Finite Group Databasebeta

← #25974779

Subgroups — #25974779

Order 11008.

2110 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148459C211yesmaximal, characteristic, complemented
2#19148354C211yesmaximal, characteristic
3#19146904C212yesmaximal, complemented
4#19146819C212yesmaximal, complemented
5#19146815C212yesmaximal, complemented
6#19146804C212yesmaximal, complemented
7#19146505C212yesmaximal, complemented
8#19146434C212yesmaximal, complemented
9#19146423C212yesmaximal, complemented
10#19146412C212yesmaximal, complemented
11#19144915C211yesmaximal, characteristic, complemented
12#19144586C211yesmaximal, characteristic, complemented
13#19144582C211yesmaximal, characteristic, complemented
14#19144389C211yesmaximal, characteristic, complemented
15#19144282C211yesmaximal, characteristic, complemented
16#19144280C211yesmaximal, characteristic, complemented
17#19144064C211yesmaximal, characteristic, complemented
18#19143868C211yesmaximal, characteristic, complemented
19C2×SD16×Dic43C211yesmaximal, characteristic, complemented
20#19143303C211yesmaximal, characteristic, complemented
21#19143121C211yesmaximal, characteristic, complemented
22#19143120C211yesmaximal, characteristic, complemented
23C43×#3009C211yesmaximal, characteristic, complemented
24C2×#13063370C2211yescharacteristic
25C2×#13063356C2211yescharacteristic, complemented
26C2×#13063333C2211yescharacteristic, complemented
27C2×#13063332C2211yescharacteristic, complemented
28#14583631—21no—
29#14583624—21no—
30#14583623—21no—
31#14583620C2212yescomplemented
32#14583618—21no—
33#14583607C2212yescomplemented
34#14583591C2212yescomplemented
35#14583583C2212yescomplemented
36#14583548—21no—
37#14583548C2212yes—
38#14583543—21no—
39#14583543C2212yes—
40#14583537—21no—
41#14583537C2212yes—
42D4×C22⋊D43—21no—
43D4×C22⋊D43C2212yes—
44#14583493—22no—
45#14583477C2211yescharacteristic
46#14583477C2211yescharacteristic
47#14583473C2211yescharacteristic, complemented
48#14583458—22no—
49#14583452C2211yescharacteristic, complemented
50#14583445C2211yescharacteristic
51#14583445C2211yescharacteristic
52#14583426—22no—
53C2×#13063297—22no—
54#14583382C2211yescharacteristic, complemented
55#14583379C2211yescharacteristic, complemented
56C2×Q8×Dic43C2211yescharacteristic, complemented
57C2×D4×Dic43C2211yescharacteristic
58#14583255C2211yescharacteristic, complemented
59#14583255C2211yescharacteristic, complemented
60#14583252C2211yescharacteristic, complemented
61#14583252C2211yescharacteristic, complemented
62#14583248C2211yescharacteristic, complemented
63#14583248C2211yescharacteristic, complemented
64#14583244C2211yescharacteristic, complemented
65#14583244C2211yescharacteristic, complemented
66#14583241C2212yescomplemented
67#14583238C2212yescomplemented
68#14583230C2212yescomplemented
69#14583228C2212yescomplemented
70#14583224C2212yescomplemented
71#14583222C2212yescomplemented
