Finite Group Databasebeta

← #25968988

Subgroups — #25968988

Order 11008.

1742 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148318C211yesmaximal, characteristic
2C2×#14583526C211yesmaximal, characteristic, complemented
3#19145883C212yesmaximal, complemented
4#19145873C212yesmaximal, complemented
5#19145849C212yesmaximal, complemented
6#19145847C212yesmaximal, complemented
7#19145819C211yesmaximal, characteristic, complemented
8#19145787C211yesmaximal, characteristic, complemented
9#19145782C211yesmaximal, characteristic, complemented
10#19145766C211yesmaximal, characteristic, complemented
11#19145759C211yesmaximal, characteristic, complemented
12#19145716C211yesmaximal, characteristic, complemented
13#19145714C211yesmaximal, characteristic, complemented
14#19145130C212yesmaximal, complemented
15#19144946C212yesmaximal, complemented
16#19144530C211yesmaximal, characteristic, complemented
17#19144519C211yesmaximal, characteristic, complemented
18#19144509C211yesmaximal, characteristic, complemented
19#480×D43C211yesmaximal, characteristic, complemented
20#19144443C212yesmaximal, complemented
21#19144421C212yesmaximal, complemented
22#19143254C211yesmaximal, characteristic, complemented
23C43×#3238C211yesmaximal, characteristic, complemented
24#14583612—21no—
25#14583600—21no—
26#14583598—21no—
27#14583574—21no—
28#14583573—21no—
29#14583547—21no—
30#14583544—21no—
31#14583541—21no—
32#14583529C2211yescharacteristic
33#14583526—21no—
34#14583526—21no—
35#14583526—21no—
36#14583526—21no—
37#14583526C2212yes—
38#14583526C2212yes—
39#14583526C2212yescomplemented
40#14583526C2212yescomplemented
41#14583521C2211yescharacteristic
42#14583518C2211yescharacteristic
43#14583505C2211yescharacteristic
44#14583500C2211yescharacteristic
45#14583467C2211yescharacteristic
46#14583449C2211yescharacteristic
47#14583444C2211yescharacteristic
48C2×#13063324C2211yescharacteristic, complemented
49C2×#13063323—21no—
50#14583435C2211yescharacteristic
51C2×#13063317C2211yescharacteristic, complemented
52C2×#13063316C2211yescharacteristic, complemented
53C2×#13063315—21no—
54#14583412C2211yescharacteristic
55C2×#13063303—21no—
56C2×#13063301—21no—
57#121×D43C2211yescharacteristic
58#14583381C2211yescharacteristic
59#14583371C2211yescharacteristic
60C2×#13063283C2211yescharacteristic
61C2×#13063282C2211yescharacteristic
62C2×C4⋊C4×D43C2211yescharacteristic
63#14583308C2212yescomplemented
64#14583307C2212yescomplemented
65#14583306C2212yescomplemented
66#14583303C2212yescomplemented
67#14583302C2212yescomplemented
68#14583299C2212yescomplemented
69#14583298C2212yescomplemented
70#14583264C2212yescomplemented
71#14583262C2212yescomplemented
72#14583260C2212yescomplemented
73#14583255C2212yescomplemented
74#14583253C2212yescomplemented
75#14583247C2212yescomplemented
76#14583244C2212yescomplemented
77#14583238C2212yescomplemented
78#14583233C2212yescomplemented
79#14583232C2211yescharacteristic, complemented
80#14583227C2211yescharacteristic, complemented
81#14583226C2212yes—
82#14583225C2212yescomplemented
83#14583222C2212yes—
84#14583219C2212yescomplemented
85#14583218C2211yescharacteristic
86#14583218C2211yescharacteristic, complemented
87#14583215C2211yescharacteristic
88#14583214C2212yes—
89#14583213C2211yescharacteristic
90#14583213C2211yescharacteristic, complemented
91#14583212C2211yescharacteristic
92#14583212C2211yescharacteristic
93#14583212C2211yescharacteristic, complemented
94#14583212C2211yescharacteristic, complemented
95#14583211C2212yes—
96#14583210C2211yescharacteristic
97#14583206C2212yescomplemented
98#14583204C2212yescomplemented
99#14583202C2212yescomplemented
