Finite Group Databasebeta

← #25969253

Subgroups — #25969253

Order 11008.

1736 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148411C211yesmaximal, characteristic, complemented
2#19148009C211yesmaximal, characteristic
3#19145881C212yesmaximal, complemented
4#19145874C212yesmaximal, complemented
5#19145844C212yesmaximal, complemented
6#19145841C212yesmaximal, complemented
7#19145825C211yesmaximal, characteristic, complemented
8#19145824C211yesmaximal, characteristic, complemented
9#19145792C211yesmaximal, characteristic, complemented
10#19145789C211yesmaximal, characteristic, complemented
11#19145776C211yesmaximal, characteristic, complemented
12#19145772C211yesmaximal, characteristic, complemented
13#19145715C211yesmaximal, characteristic, complemented
14#19145128C212yesmaximal, complemented
15#19144944C212yesmaximal, complemented
16#19144568C212yesmaximal, complemented
17#19144546C212yesmaximal, complemented
18#19144403C211yesmaximal, characteristic, complemented
19#19144387C211yesmaximal, characteristic, complemented
20#19144376C211yesmaximal, characteristic, complemented
21#474×D43C211yesmaximal, characteristic, complemented
22#19143256C211yesmaximal, characteristic, complemented
23C43×#3226C211yesmaximal, characteristic, complemented
24#14583629—21no—
25#14583624—21no—
26#14583610—21no—
27#14583604—21no—
28#14583604—21no—
29#14583564—21no—
30Q8×C22⋊D43—21no—
31Q8×C22⋊D43—21no—
32#14583530C2212yescomplemented
33#14583526C2212yes—
34#14583526C2211yescharacteristic
35#14583526C2212yescomplemented
36#14583523C2211yescharacteristic
37#14583516C2211yescharacteristic
38#14583513—21no—
39#14583503C2211yescharacteristic
40#14583502C2211yescharacteristic
41#14583499—21no—
42#14583483—21no—
43#14583481—21no—
44#14583478C2211yescharacteristic
45#14583465C2211yescharacteristic
46#14583462C2211yescharacteristic
47#14583456C2211yescharacteristic, complemented
48#14583454C2211yescharacteristic
49#14583454C2211yescharacteristic, complemented
50#14583446C2211yescharacteristic
51#14583445—21no—
52C4⋊Q8×D43C2211yescharacteristic
53C4⋊Q8×D43C2211yescharacteristic, complemented
54#14583433C2211yescharacteristic
55#14583431C2211yescharacteristic
56#14583429—21no—
57#14583408—21no—
58#14583406—21no—
59#14583380C2212yes—
60C4×#10621898C2211yescharacteristic
61C4×#10621900C2211yescharacteristic
62C4×D4×D43C2211yescharacteristic
63#14583307C2212yescomplemented
64#14583307C2212yescomplemented
65#14583305C2212yescomplemented
66#14583305C2212yescomplemented
67#14583303C2212yescomplemented
68#14583301C2212yescomplemented
69#14583300C2212yescomplemented
70#14583263C2212yes—
71#14583262C2212yes—
72#14583261C2212yes—
73#14583257C2212yes—
74#14583254C2212yes—
75#14583252C2212yes—
76#14583244C2212yes—
77#14583242C2212yescomplemented
78#14583241C2212yescomplemented
79#14583236C2212yescomplemented
80#14583234C2212yescomplemented
81#14583226C2212yes—
82#14583224C2212yes—
83#14583222C2212yescomplemented
84#14583221C2212yes—
85#14583220C2212yes—
86#14583220C2212yescomplemented
87#14583217C2212yes—
88#14583216C2212yes—
89#14583214C2212yes—
90#14583211C2212yescomplemented
91#14583205C2212yescomplemented
92#14583202C2212yes—
93#14583201C2212yes—
94#14583197C2212yescomplemented
95#14583195C2211yescharacteristic, complemented
96#14583193C2212yescomplemented
97#14583190C2211yescharacteristic
98#14583189C2211yescharacteristic
99#14583189C2211yescharacteristic, complemented
100#14583187C2212yescomplemented
101#14583185C2211yescharacteristic, complemented
102#14583181C2211yescharacteristic, complemented
103#14583181C2211yescharacteristic, complemented
104#14583180C2211yescharacteristic
105#14583179C2211yescharacteristic
