacteristic
221#13063296C2312yes—
222#13063296C2312yes—
223#13063295—21no—
224#13063294—22no—
225#13063294—22no—
226#13063293—21no—
227Q8×Dic43C2311yescharacteristic
228C4×Dic86—21no—
229C4×Dic86—21no—
230C4×Dic86—21no—
231C4×Dic86D411yescharacteristic
232C4×Dic86D411yescharacteristic
233C4×Dic86C2311yescharacteristic
234#13063290—21no—
235#13063290—21no—
236#13063290—21no—
237#13063290C2311yescharacteristic
238C4×D172D411yescharacteristic
239C4×D172D411yescharacteristic
240C4×D172C2311yescharacteristic
241D4×Dic43—22no—
242D4×Dic43—22no—
243D4×Dic43—21no—
244D4×Dic43—21no—
245D4×Dic43—21no—
246D4×Dic43—21no—
247D4×Dic43C2312yes—
248D4×Dic43C2312yes—
249D4×Dic43C2311yescharacteristic
250D4×Dic43C2312yes—
251D4×Dic43C2312yes—
252#13063287—21no—
253#13063287C2311yescharacteristic
254C4×C22⋊D43—21no—
255C4×C22⋊D43—21no—
256C4×C22⋊D43D411yescharacteristic
257C4×C22⋊D43D411yescharacteristic
258C4×C22⋊D43D411yescharacteristic
259C4×C22⋊D43D411yescharacteristic
260(C22⋊D43)⋊C4—21no—
261(C22⋊D43)⋊C4—21no—
262#13063284C2312yes—
263#13063284C2311yescharacteristic
264#13063283—21no—
265#13063283—21no—
266#13063283C2311yescharacteristic
267#13063283C2311yescharacteristic
268#13063282—21no—
269#13063282—21no—
270#13063282C2311yescharacteristic
271#13063282C2311yescharacteristic
272#13063281—21no—
273C2×C22⋊Dic43—22no—
274C2×C22⋊Dic43—22no—
275C2×(C2×D43)⋊C4—21no—
276C22⋊C4×D43—21no—
277C22⋊C4×D43—21no—
278C22⋊C4×D43—21no—
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#13063250C2312yes—
293#13063250C2312yes—
294#13063249C2312yes—
295#13063249C2312yes—
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—
311C22×D4×C43—21no—
312C22×D4×C43—21no—
313C22×D4×C43C2312yes—
314C2×SD16×C43C2312yes—
315C2×SD16×C43C2312yes—
316C2×D8×C43C2312yes—
317C2×D8×C43C2312yes—
318#127×C43—21no—
319#127×C43—21no—
320#127×C43C2312yes—
321#127×C43C2311yescharacteristic
322#127×C43C2311yescharacteristic
323#126×C43—21no—
324#125×C43C2311yescharacteristic
325#124×C43C2311yescharacteristic
326#123×C43—21no—
327C22⋊Q8×C43C2311yescharacteristic
328#121×C43C2311yescharacteristic
329C4×Q8×C43C2311yescharacteristic
330C4×D4×C43—21no—
331C4×D4×C43C2311yescharacteristic
332#117×C43—21no—
333C2×C42×C43C2311yescharacteristic
334C4⋊C8×C43C2312yes—
335#102×C43C2312yes—
336#102×C43C2312yes—
337#102×C43C2312yes—
338#102×C43C2312yes—
339C22⋊C8×C43C2312yes—
340#97×C43C2311yescharacteristic
341#97×C43C2311yescharacteristic
342C24×C43—22no—
343C23×D43—21no—
344C2×Q8×C43C2411yescharacteristic
345C2×D4×C43—22no—
346C2×D4×C43—21no—
347C2×D4×C43—21no—
348C2×D4×C43—21no—
349C2×D4×C43—21no—
350C2×D4×C43—22no—
351C2×D4×C43—22no—
352C2×D4×C43—21no—
353C2×D4×C43—42no—
354C2×D4×C43—42no—
355C2×D4×C43—82no—
356C2×D4×C43—82no—
357C2×D4×C43C2412yes—
358C2×D4×C43C2412yes—
359C2×D4×C43C2411yescharacteristic
360C22×C4×C43—21no—
361C22×C4×C43C2×D411yescharacteristic
362C22×C4×C43C2×D411yescharacteristic
363C22×C4×C43C2411yescharacteristic