72#14583218C2212yescomplemented
73#14583216C2212yescomplemented
74#14583201C2212yescomplemented
75#14583197C2212yescomplemented
76#14583187C2212yescomplemented
77#14583177C2212yescomplemented
78#14583155C2212yescomplemented
79#14583154C2212yescomplemented
80#14583147C2212yescomplemented
81#14583142C2212yescomplemented
82#14583138C2212yescomplemented
83#14583137C2212yescomplemented
84#14583130C2212yescomplemented
85#14583125C2212yescomplemented
86#14583123C2212yescomplemented
87#14583119C2212yescomplemented
88#14583107C2212yescomplemented
89#14583097C2212yescomplemented
90#14583058C2212yescomplemented
91#14583058C2212yescomplemented
92#14583048C2212yescomplemented
93#14583048C2212yescomplemented
94SD16×Dic43C2212yescomplemented
95SD16×Dic43C2212yescomplemented
96SD16×Dic43C2212yescomplemented
97SD16×Dic43C2212yescomplemented
98#14582974C2212yescomplemented
99#14582974C2212yescomplemented
100(C22⋊D43)⋊C8C2212yescomplemented
101(C22⋊D43)⋊C8C2212yescomplemented
102#14582942C2211yescharacteristic, complemented
103#14582941C2211yescharacteristic, complemented
104C2×#13063257C2211yescharacteristic, complemented
105#14582922C2211yescharacteristic, complemented
106#14582904C2211yescharacteristic
107#14582904C2212yescomplemented
108#14582902C2212yescomplemented
109#14582901C2211yescharacteristic, complemented
110#14582900C2212yescomplemented
111#14582900C2211yescharacteristic, complemented
112#14582897C2212yescomplemented
113#14582896C2211yescharacteristic, complemented
114#14582895C2212yescomplemented
115#14582895C2211yescharacteristic, complemented
116#14582893C2211yescharacteristic, complemented
117#14582892C2212yescomplemented
118C2×#13063249C2211yescharacteristic, complemented
119C2×#13063246C2211yescharacteristic
120C2×#13063246C2212yescomplemented
121#102×D43C2212yescomplemented
122#14582865C2211yescharacteristic, complemented
123C2×C8×Dic43C2211yescharacteristic, complemented
124C2×H(5,𝔽2)×C43C2211yescharacteristic
125C2×#137×C43C2211yescharacteristic, complemented
126C22×SD16×C43C2211yescharacteristic
127C43×#536C2211yescharacteristic, complemented
128C43×#452C2212yescomplemented
129C43×#452C2212yescomplemented
130C43×#450C2212yescomplemented
131C43×#450C2212yescomplemented
132C43×#418C2211yescharacteristic
133C43×#416C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic, complemented
135#13063370—24no—
136#13063370—42no—
137C2×#10621898C2311yescharacteristic
138C2×#10621898C2311yescharacteristic
139C2×#10621900—21no—
140C2×#10621900C2312yes—
141C22×C22⋊D43—22no—
142C22×C22⋊D43—22no—
143C2×D4×D43—21no—
144C2×D4×D43C2312yes—
145C23×Dic43—21no—
146#13063356—42no—
147C2×#10621885C2312yes—
148C2×#10621884C2312yes—
149#13063333—42no—
150#13063332—42no—
151C2×#10621877C2311yescharacteristic
152C2×#10621877C2312yes—
153C2×#10621872C2312yes—
154C22×C43⋊C8C2311yescharacteristic
155C22×C43⋊C8C2312yes—
156C2×C8×D43C2312yes—