100#14583201C2212yescomplemented
101#14583200C2212yescomplemented
102#14583200C2212yescomplemented
103#14583199C2212yescomplemented
104#14583198C2212yescomplemented
105#14583192C2212yescomplemented
106#14583188C2212yescomplemented
107#14583178C2212yescomplemented
108#14583177C2212yescomplemented
109#14583176C2212yescomplemented
110#14583176C2212yescomplemented
111#14582961C2212yescomplemented
112#14582959C2212yescomplemented
113#14582953C2211yescharacteristic, complemented
114#14582952C2211yescharacteristic, complemented
115#14582949C2211yescharacteristic, complemented
116#14582940C2212yes—
117#14582938C2212yes—
118#14582934C2212yes—
119#107×D43C2212yes—
120#14582924C2212yes—
121#14582902C2212yes—
122#14582899C2212yes—
123#14582894C2212yes—
124#102×D43C2212yes—
125#14582861C2211yescharacteristic
126C22⋊C8×D43C2211yescharacteristic
127#14582856C2212yes—
128C2×C4⋊Q8×C43C2211yescharacteristic, complemented
129C43×#529C2211yescharacteristic
130C43×#501C2212yescomplemented
131C43×#489C2212yescomplemented
132C43×#483C2211yescharacteristic, complemented
133C43×#483C2211yescharacteristic, complemented
134C43×#480C2211yescharacteristic
135C43×#480C2211yescharacteristic
136C43×#477C2212yescomplemented
137C43×#476C2212yescomplemented
138C43×#432C2211yescharacteristic, complemented
139C2×#10621902C2311yescharacteristic
140C2×#10621898—21no—
141C2×#10621900—21no—
142C22×Dic86—21no—
143C2×D4×D43—21no—
144C2×D4×D43C2311yescharacteristic
145C22×C4×D43—21no—
146C22×C4×D43C2311yescharacteristic
147C2×#10621872C2312yes—
148C2×C8×D43C2312yes—
149#13063325C2311yescharacteristic
150#13063324—21no—
151#13063324—21no—
152#13063324—21no—
153#13063324C2311yescharacteristic
154#13063324C2312yes—
155#13063324C2312yes—
156#13063323—22no—
157#13063323—22no—
158#13063323—22no—
159#13063323—22no—
160#13063322C2311yescharacteristic
161#13063321C2311yescharacteristic
162#13063320—21no—
163#13063319—21no—
164#13063318—21no—
165#13063317—21no—
166#13063317—21no—
167#13063317C2312yes—
168#13063317C2312yes—
169#13063316—21no—
170#13063316—21no—
171#13063316C2311yescharacteristic
172#13063316C2312yes—
173#13063316C2312yes—
174#13063315—21no—
175#13063315—22no—
176#13063315—22no—
177#13063315—22no—
178#13063315—22no—
179#13063314C2311yescharacteristic
180#13063313—21no—
181#13063313—21no—
182#13063311—21no—
183#13063311—21no—
184#13063310—21no—
185#13063310—21no—
186#13063310—21no—
187#13063310—21no—
188#13063309—21no—
189#13063309—21no—
190#13063308—21no—
191#13063307—21no—
192#13063305—21no—
193#13063303—21no—
194#13063303—22no—
195#13063303—22no—
196#13063303—22no—
197#13063303—22no—
198#13063303—21no—
199#13063302—21no—
200#13063301—22no—
201#13063301—22no—
202#13063301—22no—
203#13063301—22no—
204#13063301C2311yescharacteristic
205#13063300—21no—
206#13063300—21no—
207#13063300C2311yescharacteristic
208#13063300C2311yescharacteristic
209#13063299—21no—
210#13063299—21no—
211#13063299C2311yescharacteristic
212#13063299C2311yescharacteristic
213#13063298—21no—
214#13063298—21no—
215#13063298—21no—
216#13063298—21no—
217#13063297—21no—
218#13063297—21no—
219#13063296C2311yescharacteristic
220#13063295—21no—
221#13063295—21no—
222#13063295—21no—
223Q8×Dic43C2311yescharacteristic
224C4×D172—21no—
225C4×D172—21no—
226C4×D172C2311yescharacteristic
227C4×D172C2311yescharacteristic
228D4×Dic43C2311yescharacteristic
229#13063287—21no—
230#13063287—21no—
231#13063287C2311yescharacteristic
232#13063287C2311yescharacteristic
233C4×C22⋊D43—21no—
234(C22⋊D43)⋊C4—21no—
235(C22⋊D43)⋊C4—21no—
236(C22⋊D43)⋊C4—21no—
237(C22⋊D43)⋊C4—21no—
238#13063283—21no—
239#13063283—21no—
240#13063283—21no—
241#13063283C2312yes—
242#13063283C2312yes—