364C2×C22⋊D43—21no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43—21no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—22no—
369C2×C22⋊D43—22no—
370C2×C22⋊D43—22no—
371C2×C22⋊D43C2×D411yescharacteristic
372C2×C22⋊D43C2×D411yescharacteristic
373C22×Dic43—21no—
374C22×Dic43—22no—
375C22×Dic43—22no—
376C22×Dic43—22no—
377C22×Dic43—22no—
378Q8×D43—42no—
379#10621900—82no—
380#10621900—82no—
381#10621900—82no—
382#10621900—82no—
383D4×D43—42no—
384#10621898—42no—
385C2×D172—21no—
386C2×D172C2×D411yescharacteristic
387C2×D172C2411yescharacteristic
388C2×C4×D43—21no—
389C2×C4×D43—21no—
390C2×C4×D43—21no—
391C2×C4×D43C2×D411yescharacteristic
392C2×C4×D43C2×D411yescharacteristic
393C2×C4×D43C2×D411yescharacteristic
394C2×C4×D43C2×D411yescharacteristic
395C2×C4×D43C2411yescharacteristic
396C2×C4×D43C2411yescharacteristic
397C2×Dic86—21no—
398C2×Dic86—21no—
399C2×Dic86—21no—
400C2×Dic86—21no—
401C2×Dic86—21no—
402C2×Dic86C2×D411yescharacteristic
403C2×Dic86C2411yescharacteristic
404SD16×C43—42no—
405SD16×C43—42no—
406D8×C43—42no—
407D8×C43—42no—
408C2×C8×C43C2412yes—
409C2×C8×C43C2412yes—
410C4⋊C4×C43—21no—
411C4⋊C4×C43—21no—
412C4⋊C4×C43—21no—
413C4⋊C4×C43—21no—
414C4⋊C4×C43C2411yescharacteristic
415C4⋊C4×C43C2411yescharacteristic
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43—21no—
419C22⋊C4×C43—21no—
420C22⋊C4×C43—21no—
421C42×C43—21no—
422C42×C43C2×D411yescharacteristic
423C42×C43C2×D411yescharacteristic
424C42×C43C2411yescharacteristic
425C42×C43C2411yescharacteristic
426C22⋊Dic43—21no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—22no—
430C22⋊Dic43—22no—
431C22⋊Dic43—22no—
432C22⋊Dic43—22no—
433C22⋊Dic43—21no—
434C22⋊Dic43—22no—
435C22⋊Dic43—22no—
436C22⋊Dic43—22no—
437C22⋊Dic43—22no—
438C22⋊Dic43—22no—
439C22⋊Dic43—21no—
440C22⋊Dic43C2×D411yescharacteristic
441C22⋊Dic43C2×D411yescharacteristic
442#10621883—42no—
443#10621883—42no—
444#10621882—42no—
445#10621882—42no—
446(C2×D43)⋊C4—21no—
447(C2×D43)⋊C4—21no—
448(C2×D43)⋊C4—21no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—21no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4—21no—
454(C2×D43)⋊C4—21no—
455(C2×D43)⋊C4—21no—
456(C2×D43)⋊C4—21no—
457(C2×D43)⋊C4—21no—
458(C2×D43)⋊C4C2×D411yescharacteristic
459(C2×D43)⋊C4C2×D411yescharacteristic
460(C2×D43)⋊C4C2×D411yescharacteristic
461(C2×D43)⋊C4C2×D411yescharacteristic
462C4⋊Dic43—21no—
463C4⋊Dic43—21no—
464C4⋊Dic43—21no—
465C4⋊Dic43—21no—
466C4⋊Dic43C2×D411yescharacteristic
467C4⋊Dic43C2×D411yescharacteristic
468C4⋊Dic43C2411yescharacteristic
469C4⋊Dic43C2411yescharacteristic
470C4⋊Dic43C2412yes—
471C4⋊Dic43C2412yes—
472Dic43⋊C4—21no—
473Dic43⋊C4—21no—
474Dic43⋊C4—21no—
475Dic43⋊C4—21no—
476Dic43⋊C4—22no—
477Dic43⋊C4—22no—
478Dic43⋊C4—21no—
479Dic43⋊C4—21no—
480Dic43⋊C4—21no—
481Dic43⋊C4—21no—
482Dic43⋊C4C2×D411yescharacteristic
483Dic43⋊C4C2×D411yescharacteristic
484Dic43⋊C4C2×D411yescharacteristic