157#13063324C2311yescharacteristic
158#13063324C2311yescharacteristic
159#13063323—21no—
160#13063323D411yescharacteristic
161#13063323C2311yescharacteristic
162#13063321D411yescharacteristic
163#13063321C2311yescharacteristic
164#13063320—22no—
165#13063320—22no—
166#13063318—22no—
167#13063318—22no—
168#13063316—22no—
169#13063316C2311yescharacteristic
170#13063316C2311yescharacteristic
171#13063315—22no—
172#13063315—22no—
173#13063314—21no—
174#13063314D411yescharacteristic
175#13063314C2311yescharacteristic
176#13063312D411yescharacteristic
177#13063312C2311yescharacteristic
178#13063311—22no—
179#13063309—22no—
180#13063308—22no—
181#13063308—22no—
182#13063308—22no—
183#13063307—22no—
184#13063306—22no—
185#13063306—22no—
186#13063305—22no—
187#13063304—21no—
188#13063304C2312yes—
189#13063302—21no—
190#13063302—21no—
191#13063302—22no—
192#13063301—21no—
193#13063301C2312yes—
194#13063301C2312yes—
195#13063301C2312yes—
196#13063299—21no—
197#13063299C2312yes—
198#13063297—22no—
199#13063297—22no—
200#13063297—22no—
201#13063297—21no—
202#13063297—21no—
203#13063297—22no—
204#13063297—22no—
205#13063297—22no—
206#13063297D412yes—
207#13063297D412yes—
208#13063296—21no—
209#13063296C2312yes—
210#13063294—22no—
211#13063294—22no—
212#13063293—22no—
213#13063293—22no—
214Q8×Dic43—21no—
215Q8×Dic43—21no—
216Q8×Dic43—21no—
217Q8×Dic43C2312yes—
218Q8×Dic43C2312yes—
219C4×Dic86—21no—
220C4×Dic86—21no—
221C4×Dic86—21no—
222#13063290—22no—
223C4×D172—21no—
224D4×Dic43—21no—
225D4×Dic43—22no—
226D4×Dic43—21no—
227D4×Dic43—21no—
228D4×Dic43C2312yes—
229D4×Dic43C2312yes—
230C4×C22⋊D43—21no—
231C4×C22⋊D43—21no—
232C4×C22⋊D43C2312yes—
233C4×C22⋊D43C2312yes—
234(C22⋊D43)⋊C4—22no—
235(C22⋊D43)⋊C4—22no—
236#13063284C2312yes—
237#13063284C2311yescharacteristic
238#13063283—22no—
239#13063283C2312yes—
240#13063281—22no—
241C2×C4⋊Dic43—21no—
242C2×C4⋊Dic43C2312yes—
243C2×C4⋊Dic43C2311yescharacteristic
244C2×C4⋊Dic43C2311yescharacteristic
245C2×Dic43⋊C4—22no—
246C4⋊C4×D43C2312yes—
247C2×C22⋊Dic43—21no—
248C2×C22⋊Dic43—22no—
249C2×(C2×D43)⋊C4—22no—
250C2×C4×Dic43—21no—
251C2×C4×Dic43C2311yescharacteristic
252#13063259C2312yes—
253#13063258C2312yes—
254#13063257C2312yes—
255#13063257C2312yes—
256#13063257C2312yes—
257#13063256C2312yes—
258Dic43⋊C8C2312yes—
259Dic43⋊C8C2312yes—
260#13063250C2311yescharacteristic
261#13063250C2311yescharacteristic
262#13063250C2312yes—
263#13063249C2312yes—
264#13063249C2312yes—
265#13063249C2311yescharacteristic
266#13063249C2312yes—
267#13063249C2311yescharacteristic
268#13063248C2311yescharacteristic
269#13063248C2311yescharacteristic
270#13063247C2311yescharacteristic
271#13063247C2311yescharacteristic
272#13063247C2312yes—
273#13063246C2312yes—
274#13063246C2312yes—
275#13063246C2312yes—
276#13063246C2311yescharacteristic
277#13063246C2312yes—
278#13063246C2312yes—
279#13063246C2311yescharacteristic