106#14583179C2211yescharacteristic, complemented
107#14583178C2212yes—
108#14583177C2212yes—
109#14583176C2211yescharacteristic
110#14583176C2211yescharacteristic
111#14582958C2212yescomplemented
112#14582957C2212yescomplemented
113#14582956C2211yescharacteristic, complemented
114#14582955C2211yescharacteristic, complemented
115#14582951C2211yescharacteristic, complemented
116#14582940C2212yes—
117#14582940C2212yes—
118#14582936C2212yes—
119#107×D43C2212yes—
120#14582921C2211yescharacteristic
121C4⋊C8×D43C2211yescharacteristic
122#14582902C2212yes—
123#14582897C2212yes—
124#14582892C2212yes—
125#102×D43C2212yes—
126#14582864C2212yes—
127#14582853C2212yes—
128C43×#532C2211yescharacteristic
129C2×C4⋊Q8×C43C2211yescharacteristic, complemented
130C43×#500C2212yescomplemented
131C43×#486C2212yes—
132C43×#480C2212yes—
133C43×#480C2212yescomplemented
134C43×#474C2211yescharacteristic
135C43×#474C2211yescharacteristic
136C43×#474C2211yescharacteristic, complemented
137C43×#474C2211yescharacteristic, complemented
138C43×#431C2211yescharacteristic, complemented
139C2×#10621898—21no—
140C2×#10621898C2311yescharacteristic
141C2×#10621900C2311yescharacteristic
142C2×Q8×D43—21no—
143C2×Q8×D43—21no—
144C2×D4×D43C2311yescharacteristic
145C22×C4×D43—21no—
146C2×#10621872C2312yes—
147C2×C8×D43C2312yes—
148#13063325C2311yescharacteristic
149#13063325C2311yescharacteristic
150#13063324—22no—
151#13063324—21no—
152#13063324—21no—
153#13063324C2311yescharacteristic
154#13063324C2312yes—
155#13063324C2312yes—
156#13063323—22no—
157#13063323—22no—
158#13063323—21no—
159#13063323—21no—
160#13063323—21no—
161#13063321—21no—
162#13063321C2311yescharacteristic
163#13063320—21no—
164#13063319—21no—
165#13063318—21no—
166#13063318—21no—
167#13063317C2311yescharacteristic
168#13063317C2312yes—
169#13063316—22no—
170#13063316C2311yescharacteristic
171#13063316C2312yes—
172#13063316C2312yes—
173#13063315—22no—
174#13063315—22no—
175#13063315—21no—
176#13063314—21no—
177#13063313C2311yescharacteristic
178#13063312—21no—
179#13063312C2311yescharacteristic
180#13063311—21no—
181#13063311—21no—
182#13063310—21no—
183#13063309—21no—
184#13063308—21no—
185#13063307—21no—
186#13063307—21no—
187#13063306—21no—
188#13063306—21no—
189#13063306—21no—
190#13063305—21no—
191#13063305—21no—
192#13063305C2311yescharacteristic
193#13063304—21no—
194#13063304—21no—
195#13063304—22no—
196#13063304—22no—
197#13063304C2311yescharacteristic
198#13063303—22no—
199#13063303—22no—
200#13063303—21no—
201#13063302—21no—
202#13063302—21no—
203#13063301—21no—
204#13063301—21no—
205#13063301—22no—
206#13063301—22no—
207#13063301—21no—
208#13063301—21no—
209#13063300C2311yescharacteristic
210#13063299C2311yescharacteristic
211#13063298—21no—
212#13063298—21no—
213#13063297—21no—
214#13063297—21no—
215#13063297—21no—
216#13063297—21no—
217#13063297—21no—
218#13063297—21no—
219#13063296—21no—
220#13063296—21no—
221#13063296C2311yescharacteristic
222#13063296C2311yescharacteristic
223#13063295—21no—
224#13063293—21no—
225#13063293—21no—
226#13063293—21no—
227Q8×Dic43—21no—
228Q8×Dic43—21no—
229C4×Dic86—21no—
230C4×Dic86—21no—
231C4×Dic86D411yescharacteristic
232C4×Dic86D411yescharacteristic
233C4×Dic86C2311yescharacteristic
234#13063290—22no—
235#13063290—21no—
236#13063290—21no—
237#13063290C2311yescharacteristic
238C4×D172D411yescharacteristic
239C4×D172D411yescharacteristic
240C4×D172C2311yescharacteristic
241D4×Dic43C2311yescharacteristic
242D4×Dic43C2311yescharacteristic
243#13063287—22no—
244#13063287C2311yescharacteristic
245C4×C22⋊D43—21no—
246C4×C22⋊D43—22no—
247C4×C22⋊D43—22no—
248C4×C22⋊D43—21no—
249C4×C22⋊D43—21no—
250C4×C22⋊D43—21no—