485Dic43⋊C4C2×D411yescharacteristic
486C4×Dic43—21no—
487C4×Dic43—22no—
488C4×Dic43—21no—
489C4×Dic43—21no—
490C4×Dic43—21no—
491C4×Dic43—21no—
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—22no—
504C23×C43—22no—
505C23×C43—44no—
506C23×C43—82no—
507C23×C43—82no—
508C23×C43C22×D411yescharacteristic
509C22×D43—21no—
510C22×D43—42no—
511C22×D43—81no—
512C22×D43—81no—
513C22×D43C22×D411yescharacteristic
514C22×D43C22×D411yescharacteristic
515Q8×C43—22no—
516D4×C43—22no—
517D4×C43—22no—
518D4×C43—22no—
519D4×C43—22no—
520D4×C43—22no—
521D4×C43—42no—
522D4×C43—42no—
523D4×C43—42no—
524D4×C43—42no—
525D4×C43—44no—
526D4×C43—82no—
527D4×C43—82no—
528D4×C43—81no—
529C2×C4×C43—22no—
530C2×C4×C43—21no—
531C2×C4×C43—21no—
532C2×C4×C43—21no—
533C2×C4×C43—41no—
534C2×C4×C43—41no—
535C2×C4×C43—81no—
536C2×C4×C43C22×D411yescharacteristic
537C2×C4×C43C22×D411yescharacteristic
538C2×C4×C43C22×D411yescharacteristic
539C2×C4×C43C22×D411yescharacteristic
540C2×C4×C43C22×D411yescharacteristic
541C2×C4×C43C2511yescharacteristic
542C22⋊D43—41no—
543C22⋊D43—41no—
544C22⋊D43—42no—
545C22⋊D43—82no—
546C22⋊D43—82no—
547C22⋊D43—82no—
548C22⋊D43—82no—
549C22⋊D43—81no—
550C22⋊D43—81no—
551C2×Dic43—21no—
552C2×Dic43—21no—
553C2×Dic43—21no—
554C2×Dic43—22no—
555C2×Dic43—22no—
556C2×Dic43—82no—
557C2×Dic43—82no—
558C2×Dic43—82no—
559C2×Dic43—82no—
560C2×Dic43—81no—
561C2×Dic43C22×D411yescharacteristic
562C2×Dic43C22×D411yescharacteristic
563C2×Dic43C22×D411yescharacteristic
564C2×Dic43C22×D411yescharacteristic
565C2×Dic43C22×D411yescharacteristic
566C2×Dic43C22×D411yescharacteristic
567D172—22no—
568D172—41no—
569D172—81no—
570C4×D43—22no—
571C4×D43—22no—
572C4×D43—41no—
573C4×D43—41no—
574C4×D43—41no—
575C4×D43—41no—
576C4×D43—42no—
577C4×D43—81no—
578C4×D43—81no—
579Dic86—22no—
580Dic86—41no—
581Dic86—42no—
582Dic86—42no—
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—41no—
595C22×C43—41no—
596C22×C43—42no—
597C22×C43—42no—
598C22×C43—42no—
599C22×C43—42no—
600C22×C43—41no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—164no—
604C22×C43C23×D411yescharacteristic
605C2×D43—21no—
606C2×D43—21no—
607C2×D43—21no—
608C2×D43—21no—
609C2×D43—21no—
610C2×D43—21no—
611C2×D43—41no—
612C2×D43—41no—
613C2×D43—41no—
614C2×D43—162no—
615C4×C43—21no—
616C4×C43—21no—
617C4×C43—21no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—41no—
621C4×C43—41no—
622C4×C43—41no—
623C4×C43#58512yes—
624Dic43—21no—
625Dic43—21no—
626Dic43—21no—
627Dic43—21no—
628Dic43—21no—
629Dic43—21no—
630Dic43—42no—
631Dic43—42no—
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#3217D4311yescharacteristic, complemented
645#3213—431no—
646#3213—431no—
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—81no—
660C2×C43—82no—
661C2×C43—82no—
662C2×C43#344911yescharacteristic
663C2×C43#358511yescharacteristic
664C2×C43#358511yescharacteristic
665D43—41no—
666D43—41no—
667D43—81no—
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—432no—