280#13063245C2311yescharacteristic
281#13063245C2311yescharacteristic
282(C2×D43)⋊C8C2312yes—
283(C2×D43)⋊C8C2312yes—
284C8×Dic43C2311yescharacteristic
285C8×Dic43C2311yescharacteristic
286C8×Dic43C2311yescharacteristic
287C8×Dic43C2311yescharacteristic
288H(5,𝔽2)×C43—24no—
289H(5,𝔽2)×C43—42no—
290C2×#41×C43—21no—
291C2×#41×C43C2311yescharacteristic
292C2×#41×C43C2312yes—
293C2×#41×C43C2311yescharacteristic
294C22×Q8×C43C2311yescharacteristic
295C22×D4×C43—22no—
296C22×D4×C43—21no—
297C22×D4×C43C2312yes—
298C22×D4×C43C2311yescharacteristic
299#137×C43—42no—
300C2×Q16×C43C2312yes—
301C2×SD16×C43—24no—
302C2×SD16×C43C2312yes—
303C2×SD16×C43C2312yes—
304C2×SD16×C43C2312yes—
305C2×M16×C43C2311yescharacteristic
306C22×C8×C43C2311yescharacteristic
307C4⋊Q8×C43—21no—
308#124×C43—21no—
309#123×C43—22no—
310C22⋊Q8×C43C2312yes—
311C22⋊Q8×C43C2312yes—
312#117×C43C2311yescharacteristic
313#103×C43C2311yescharacteristic
314#103×C43C2311yescharacteristic
315#102×C43C2312yes—
316#102×C43C2312yes—
317#102×C43C2311yescharacteristic
318#102×C43C2311yescharacteristic
319C22⋊C8×C43C2312yes—
320C22⋊C8×C43C2312yes—
321C24×C43—21no—
322C24×C43—22no—
323C23×D43—22no—
324#41×C43—22no—
325#41×C43—22no—
326#41×C43—24no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—42no—
330#41×C43—44no—
331C2×Q8×C43—21no—
332C2×Q8×C43—22no—
333C2×Q8×C43—22no—
334C2×Q8×C43C2×D411yescharacteristic
335C2×Q8×C43C2411yescharacteristic
336C2×Q8×C43C2412yes—
337C2×D4×C43—21no—
338C2×D4×C43—22no—
339C2×D4×C43—22no—
340C2×D4×C43—22no—
341C2×D4×C43—21no—
342C2×D4×C43—24no—
343C2×D4×C43—48no—
344C2×D4×C43—42no—
345C2×D4×C43—44no—
346C2×D4×C43C2×D412yes—
347C2×D4×C43C2×D411yescharacteristic
348C2×D4×C43#4114yes—
349C2×D4×C43C2411yescharacteristic
350C2×D4×C43C2412yes—
351C22×C4×C43—22no—
352C22×C4×C43—21no—
353C22×C4×C43—21no—
354C22×C4×C43C2412yes—
355C22×C4×C43C2411yescharacteristic
356C2×C22⋊D43—21no—
357C2×C22⋊D43—22no—
358C2×C22⋊D43—21no—
359C2×C22⋊D43—21no—
360C2×C22⋊D43—22no—
361C2×C22⋊D43—22no—
362C2×C22⋊D43—22no—
363C2×C22⋊D43—48no—
364C2×C22⋊D43—84no—
365C2×C22⋊D43C2×D412yes—
366C2×C22⋊D43C2×D412yes—
367C2×C22⋊D43C2×D412yes—
368C22×Dic43—22no—
369C22×Dic43—22no—
370C22×Dic43—22no—
371C22×Dic43—21no—
372C22×Dic43—21no—
373C22×Dic43—22no—
374C22×Dic43—82no—
375C22×Dic43C2×D411yescharacteristic
376C22×Dic43C2×D411yescharacteristic
377#10621900—24no—
378#10621900—42no—
379#10621900—44no—
380D4×D43—24no—
381D4×D43—42no—
382D4×D43—44no—
383#10621898—22no—
384#10621898—22no—
385#10621898—22no—
386#10621898—22no—
387C2×D172C2×D411yescharacteristic
388C2×D172C2411yescharacteristic
389C2×C4×D43—21no—
390C2×C4×D43—22no—
391C2×C4×D43C2412yes—
392C2×Dic86—21no—
393C2×Dic86—21no—
394C2×Dic86C2×D411yescharacteristic
395C2×Dic86C2411yescharacteristic
396Q16×C43—42no—
397SD16×C43—24no—
398SD16×C43—24no—
399SD16×C43—42no—
400M16×C43—22no—
401C2×C8×C43—22no—
402C2×C8×C43C2412yes—