251C4×C22⋊D43—21no—
252C4×C22⋊D43D411yescharacteristic
253C4×C22⋊D43D411yescharacteristic
254C4×C22⋊D43D411yescharacteristic
255C4×C22⋊D43D411yescharacteristic
256(C22⋊D43)⋊C4—21no—
257(C22⋊D43)⋊C4—21no—
258#13063284—21no—
259#13063284C2312yes—
260#13063284C2311yescharacteristic
261#13063283C2311yescharacteristic
262#13063283C2312yes—
263#13063283C2312yes—
264#13063282—21no—
265#13063282C2311yescharacteristic
266#13063282C2311yescharacteristic
267#13063281—21no—
268C4⋊C4×D43—21no—
269C4⋊C4×D43—21no—
270C4⋊C4×D43C2311yescharacteristic
271C4⋊C4×D43C2312yes—
272C4⋊C4×D43C2312yes—
273C22⋊C4×D43—21no—
274C2×C4×Dic43—21no—
275C42×D43C2311yescharacteristic
276C42×D43C2311yescharacteristic
277#13063259C2312yes—
278#13063259C2312yes—
279#13063258C2312yes—
280#13063258C2312yes—
281#13063258C2312yes—
282#13063258C2312yes—
283#13063257C2312yes—
284#13063257C2312yes—
285#13063256C2312yes—
286#13063256C2312yes—
287#13063256C2312yes—
288#13063256C2312yes—
289C4⋊(C43⋊C8)C2311yescharacteristic
290C4⋊(C43⋊C8)C2311yescharacteristic
291Dic43⋊C8C2312yes—
292Dic43⋊C8C2312yes—
293#13063250C2312yes—
294#13063250C2312yes—
295#13063248C2312yes—
296#13063248C2312yes—
297#13063247C2312yes—
298#13063247C2312yes—
299#13063246C2312yes—
300#13063246C2312yes—
301#13063246C2312yes—
302#13063246C2312yes—
303#13063245C2312yes—
304#13063245C2312yes—
305C22⋊(C43⋊C8)C2312yes—
306(C2×D43)⋊C8C2312yes—
307(C2×D43)⋊C8C2312yes—
308#13063236C2312yes—
309#13063235C2312yes—
310C8×Dic43C2312yes—
311C2×#41×C43—21no—
312C22×Q8×C43—21no—
313C4⋊Q8×C43—21no—
314C4⋊Q8×C43—21no—
315C4⋊Q8×C43C2311yescharacteristic
316C4⋊Q8×C43C2312yes—
317C4⋊Q8×C43C2311yescharacteristic
318C4⋊Q8×C43C2311yescharacteristic
319#127×C43C2311yescharacteristic
320#124×C43—21no—
321#121×C43—21no—
322#121×C43C2311yescharacteristic
323#121×C43C2311yescharacteristic
324C4×D4×C43—21no—
325C4×D4×C43C2311yescharacteristic
326C4×D4×C43C2311yescharacteristic
327C2×C4⋊C4×C43—21no—
328C2×C4⋊C4×C43C2312yes—
329C2×C42×C43C2311yescharacteristic
330#107×C43C2312yes—
331#107×C43C2312yes—
332#107×C43C2312yes—
333#107×C43C2312yes—
334C4⋊C8×C43C2311yescharacteristic
335C4⋊C8×C43C2311yescharacteristic
336#102×C43C2312yes—
337#102×C43C2312yes—
338#102×C43C2312yes—
339#102×C43C2312yes—
340C22⋊C8×C43C2312yes—
341C4×C8×C43C2312yes—
342C23×D43—21no—
343#41×C43—82no—
344C2×Q8×C43—21no—
345C2×Q8×C43—21no—
346C2×Q8×C43—21no—
347C2×Q8×C43—22no—
348C2×Q8×C43—82no—
349C2×D4×C43—21no—
350C2×D4×C43—21no—
351C2×D4×C43—21no—
352C2×D4×C43—21no—
353C2×D4×C43C2411yescharacteristic
354C2×D4×C43C2411yescharacteristic
355C22×C4×C43—21no—
356C22×C4×C43—21no—
357C22×C4×C43—22no—
358C22×C4×C43C2×D411yescharacteristic
359C22×C4×C43C2×D411yescharacteristic
360C22×C4×C43C2411yescharacteristic
361C2×C22⋊D43—21no—
362C2×C22⋊D43—21no—
363C2×C22⋊D43—21no—
364C2×C22⋊D43—21no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43—21no—
367C2×C22⋊D43—21no—
368C2×C22⋊D43C2×D411yescharacteristic
369C2×C22⋊D43C2×D411yescharacteristic
370C22×Dic43—21no—
371C22×Dic43—21no—
372C22×Dic43—21no—
373Q8×D43—82no—
374Q8×D43—82no—
375#10621900—22no—
376#10621900—22no—
377D4×D43—22no—
378D4×D43—22no—
379#10621898—22no—
380#10621898—22no—
381#10621898—82no—
382C2×D172—21no—
383C2×D172C2×D411yescharacteristic
384C2×D172C2411yescharacteristic
385C2×C4×D43—21no—
386C2×C4×D43—21no—
387C2×C4×D43—21no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—82no—
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—22no—
401C2×Dic86—22no—
402C2×Dic86C2×D411yescharacteristic
403C2×Dic86C2411yescharacteristic
404C2×C8×C43C2412yes—
405C2×C8×C43C2412yes—
406C4⋊C4×C43—21no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—22no—
409C4⋊C4×C43—22no—