243#13063283C2311yescharacteristic
244#13063282—21no—
245#13063282D411yescharacteristic
246#13063282D411yescharacteristic
247#13063282D411yescharacteristic
248#13063282D411yescharacteristic
249#13063282C2311yescharacteristic
250#13063282C2311yescharacteristic
251#13063282C2311yescharacteristic
252#13063282C2311yescharacteristic
253C2×C4⋊Dic43—21no—
254C2×C4⋊Dic43C2311yescharacteristic
255C2×C4⋊Dic43C2311yescharacteristic
256C2×Dic43⋊C4—21no—
257C2×Dic43⋊C4—21no—
258C2×Dic43⋊C4—21no—
259C2×Dic43⋊C4—21no—
260C2×Dic43⋊C4—21no—
261C2×Dic43⋊C4D411yescharacteristic
262C2×Dic43⋊C4D411yescharacteristic
263C4⋊C4×D43—21no—
264C4⋊C4×D43—21no—
265C4⋊C4×D43—21no—
266C4⋊C4×D43C2312yes—
267C4⋊C4×D43C2312yes—
268C4⋊C4×D43C2311yescharacteristic
269C2×(C2×D43)⋊C4—21no—
270C2×(C2×D43)⋊C4—21no—
271C2×(C2×D43)⋊C4D411yescharacteristic
272C2×(C2×D43)⋊C4D411yescharacteristic
273C22⋊C4×D43—21no—
274C22⋊C4×D43—21no—
275C2×C4×Dic43—21no—
276C2×C4×Dic43C2311yescharacteristic
277#13063259C2312yes—
278#13063259C2312yes—
279#13063258C2312yes—
280#13063258C2312yes—
281#13063258C2312yes—
282#13063258C2312yes—
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#13063245C2312yes—
301#13063245C2312yes—
302#13063245C2312yes—
303#13063245C2312yes—
304C22⋊(C43⋊C8)C2311yescharacteristic
305C22⋊(C43⋊C8)C2311yescharacteristic
306(C2×D43)⋊C8C2312yes—
307(C2×D43)⋊C8C2312yes—
308#13063235C2312yes—
309C4×C43⋊C8C2312yes—
310C8×Dic43C2312yes—
311C22×Q8×C43—21no—
312C4⋊Q8×C43—21no—
313C4⋊Q8×C43—21no—
314C4⋊Q8×C43C2312yes—
315C4⋊Q8×C43C2312yes—
316#126×C43—21no—
317#125×C43C2311yescharacteristic
318#124×C43C2311yescharacteristic
319#123×C43—21no—
320C22⋊Q8×C43C2311yescharacteristic
321#121×C43C2311yescharacteristic
322C4×Q8×C43C2311yescharacteristic
323C4×D4×C43—21no—
324C4×D4×C43C2311yescharacteristic
325#117×C43—21no—
326C2×C4⋊C4×C43—21no—
327C2×C4⋊C4×C43C2311yescharacteristic
328C2×C4⋊C4×C43C2311yescharacteristic
329C2×C42×C43C2311yescharacteristic
330#107×C43C2312yes—
331#107×C43C2312yes—
332#106×C43C2312yes—
333#106×C43C2312yes—
334C4⋊C8×C43C2312yes—
335#103×C43C2312yes—
336#103×C43C2312yes—
337#102×C43C2312yes—
338#102×C43C2312yes—
339C22⋊C8×C43C2311yescharacteristic
340C22⋊C8×C43C2311yescharacteristic
341#97×C43C2312yes—
342C23×D43—21no—
343C23×D43C2×D411yescharacteristic
344C2×Q8×C43—22no—
345C2×Q8×C43—22no—
346C2×Q8×C43—82no—
347C2×Q8×C43C2411yescharacteristic
348C2×D4×C43—21no—
349C2×D4×C43C2411yescharacteristic
350C22×C4×C43—21no—
351C22×C4×C43—21no—
352C22×C4×C43—21no—
353C22×C4×C43C2×D411yescharacteristic
354C22×C4×C43C2×D411yescharacteristic
355C22×C4×C43C2411yescharacteristic
356C2×C22⋊D43—21no—
357C2×C22⋊D43—21no—
358C2×C22⋊D43—21no—
359C2×C22⋊D43—21no—
360C2×C22⋊D43—21no—
361C2×C22⋊D43—21no—
362C22×Dic43—21no—
363C22×Dic43—21no—
364C22×Dic43—21no—
365C22×Dic43C2×D411yescharacteristic
366C22×Dic43C2×D411yescharacteristic
367C22×Dic43C2×D411yescharacteristic
368#10621902—24no—
369#10621900—82no—
370D4×D43—24no—
371D4×D43—82no—
372#10621898—82no—
373C2×D172—21no—
374C2×D172—21no—
375C2×D172—21no—
376C2×D172—21no—
377C2×D172—21no—
378C2×D172C2411yescharacteristic
379C2×D172C2411yescharacteristic
380C2×C4×D43—24no—
381C2×C4×D43—21no—
382C2×C4×D43—21no—
383C2×C4×D43—21no—
384C2×C4×D43—21no—
385C2×C4×D43—21no—
386C2×C4×D43—21no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—82no—
390C2×C4×D43C2×D411yescharacteristic
391C2×C4×D43C2×D411yescharacteristic
392C2×C4×D43C2411yescharacteristic
393C2×C4×D43C2411yescharacteristic
394C2×Dic86—21no—
395C2×Dic86—22no—
396C2×Dic86—22no—
397C2×Dic86—21no—
398C2×Dic86—82no—
399C2×C8×C43C2412yes—
400C2×C8×C43C2412yes—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—22no—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43—21no—
