Finite Group Databasebeta

← #25979511

Subgroups — #25979511

Order 11008.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148646C211yesmaximal, characteristic, complemented
2#19147611C211yesmaximal, characteristic, complemented
3#19147494C211yesmaximal, characteristic, complemented
4#19147244C211yesmaximal, characteristic, complemented
5#19147226C211yesmaximal, characteristic, complemented
6#19147184C211yesmaximal, characteristic, complemented
7#19147080C212yesmaximal, complemented
8#19146517C211yesmaximal, characteristic, complemented
9#19146439C212yesmaximal, complemented
10#19146419C212yesmaximal, complemented
11#19146408C211yesmaximal, characteristic, complemented
12#19146191C211yesmaximal, characteristic, complemented
13#19146071C212yesmaximal, complemented
14#19145280C212yesmaximal, complemented
15#19145150C211yesmaximal, characteristic, complemented
16#19144788C212yesmaximal, complemented
17#19144779C212yesmaximal, complemented
18#19144694C211yesmaximal, characteristic, complemented
19#19144682C211yesmaximal, characteristic, complemented
20#19143571C211yesmaximal, characteristic, complemented
21#19143427C212yesmaximal, complemented
22C2×C4×#10621882C211yesmaximal, characteristic, complemented
23C43×#3519C211yesmaximal, characteristic, complemented
24C2×#13063351C2212yes—
25C22×#10621882C2211yescharacteristic
26#14583622C2211yescharacteristic, complemented
27#14583606C2212yescomplemented
28#14583587—21no—
29#14583572—22no—
30Q8×D172C2211yescharacteristic, complemented
31#14583557—21no—
32#14583554C2211yescharacteristic, complemented
33#14583553C2211yescharacteristic, complemented
34#14583545C2212yescomplemented
35#14583520C2212yescomplemented
36#14583490—22no—
37#14583456C2211yescharacteristic, complemented
38#14583409—21no—
39C22⋊Q8×D43—21no—
40#14583379C2212yescomplemented
41C2×C4×D172C2211yescharacteristic, complemented
42#14583309C2212yescomplemented
43#14583295C2211yescharacteristic, complemented
44#14583286C2212yescomplemented
45#14583271C2211yescharacteristic, complemented
46#14583256C2212yescomplemented
47#14583251C2211yescharacteristic, complemented
48#14583245C2212yescomplemented
49#14583245C2211yescharacteristic, complemented
50#14583240C2212yescomplemented
51#14583234C2212yescomplemented
52#14583223C2212yescomplemented
53#14583215C2212yescomplemented
54#14583215C2212yescomplemented
55#14583210C2212yescomplemented
56#14583203C2212yescomplemented
57#14583196C2212yescomplemented
58#14583189C2212yescomplemented
59#14583186C2211yescharacteristic, complemented
60#14583186C2211yescharacteristic, complemented
61#14583179C2212yescomplemented
62#14583179C2211yescharacteristic, complemented
63#14583179C2211yescharacteristic, complemented
64#14583150C2212yescomplemented
65#14583143C2212yescomplemented
66#14583133C2212yescomplemented
67#14583126C2212yescomplemented
68#14583126C2212yescomplemented
69#14583126C2212yescomplemented
70#14583114C2212yes—
71#14583114C2212yescomplemented
72#14583104C2211yescharacteristic, complemented
73#14583104C2211yescharacteristic, complemented
74#14583096C2212yescomplemented
75#14583091C2212yescomplemented
76#14583091C2211yescharacteristic, complemented
77#14583091C2211yescharacteristic, complemented
78#14583050C2212yes—
79#14583050C2212yescomplemented
80#14583042C2212yescomplemented
81#14583042C2212yescomplemented
82#14583033C2212yes—
83#14583032C2212yescomplemented
84#14583030C2211yescharacteristic, complemented
85Q8×C43⋊C8C2211yescharacteristic, complemented
86#14583009C2212yes—
87#14583009C2212yescomplemented
88#14583009C2212yescomplemented
89#14582999C2212yescomplemented
90#14582999C2212yescomplemented
91#14582999C2212yescomplemented
92C4×#10621883C2212yescomplemented
93C4×#10621883C2212yescomplemented
94C4×#10621883C2212yescomplemented