403C2×C8×C43C2411yescharacteristic
404C2×C8×C43C2411yescharacteristic
405C4⋊C4×C43—22no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43C2411yescharacteristic
408C4⋊C4×C43C2411yescharacteristic
409C22⋊C4×C43—21no—
410C22⋊C4×C43—22no—
411C22⋊C4×C43—22no—
412C42×C43—21no—
413C22⋊Dic43—21no—
414C22⋊Dic43—22no—
415C22⋊Dic43—22no—
416C22⋊Dic43—22no—
417C22⋊Dic43—21no—
418C22⋊Dic43—22no—
419C22⋊Dic43—21no—
420C22⋊Dic43—22no—
421C22⋊Dic43C2×D412yes—
422C22⋊Dic43C2×D412yes—
423#10621885—42no—
424#10621884—42no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—21no—
427(C2×D43)⋊C4—21no—
428(C2×D43)⋊C4—22no—
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4C2×D412yes—
433(C2×D43)⋊C4C2×D412yes—
434C4⋊Dic43—21no—
435C4⋊Dic43—21no—
436C4⋊Dic43—22no—
437C4⋊Dic43—22no—
438C4⋊Dic43—22no—
439C4⋊Dic43—21no—
440C4⋊Dic43—21no—
441C4⋊Dic43C2412yes—
442C4⋊Dic43C2411yescharacteristic
443C4⋊Dic43C2411yescharacteristic
444C4⋊Dic43C2412yes—
445Dic43⋊C4—22no—
446Dic43⋊C4—22no—
447Dic43⋊C4—21no—
448Dic43⋊C4—22no—
449Dic43⋊C4—21no—
450Dic43⋊C4—22no—
451Dic43⋊C4—21no—
452Dic43⋊C4—21no—
453Dic43⋊C4—22no—
454Dic43⋊C4—21no—
455Dic43⋊C4—21no—
456Dic43⋊C4C2×D412yes—
457Dic43⋊C4C2×D412yes—
458C4×Dic43—22no—
459C4×Dic43—21no—
460C4×Dic43—22no—
461C4×Dic43—22no—
462C4×Dic43—22no—
463C4×Dic43C2×D411yescharacteristic
464C4×Dic43C2×D411yescharacteristic
465C4×Dic43C2411yescharacteristic
466C4×Dic43C2411yescharacteristic
467#10621877—22no—
468#10621877—42no—
469C2×C43⋊C8—22no—
470C2×C43⋊C8—42no—
471C2×C43⋊C8C2411yescharacteristic
472C2×C43⋊C8C2411yescharacteristic
473C2×C43⋊C8C2412yes—
474#10621872—42no—
475C8×D43—42no—
476C23×C43—22no—
477C23×C43—24no—
478C23×C43—21no—
479C23×C43—44no—
480C23×C43—81no—
481C23×C43—81no—
482C23×C43—82no—
483C23×C43—82no—
484C23×C43C22×D412yes—
485C23×C43C22×D411yescharacteristic
486C22×D43—21no—
487C22×D43—44no—
488C22×D43—82no—
489C22×D43—82no—
490C22×D43C22×D412yes—
491Q8×C43—22no—
492Q8×C43—22no—
493Q8×C43—21no—
494Q8×C43—22no—
495Q8×C43—21no—
496Q8×C43—42no—
497D4×C43—24no—
498D4×C43—24no—
499D4×C43—22no—
500D4×C43—21no—
501D4×C43—22no—
502D4×C43—21no—
503D4×C43—44no—
504D4×C43—44no—
505D4×C43—42no—
506D4×C43C2×#4114yes—
507C2×C4×C43—22no—
508C2×C4×C43—22no—
509C2×C4×C43—22no—
510C2×C4×C43—21no—
511C2×C4×C43—21no—
512C2×C4×C43—21no—
513C2×C4×C43—44no—
514C2×C4×C43—42no—
515C2×C4×C43—42no—
516C2×C4×C43C22×D412yes—
517C2×C4×C43C22×D411yescharacteristic
518C2×C4×C43C2×#4112yes—
519C2×C4×C43H(5,𝔽2)12yes—
520C2×C4×C43C2511yescharacteristic
521C22⋊D43—24no—
522C22⋊D43—24no—
523C22⋊D43—42no—
524C22⋊D43—44no—
525C22⋊D43—44no—
526C22⋊D43—42no—
527C22⋊D43—42no—
528C22⋊D43—81no—
529C22⋊D43—82no—
530C22⋊D43—82no—
531C2×Dic43—22no—
532C2×Dic43—22no—
533C2×Dic43—21no—
534C2×Dic43—21no—
535C2×Dic43—21no—
536C2×Dic43—22no—
537C2×Dic43—41no—
538C2×Dic43—44no—
539C2×Dic43—44no—
540C2×Dic43—82no—
541C2×Dic43—82no—
542C2×Dic43—81no—
543C2×Dic43—81no—