406C4⋊C4×C43—21no—
407C4⋊C4×C43—21no—
408C4⋊C4×C43—21no—
409C4⋊C4×C43C2412yes—
410C4⋊C4×C43C2412yes—
411C4⋊C4×C43C2411yescharacteristic
412C4⋊C4×C43C2411yescharacteristic
413C22⋊C4×C43—21no—
414C22⋊C4×C43—21no—
415C22⋊C4×C43—21no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43—21no—
418C42×C43—21no—
419C42×C43C2×D411yescharacteristic
420C42×C43C2×D411yescharacteristic
421C42×C43C2411yescharacteristic
422C42×C43C2411yescharacteristic
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425(C2×D43)⋊C4—21no—
426(C2×D43)⋊C4—21no—
427(C2×D43)⋊C4—21no—
428(C2×D43)⋊C4—21no—
429(C2×D43)⋊C4—21no—
430(C2×D43)⋊C4—21no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—21no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—21no—
439(C2×D43)⋊C4C2×D411yescharacteristic
440(C2×D43)⋊C4C2×D411yescharacteristic
441(C2×D43)⋊C4C2×D411yescharacteristic
442(C2×D43)⋊C4C2×D411yescharacteristic
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⋊Dic43—21no—
454C4⋊Dic43C2412yes—
455C4⋊Dic43C2412yes—
456C4⋊Dic43C2411yescharacteristic
457C4⋊Dic43C2411yescharacteristic
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4—21no—
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—22no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4C2×D411yescharacteristic
473Dic43⋊C4C2×D411yescharacteristic
474Dic43⋊C4C2×D411yescharacteristic
475Dic43⋊C4C2×D411yescharacteristic
476Dic43⋊C4C2×D411yescharacteristic
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479Dic43⋊C4C2×D411yescharacteristic
480C4×Dic43—22no—
481C4×Dic43—22no—
482C4×Dic43—21no—
483C4×Dic43—21no—
484C4×Dic43C2×D411yescharacteristic
485C4×Dic43C2×D411yescharacteristic
486C4×Dic43C2411yescharacteristic
487C4×Dic43C2411yescharacteristic
488C2×C43⋊C8C2412yes—
489C2×C43⋊C8C2412yes—
490#10621872—24no—
491C8×D43—24no—
492C23×C43—21no—
493C23×C43C22×D411yescharacteristic
494C22×D43—22no—
495C22×D43—22no—
496C22×D43—21no—
497C22×D43—21no—
498C22×D43—41no—
499C22×D43—42no—
500C22×D43—81no—
501C22×D43—81no—
502C22×D43C22×D411yescharacteristic
503C22×D43C22×D411yescharacteristic
504Q8×C43—22no—
505Q8×C43—82no—
506Q8×C43—82no—
507D4×C43—22no—
508D4×C43—42no—
509C2×C4×C43—22no—
510C2×C4×C43—22no—
511C2×C4×C43—22no—
512C2×C4×C43—21no—
513C2×C4×C43—21no—
514C2×C4×C43—22no—
515C2×C4×C43—21no—
516C2×C4×C43—41no—
517C2×C4×C43—42no—
518C2×C4×C43—42no—
519C2×C4×C43—81no—
520C2×C4×C43C22×D411yescharacteristic
521C2×C4×C43C22×D411yescharacteristic
522C2×C4×C43C22×D411yescharacteristic
523C2×C4×C43C22×D411yescharacteristic
524C2×C4×C43C22×D411yescharacteristic
525C2×C4×C43C2511yescharacteristic
526C22⋊D43—42no—
527C22⋊D43—42no—
528C22⋊D43—42no—
529C22⋊D43—81no—
530C22⋊D43—81no—
531C22⋊D43—81no—
532C2×Dic43—22no—
533C2×Dic43—22no—
534C2×Dic43—22no—
535C2×Dic43—21no—
536C2×Dic43—21no—
537C2×Dic43—22no—
538C2×Dic43—41no—
539C2×Dic43—42no—
540C2×Dic43—42no—
541C2×Dic43—81no—
542C2×Dic43C22×D411yescharacteristic
543C2×Dic43C22×D411yescharacteristic
544C2×Dic43C22×D411yescharacteristic
545C2×Dic43C22×D411yescharacteristic
546C2×Dic43C22×D411yescharacteristic
547C2×Dic43C22×D411yescharacteristic
548D172—22no—
549D172—22no—
550D172—42no—
551D172—81no—
552D172—81no—
553D172—81no—
554D172—81no—
555C4×D43—22no—
556C4×D43—22no—
557C4×D43—22no—
558C4×D43—42no—
559C4×D43—81no—
560C4×D43—81no—
561C4×D43—81no—
562C4×D43—81no—
563C4×D43—82no—
564C4×D43—82no—
565C4×D43—81no—
566C4×D432−1+414yes—
567Dic86—82no—
568Dic86—82no—
569Dic86—81no—
570Dic86—81no—
571C8×C43—22no—
572C8×C43—22no—
573C43⋊C8—22no—
574C43⋊C8—22no—
575#60871—431nomaximal, Sylow
576C22×C43—21no—
577C22×C43—21no—
578C22×C43—41no—