95C4×#10621882C2211yescharacteristic
96C4×#10621882C2211yescharacteristic
97C4×#10621882C2211yescharacteristic
98C4×#10621882C2211yescharacteristic
99C4×#10621882C2212yescomplemented
100C4×#10621882C2211yescharacteristic, complemented
101C4×#10621882C2211yescharacteristic, complemented
102C4×#10621882C2211yescharacteristic, complemented
103C4×#10621882C2211yescharacteristic, complemented
104#14582977C2211yescharacteristic, complemented
105#14582971C2212yescomplemented
106D4×C43⋊C8C2211yescharacteristic, complemented
107D4×C43⋊C8C2212yescomplemented
108#14582960C2212yescomplemented
109#14582956C2211yescharacteristic, complemented
110#14582942C2212yescomplemented
111C2×#13063258C2211yescharacteristic, complemented
112#14582893C2212yescomplemented
113C2×#13063246C2211yescharacteristic
114C2×#13063246C2212yescomplemented
115C2×#13063245C2211yescharacteristic, complemented
116#14582855C2212yescomplemented
117C2×C4×C43⋊C8C2211yescharacteristic, complemented
118C43×#555C2211yescharacteristic, complemented
119C43×#554C2211yescharacteristic, complemented
120C43×#553—21no—
121C43×#553C2212yes—
122C43×#550C2211yescharacteristic, complemented
123C43×#546—21no—
124C43×#546—22no—
125D42×C43C2212yes—
126D42×C43C2211yescharacteristic, complemented
127C43×#540C2212yescomplemented
128C43×#538—22no—
129C43×#532C2211yescharacteristic
130C43×#529C2211yescharacteristic
131C43×#525—21no—
132C2×#121×C43—21no—
133C43×#518C2212yescomplemented
134C2×C4×D4×C43C2211yescharacteristic
135C2×#10621898C2312yes—
136C2×#10621900—21no—
137C2×Q8×D43—21no—
138C22×D172C2311yescharacteristic
139C22×C4×D43—21no—
140#13063351—28no—
141C2×#10621883C2312yes—
142C2×#10621883C2312yes—
143C2×#10621883C2312yes—
144C2×#10621883C2312yes—
145C2×#10621882—24no—
146C2×#10621882C2311yescharacteristic
147C2×#10621882C2312yes—
148C2×#10621882C2311yescharacteristic
149C2×#10621882C2311yescharacteristic
150C2×#10621882C2312yes—
151C2×#10621882C2311yescharacteristic
152C2×#10621877C2312yes—
153C22×C43⋊C8C2311yescharacteristic
154C22×C43⋊C8C2311yescharacteristic
155C22×C43⋊C8C2312yes—
156#13063325C2311yescharacteristic
157#13063325C2311yescharacteristic
158#13063325C2312yes—
159#13063320—22no—
160#13063320—22no—
161#13063317—21no—
162#13063316—22no—
163#13063313C2312yes—
164#13063311—22no—
165#13063310—22no—
166#13063309—22no—
167#13063307—22no—
168#13063307—22no—
169#13063305—21no—
170#13063305—22no—
171#13063305—21no—
172#13063304—21no—
173#13063304C2312yes—
174#13063304C2312yes—
175#13063303—22no—
176#13063302—22no—
177#13063302—22no—
178#13063301—21no—
179#13063299C2312yes—
180#13063298—22no—
181#13063296—21no—
182#13063293—22no—
183C4×Dic86—21no—
184C4×Dic86C2312yes—
185C4×Dic86C2312yes—
186C4×D172—21no—
187C4×D172—21no—
188C4×D172C2311yescharacteristic
189C4×D172C2311yescharacteristic
190C4×D172C2312yes—
191C4×D172C2311yescharacteristic
192C4×D172C2311yescharacteristic
193D4×Dic43—22no—
194(C22⋊D43)⋊C4—22no—
195(C22⋊D43)⋊C4—22no—
196#13063284—21no—
197#13063283—22no—
198#13063283—21no—
199C2×C4⋊Dic43C2312yes—
200C2×C4⋊Dic43C2311yescharacteristic
201C4⋊C4×D43—21no—
202C4⋊C4×D43—22no—
203C2×(C2×D43)⋊C4—21no—
204C22⋊C4×D43—22no—
205#13063258C2311yescharacteristic
206#13063258C2312yes—
207#13063258C2311yescharacteristic
208#13063258C2312yes—
209#13063258C2311yescharacteristic
210#13063258C2311yescharacteristic
211#13063256C2312yes—
212#13063256C2312yes—
213#13063256C2312yes—
214#13063256C2312yes—
215C4⋊(C43⋊C8)C2311yescharacteristic
216C4⋊(C43⋊C8)C2311yescharacteristic
217C4⋊(C43⋊C8)C2312yes—
218C4⋊(C43⋊C8)C2312yes—
219#13063248C2312yes—
220#13063248C2312yes—
221#13063248C2312yes—
222#13063248C2312yes—
223#13063246C2312yes—
224#13063246C2312yes—
225#13063246C2311yescharacteristic
226#13063246C2312yes—
227#13063246C2312yes—