692#535—431no—
693#533—431no—
694#533—431no—
695#532—431no—
696#532—431no—
697#532—431no—
698#532—431no—
699C2×#127C2×D4311yescharacteristic, complemented
700#529—431no—
701#529—431no—
702#529—431no—
703#529C2×D4311yescharacteristic
704C2×#124—431no—
705#519—431no—
706#518—432no—
707#518—431no—
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#490C2×D4311yescharacteristic, complemented
720#490C2×D4311yescharacteristic, complemented
721#489—431no—
722#489—431no—
723#489—431no—
724#489—431no—
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#463—432no—
752#463—432no—
753#460—432no—
754#460C2×D4312yescomplemented
755#459—432no—
756#459C2×D4312yes—
757#450—432no—
758#450C2×D4312yescomplemented
759#448—432no—
760#448—432no—
761#447—432no—
762#447—432no—
763#447—432no—
764#447C2×D4312yes—
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—431no—
785C2×#41—861no—
786C2×#41—861no—
787C2×#41—861no—
788C2×#41—861no—
789C22×Q8—431no—
790C22×D4—21no—
791C22×D4—21no—
792C22×D4—431no—
793C22×D4C22×D4312yes—
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—431no—
808C4⋊Q8—861no—
809#127—21no—
810#127—21no—
811#127—862no—
812#127—861no—
813#127C22×D4311yescharacteristic
814#127C22×D4311yescharacteristic
815#127C22×D4312yes—
816#126—21no—
817#126—861no—
818#126—861no—
819#126—861no—
820#126—861no—
821#126—861no—
822#126—861no—
823#126—861no—
824#125—431no—
825#125—432no—
826#125C22×D4311yescharacteristic
827#124—431no—
828#124—431no—
829#124—431no—
830#124—861no—
831#124—861no—
832#124—861no—
833#124—861no—
834#124—861no—
835#124—861no—
836#124—861no—
837#124—861no—
838#124—861no—
839#124—861no—
840#124—861no—
841#124—861no—
842#124—862no—
843#124C22×D4311yescharacteristic
844#123—21no—
845#123—861no—
846#123—861no—
847#123—861no—
848#123—861no—
849#123—861no—
850#123—861no—
851#123—861no—
852#123—861no—
853#123—862no—
854#123—862no—
855#123—862no—
856#123—862no—
857#123—861no—
858C22⋊Q8—431no—
859C22⋊Q8—431no—
860C22⋊Q8—431no—
861C22⋊Q8—861no—
862C22⋊Q8—861no—
863C22⋊Q8—861no—
864C22⋊Q8—861no—
865C22⋊Q8—861no—
866C22⋊Q8—861no—
867C22⋊Q8—861no—
868C22⋊Q8—861no—
869C22⋊Q8C22×D4311yescharacteristic
870#121—431no—
871#121—432no—
872#121—432no—
873#121—432no—
874#121—432no—
875#121—431no—
876#121—431no—
877#121—862no—
878#121—862no—
879#121—862no—
880#121—862no—
881#121—861no—
882#121—861no—
883#121—861no—
884#121—861no—
885#121C22×D4311yescharacteristic
886#120—861no—
887#120—861no—
888#120—862no—
889#120—862no—
890C4×Q8—431no—
891C4×Q8—431no—
892C4×Q8—431no—
893C4×Q8—431no—
894C4×Q8—431no—
895C4×Q8—861no—
896C4×Q8—861no—
897C4×Q8—861no—
898C4×Q8—861no—
899C4×Q8—861no—
900C4×Q8—861no—
901C4×Q8C22×D4311yescharacteristic
902C4×D4—21no—
903C4×D4—431no—
904C4×D4—431no—
905C4×D4—431no—
906C4×D4—431no—
907C4×D4—431no—
908C4×D4—432no—
909C4×D4—432no—
910C4×D4—432no—
911C4×D4—432no—
912C4×D4—431no—
913C4×D4—431no—
914C4×D4—431no—
915C4×D4—431no—