579C22×C43—41no—
580C22×C43—41no—
581C22×C43#57612yes—
582C22×C43C23×D411yescharacteristic
583C2×D43—21no—
584C2×D43—21no—
585C2×D43—21no—
586C2×D43—21no—
587C2×D43—21no—
588C2×D43—44no—
589C2×D43—41no—
590C2×D43—41no—
591C2×D43—41no—
592C2×D43—41no—
593C2×D43—41no—
594C2×D43—41no—
595C2×D43—162no—
596C2×D43#53612yes—
597C4×C43—21no—
598C4×C43—21no—
599C4×C43—21no—
600C4×C43—21no—
601C4×C43—21no—
602C4×C43—41no—
603C4×C43—41no—
604C4×C43—42no—
605C4×C43—41no—
606C4×C43—42no—
607C4×C43C2×2−1+412yes—
608Dic43—21no—
609Dic43—21no—
610Dic43—21no—
611Dic43—21no—
612Dic43—21no—
613Dic43—42no—
614Dic43—42no—
615Dic43—41no—
616Dic43—41no—
617Dic43#53612yes—
618#3494—431no—
619C2×#544—431no—
620#3243—432no—
621#3243—432no—
622#3241—432no—
623#3241—432no—
624#3238—431no—
625#3238D4311yescharacteristic, complemented
626#3234—431no—
627#3234—431no—
628#3232—431no—
629#3232—431no—
630#3226—431no—
631#3226—431no—
632#3164—432no—
633#3136—432no—
634#3094—431no—
635#3092—431no—
636#3091—431no—
637C2×#480—431no—
638#3083—432no—
639#3081—432no—
640#2924—431no—
641C2×C43—22no—
642C2×C43—81no—
643C2×C43C2×#53611yescharacteristic
644C2×C43C2×#57611yescharacteristic
645C2×C43#358611yescharacteristic
646D43—22no—
647D43—41no—
648D43—81no—
649D43—81no—
650#555—861no—
651#553—861no—
652#553—861no—
653#551—861no—
654#551—861no—
655#547—861no—
656#546—861no—
657#546—861no—
658#544—432no—
659#544—432no—
660#544—432no—
661#544—432no—
662#544—431no—
663#544—861no—
664#544—861no—
665#544—861no—
666#544—861no—
667#542—431no—
668#542—431no—
669#540—431no—
670#540—431no—
671#535—431no—
672#532—431no—
673#532—431no—
674C2×C4⋊Q8—431no—
675C2×C4⋊Q8—861no—
676C2×C4⋊Q8C2×D4311yescharacteristic, complemented
677#529—431no—
678#529C2×D4311yescharacteristic
679C2×#125—431no—
680C2×#125—431no—
681C2×#125—861no—
682#525—431no—
683C2×C22⋊Q8—861no—
684C2×C22⋊Q8—861no—
685C2×#121—431no—
686#520—431no—
687#518—431no—
688C2×#117—431no—
689C2×#117—431no—
690C22×C4⋊C4—431no—
691#501—432no—
692#501—432no—
693#501—432no—
694#501C2×D4312yescomplemented
695#500—432no—
696#500—432no—
697#499—432no—
698#499—432no—
699#490—432no—
700#490—432no—
701#489—432no—
702#489C2×D4312yescomplemented
703#488—432no—
704#488—432no—
705#486—432no—
706#486—432no—
707#485—432no—
708#484—431no—
709#484—432no—
710#483—431no—
711#483C2×D4311yescharacteristic, complemented
712#483C2×D4311yescharacteristic, complemented
713#482—432no—
714#482—432no—
715#482—432no—
716#481—431no—
717#481—432no—
718#481—431no—
719#481—431no—
720#480—431no—
721#480—431no—
722#480—431no—
723#480—431no—
724#480—431no—
725#480—432no—
726#480—432no—
727#480—431no—
728#480—431no—
729#480C2×D4311yescharacteristic
730#480C2×D4311yescharacteristic
731#479—432no—
732#479—432no—
733#478—432no—
734#478—432no—
735#478—432no—
736#478—432no—
737#478—432no—
738#478—432no—
739#477—432no—
740#477C2×D4312yescomplemented
741#476—432no—
742#476C2×D4312yescomplemented
743#474—432no—
744#474—432no—
745#474—432no—
746#474—432no—
747#433—432no—
748#433—432no—
749#432—431no—
750#432C2×D4311yescharacteristic, complemented
751#431—431no—
752#431—431no—
753#428—432no—
754#428—432no—
755#427—432no—
756C2×#107—432no—
757#424—432no—
758#418—432no—
759#417—432no—
760#416—432no—
761C2×#102—432no—
762#407—431no—
763C2×C22⋊C8—431no—
764#405—432no—
765C43#6087111yescharacteristic, complemented, Sylow
766C2×#41—431no—
767C2×#41—861no—
768C2×#41—861no—
769C22×Q8—21no—
770C22×Q8—861no—
771C22×D4—431no—
772C22×D4—861no—
773C23×C4—431no—
774C23×C4—861no—
775C2×M16—432no—
776C22×C8—432no—
777C4⋊Q8—21no—
778C4⋊Q8—21no—
779C4⋊Q8—432no—
780C4⋊Q8—432no—
781C4⋊Q8—431no—
782C4⋊Q8—431no—
783C4⋊Q8—861no—
784C4⋊Q8—861no—