544C2×Dic43C22×D411yescharacteristic
545C2×Dic43C22×D412yes—
546C2×Dic43C22×D411yescharacteristic
547C2×Dic43C22×D411yescharacteristic
548C2×Dic43C22×D411yescharacteristic
549D172—22no—
550D172—21no—
551D172—21no—
552C4×D43—22no—
553C4×D43—22no—
554C4×D43—42no—
555C4×D43—82no—
556Dic86—22no—
557Dic86—21no—
558Dic86—21no—
559Dic86—42no—
560Dic86—81no—
561C8×C43—21no—
562C8×C43—21no—
563C8×C43—22no—
564C43⋊C8—21no—
565C43⋊C8—21no—
566C43⋊C8—22no—
567#61212—431nomaximal, Sylow
568C22×C43—21no—
569C22×C43—21no—
570C22×C43—22no—
571C22×C43—24no—
572C22×C43—22no—
573C22×C43—22no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—41no—
577C22×C43—41no—
578C22×C43—41no—
579C22×C43—84no—
580C22×C43—164no—
581C22×C43#54612yes—
582C22×C43C23×D411yescharacteristic
583C2×D43—22no—
584C2×D43—22no—
585C2×D43—22no—
586C2×D43—41no—
587C2×D43—41no—
588C2×D43—41no—
589C2×D43—164no—
590C4×C43—22no—
591C4×C43—41no—
592C4×C43—41no—
593C4×C43—42no—
594C4×C43—41no—
595C4×C43#54612yes—
596C4×C43C22×#4111yescharacteristic
597C4×C43C2×H(5,𝔽2)11yescharacteristic
598Dic43—21no—
599Dic43—21no—
600Dic43—22no—
601Dic43—21no—
602Dic43—41no—
603Dic43—42no—
604Dic43—41no—
605Dic43—41no—
606Dic43—42no—
607Dic43#57712yes—
608#3507—431no—
609#3496—431no—
610#3331—432no—
611#3324—432no—
612#3323—432no—
613#3323—432no—
614#3302—432no—
615#3296—432no—
616#3296—432no—
617#3295—432no—
618#3131—431no—
619#3099—431no—
620#3099—431no—
621#3077—431no—
622#3063—431no—
623#3063—431no—
624#3037—431no—
625#3009—431no—
626#3009D4311yescharacteristic, complemented
627C2×C4×SD16—431no—
628#2931—431no—
629#2897—431no—
630#2897—431no—
631C2×C43—22no—
632C2×C43—44no—
633C2×C43—42no—
634C2×C43—81no—
635C2×C43C2×#54611yescharacteristic
636C2×C43C2×#57711yescharacteristic
637C2×C43#358411yescharacteristic
638D43—42no—
639D43—81no—
640C2×H(5,𝔽2)—431no—
641C2×H(5,𝔽2)C2×D4311yescharacteristic
642C2×#137—431no—
643C2×#137C2×D4311yescharacteristic, complemented
644C22×SD16C2×D4311yescharacteristic
645C2×#131—431no—
646C2×#131—431no—
647#559—861no—
648#557—861no—
649#556—432no—
650#556—861no—
651#556—861no—
652#554—432no—
653#552—432no—
654#552—432no—
655#547—432no—
656#547—861no—
657#546—432no—
658#546—432no—
659#546—861no—
660#546—861no—
661D42—432no—
662D42—861no—
663#539—862no—
664#537—431no—
665#537—431no—
666#536—431no—
667#536C2×D4311yescharacteristic, complemented
668#534—862no—
669#533—431no—
670#532—431no—
671#532—431no—
672#529—862no—
673C2×#121—862no—
674#520—431no—
675#520—431no—
676C2×C4×Q8—431no—
677C2×C4×D4—431no—
678#488—431no—
679#488—431no—
680#488—431no—
681#488—431no—
682#487—431no—
683#487—431no—
684#486—431no—
685#486—431no—
686#485—432no—
687#485—432no—
688#483—432no—
689#483—432no—
690#482—432no—
691#482—432no—
692#481—432no—
693#481—432no—
694#478—432no—
695#478—432no—
696#476—432no—
697#474—432no—
698#470—432no—
699#470—432no—
700#468—432no—
701#468—432no—
702#467—432no—