410C4⋊C4×C43—21no—
411C4⋊C4×C43C2412yes—
412C4⋊C4×C43C2412yes—
413C4⋊C4×C43C2411yescharacteristic
414C4⋊C4×C43C2411yescharacteristic
415C22⋊C4×C43—21no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C22⋊C4×C43—21no—
419C42×C43C2×D411yescharacteristic
420C42×C43C2×D411yescharacteristic
421C42×C43C2411yescharacteristic
422C42×C43C2411yescharacteristic
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425C22⋊Dic43—21no—
426C22⋊Dic43—21no—
427C22⋊Dic43—21no—
428C22⋊Dic43—21no—
429C22⋊Dic43—22no—
430C22⋊Dic43—21no—
431C22⋊Dic43C2×D411yescharacteristic
432C22⋊Dic43C2×D411yescharacteristic
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—21no—
437(C2×D43)⋊C4—21no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4—21no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4—21no—
443(C2×D43)⋊C4C2×D411yescharacteristic
444(C2×D43)⋊C4C2×D411yescharacteristic
445(C2×D43)⋊C4C2×D411yescharacteristic
446(C2×D43)⋊C4C2×D411yescharacteristic
447C4⋊Dic43—21no—
448C4⋊Dic43—21no—
449C4⋊Dic43—21no—
450C4⋊Dic43—21no—
451C4⋊Dic43—22no—
452C4⋊Dic43—22no—
453C4⋊Dic43C2×D411yescharacteristic
454C4⋊Dic43C2×D411yescharacteristic
455C4⋊Dic43C2412yes—
456C4⋊Dic43C2412yes—
457C4⋊Dic43C2411yescharacteristic
458C4⋊Dic43C2411yescharacteristic
459Dic43⋊C4—21no—
460Dic43⋊C4—21no—
461Dic43⋊C4—21no—
462Dic43⋊C4—21no—
463Dic43⋊C4—22no—
464Dic43⋊C4—22no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—21no—
468Dic43⋊C4—22no—
469Dic43⋊C4—22no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4—21no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4C2×D411yescharacteristic
476Dic43⋊C4C2×D411yescharacteristic
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479C4×Dic43—21no—
480C4×Dic43—22no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483C4×Dic43—22no—
484C4×Dic43—22no—
485C4×Dic43C2×D411yescharacteristic
486C4×Dic43C2×D411yescharacteristic
487C4×Dic43C2×D411yescharacteristic
488C4×Dic43C2×D411yescharacteristic
489C4×Dic43C2411yescharacteristic
490C4×Dic43C2411yescharacteristic
491C2×C43⋊C8C2412yes—
492C2×C43⋊C8C2412yes—
493#10621872—24no—
494C8×D43—24no—
495C23×C43—21no—
496C23×C43—21no—
497C23×C43C22×D411yescharacteristic
498C22×D43—21no—
499C22×D43—42no—
500C22×D43—81no—
501C22×D43—81no—
502C22×D43C22×D411yescharacteristic
503C22×D43C22×D411yescharacteristic
504Q8×C43—42no—
505Q8×C43—42no—
506Q8×C43—82no—
507Q8×C43—81no—
508D4×C43—21no—
509D4×C43—21no—
510D4×C43—21no—
511D4×C43—21no—
512D4×C43—81no—
513D4×C43—81no—
514D4×C43—81no—
515D4×C43—81no—
516C2×C4×C43—22no—
517C2×C4×C43—21no—
518C2×C4×C43—21no—
519C2×C4×C43—21no—
520C2×C4×C43—22no—
521C2×C4×C43—22no—
522C2×C4×C43—21no—
523C2×C4×C43—41no—
524C2×C4×C43—42no—
525C2×C4×C43—42no—
526C2×C4×C43—82no—
527C2×C4×C43C22×D411yescharacteristic
528C2×C4×C43C22×D411yescharacteristic
529C2×C4×C43C22×D411yescharacteristic
530C2×C4×C43C22×D411yescharacteristic
531C2×C4×C43C22×D411yescharacteristic
532C2×C4×C43C2511yescharacteristic
533C22⋊D43—22no—
534C22⋊D43—22no—
535C22⋊D43—42no—
536C22⋊D43—42no—
537C22⋊D43—81no—
538C22⋊D43—81no—
539C22⋊D43—81no—
540C22⋊D43—81no—
541C22⋊D43—81no—
542C2×Dic43—22no—
543C2×Dic43—21no—
544C2×Dic43—21no—
545C2×Dic43—22no—
546C2×Dic43—21no—
547C2×Dic43—42no—
548C2×Dic43—81no—
549C2×Dic43—81no—
550C2×Dic43C22×D411yescharacteristic
551C2×Dic43C22×D411yescharacteristic
552C2×Dic43C22×D411yescharacteristic
553C2×Dic43C22×D411yescharacteristic
554C2×Dic43C22×D411yescharacteristic
555C2×Dic43C22×D411yescharacteristic
556D172—22no—
557D172—21no—
558D172—21no—
559D172—81no—
560C4×D43—22no—
561C4×D43—22no—
562C4×D43—21no—
563C4×D43—21no—
564C4×D43—41no—
565C4×D43—41no—
566C4×D43—42no—
567C4×D43—81no—
568C4×D43—81no—
569C4×D43—82no—