228#13063246C2312yes—
229#13063246C2311yescharacteristic
230#13063246C2311yescharacteristic
231#13063246C2312yes—
232#13063246C2311yescharacteristic
233#13063245C2311yescharacteristic
234#13063245C2312yes—
235#13063245C2312yes—
236#13063245C2311yescharacteristic
237#13063245C2311yescharacteristic
238#13063245C2311yescharacteristic
239C22⋊(C43⋊C8)C2312yes—
240C22⋊(C43⋊C8)C2312yes—
241C22⋊(C43⋊C8)C2312yes—
242#13063236C2312yes—
243#13063236C2312yes—
244C4×C43⋊C8C2311yescharacteristic
245C4×C43⋊C8C2311yescharacteristic
246C4×C43⋊C8C2311yescharacteristic
247C4×C43⋊C8C2311yescharacteristic
248C4×C43⋊C8C2312yes—
249C2×#41×C43—21no—
250C2×#41×C43—21no—
251C22×D4×C43—22no—
252C22×D4×C43—21no—
253C22×D4×C43C2311yescharacteristic
254C22×D4×C43C2312yes—
255C23×C4×C43—21no—
256C4⋊Q8×C43C2311yescharacteristic
257#127×C43C2311yescharacteristic
258#127×C43C2312yes—
259#126×C43—22no—
260#126×C43D412yes—
261#125×C43D411yescharacteristic
262#125×C43C2312yes—
263#124×C43—22no—
264#124×C43—21no—
265#124×C43D411yescharacteristic
266#123×C43—22no—
267#123×C43—22no—
268#123×C43—22no—
269#123×C43D412yes—
270C22⋊Q8×C43—21no—
271C22⋊Q8×C43—22no—
272C22⋊Q8×C43D411yescharacteristic
273#121×C43—22no—
274#121×C43—21no—
275#121×C43—21no—
276#121×C43—21no—
277#121×C43—21no—
278#121×C43—22no—
279#121×C43—22no—
280#121×C43—22no—
281#121×C43—22no—
282#121×C43D411yescharacteristic
283#121×C43C2312yes—
284#121×C43C2312yes—
285#121×C43C2312yes—
286#120×C43—22no—
287#120×C43—22no—
288#120×C43—22no—
289C4×Q8×C43C2311yescharacteristic
290C4×D4×C43—22no—
291C4×D4×C43—22no—
292C4×D4×C43—22no—
293C4×D4×C43—21no—
294C4×D4×C43—21no—
295C4×D4×C43—21no—
296C4×D4×C43C2311yescharacteristic
297C4×D4×C43C2311yescharacteristic
298C4×D4×C43C2311yescharacteristic
299C4×D4×C43C2311yescharacteristic
300C4×D4×C43C2312yes—
301C4×D4×C43C2312yes—
302C4×D4×C43C2312yes—
303C4×D4×C43C2311yescharacteristic
304C4×D4×C43C2312yes—
305#117×C43—21no—
306#117×C43C2312yes—
307#117×C43C2312yes—
308C2×C4⋊C4×C43—21no—
309C2×C4⋊C4×C43C2311yescharacteristic
310C2×C22⋊C4×C43—21no—
311C2×C22⋊C4×C43—22no—
312C2×C22⋊C4×C43—22no—
313C2×C42×C43C2311yescharacteristic
314C24×C43—21no—
315C24×C43—22no—
316C23×D43—21no—
317#41×C43—82no—
318#41×C43—82no—
319C2×Q8×C43—21no—
320C2×Q8×C43C2×D411yescharacteristic
321C2×D4×C43—21no—
322C2×D4×C43—22no—
323C2×D4×C43—21no—
324C2×D4×C43—22no—
325C2×D4×C43—21no—
326C2×D4×C43—22no—
327C2×D4×C43—22no—
328C2×D4×C43—22no—
329C2×D4×C43—22no—
330C2×D4×C43—22no—
331C2×D4×C43—24no—
332C2×D4×C43—41no—
333C2×D4×C43—42no—
334C2×D4×C43—84no—
335C2×D4×C43—82no—
336C2×D4×C43C2×D412yes—
337C2×D4×C43C2×D411yescharacteristic
338C2×D4×C43C2411yescharacteristic
339C2×D4×C43C2412yes—
340C2×D4×C43C2411yescharacteristic
341C22×C4×C43—21no—
342C22×C4×C43—21no—
343C22×C4×C43—21no—
344C22×C4×C43—22no—
345C22×C4×C43—22no—
346C22×C4×C43—22no—
347C22×C4×C43—21no—
348C22×C4×C43—21no—
349C22×C4×C43—82no—
350C22×C4×C43C2×D411yescharacteristic
351C22×C4×C43C2×D411yescharacteristic
352C22×C4×C43C2411yescharacteristic
353C22×C4×C43C2412yes—
354C2×C22⋊D43—22no—
355C2×C22⋊D43—22no—
356C22×Dic43—21no—
357C22×Dic43—22no—
358Q8×D43—82no—
359#10621900—82no—
360#10621898—24no—
361#10621898—42no—
362C2×D172—21no—
363C2×D172—22no—
364C2×D172—41no—
365C2×D172C2411yescharacteristic
366C2×D172C2411yescharacteristic
367C2×C4×D43—22no—
368C2×C4×D43—21no—
369C2×C4×D43—21no—
370C2×C4×D43—22no—
371C2×C4×D43—21no—
372C2×C4×D43—21no—
373C2×C4×D43—82no—
374C2×Dic86—21no—
375C2×Dic86—22no—
376C2×Dic86C2412yes—
377C4⋊C4×C43—21no—
378C4⋊C4×C43—22no—
379C4⋊C4×C43—21no—
380C4⋊C4×C43—22no—
381C4⋊C4×C43C2×D411yescharacteristic
382C4⋊C4×C43C2×D411yescharacteristic
383C4⋊C4×C43C2×D412yes—
384C4⋊C4×C43C2×D412yes—
385C4⋊C4×C43C2×D412yes—
386C4⋊C4×C43C2×D412yes—