916C4×D4—861no—
917C4×D4—861no—
918C4×D4—861no—
919C4×D4—861no—
920C4×D4—861no—
921C4×D4—861no—
922C4×D4—861no—
923C4×D4—861no—
924C4×D4—862no—
925C4×D4—862no—
926C4×D4—861no—
927C4×D4C22×D4311yescharacteristic
928#117—21no—
929#117—431no—
930#117—431no—
931#117—431no—
932#117—432no—
933#117—431no—
934#117—431no—
935#117—861no—
936#117—861no—
937#117—861no—
938#117—861no—
939#117—861no—
940C2×C22⋊C4—861no—
941C2×C22⋊C4—861no—
942C2×C22⋊C4—861no—
943C2×C22⋊C4—861no—
944C2×C22⋊C4—862no—
945C2×C22⋊C4—862no—
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#103—432no—
964#103—432no—
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#102C22×D4312yes—
974#102C22×D4312yes—
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—22no—
988C24—861no—
989#41—3442no—
990#41—3442no—
991#41—3442no—
992#41—3442no—
993#41—1722no—
994C2×Q8—431no—
995C2×Q8—431no—
996C2×Q8—861no—
997C2×Q8—861no—
998C2×Q8—861no—
999C2×Q8—861no—
1000C2×Q8—861no—
1001C2×Q8—1722no—
1002C2×Q8C23×D4311yescharacteristic
1003C2×D4—21no—
1004C2×D4—22no—
1005C2×D4—21no—
1006C2×D4—21no—
1007C2×D4—21no—
1008C2×D4—21no—
1009C2×D4—22no—
1010C2×D4—22no—
1011C2×D4—42no—
1012C2×D4—42no—
1013C2×D4—82no—
1014C2×D4—82no—
1015C2×D4—431no—
1016C2×D4—431no—
1017C2×D4—431no—
1018C2×D4—431no—
1019C2×D4—861no—
1020C2×D4—861no—
1021C2×D4—861no—
1022C2×D4—862no—
1023C2×D4—862no—
1024C2×D4—862no—
1025C2×D4—862no—
1026C2×D4—861no—
1027C2×D4—1722no—
1028C2×D4C23×D4311yescharacteristic
1029C2×D4C23×D4312yes—
1030C2×D4C23×D4312yes—
1031C22×C4—21no—
1032C22×C4—431no—
1033C22×C4—431no—
1034C22×C4—431no—
1035C22×C4—431no—
1036C22×C4—431no—
1037C22×C4—431no—
1038C22×C4—861no—
1039C22×C4—861no—
1040C22×C4—861no—
1041C22×C4—862no—
1042C22×C4—862no—
1043C22×C4—862no—
1044C22×C4—862no—
1045C22×C4—861no—
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—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—431no—
1068C4⋊C4—431no—
1069C4⋊C4—431no—
1070C4⋊C4—431no—
1071C4⋊C4—431no—
1072C4⋊C4—431no—
1073C4⋊C4—431no—
1074C4⋊C4—431no—
1075C4⋊C4—432no—
1076C4⋊C4—432no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4—861no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—861no—
1083C4⋊C4—861no—
1084C4⋊C4—861no—
1085C4⋊C4—861no—
1086C4⋊C4—861no—
1087C4⋊C4—861no—
1088C4⋊C4—861no—
1089C4⋊C4—862no—
1090C4⋊C4—862no—
1091C4⋊C4C23×D4311yescharacteristic
1092C4⋊C4C23×D4311yescharacteristic
1093C22⋊C4—21no—
1094C22⋊C4—21no—
1095C22⋊C4—21no—
1096C22⋊C4—21no—
1097C22⋊C4—21no—
1098C22⋊C4—431no—
1099C22⋊C4—431no—
1100C22⋊C4—431no—
1101C22⋊C4—431no—
1102C22⋊C4—431no—
1103C22⋊C4—431no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C22⋊C4—861no—
1107C22⋊C4—861no—
1108C22⋊C4—861no—
1109C22⋊C4—861no—
1110C22⋊C4—861no—
1111C22⋊C4—861no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
1116C22⋊C4—861no—
1117C22⋊C4—861no—
1118C22⋊C4—861no—
1119C22⋊C4—861no—
1120C22⋊C4—862no—
1121C22⋊C4—862no—
1122C22⋊C4—862no—
1123C22⋊C4—862no—
1124C22⋊C4—862no—