785C4⋊Q8—861no—
786C4⋊Q8—862no—
787C4⋊Q8—862no—
788C4⋊Q8—862no—
789C4⋊Q8—862no—
790C4⋊Q8C22×D4312yes—
791C4⋊Q8C22×D4312yes—
792#127—431no—
793#127—431no—
794#126—21no—
795#126—861no—
796#126—861no—
797#126—861no—
798#125—432no—
799#125—432no—
800#125—431no—
801#125—432no—
802#125—432no—
803#125—861no—
804#125—861no—
805#125—862no—
806#125—862no—
807#125—862no—
808#125—862no—
809#125—861no—
810#125—861no—
811#125—861no—
812#125C22×D4311yescharacteristic
813#124—431no—
814#124—861no—
815#124—861no—
816#124—861no—
817#124—861no—
818#124C22×D4311yescharacteristic
819#123—21no—
820#123—861no—
821#123—861no—
822#123—861no—
823#123—861no—
824#123—861no—
825#123—861no—
826#123—861no—
827#123—861no—
828C22⋊Q8—431no—
829C22⋊Q8—861no—
830C22⋊Q8—862no—
831C22⋊Q8—862no—
832C22⋊Q8—862no—
833C22⋊Q8—862no—
834C22⋊Q8—861no—
835C22⋊Q8—861no—
836C22⋊Q8—862no—
837C22⋊Q8—862no—
838C22⋊Q8—862no—
839C22⋊Q8—862no—
840C22⋊Q8—861no—
841C22⋊Q8C22×D4311yescharacteristic
842#121—431no—
843#121—431no—
844#121—431no—
845#121—431no—
846#121—431no—
847#121—861no—
848#121—861no—
849#121—861no—
850#121—861no—
851#121—861no—
852#121—861no—
853#121—861no—
854#121—861no—
855#121—861no—
856#121—861no—
857#121C22×D4311yescharacteristic
858#120—861no—
859#120—861no—
860#120—861no—
861C4×Q8—431no—
862C4×Q8C22×D4311yescharacteristic
863C4×D4—21no—
864C4×D4—431no—
865C4×D4—431no—
866C4×D4—431no—
867C4×D4—431no—
868C4×D4—431no—
869C4×D4—861no—
870C4×D4—861no—
871C4×D4—861no—
872C4×D4—861no—
873C4×D4—861no—
874C4×D4—861no—
875C4×D4—861no—
876C4×D4—861no—
877C4×D4—861no—
878C4×D4C22×D4311yescharacteristic
879#117—21no—
880#117—431no—
881#117—431no—
882#117—431no—
883#117—431no—
884#117—431no—
885#117—431no—
886#117—431no—
887#117—431no—
888#117—432no—
889#117—432no—
890#117—431no—
891#117—861no—
892#117—861no—
893#117—861no—
894#117—861no—
895C2×C4⋊C4—21no—
896C2×C4⋊C4—431no—
897C2×C4⋊C4—431no—
898C2×C4⋊C4—431no—
899C2×C4⋊C4—431no—
900C2×C4⋊C4—432no—
901C2×C4⋊C4—432no—
902C2×C4⋊C4—431no—
903C2×C4⋊C4—861no—
904C2×C4⋊C4—861no—
905C2×C4⋊C4—861no—
906C2×C4⋊C4—861no—
907C2×C4⋊C4—861no—
908C2×C4⋊C4—861no—
909C2×C4⋊C4—861no—
910C2×C4⋊C4—861no—
911C2×C4⋊C4—861no—
912C2×C4⋊C4C22×D4311yescharacteristic
913C2×C4⋊C4C22×D4311yescharacteristic
914C2×C22⋊C4—431no—
915C2×C22⋊C4—431no—
916C2×C22⋊C4—861no—
917C2×C22⋊C4—861no—
918C2×C22⋊C4—861no—
919C2×C22⋊C4—861no—
920C2×C42—431no—
921C2×C42—861no—
922C2×C42C22×D4311yescharacteristic
923#107—432no—
924#107—432no—
925#107—432no—
926#107—432no—
927#107—432no—
928#107—432no—
929#107—432no—
930#107—432no—
931#107C22×D4312yes—
932#107C22×D4312yes—
933#106—432no—
934#106—432no—
935#106—432no—
936#106—432no—
937#106C22×D4312yes—
938#106C22×D4312yes—
939C4⋊C8—432no—
940C4⋊C8—432no—
941C4⋊C8—432no—
942C4⋊C8C22×D4312yes—
943#103—432no—
944#103—432no—
945#103C22×D4312yes—
946#103C22×D4312yes—
947#102—432no—
948#102—432no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102—432no—
955#102—432no—
956#102—432no—
957#102C22×D4312yes—
958#102C22×D4312yes—
959C22⋊C8—431no—
960C22⋊C8—431no—
961C22⋊C8—432no—
962C22⋊C8—432no—
963C22⋊C8C22×D4311yescharacteristic
964C22⋊C8C22×D4311yescharacteristic
965#97—432no—
966#97C22×D4312yes—
967C4×C8—432no—
968C4×C8—432no—
969C24—431no—
970C24—861no—
971#41—864no—
972#41—3442no—
973#41—3442no—
974C2×Q8—22no—
975C2×Q8—22no—
976C2×Q8—82no—
977C2×Q8—861no—
978C2×Q8—862no—
979C2×Q8—862no—
980C2×Q8—861no—
981C2×Q8—3442no—
982C2×Q8C23×D4311yescharacteristic
983C2×D4—21no—
984C2×D4—431no—
985C2×D4—431no—
986C2×D4—861no—
987C2×D4—861no—
988C2×D4—861no—
989C2×D4—864no—
990C2×D4—861no—
991C2×D4—861no—
992C2×D4—861no—
993C2×D4—861no—
994C2×D4—861no—
995C2×D4—861no—
996C2×D4—861no—