387C4⋊C4×C43C2411yescharacteristic
388C4⋊C4×C43C2411yescharacteristic
389C4⋊C4×C43C2412yes—
390C22⋊C4×C43—21no—
391C22⋊C4×C43—22no—
392C22⋊C4×C43—21no—
393C22⋊C4×C43—22no—
394C22⋊C4×C43—21no—
395C22⋊C4×C43—22no—
396C22⋊C4×C43—21no—
397C22⋊C4×C43—22no—
398C22⋊C4×C43—22no—
399C22⋊C4×C43—22no—
400C22⋊C4×C43—22no—
401C22⋊C4×C43C2×D412yes—
402C22⋊C4×C43C2×D412yes—
403C22⋊C4×C43C2×D412yes—
404C22⋊C4×C43C2×D412yes—
405C22⋊C4×C43C2×D412yes—
406C42×C43—22no—
407C42×C43C2×D411yescharacteristic
408C42×C43C2×D411yescharacteristic
409C42×C43C2411yescharacteristic
410C42×C43C2411yescharacteristic
411C42×C43C2412yes—
412C22⋊Dic43—22no—
413C22⋊Dic43—22no—
414#10621883—24no—
415#10621883—24no—
416#10621883—42no—
417#10621883—42no—
418#10621882—22no—
419#10621882—22no—
420#10621882—24no—
421#10621882—22no—
422#10621882—42no—
423#10621882#4114yescomplemented
424(C2×D43)⋊C4—22no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—21no—
427(C2×D43)⋊C4—21no—
428(C2×D43)⋊C4—21no—
429(C2×D43)⋊C4—21no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432C4⋊Dic43—22no—
433C4⋊Dic43—21no—
434C4⋊Dic43—21no—
435C4⋊Dic43—21no—
436C4⋊Dic43—21no—
437C4⋊Dic43—22no—
438C4⋊Dic43C2411yescharacteristic
439C4⋊Dic43C2411yescharacteristic
440C4⋊Dic43C2412yes—
441Dic43⋊C4—22no—
442Dic43⋊C4—22no—
443Dic43⋊C4—22no—
444Dic43⋊C4—22no—
445C4×Dic43—22no—
446C4×Dic43—22no—
447#10621877—24no—
448C2×C43⋊C8—22no—
449C2×C43⋊C8—42no—
450C2×C43⋊C8—41no—
451C2×C43⋊C8C2411yescharacteristic
452C2×C43⋊C8C2411yescharacteristic
453C2×C43⋊C8C2411yescharacteristic
454C2×C43⋊C8C2412yes—
455C2×C43⋊C8C2412yes—
456C2×C43⋊C8C2411yescharacteristic
457C23×C43—21no—
458C23×C43—21no—
459C23×C43—22no—
460C23×C43—42no—
461C23×C43—44no—
462C23×C43—42no—
463C23×C43—81no—
464C23×C43—82no—
465C23×C43—82no—
466C23×C43C22×D412yes—
467C23×C43C22×D411yescharacteristic
468C22×D43—21no—
469C22×D43—21no—
470C22×D43—42no—
471C22×D43—42no—
472C22×D43—81no—
473Q8×C43—22no—
474Q8×C43—81no—
475D4×C43—24no—
476D4×C43—22no—
477D4×C43—21no—
478D4×C43—22no—
479D4×C43—21no—
480D4×C43—22no—
481D4×C43—21no—
482D4×C43—44no—
483D4×C43—42no—
484D4×C43—44no—
485D4×C43—42no—
486D4×C43—82no—
487D4×C43—82no—
488D4×C43—81no—
489D4×C43—82no—
490D4×C43—82no—
491D4×C43C2×#4112yes—
492C2×C4×C43—22no—
493C2×C4×C43—22no—
494C2×C4×C43—21no—
495C2×C4×C43—22no—
496C2×C4×C43—21no—
497C2×C4×C43—22no—
498C2×C4×C43—21no—
499C2×C4×C43—22no—
500C2×C4×C43—21no—
501C2×C4×C43—42no—
502C2×C4×C43—42no—
503C2×C4×C43—81no—
504C2×C4×C43—81no—
505C2×C4×C43—82no—
506C2×C4×C43—82no—
507C2×C4×C43—82no—
508C2×C4×C43—81no—
509C2×C4×C43C22×D411yescharacteristic
510C2×C4×C43C22×D412yes—
511C2×C4×C43C22×D411yescharacteristic
512C2×C4×C43C22×D411yescharacteristic
513C2×C4×C43C22×D412yes—
514C2×C4×C43C22×D412yes—
515C2×C4×C43C22×D411yescharacteristic
516C2×C4×C43C22×D411yescharacteristic
517C2×C4×C43C2511yescharacteristic
518C22⋊D43—44no—
519C22⋊D43—82no—
520C2×Dic43—22no—
521C2×Dic43—21no—
522C2×Dic43—22no—
523C2×Dic43—21no—
524C2×Dic43—81no—
525C2×Dic43—82no—
526D172—21no—
527D172—21no—
528D172—21no—
529D172—42no—
530D172C2×#4112yes—
531C4×D43—44no—
532C4×D43—42no—
533C4×D43—42no—
534C4×D43—81no—
535C4×D43—81no—
536C4×D43—82no—
537Dic86—22no—
538Dic86—22no—
539Dic86—42no—
540Dic86—82no—
541C43⋊C8—21no—
542C43⋊C8—22no—
543C43⋊C8—21no—
544C43⋊C8—22no—
545C43⋊C8—21no—
546C43⋊C8C2×#4112yes—
547#61496—431nomaximal, Sylow
548C22×C43—21no—
549C22×C43—21no—
550C22×C43—22no—
551C22×C43—22no—
552C22×C43—22no—
553C22×C43—22no—
554C22×C43—41no—
555C22×C43—41no—
556C22×C43—41no—
557C22×C43—42no—
558C22×C43—41no—
559C22×C43—42no—
560C22×C43—41no—
561C22×C43—42no—
562C22×C43—84no—
563C22×C43—164no—
564C22×C43#57712yes—
565C22×C43C23×D411yescharacteristic
566C2×D43—22no—
567C2×D43—41no—
568C2×D43—41no—
569C2×D43—41no—