570C4×D43—82no—
571C4×D432−1+412yes—
572C4×D432−1+412yes—
573Dic86—22no—
574Dic86—21no—
575Dic86—21no—
576Dic86—42no—
577Dic86—42no—
578Dic86—81no—
579Dic86—82no—
580Dic86—82no—
581C8×C43—22no—
582C8×C43—22no—
583C43⋊C8—22no—
584C43⋊C8—22no—
585#60888—431nomaximal, Sylow
586C22×C43—21no—
587C22×C43—21no—
588C22×C43—21no—
589C22×C43—41no—
590C22×C43—41no—
591C22×C43—41no—
592C22×C43—41no—
593C22×C43—41no—
594C22×C43—41no—
595C22×C43C23×D411yescharacteristic
596C2×D43—21no—
597C2×D43—21no—
598C2×D43—21no—
599C2×D43—21no—
600C2×D43—21no—
601C2×D43—41no—
602C2×D43—41no—
603C2×D43—41no—
604C2×D43—84no—
605C2×D43#53612yes—
606C4×C43—21no—
607C4×C43—21no—
608C4×C43—21no—
609C4×C43—21no—
610C4×C43—42no—
611C4×C43—42no—
612C4×C43—41no—
613C4×C43—41no—
614C4×C43#57612yes—
615C4×C43C2×2−1+411yescharacteristic
616C4×C43C2×2−1+411yescharacteristic
617Dic43—21no—
618Dic43—21no—
619Dic43—21no—
620Dic43—21no—
621Dic43—21no—
622Dic43—42no—
623Dic43—41no—
624Dic43—41no—
625Dic43—42no—
626Dic43—41no—
627Dic43#53612yes—
628#3503—431no—
629#3460—431no—
630#3243—432no—
631#3243—432no—
632#3241—432no—
633#3241—432no—
634#3239—431no—
635#3239—431no—
636#3235—431no—
637#3235—431no—
638#3233—431no—
639#3233—431no—
640#3226—431no—
641#3226D4311yescharacteristic, complemented
642#3164—432no—
643#3136—432no—
644#3098—432no—
645#3096—432no—
646#3079—431no—
647#3077—431no—
648#3076—431no—
649C2×#474—431no—
650#2925—431no—
651C2×C43—41no—
652C2×C43—81no—
653C2×C43—81no—
654C2×C43C2×#53611yescharacteristic
655C2×C43C2×#57611yescharacteristic
656C2×C43#358611yescharacteristic
657D43—22no—
658D43—41no—
659D43—81no—
660Q82—861no—
661#557—861no—
662#554—861no—
663#554—861no—
664#554—861no—
665D4×Q8—861no—
666D4×Q8—861no—
667D4×Q8—861no—
668#544—432no—
669#544—431no—
670#544—432no—
671#544—432no—
672#542—431no—
673#542—431no—
674#542—861no—
675#540—431no—
676#540—431no—
677#540—861no—
678#538—861no—
679#538—861no—
680#537—431no—
681#535—431no—
682#535—431no—
683#533—431no—
684#533—431no—
685#533—431no—
686#532—431no—
687#532—861no—
688#532C2×D4311yescharacteristic
689C2×C4⋊Q8—431no—
690C2×C4⋊Q8—431no—
691C2×C4⋊Q8C2×D4311yescharacteristic, complemented
692#529—431no—
693#529—431no—
694#529—861no—
695#525—861no—
696#525—861no—
697#520—432no—
698C4×#41—431no—
699C4×#41—431no—
700C2×C4×D4—431no—
701#501—432no—
702#501—432no—
703#501—432no—
704#501—432no—
705#500—432no—
706#500C2×D4312yescomplemented
707#499—432no—
708#499—432no—
709#490—432no—
710#490—432no—
711#489—432no—
712#489—432no—
713#488—432no—
714#488—432no—
715#486—432no—
716#486C2×D4312yes—
717#485—432no—
718#485—432no—
719#484—432no—
720#484—432no—
721#482—432no—
722#482—432no—
723#482—432no—
724#482—432no—
725#482—432no—
726#482—432no—
727#481—432no—
728#481—432no—
729#480—432no—
730#480—432no—
731#480C2×D4312yes—
732#480C2×D4312yescomplemented
733#479—432no—
734#478—432no—
735#478—432no—
736#478—432no—
737#477—432no—
738#477—431no—
739#476—431no—
740#476—431no—
741#476—431no—
742#476—432no—
743#475—431no—
744#475—431no—
745#475—431no—
746#474—431no—
747#474—431no—
748#474—431no—
749#474—431no—
750#474—432no—
751#474—431no—
752#474—432no—
753#474C2×D4311yescharacteristic
754#474C2×D4311yescharacteristic
755#474C2×D4311yescharacteristic, complemented
756#474C2×D4311yescharacteristic, complemented
757#433—432no—
758#433—432no—
759#432—431no—
760#432—431no—
761#431—431no—
762#431C2×D4311yescharacteristic, complemented
763#428—432no—
764#428—432no—
765#427—432no—
766C2×#107—432no—
767#423—431no—
768C2×C4⋊C8—431no—
769#418—432no—
770#417—432no—
771#416—432no—
772C2×#102—432no—
773#408—432no—
774#405—432no—
775C43#6088811yescharacteristic, complemented, Sylow
776C2×#41—21no—