703#467—432no—
704#465—432no—
705#465—432no—
706#464—432no—
707#464—432no—
708#462—432no—
709#460—432no—
710#452—432no—
711#452—432no—
712#452C2×D4312yescomplemented
713#452C2×D4312yescomplemented
714#450—432no—
715#450—432no—
716#450C2×D4312yescomplemented
717#450C2×D4312yescomplemented
718C4×SD16—432no—
719C4×SD16—432no—
720C4×SD16—432no—
721C4×SD16—432no—
722#436—432no—
723#436—432no—
724C8×D4—432no—
725C8×D4—432no—
726#428—431no—
727#428—431no—
728C2×#106—431no—
729#423—431no—
730#418—431no—
731#418—432no—
732#418—432no—
733#418C2×D4311yescharacteristic
734#417—432no—
735#417—431no—
736#417—431no—
737#417—432no—
738#416—431no—
739#416—432no—
740#416—431no—
741#416—431no—
742#416—432no—
743#416C2×D4311yescharacteristic, complemented
744C2×#103—431no—
745C2×#102—431no—
746C2×#102—432no—
747C2×#102—432no—
748#408—431no—
749#408C2×D4311yescharacteristic, complemented
750C2×C4×C8—431no—
751C43#6121211yescharacteristic, complemented, Sylow
752H(5,𝔽2)—24no—
753H(5,𝔽2)—42no—
754H(5,𝔽2)—864no—
755H(5,𝔽2)—1722no—
756C2×#41—21no—
757C2×#41—431no—
758C2×#41—432no—
759C2×#41—431no—
760C2×#41—861no—
761C2×#41C22×D4311yescharacteristic
762C2×#41C22×D4312yes—
763C2×#41C22×D4311yescharacteristic
764C22×Q8C22×D4311yescharacteristic
765C22×D4—22no—
766C22×D4—21no—
767C22×D4—432no—
768C22×D4—861no—
769C22×D4—862no—
770C22×D4—862no—
771C22×D4C22×D4312yes—
772C22×D4C22×D4311yescharacteristic
773C23×C4—861no—
774#137—42no—
775#137—1722no—
776C2×Q16—432no—
777C2×Q16C22×D4312yes—
778C2×SD16—24no—
779C2×SD16—432no—
780C2×SD16C22×D4312yes—
781C2×SD16C22×D4312yes—
782C2×SD16C22×D4312yes—
783#131—1722no—
784#131—1722no—
785C2×M16—431no—
786C2×M16—432no—
787C2×M16—432no—
788C2×M16C22×D4311yescharacteristic
789C22×C8—431no—
790C22×C8—432no—
791C22×C8—432no—
792C22×C8C22×D4311yescharacteristic
793C4⋊Q8—21no—
794C4⋊Q8—431no—
795C4⋊Q8—431no—
796C4⋊Q8—431no—
797C4⋊Q8—431no—
798C4⋊Q8—861no—
799#127—431no—
800#127—431no—
801#126—862no—
802#126—862no—
803#126—862no—
804#126—862no—
805#125—431no—
806#125—431no—
807#125—862no—
808#125—862no—
809#125—862no—
810#124—21no—
811#124—431no—
812#124—431no—
813#124—431no—
814#124—431no—
815#124—862no—
816#124—861no—
817#123—22no—
818#123—862no—
819#123—862no—
820#123—862no—
821#123—862no—
822#123—862no—
823#123—862no—
824#123—862no—
825C22⋊Q8—432no—
826C22⋊Q8—432no—
827C22⋊Q8—432no—
828C22⋊Q8—432no—
829C22⋊Q8—862no—
830C22⋊Q8—861no—
831C22⋊Q8—861no—
832C22⋊Q8—862no—
833C22⋊Q8—861no—
834C22⋊Q8—861no—
835C22⋊Q8C22×D4312yes—
836C22⋊Q8C22×D4312yes—
837#121—432no—
838#121—432no—
839#121—432no—
840#121—432no—
841#121—862no—
842#121—862no—
843#121—862no—
844#121—861no—
845#121—861no—
846#121—861no—
847#121—862no—
848#121—862no—
849#121—862no—
850#121—861no—
851#120—862no—
852#120—862no—
853#120—862no—
854#120—862no—
855C4×Q8—432no—
856C4×Q8—432no—
857C4×Q8—861no—
858C4×Q8—861no—
859C4×Q8—861no—
860C4×Q8—861no—
861C4×Q8—861no—