570C2×D43—41no—
571C2×D43—41no—
572C2×D43—84no—
573C4×C43—22no—
574C4×C43—21no—
575C4×C43—22no—
576C4×C43—21no—
577C4×C43—21no—
578C4×C43—21no—
579C4×C43—22no—
580C4×C43—41no—
581C4×C43—41no—
582C4×C43—42no—
583C4×C43#57612yes—
584C4×C43C22×#4111yescharacteristic
585C4×C43#58511yescharacteristic
586Dic43—42no—
587Dic43—42no—
588Dic43—41no—
589Dic43—41no—
590#3520—431no—
591#3519D4311yescharacteristic, complemented
592#3397—431no—
593#3384—431no—
594#3360—431no—
595#3358—431no—
596#3354—431no—
597#3346—432no—
598#3303—431no—
599#3297—432no—
600#3295—432no—
601#3294—431no—
602#3272—431no—
603#3264—432no—
604#3179—432no—
605#3167—431no—
606#3119—432no—
607#3118—432no—
608#3110—431no—
609#3109—431no—
610#2966—431no—
611#2946—432no—
612C2×C4×D8—431no—
613C2×C43—22no—
614C2×C43—42no—
615C2×C43—42no—
616C2×C43—81no—
617C2×C43—82no—
618C2×C43D4×#4111yescharacteristic
619C2×C43C2×#57611yescharacteristic
620C2×C43C2×#57711yescharacteristic
621D43—42no—
622D43—81no—
623C2×AGL(1,ℤ/8)—432no—
624C22×D8—431no—
625#556—431no—
626#555C2×D4311yescharacteristic, complemented
627#554—432no—
628#554C2×D4311yescharacteristic, complemented
629#553—21no—
630#553C2×D4312yes—
631#552—861no—
632#551—862no—
633#550C2×D4311yescharacteristic, complemented
634D4×Q8—431no—
635#548—861no—
636#547—431no—
637#547—431no—
638#546—21no—
639#546—22no—
640#546—432no—
641D42C2×D4312yes—
642D42C2×D4311yescharacteristic, complemented
643#542—432no—
644#540C2×D4312yescomplemented
645#539—862no—
646#538—22no—
647#533—431no—
648#532C2×D4311yescharacteristic
649#529C2×D4311yescharacteristic
650#525—21no—
651#525—861no—
652C2×C22⋊Q8—861no—
653C2×#121—21no—
654#520—432no—
655#518C2×D4312yescomplemented
656C2×C4×D4—431no—
657C2×C4×D4C2×D4311yescharacteristic
658#501—432no—
659#498—431no—
660#496—432no—
661#492—431no—
662#488—432no—
663#487—431no—
664#486—431no—
665#486—432no—
666#485—432no—
667#484—432no—
668#482—432no—
669#481—432no—
670#481—432no—
671#480—432no—
672#479—432no—
673#478—432no—
674#476—431no—
675#476—431no—
676#476—432no—
677#474—432no—
678#474—431no—
679#474—431no—
680#469—432no—
681#468—432no—
682#466—432no—
683#465—432no—
684#465—432no—
685#465—432no—
686#463—432no—
687#463—432no—
688#461—431no—
689#461—431no—
690#460—432no—
691#459—431no—
692#459—432no—
693#459—431no—
694#450—432no—
695#450—432no—
696#449—432no—
697#449—432no—
698#447—432no—
699#447—432no—
700#446—431no—
701C8×Q8—431no—
702#442—432no—
703#442—432no—
704#442—432no—
705#440—432no—
706#440—432no—
707#440—432no—
708C4×SD16—432no—
709C4×SD16—432no—
710C4×SD16—432no—
711C4×D8—431no—
712C4×D8—431no—
713C4×D8—432no—
714C4×D8—431no—
715C4×D8—431no—
716C4×D8—431no—
717C4×D8—431no—
718C4×D8—431no—
719C4×D8—431no—
720#436—431no—
721#435—432no—
722C8×D4—431no—
723C8×D4—432no—
724#433—432no—
725#432—431no—
726#428—432no—
727C2×#107—431no—
728#416—432no—
729C2×#102—431no—
730C2×#102—432no—
731C2×#102—431no—
732#405—432no—
733C2×C4×C8—431no—
734C43#6149611yescharacteristic, complemented, Sylow
735C2×#41—21no—
736C2×#41—21no—
737C2×#41—432no—
738C2×#41—861no—
739C22×Q8—861no—
740C22×D4—22no—
741C22×D4—21no—
742C22×D4—431no—
743C22×D4C22×D4311yescharacteristic
744C22×D4C22×D4312yes—
745C23×C4—21no—
746C23×C4—861no—
747AGL(1,ℤ/8)—868no—
748C2×SD16—432no—
749C2×SD16—432no—
750C2×SD16—432no—
751C2×SD16—432no—
752C2×D8—431no—
753C2×D8—431no—
754C2×D8—431no—
755C2×D8—431no—
756C2×D8—432no—
757C2×D8—432no—
758C2×D8—864no—
759C2×M16—432no—
760C22×C8—431no—
761C22×C8—431no—
762C22×C8—432no—
763C4⋊Q8—431no—
764C4⋊Q8—432no—
765C4⋊Q8—431no—
766C4⋊Q8C22×D4311yescharacteristic
767#127C22×D4311yescharacteristic
768#127C22×D4312yes—
769#126—22no—
770#126—862no—
771#126—862no—
772#126C22⋊D4312yes—
773#125—862no—
774#125—861no—
775#125C22⋊D4311yescharacteristic
776#125C22×D4312yes—