1125C22⋊C4—861no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—861no—
1130C42—21no—
1131C42—431no—
1132C42—431no—
1133C42—431no—
1134C42—431no—
1135C42—431no—
1136C42—431no—
1137C42—861no—
1138C42—861no—
1139C42—861no—
1140C42—861no—
1141C42—862no—
1142C42—861no—
1143C42D4×D4311yescharacteristic
1144C42D4×D4311yescharacteristic
1145C42C23×D4311yescharacteristic
1146C42C23×D4311yescharacteristic
1147C23—21no—
1148C23—22no—
1149C23—22no—
1150C23—44no—
1151C23—82no—
1152C23—82no—
1153C23—431no—
1154C23—431no—
1155C23—861no—
1156C23—3441no—
1157C23—3441no—
1158C23—1722no—
1159C23C2×D4×D4311yescharacteristic
1160Q8—22no—
1161Q8—862no—
1162Q8—3441no—
1163Q8—3441no—
1164Q8—1721no—
1165Q8—1722no—
1166Q8—1722no—
1167Q8—1722no—
1168D4—22no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—22no—
1173D4—44no—
1174D4—42no—
1175D4—42no—
1176D4—42no—
1177D4—42no—
1178D4—82no—
1179D4—82no—
1180D4—81no—
1181D4—862no—
1182D4—3441no—
1183D4—3441no—
1184D4—3442no—
1185D4—3442no—
1186D4—3442no—
1187D4—3442no—
1188D4—3441no—
1189D4—1721no—
1190D4—1721no—
1191D4—1721no—
1192D4—1722no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—81no—
1200C2×C4—431no—
1201C2×C4—431no—
1202C2×C4—431no—
1203C2×C4—431no—
1204C2×C4—431no—
1205C2×C4—431no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—861no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—862no—
1212C2×C4—862no—
1213C2×C4—3441no—
1214C2×C4—3441no—
1215C2×C4—3442no—
1216C2×C4—3442no—
1217C2×C4—3442no—
1218C2×C4—3442no—
1219C2×C4—3441no—
1220C2×C4—1721no—
1221C2×C4—1721no—
1222C2×C4—1721no—
1223C2×C4—1721no—
1224C2×C4—1722no—
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—41no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—41no—
1244C22—42no—
1245C22—42no—
1246C22—41no—
1247C22—164no—
1248C22—861no—
1249C22—861no—
1250C22—861no—
1251C22—861no—
1252C22—861no—
1253C22—861no—
1254C22—1721no—
1255C22—1721no—
1256C22—1721no—
1257C22—6882no—
1258C22C22×D4×D4311yescharacteristic
1259C4—21no—
1260C4—21no—
1261C4—21no—
1262C4—21no—
1263C4—21no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—861no—
1268C4—861no—
1269C4—861no—
1270C4—861no—
1271C4—861no—
1272C4—861no—
1273C4—1722no—
1274C4—1722no—
1275C4—1721no—
1276C4—1721no—
1277C4—1721no—
1278C4#1458373412yes—
1279C2—41no—
1280C2—82no—
1281C2—82no—
1282C2—81no—
1283C2—3441no—
1284C2—1721no—
1285C2—1721no—
1286C2#1914792611yescharacteristic
1287C2#1914937111yescharacteristic
1288C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3217C2
socleC22×C43C23×D4
hypercenter#3217D43
hypocenterC43#61017
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3217

Complements

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

NH ≅ G/Ntype
1. #19148484C2semidirect
2. #19148469C2semidirect
3. #19146004C2semidirect
4. #19146002C2semidirect
5. #19145837C2semidirect
6. #19145831C2semidirect
7. #19145788C2semidirect
8. #19145788C2semidirect
9. #19145613C2semidirect