777C2×#41—431no—
778C2×#41—431no—
779C2×#41—861no—
780C22×Q8—21no—
781C22×Q8—861no—
782C22×Q8—861no—
783C22×D4—431no—
784C23×C4—861no—
785C2×M16—432no—
786C22×C8—432no—
787C4⋊Q8—21no—
788C4⋊Q8—21no—
789C4⋊Q8—432no—
790C4⋊Q8—432no—
791C4⋊Q8—431no—
792C4⋊Q8—431no—
793C4⋊Q8—431no—
794C4⋊Q8—861no—
795C4⋊Q8—861no—
796C4⋊Q8—861no—
797C4⋊Q8—861no—
798C4⋊Q8—862no—
799C4⋊Q8—861no—
800C4⋊Q8—862no—
801C4⋊Q8—862no—
802C4⋊Q8C22×D4311yescharacteristic
803C4⋊Q8C22×D4311yescharacteristic
804C4⋊Q8C22×D4312yes—
805C4⋊Q8C22×D4311yescharacteristic
806#127—431no—
807#127—861no—
808#127C22×D4311yescharacteristic
809#126—861no—
810#126—861no—
811#126—861no—
812#126—861no—
813#125—431no—
814#125—432no—
815#125—432no—
816#125—431no—
817#125—432no—
818#125—861no—
819#125—862no—
820#125—862no—
821#125—862no—
822#124—21no—
823#124—431no—
824#124—431no—
825#124—861no—
826#124—861no—
827#124—861no—
828#124—861no—
829#123—861no—
830#123—861no—
831#123—861no—
832#123—861no—
833#123—861no—
834#123—861no—
835#123—861no—
836#123—861no—
837C22⋊Q8—431no—
838C22⋊Q8—431no—
839C22⋊Q8—861no—
840C22⋊Q8—861no—
841C22⋊Q8—861no—
842C22⋊Q8—862no—
843C22⋊Q8—862no—
844C22⋊Q8—862no—
845C22⋊Q8—862no—
846C22⋊Q8—861no—
847C22⋊Q8—862no—
848C22⋊Q8—862no—
849C22⋊Q8—861no—
850C22⋊Q8—861no—
851C22⋊Q8—861no—
852C22⋊Q8—861no—
853C22⋊Q8—861no—
854C22⋊Q8—861no—
855C22⋊Q8—861no—
856#121—21no—
857#121—431no—
858#121—431no—
859#121—431no—
860#121—431no—
861#121—861no—
862#121—861no—
863#121—861no—
864#121—861no—
865#121—861no—
866#121—861no—
867#121—861no—
868#121—861no—
869#121—861no—
870#121—861no—
871#121C22×D4311yescharacteristic
872#121C22×D4311yescharacteristic
873#120—861no—
874#120—861no—
875#120—861no—
876#120—861no—
877C4×Q8—431no—
878C4×Q8—431no—
879C4×Q8—431no—
880C4×Q8—431no—
881C4×Q8—861no—
882C4×Q8—861no—
883C4×Q8—861no—
884C4×Q8—861no—
885C4×Q8—862no—
886C4×Q8—861no—
887C4×Q8—861no—
888C4×D4—21no—
889C4×D4—431no—
890C4×D4—431no—
891C4×D4—431no—
892C4×D4—431no—
893C4×D4—431no—
894C4×D4—431no—
895C4×D4—431no—
896C4×D4—431no—
897C4×D4—431no—
898C4×D4—431no—
899C4×D4—861no—
900C4×D4—861no—
901C4×D4—861no—
902C4×D4—861no—
903C4×D4—862no—
904C4×D4—861no—
905C4×D4—861no—
906C4×D4—862no—
907C4×D4—862no—
908C4×D4—861no—
909C4×D4C22×D4311yescharacteristic
910C4×D4C22×D4311yescharacteristic
911#117—431no—
912#117—431no—
913#117—431no—
914#117—432no—
915#117—431no—
916#117—432no—
917#117—432no—
918#117—861no—
919#117—861no—
920#117—861no—
921C2×C4⋊C4—21no—
922C2×C4⋊C4—431no—
923C2×C4⋊C4—432no—
924C2×C4⋊C4—432no—
925C2×C4⋊C4—861no—
926C2×C4⋊C4—861no—
927C2×C4⋊C4C22×D4312yes—
928C2×C22⋊C4—861no—
929C2×C42—431no—
930C2×C42—431no—
931C2×C42—861no—
932C2×C42C22×D4311yescharacteristic
933#107—432no—
934#107—432no—
935#107—432no—
936#107—432no—
937#107—432no—
938#107—432no—
939#107C22×D4312yes—
940#107C22×D4312yes—
941#107C22×D4312yes—
942#107C22×D4312yes—
943#106—432no—
944#106—432no—
945#106—432no—
946#106—432no—
947#106—432no—
948#106—432no—
949C4⋊C8—432no—
950C4⋊C8—432no—
951C4⋊C8—431no—
952C4⋊C8—431no—
953C4⋊C8C22×D4311yescharacteristic
954C4⋊C8C22×D4311yescharacteristic
955#103—432no—
956#103—432no—
957#103—432no—
958#103—432no—
959#102—432no—
960#102—432no—
961#102—432no—
962#102—432no—
963#102—432no—
964#102—432no—
965#102—432no—
966#102—432no—
967#102C22×D4312yes—
968#102C22×D4312yes—
969#102C22×D4312yes—
970#102C22×D4312yes—
971C22⋊C8—432no—
972C22⋊C8—432no—
973C22⋊C8—432no—
974C22⋊C8C22×D4312yes—
975#97—432no—
976#97—432no—
977C4×C8—432no—
978C4×C8C22×D4312yes—
979C24—861no—
980#41—82no—
981#41—862no—
982#41—862no—
983#41—862no—
984#41—862no—
985#41—3442no—
986C2×Q8—21no—
987C2×Q8—21no—
988C2×Q8—21no—
989C2×Q8—22no—
990C2×Q8—82no—