777#124—22no—
778#124—21no—
779#124—432no—
780#124—862no—
781#124C22⋊D4311yescharacteristic
782#123—22no—
783#123—22no—
784#123—22no—
785#123—862no—
786#123—862no—
787#123—862no—
788#123—862no—
789#123C22⋊D4312yes—
790C22⋊Q8—21no—
791C22⋊Q8—22no—
792C22⋊Q8—432no—
793C22⋊Q8—432no—
794C22⋊Q8—861no—
795C22⋊Q8—861no—
796C22⋊Q8—862no—
797C22⋊Q8—861no—
798C22⋊Q8—861no—
799C22⋊Q8—862no—
800C22⋊Q8—862no—
801C22⋊Q8—862no—
802C22⋊Q8C22⋊D4311yescharacteristic
803#121—22no—
804#121—21no—
805#121—21no—
806#121—21no—
807#121—21no—
808#121—22no—
809#121—22no—
810#121—22no—
811#121—22no—
812#121—432no—
813#121—861no—
814#121—862no—
815#121C22⋊D4311yescharacteristic
816#121C22×D4312yes—
817#121C22×D4312yes—
818#121C22×D4312yes—
819#120—22no—
820#120—22no—
821#120—22no—
822#120—862no—
823C4×Q8—432no—
824C4×Q8—432no—
825C4×Q8—861no—
826C4×Q8C22×D4311yescharacteristic
827C4×D4—22no—
828C4×D4—22no—
829C4×D4—22no—
830C4×D4—21no—
831C4×D4—21no—
832C4×D4—21no—
833C4×D4—431no—
834C4×D4—431no—
835C4×D4—431no—
836C4×D4—431no—
837C4×D4—432no—
838C4×D4—862no—
839C4×D4—862no—
840C4×D4—862no—
841C4×D4—861no—
842C4×D4—861no—
843C4×D4C22×D4311yescharacteristic
844C4×D4C22×D4311yescharacteristic
845C4×D4C22×D4311yescharacteristic
846C4×D4C22×D4311yescharacteristic
847C4×D4C22×D4312yes—
848C4×D4C22×D4312yes—
849C4×D4C22×D4312yes—
850C4×D4C22×D4312yes—
851C4×D4C22×D4311yescharacteristic
852#117—21no—
853#117—861no—
854#117—862no—
855#117—861no—
856#117C22×D4312yes—
857#117C22×D4312yes—
858C2×C4⋊C4—21no—
859C2×C4⋊C4—431no—
860C2×C4⋊C4—432no—
861C2×C4⋊C4—862no—
862C2×C4⋊C4—861no—
863C2×C4⋊C4C22×D4311yescharacteristic
864C2×C22⋊C4—21no—
865C2×C22⋊C4—22no—
866C2×C22⋊C4—22no—
867C2×C22⋊C4—861no—
868C2×C22⋊C4—862no—
869C2×C42C22×D4311yescharacteristic
870#107—431no—
871#107—431no—
872#107—431no—
873#107—431no—
874#107—432no—
875#107—432no—
876#106—432no—
877#106—432no—
878#106—432no—
879#106—432no—
880C4⋊C8—431no—
881C4⋊C8—431no—
882C4⋊C8—432no—
883C4⋊C8—432no—
884#103—432no—
885#103—432no—
886#103—432no—
887#103—432no—
888#102—431no—
889#102—431no—
890#102—431no—
891#102—431no—
892#102—432no—
893#102—432no—
894#102—432no—
895#102—432no—
896#102—432no—
897#102—432no—
898#102—431no—
899#102—431no—
900#102—431no—
901#102—431no—
902#102—432no—
903#102—432no—
904C22⋊C8—432no—
905C22⋊C8—432no—
906C22⋊C8—432no—
907#97—432no—
908#97—432no—
909C4×C8—431no—
910C4×C8—431no—
911C4×C8—431no—
912C4×C8—431no—
913C4×C8—432no—
914C24—21no—
915C24—22no—
916C24—861no—
917#41—82no—
918#41—82no—
919#41—864no—
920#41—3442no—
921#41—1722no—
922C2×Q8—21no—
923C2×Q8—432no—
924C2×Q8—862no—
925C2×Q8—861no—
926C2×Q8—3442no—
927C2×Q8C2×C22⋊D4311yescharacteristic
928C2×D4—22no—
929C2×D4—24no—
930C2×D4—22no—
931C2×D4—22no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—21no—
935C2×D4—21no—
936C2×D4—22no—
937C2×D4—21no—
938C2×D4—22no—
939C2×D4—41no—
940C2×D4—42no—
941C2×D4—82no—
942C2×D4—84no—
943C2×D4—431no—
944C2×D4—431no—
945C2×D4—862no—
946C2×D4—862no—
947C2×D4—862no—
948C2×D4—861no—
949C2×D4—1721no—
950C2×D4C2×C22⋊D4312yes—
951C2×D4C2×C22⋊D4311yescharacteristic
952C2×D4C23×D4311yescharacteristic
953C2×D4C23×D4312yes—
954C2×D4C23×D4311yescharacteristic
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—22no—
960C22×C4—22no—
961C22×C4—22no—
962C22×C4—21no—
963C22×C4—82no—
964C22×C4—861no—
965C22×C4—862no—
966C22×C4—862no—
967C22×C4—861no—
968C22×C4—861no—
969C22×C4—862no—
970C22×C4—861no—
971C22×C4—861no—
972C22×C4—3442no—
973C22×C4C2×C22⋊D4311yescharacteristic
974C22×C4C2×C22⋊D4311yescharacteristic
975C22×C4C23×D4311yescharacteristic
976C22×C4C23×D4312yes—
977SD16—864no—
978SD16—864no—
979SD16—1722no—
980SD16—1722no—
981D8—434no—
982D8—862no—
983D8—862no—
984D8—864no—
985D8—862no—
986D8—1722no—
987M16—864no—
988C2×C8—431no—