10. #19145577C2semidirect
11. #19145577C2semidirect
12. #19145464C2semidirect
13. #19145458C2semidirect
14. #19145292C2semidirect
15. #19145290C2semidirect
16. #19145189C2semidirect
17. #19145187C2semidirect
18. #19144884C2semidirect
19. #19144836C2semidirect
20. #19144780C2semidirect
21. #19144772C2semidirect
22. #19143241C2semidirect
23. C43×#3217C2semidirect
41. #14583521C22semidirect
43. #14583514C22semidirect
45. #14583503C22semidirect
49. #14583456C22semidirect
50. #14583455C22semidirect
53. #14583447C22semidirect
54. #14583447C22semidirect
55. #14583434C22semidirect
57. #14583428C22semidirect
58. #124×D43C22semidirect
59. #14583375C22semidirect
60. #14583374C22semidirect
61. #14583371C22semidirect
63. #14583309C22semidirect
64. #14583309C22semidirect
65. #14583308C22semidirect
66. #14583308C22semidirect
69. #14583263C22semidirect
70. #14583263C22semidirect
71. #14583259C22semidirect
72. #14583259C22semidirect
73. #14583258C22semidirect
74. #14583258C22semidirect
75. #14583241C22semidirect
76. #14583237C22semidirect
78. #14583222C22semidirect
79. #14583222C22semidirect
80. #14583221C22semidirect
81. #14583221C22semidirect
83. #14583207C22semidirect
84. #14583206C22semidirect
85. #14583200C22semidirect
86. #14583199C22semidirect
87. #14583187C22semidirect
88. #14583187C22semidirect
89. #14583177C22semidirect
90. #14583177C22semidirect
91. #14583151C22semidirect
92. #14583149C22semidirect
93. #14583144C22semidirect
94. #14583142C22semidirect
95. #14583134C22semidirect
96. #14583132C22semidirect
97. #14583127C22semidirect
98. #14583125C22semidirect
99. #14583116C22semidirect
100. #14583116C22semidirect
101. #14583112C22semidirect
102. #14583112C22semidirect
103. #14583096C22semidirect
105. #14583050C22semidirect
106. #14583036C22semidirect
107. #14583036C22semidirect
109. #14583031C22semidirect
110. #14583031C22semidirect
111. #14583011C22semidirect
112. #14583008C22semidirect
113. #14583000C22semidirect
114. #14582996C22semidirect
115. #14582990C22semidirect
116. SD16×Dic43C22semidirect
117. D8×Dic43C22semidirect
118. #14582979C22semidirect
119. #14582959C22semidirect
120. #14582957C22semidirect
121. #14582956C22semidirect
122. #14582954C22semidirect
123. #14582954C22semidirect
124. #14582924C22semidirect
126. #14582851C22semidirect
127. #97×D43C22semidirect
128. C2×#127×C43C22semidirect
132. C43×#490C22semidirect
133. C43×#490C22semidirect
134. C43×#460C22semidirect
136. C43×#450C22semidirect
138. C43×#432C22semidirect
644. #3217D43semidirect
699. C2×#127C2×D43semidirect
719. #490C2×D43semidirect
720. #490C2×D43semidirect
754. #460C2×D43semidirect
758. #450C2×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
#191484842
#191484692
#191460042
#191460022
#191458372
#191458312
#191457882
#191456132
#191455772
#191454642
#191454582
#191452922
#191452902
#191451892
#191451872
#191448842
#191448362
#191447802
#191447722
#191432412
C43×#32172
#6101743