991C2×Q8—431no—
992C2×Q8—431no—
993C2×Q8—861no—
994C2×Q8—862no—
995C2×Q8—862no—
996C2×Q8—861no—
997C2×Q8—861no—
998C2×Q8—3442no—
999C2×Q8—3442no—
1000C2×D4—21no—
1001C2×D4—21no—
1002C2×D4—21no—
1003C2×D4—21no—
1004C2×D4—431no—
1005C2×D4—431no—
1006C2×D4—431no—
1007C2×D4—431no—
1008C2×D4—861no—
1009C2×D4—862no—
1010C2×D4—862no—
1011C2×D4—861no—
1012C2×D4—861no—
1013C2×D4—861no—
1014C2×D4—861no—
1015C2×D4—861no—
1016C2×D4—861no—
1017C2×D4—861no—
1018C2×D4C23×D4311yescharacteristic
1019C2×D4C23×D4311yescharacteristic
1020C22×C4—22no—
1021C22×C4—21no—
1022C22×C4—21no—
1023C22×C4—431no—
1024C22×C4—431no—
1025C22×C4—431no—
1026C22×C4—431no—
1027C22×C4—431no—
1028C22×C4—431no—
1029C22×C4—861no—
1030C22×C4—861no—
1031C22×C4—862no—
1032C22×C4—862no—
1033C22×C4—861no—
1034C22×C4—861no—
1035C22×C4—861no—
1036C22×C4—861no—
1037C22×C4—3442no—
1038C22×C4D4×D4311yescharacteristic
1039C22×C4D4×D4311yescharacteristic
1040C22×C4C23×D4311yescharacteristic
1041M16—864no—
1042C2×C8—432no—
1043C2×C8—432no—
1044C2×C8—864no—
1045C2×C8C23×D4312yes—
1046C2×C8C23×D4312yes—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—22no—
1050C4⋊C4—22no—
1051C4⋊C4—21no—
1052C4⋊C4—431no—
1053C4⋊C4—431no—
1054C4⋊C4—431no—
1055C4⋊C4—431no—
1056C4⋊C4—431no—
1057C4⋊C4—431no—
1058C4⋊C4—432no—
1059C4⋊C4—432no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—861no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—861no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—862no—
1073C4⋊C4—862no—
1074C4⋊C4—862no—
1075C4⋊C4—862no—
1076C4⋊C4—861no—
1077C4⋊C4—861no—
1078C4⋊C4—861no—
1079C4⋊C4—861no—
1080C4⋊C4—861no—
1081C4⋊C4—861no—
1082C4⋊C4—862no—
1083C4⋊C4—862no—
1084C4⋊C4C23×D4312yes—
1085C4⋊C4C23×D4312yes—
1086C4⋊C4C23×D4311yescharacteristic
1087C4⋊C4C23×D4311yescharacteristic
1088C22⋊C4—21no—
1089C22⋊C4—21no—
1090C22⋊C4—21no—
1091C22⋊C4—21no—
1092C22⋊C4—431no—
1093C22⋊C4—431no—
1094C22⋊C4—431no—
1095C22⋊C4—431no—
1096C22⋊C4—431no—
1097C22⋊C4—431no—
1098C22⋊C4—861no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—862no—
1102C22⋊C4—862no—
1103C22⋊C4—861no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C22⋊C4—861no—
1107C22⋊C4—861no—
1108C22⋊C4—861no—
1109C22⋊C4—861no—
1110C22⋊C4—862no—
1111C22⋊C4—861no—
1112C22⋊C4—861no—
1113C22⋊C4—861no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C42—431no—
1117C42—431no—
1118C42—431no—
1119C42—431no—
1120C42—431no—
1121C42—431no—
1122C42—861no—
1123C42—861no—
1124C42—862no—
1125C42—862no—
1126C42—861no—
1127C42—862no—
1128C42D4×D4311yescharacteristic
1129C42D4×D4311yescharacteristic
1130C42C23×D4311yescharacteristic
1131C42C23×D4311yescharacteristic
1132C23—21no—
1133C23—21no—
1134C23—431no—
1135C23—431no—
1136C23—861no—
1137C23—3441no—
1138C23—3441no—
1139C23—1722no—
1140C23C2×D4×D4311yescharacteristic
1141Q8—42no—
1142Q8—42no—
1143Q8—82no—
1144Q8—81no—
1145Q8—862no—
1146Q8—861no—
1147Q8—861no—
1148Q8—3442no—
1149Q8—3442no—
1150Q8—3441no—
1151Q8—1722no—
1152Q8—1722no—
1153D4—21no—
1154D4—21no—
1155D4—21no—
1156D4—21no—
1157D4—81no—
1158D4—81no—
1159D4—81no—
1160D4—81no—
1161D4—862no—
1162D4—862no—
1163D4—862no—
1164D4—861no—
1165D4—861no—
1166D4—3441no—
1167D4—3441no—
1168D4—3441no—
1169D4—3441no—
1170D4—3441no—
1171D4—3441no—
1172D4—1722no—
1173D4—1722no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—21no—
1181C2×C4—41no—
1182C2×C4—42no—
1183C2×C4—42no—
1184C2×C4—82no—
1185C2×C4—431no—
1186C2×C4—432no—
1187C2×C4—432no—
1188C2×C4—431no—
1189C2×C4—431no—
1190C2×C4—431no—
1191C2×C4—431no—
1192C2×C4—431no—
1193C2×C4—862no—
1194C2×C4—862no—
1195C2×C4—861no—
1196C2×C4—861no—
1197C2×C4—862no—
1198C2×C4—861no—
1199C2×C4—861no—
1200C2×C4—862no—
1201C2×C4—861no—
1202C2×C4—3441no—