997C2×D4—861no—
998C2×D4—3442no—
999C2×D4C23×D4311yescharacteristic
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—431no—
1004C22×C4—431no—
1005C22×C4—431no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—864no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—861no—
1014C22×C4—861no—
1015C22×C4—862no—
1016C22×C4—862no—
1017C22×C4—861no—
1018C22×C4—861no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—3442no—
1023C22×C4D4×D4311yescharacteristic
1024C22×C4D4×D4311yescharacteristic
1025C22×C4C23×D4311yescharacteristic
1026M16—864no—
1027C2×C8—432no—
1028C2×C8—432no—
1029C2×C8—864no—
1030C2×C8C23×D4312yes—
1031C2×C8C23×D4312yes—
1032C4⋊C4—22no—
1033C4⋊C4—22no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—431no—
1041C4⋊C4—431no—
1042C4⋊C4—431no—
1043C4⋊C4—431no—
1044C4⋊C4—431no—
1045C4⋊C4—431no—
1046C4⋊C4—431no—
1047C4⋊C4—431no—
1048C4⋊C4—432no—
1049C4⋊C4—432no—
1050C4⋊C4—431no—
1051C4⋊C4—431no—
1052C4⋊C4—862no—
1053C4⋊C4—862no—
1054C4⋊C4—861no—
1055C4⋊C4—861no—
1056C4⋊C4—862no—
1057C4⋊C4—862no—
1058C4⋊C4—862no—
1059C4⋊C4—862no—
1060C4⋊C4—862no—
1061C4⋊C4—862no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4—861no—
1065C4⋊C4—861no—
1066C4⋊C4—861no—
1067C4⋊C4—861no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4—861no—
1073C4⋊C4C23×D4312yes—
1074C4⋊C4C23×D4312yes—
1075C4⋊C4C23×D4311yescharacteristic
1076C4⋊C4C23×D4311yescharacteristic
1077C22⋊C4—21no—
1078C22⋊C4—21no—
1079C22⋊C4—21no—
1080C22⋊C4—21no—
1081C22⋊C4—21no—
1082C22⋊C4—431no—
1083C22⋊C4—431no—
1084C22⋊C4—431no—
1085C22⋊C4—431no—
1086C22⋊C4—431no—
1087C22⋊C4—431no—
1088C22⋊C4—431no—
1089C22⋊C4—431no—
1090C22⋊C4—861no—
1091C22⋊C4—861no—
1092C22⋊C4—861no—
1093C22⋊C4—861no—
1094C22⋊C4—861no—
1095C22⋊C4—861no—
1096C22⋊C4—861no—
1097C22⋊C4—862no—
1098C22⋊C4—862no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—861no—
1103C22⋊C4—861no—
1104C22⋊C4—861no—
1105C22⋊C4—861no—
1106C42—21no—
1107C42—431no—
1108C42—431no—
1109C42—431no—
1110C42—431no—
1111C42—862no—
1112C42—862no—
1113C42—861no—
1114C42—861no—
1115C42D4×D4311yescharacteristic
1116C42D4×D4311yescharacteristic
1117C42C23×D4311yescharacteristic
1118C42C23×D4311yescharacteristic
1119C23—21no—
1120C23—431no—
1121C23—431no—
1122C23—862no—
1123C23—862no—
1124C23—861no—
1125C23—861no—
1126C23—3441no—
1127C23—3441no—
1128C23—1721no—
1129C23—1722no—
1130C23C2×D4×D4311yescharacteristic
1131Q8—22no—
1132Q8—82no—
1133Q8—82no—
1134Q8—3441no—
1135Q8—3442no—
1136Q8—3442no—
1137Q8—3441no—
1138D4—22no—
1139D4—42no—
1140D4—862no—
1141D4—862no—
1142D4—3441no—
1143D4—3441no—
1144D4—3441no—
1145D4—3441no—
1146D4—3441no—
1147D4—3441no—
1148D4—3441no—
1149D4—1722no—
1150D4—1722no—
1151D4—1722no—
1152D4—1722no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—41no—
1161C2×C4—42no—
1162C2×C4—42no—
1163C2×C4—81no—
1164C2×C4—431no—
1165C2×C4—434no—
1166C2×C4—431no—
1167C2×C4—431no—
1168C2×C4—431no—
1169C2×C4—431no—
1170C2×C4—431no—
1171C2×C4—862no—
1172C2×C4—862no—
1173C2×C4—862no—
1174C2×C4—862no—
1175C2×C4—862no—
1176C2×C4—862no—
1177C2×C4—861no—
1178C2×C4—861no—
1179C2×C4—862no—
1180C2×C4—3441no—
1181C2×C4—3441no—
1182C2×C4—3441no—
1183C2×C4—3441no—
1184C2×C4—3442no—
1185C2×C4—3442no—
1186C2×C4—3441no—
1187C2×C4—3441no—
1188C2×C4—1722no—
1189C2×C4—1721no—
1190C2×C4—1722no—
1191C2×C4—1722no—
1192C2×C4C2×D4×D4311yescharacteristic
1193C2×C4C2×D4×D4311yescharacteristic
1194C2×C4C2×D4×D4311yescharacteristic
1195C2×C4C2×D4×D4311yescharacteristic
1196C2×C4C2×D4×D4311yescharacteristic
1197C2×C4C24×D4311yescharacteristic
1198C8—22no—
1199C8—22no—
1200C8—862no—
1201C8—862no—
1202C22—21no—
1203C22—21no—
1204C22—41no—
1205C22—41no—
1206C22—41no—
1207C22—432no—