989C2×C8—431no—
990C2×C8—431no—
991C2×C8—431no—
992C2×C8—432no—
993C2×C8—432no—
994C2×C8—862no—
995C2×C8—1722no—
996C2×C8—1721no—
997C4⋊C4—21no—
998C4⋊C4—22no—
999C4⋊C4—21no—
1000C4⋊C4—22no—
1001C4⋊C4—431no—
1002C4⋊C4—431no—
1003C4⋊C4—432no—
1004C4⋊C4—862no—
1005C4⋊C4—861no—
1006C4⋊C4—861no—
1007C4⋊C4—862no—
1008C4⋊C4—862no—
1009C4⋊C4—862no—
1010C4⋊C4—861no—
1011C4⋊C4—861no—
1012C4⋊C4—862no—
1013C4⋊C4—862no—
1014C4⋊C4C2×C22⋊D4311yescharacteristic
1015C4⋊C4C2×C22⋊D4311yescharacteristic
1016C4⋊C4C2×C22⋊D4312yes—
1017C4⋊C4C2×C22⋊D4312yes—
1018C4⋊C4C2×C22⋊D4312yes—
1019C4⋊C4C2×C22⋊D4312yes—
1020C4⋊C4C23×D4312yes—
1021C4⋊C4C23×D4311yescharacteristic
1022C4⋊C4C23×D4311yescharacteristic
1023C22⋊C4—22no—
1024C22⋊C4—21no—
1025C22⋊C4—22no—
1026C22⋊C4—21no—
1027C22⋊C4—22no—
1028C22⋊C4—21no—
1029C22⋊C4—22no—
1030C22⋊C4—21no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—862no—
1035C22⋊C4—862no—
1036C22⋊C4—861no—
1037C22⋊C4—861no—
1038C22⋊C4—861no—
1039C22⋊C4—861no—
1040C22⋊C4—862no—
1041C22⋊C4—862no—
1042C22⋊C4—862no—
1043C22⋊C4—862no—
1044C22⋊C4C2×C22⋊D4312yes—
1045C22⋊C4C2×C22⋊D4312yes—
1046C22⋊C4C2×C22⋊D4312yes—
1047C22⋊C4C2×C22⋊D4312yes—
1048C22⋊C4C2×C22⋊D4312yes—
1049C42—22no—
1050C42—862no—
1051C42—862no—
1052C42C2×C22⋊D4311yescharacteristic
1053C42C2×C22⋊D4311yescharacteristic
1054C42C23×D4311yescharacteristic
1055C42C23×D4311yescharacteristic
1056C42C23×D4312yes—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—42no—
1061C23—44no—
1062C23—42no—
1063C23—81no—
1064C23—82no—
1065C23—82no—
1066C23—861no—
1067C23—861no—
1068C23—3441no—
1069C23—1722no—
1070C23—1722no—
1071C23C22×C22⋊D4312yes—
1072C23C22×C22⋊D4311yescharacteristic
1073Q8—22no—
1074Q8—81no—
1075Q8—862no—
1076Q8—862no—
1077Q8—3442no—
1078Q8—1722no—
1079D4—24no—
1080D4—22no—
1081D4—21no—
1082D4—22no—
1083D4—21no—
1084D4—22no—
1085D4—21no—
1086D4—44no—
1087D4—42no—
1088D4—44no—
1089D4—42no—
1090D4—82no—
1091D4—82no—
1092D4—81no—
1093D4—82no—
1094D4—82no—
1095D4—432no—
1096D4—861no—
1097D4—861no—
1098D4—861no—
1099D4—3442no—
1100D4—1722no—
1101D4—1724no—
1102D4#41×D4312yes—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—21no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—42no—
1113C2×C4—42no—
1114C2×C4—81no—
1115C2×C4—81no—
1116C2×C4—82no—
1117C2×C4—82no—
1118C2×C4—82no—
1119C2×C4—81no—
1120C2×C4—862no—
1121C2×C4—861no—
1122C2×C4—862no—
1123C2×C4—861no—
1124C2×C4—3441no—
1125C2×C4—3441no—
1126C2×C4—3442no—
1127C2×C4—3441no—
1128C2×C4—3442no—
1129C2×C4—1724no—
1130C2×C4—1722no—
1131C2×C4—1722no—
1132C2×C4C22×C22⋊D4312yes—
1133C2×C4C22×C22⋊D4311yescharacteristic
1134C2×C4C22×C22⋊D4312yes—
1135C2×C4C22×C22⋊D4311yescharacteristic
1136C2×C4C22×C22⋊D4311yescharacteristic
1137C2×C4C22×C22⋊D4311yescharacteristic
1138C2×C4C22×C22⋊D4312yes—
1139C2×C4C22×C22⋊D4311yescharacteristic
1140C2×C4C24×D4311yescharacteristic
1141C8—432no—
1142C8—861no—
1143C8—862no—
1144C8—861no—
1145C8—862no—
1146C8—861no—
1147C22—21no—
1148C22—21no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—42no—
1157C22—42no—
1158C22—41no—
1159C22—41no—
1160C22—42no—
1161C22—84no—
1162C22—164no—
1163C22—862no—
1164C22—3444no—
1165C22—1721no—
1166C22—1721no—
1167C22—1721no—
1168C22—1721no—
1169C22—1721no—
1170C22#1458371012yes—
1171C22C23×C22⋊D4311yescharacteristic
1172C4—21no—
1173C4—22no—
1174C4—21no—
1175C4—21no—
1176C4—22no—
1177C4—22no—
1178C4—21no—
1179C4—41no—
1180C4—41no—
1181C4—42no—
1182C4—1721no—
1183C4—1721no—
1184C4—1722no—
1185C4—1722no—
1186C4#1458370212yes—
1187C4C2×#41×D4311yescharacteristic
1188C4#1458373511yescharacteristic
1189C2—22no—
1190C2—42no—
1191C2—42no—
1192C2—81no—
1193C2—82no—
1194C2—3441no—
1195C2—1722no—
1196C2#41×C22⋊D4311yescharacteristic
1197C2C2×#1458370211yescharacteristic