1203C2×C4—3441no—
1204C2×C4—3442no—
1205C2×C4—3442no—
1206C2×C4—3441no—
1207C2×C4—3441no—
1208C2×C4—1721no—
1209C2×C4—1721no—
1210C2×C4—1722no—
1211C2×C4—1722no—
1212C2×C4C2×D4×D4311yescharacteristic
1213C2×C4C2×D4×D4311yescharacteristic
1214C2×C4C2×D4×D4311yescharacteristic
1215C2×C4C2×D4×D4311yescharacteristic
1216C2×C4C2×D4×D4311yescharacteristic
1217C2×C4C24×D4311yescharacteristic
1218C8—22no—
1219C8—22no—
1220C8—862no—
1221C8—862no—
1222C22—21no—
1223C22—21no—
1224C22—21no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—432no—
1232C22—861no—
1233C22—861no—
1234C22—861no—
1235C22—861no—
1236C22—861no—
1237C22—3444no—
1238C22—1721no—
1239C22—1721no—
1240C22—1721no—
1241C22C22×D4×D4311yescharacteristic
1242C4—21no—
1243C4—21no—
1244C4—21no—
1245C4—21no—
1246C4—41no—
1247C4—41no—
1248C4—42no—
1249C4—42no—
1250C4—432no—
1251C4—861no—
1252C4—861no—
1253C4—861no—
1254C4—861no—
1255C4—861no—
1256C4—1721no—
1257C4—1722no—
1258C4—1721no—
1259C4—1722no—
1260C4—1721no—
1261C4#1458370012yes—
1262C42−1+4×D4311yescharacteristic
1263C42−1+4×D4311yescharacteristic
1264C2—41no—
1265C2—81no—
1266C2—81no—
1267C2—862no—
1268C2—3441no—
1269C2—1721no—
1270C2#536×D4311yescharacteristic
1271C2C2×#1458370011yescharacteristic
1272C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3226C2
socleC22×C43C23×D4
prime radical#19148009C2
hypercenter#3226D43
hypocenterC43#60888
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
1. #19148411C2semidirect
3. #19145881C2semidirect
4. #19145874C2semidirect
5. #19145844C2semidirect
6. #19145841C2semidirect
7. #19145825C2semidirect
8. #19145824C2semidirect
9. #19145792C2semidirect
10. #19145789C2semidirect
11. #19145776C2semidirect
12. #19145772C2semidirect
13. #19145715C2semidirect
14. #19145128C2semidirect
15. #19144944C2semidirect
16. #19144568C2semidirect
17. #19144546C2semidirect
18. #19144403C2semidirect
19. #19144387C2semidirect
20. #19144376C2semidirect
21. #474×D43C2semidirect
22. #19143256C2semidirect
23. C43×#3226C2semidirect
32. #14583530C22semidirect
35. #14583526C22semidirect
47. #14583456C22semidirect
49. #14583454C22semidirect
53. C4⋊Q8×D43C22semidirect
63. #14583307C22semidirect
64. #14583307C22semidirect
65. #14583305C22semidirect
66. #14583305C22semidirect
67. #14583303C22semidirect
68. #14583301C22semidirect
69. #14583300C22semidirect
77. #14583242C22semidirect
78. #14583241C22semidirect
79. #14583236C22semidirect
80. #14583234C22semidirect
83. #14583222C22semidirect
86. #14583220C22semidirect
90. #14583211C22semidirect
91. #14583205C22semidirect
94. #14583197C22semidirect
95. #14583195C22semidirect
96. #14583193C22semidirect
99. #14583189C22semidirect
100. #14583187C22semidirect
101. #14583185C22semidirect
102. #14583181C22semidirect
103. #14583181C22semidirect
106. #14583179C22semidirect
111. #14582958C22semidirect
112. #14582957C22semidirect
113. #14582956C22semidirect
114. #14582955C22semidirect
115. #14582951C22semidirect
129. C2×C4⋊Q8×C43C22semidirect
130. C43×#500C22semidirect
133. C43×#480C22semidirect
136. C43×#474C22semidirect
137. C43×#474C22semidirect
138. C43×#431C22semidirect
641. #3226D43semidirect
691. C2×C4⋊Q8C2×D43semidirect
706. #500C2×D43semidirect
732. #480C2×D43semidirect
755. #474C2×D43semidirect
756. #474C2×D43semidirect
762. #431C2×D43semidirect
775. C43#60888semidirect

Maximal subgroups

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

subgroupindex
#191484112
#191480092
#191458812
#191458742
#191458442
#191458412
#191458252
#191458242
#191457922
#191457892
#191457762
#191457722
#191457152
#191451282
#191449442
#191445682
#191445462
#191444032
#191443872
#191443762
#474×D432
#191432562
C43×#32262
#6088843