1208C22—861no—
1209C22—861no—
1210C22—861no—
1211C22—861no—
1212C22—861no—
1213C22—1724no—
1214C22—1721no—
1215C22—1721no—
1216C22—1721no—
1217C22—1721no—
1218C22—1721no—
1219C22—1721no—
1220C22—6882no—
1221C22#1458370312yes—
1222C22C22×D4×D4311yescharacteristic
1223C4—21no—
1224C4—21no—
1225C4—21no—
1226C4—21no—
1227C4—21no—
1228C4—42no—
1229C4—42no—
1230C4—41no—
1231C4—41no—
1232C4—41no—
1233C4—432no—
1234C4—861no—
1235C4—861no—
1236C4—861no—
1237C4—861no—
1238C4—861no—
1239C4—1722no—
1240C4—1721no—
1241C4—1721no—
1242C4—1722no—
1243C42−1+4×D4312yes—
1244C2—22no—
1245C2—81no—
1246C2—862no—
1247C2—3441no—
1248C2—3441no—
1249C2—1721no—
1250C2#536×D4311yescharacteristic
1251C2C2×#1458370311yescharacteristic
1252C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3238C2
socleC22×C43C23×D4
prime radical#19148318C2
hypercenter#3238D43
hypocenterC43#60871
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
2. C2×#14583526C2semidirect
3. #19145883C2semidirect
4. #19145873C2semidirect
5. #19145849C2semidirect
6. #19145847C2semidirect
7. #19145819C2semidirect
8. #19145787C2semidirect
9. #19145782C2semidirect
10. #19145766C2semidirect
11. #19145759C2semidirect
12. #19145716C2semidirect
13. #19145714C2semidirect
14. #19145130C2semidirect
15. #19144946C2semidirect
16. #19144530C2semidirect
17. #19144519C2semidirect
18. #19144509C2semidirect
19. #480×D43C2semidirect
20. #19144443C2semidirect
21. #19144421C2semidirect
22. #19143254C2semidirect
23. C43×#3238C2semidirect
39. #14583526C22semidirect
40. #14583526C22semidirect
48. C2×#13063324C22semidirect
51. C2×#13063317C22semidirect
52. C2×#13063316C22semidirect
63. #14583308C22semidirect
64. #14583307C22semidirect
65. #14583306C22semidirect
66. #14583303C22semidirect
67. #14583302C22semidirect
68. #14583299C22semidirect
69. #14583298C22semidirect
70. #14583264C22semidirect
71. #14583262C22semidirect
72. #14583260C22semidirect
73. #14583255C22semidirect
74. #14583253C22semidirect
75. #14583247C22semidirect
76. #14583244C22semidirect
77. #14583238C22semidirect
78. #14583233C22semidirect
79. #14583232C22semidirect
80. #14583227C22semidirect
82. #14583225C22semidirect
84. #14583219C22semidirect
86. #14583218C22semidirect
90. #14583213C22semidirect
93. #14583212C22semidirect
94. #14583212C22semidirect
97. #14583206C22semidirect
98. #14583204C22semidirect
99. #14583202C22semidirect
100. #14583201C22semidirect
101. #14583200C22semidirect
102. #14583200C22semidirect
103. #14583199C22semidirect
104. #14583198C22semidirect
105. #14583192C22semidirect
106. #14583188C22semidirect
107. #14583178C22semidirect
108. #14583177C22semidirect
109. #14583176C22semidirect
110. #14583176C22semidirect
111. #14582961C22semidirect
112. #14582959C22semidirect
113. #14582953C22semidirect
114. #14582952C22semidirect
115. #14582949C22semidirect
128. C2×C4⋊Q8×C43C22semidirect
130. C43×#501C22semidirect
131. C43×#489C22semidirect
132. C43×#483C22semidirect
133. C43×#483C22semidirect
136. C43×#477C22semidirect
137. C43×#476C22semidirect
138. C43×#432C22semidirect
625. #3238D43semidirect
676. C2×C4⋊Q8C2×D43semidirect
694. #501C2×D43semidirect
702. #489C2×D43semidirect
711. #483C2×D43semidirect
712. #483C2×D43semidirect
740. #477C2×D43semidirect
742. #476C2×D43semidirect
750. #432C2×D43semidirect
765. C43#60871semidirect

Maximal subgroups

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

subgroupindex
#191483182
C2×#145835262
#191458832
#191458732
#191458492
#191458472
#191458192
#191457872
#191457822
#191457662
#191457592
#191457162
#191457142
#191451302
#191449462
#191445302
#191445192
#191445092
#480×D432
#191444432
#191444212
#191432542
C43×#32382
#6087143