1198C2C2×#1458371011yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3519C2
socleC22×C43C23×D4
hypercenter#3519D43
hypocenterC43#61496
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #529 ◁ #3519

Complements

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

NH ≅ G/Ntype
1. #19148646C2semidirect
2. #19147611C2semidirect
3. #19147494C2semidirect
4. #19147244C2semidirect
5. #19147226C2semidirect
6. #19147184C2semidirect
7. #19147080C2semidirect
8. #19146517C2semidirect
9. #19146439C2semidirect
10. #19146419C2semidirect
11. #19146408C2semidirect
12. #19146191C2semidirect
13. #19146071C2semidirect
14. #19145280C2semidirect
15. #19145150C2semidirect
16. #19144788C2semidirect
17. #19144779C2semidirect
18. #19144694C2semidirect
19. #19144682C2semidirect
20. #19143571C2semidirect
21. #19143427C2semidirect
22. C2×C4×#10621882C2semidirect
23. C43×#3519C2semidirect
26. #14583622C22semidirect
27. #14583606C22semidirect
30. Q8×D172C22semidirect
32. #14583554C22semidirect
33. #14583553C22semidirect
34. #14583545C22semidirect
35. #14583520C22semidirect
37. #14583456C22semidirect
40. #14583379C22semidirect
41. C2×C4×D172C22semidirect
42. #14583309C22semidirect
43. #14583295C22semidirect
44. #14583286C22semidirect
45. #14583271C22semidirect
46. #14583256C22semidirect
47. #14583251C22semidirect
48. #14583245C22semidirect
49. #14583245C22semidirect
50. #14583240C22semidirect
51. #14583234C22semidirect
52. #14583223C22semidirect
53. #14583215C22semidirect
54. #14583215C22semidirect
55. #14583210C22semidirect
56. #14583203C22semidirect
57. #14583196C22semidirect
58. #14583189C22semidirect
59. #14583186C22semidirect
60. #14583186C22semidirect
61. #14583179C22semidirect
62. #14583179C22semidirect
63. #14583179C22semidirect
64. #14583150C22semidirect
65. #14583143C22semidirect
66. #14583133C22semidirect
67. #14583126C22semidirect
68. #14583126C22semidirect
69. #14583126C22semidirect
71. #14583114C22semidirect
72. #14583104C22semidirect
73. #14583104C22semidirect
74. #14583096C22semidirect
75. #14583091C22semidirect
76. #14583091C22semidirect
77. #14583091C22semidirect
79. #14583050C22semidirect
80. #14583042C22semidirect
81. #14583042C22semidirect
83. #14583032C22semidirect
84. #14583030C22semidirect
85. Q8×C43⋊C8C22semidirect
87. #14583009C22semidirect
88. #14583009C22semidirect
89. #14582999C22semidirect
90. #14582999C22semidirect
91. #14582999C22semidirect
92. C4×#10621883C22semidirect
93. C4×#10621883C22semidirect
94. C4×#10621883C22semidirect
99. C4×#10621882C22semidirect
100. C4×#10621882C22semidirect
101. C4×#10621882C22semidirect
102. C4×#10621882C22semidirect
103. C4×#10621882C22semidirect
104. #14582977C22semidirect
105. #14582971C22semidirect
106. D4×C43⋊C8C22semidirect
107. D4×C43⋊C8C22semidirect
108. #14582960C22semidirect
109. #14582956C22semidirect
110. #14582942C22semidirect
111. C2×#13063258C22semidirect
112. #14582893C22semidirect
114. C2×#13063246C22semidirect
115. C2×#13063245C22semidirect
116. #14582855C22semidirect
117. C2×C4×C43⋊C8C22semidirect
118. C43×#555C22semidirect
119. C43×#554C22semidirect
122. C43×#550C22semidirect
126. D42×C43C22semidirect
127. C43×#540C22semidirect
133. C43×#518C22semidirect
423. #10621882#41semidirect
591. #3519D43semidirect
626. #555C2×D43semidirect
628. #554C2×D43semidirect
633. #550C2×D43semidirect
642. D42C2×D43semidirect
644. #540C2×D43semidirect
655. #518C2×D43semidirect
734. C43#61496semidirect

Maximal subgroups

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

subgroupindex
#191486462
#191476112
#191474942
#191472442
#191472262
#191471842
#191470802
#191465172
#191464392
#191464192
#191464082
#191461912
#191460712
#191452802
#191451502
#191447882
#191447792
#191446942
#191446822
#191435712
#191434272
C2×C4×#106218822
C43×#35192
#6149643