862C4×Q8—862no—
863C4×Q8—861no—
864C4×D4—432no—
865C4×D4—432no—
866C4×D4—432no—
867C4×D4—432no—
868C4×D4—861no—
869C4×D4—861no—
870C4×D4—861no—
871C4×D4—861no—
872C4×D4—861no—
873C4×D4—862no—
874C4×D4—862no—
875C4×D4—862no—
876C4×D4—861no—
877#117—431no—
878#117—432no—
879#117—432no—
880#117—862no—
881#117—862no—
882#117C22×D4311yescharacteristic
883C2×C4⋊C4—431no—
884C2×C4⋊C4—431no—
885C2×C4⋊C4—432no—
886C2×C4⋊C4—432no—
887C2×C4⋊C4—862no—
888C2×C4⋊C4—861no—
889C2×C22⋊C4—862no—
890C2×C22⋊C4—862no—
891C2×C22⋊C4—861no—
892C2×C42—431no—
893C2×C42—861no—
894#107—432no—
895#107—432no—
896#106—432no—
897#106—432no—
898#106—432no—
899#106—432no—
900C4⋊C8—432no—
901C4⋊C8—432no—
902#103—432no—
903#103—432no—
904#103—431no—
905#103—432no—
906#103—431no—
907#103—432no—
908#103—431no—
909#103—431no—
910#103—431no—
911#103—431no—
912#103C22×D4311yescharacteristic
913#103C22×D4311yescharacteristic
914#102—432no—
915#102—431no—
916#102—432no—
917#102—432no—
918#102—432no—
919#102—432no—
920#102—431no—
921#102—432no—
922#102—431no—
923#102—431no—
924#102—431no—
925#102—431no—
926#102C22×D4312yes—
927#102C22×D4312yes—
928#102C22×D4311yescharacteristic
929#102C22×D4311yescharacteristic
930C22⋊C8—432no—
931C22⋊C8—432no—
932C22⋊C8C22×D4312yes—
933C22⋊C8C22×D4312yes—
934C4×C8—431no—
935C4×C8—431no—
936C4×C8—431no—
937C4×C8—431no—
938C24—21no—
939C24—22no—
940C24—862no—
941#41—22no—
942#41—22no—
943#41—24no—
944#41—22no—
945#41—22no—
946#41—42no—
947#41—44no—
948#41—862no—
949#41—862no—
950#41—864no—
951#41—862no—
952#41—862no—
953#41—1722no—
954#41—1724no—
955C2×Q8—21no—
956C2×Q8—22no—
957C2×Q8—22no—
958C2×Q8—431no—
959C2×Q8—431no—
960C2×Q8—861no—
961C2×Q8—861no—
962C2×Q8D4×D4311yescharacteristic
963C2×Q8C23×D4311yescharacteristic
964C2×Q8C23×D4312yes—
965C2×D4—24no—
966C2×D4—22no—
967C2×D4—21no—
968C2×D4—21no—
969C2×D4—22no—
970C2×D4—22no—
971C2×D4—42no—
972C2×D4—44no—
973C2×D4—48no—
974C2×D4—432no—
975C2×D4—432no—
976C2×D4—432no—
977C2×D4—431no—
978C2×D4—431no—
979C2×D4—861no—
980C2×D4—861no—
981C2×D4—862no—
982C2×D4—864no—
983C2×D4—862no—
984C2×D4—862no—
985C2×D4—862no—
986C2×D4—861no—
987C2×D4—3444no—
988C2×D4—1722no—
989C2×D4—1724no—
990C2×D4—1728no—
991C2×D4D4×D4312yes—
992C2×D4D4×D4311yescharacteristic
993C2×D4#1062190014yes—
994C2×D4C23×D4311yescharacteristic
995C2×D4C23×D4312yes—
996C22×C4—21no—
997C22×C4—22no—
998C22×C4—21no—
999C22×C4—431no—
1000C22×C4—431no—
1001C22×C4—432no—
1002C22×C4—862no—
1003C22×C4—862no—
1004C22×C4—862no—
1005C22×C4—862no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—862no—
1009C22×C4—861no—
1010C22×C4—3442no—
1011C22×C4C23×D4312yes—
1012C22×C4C23×D4311yescharacteristic
1013Q16—42no—
1014Q16—1722no—
1015SD16—24no—
1016SD16—24no—
1017SD16—42no—
1018SD16—1722no—
1019M16—22no—
1020M16—862no—
1021M16—1722no—
1022M16—1722no—
1023C2×C8—22no—
1024C2×C8—431no—
1025C2×C8—431no—
1026C2×C8—432no—
1027C2×C8—862no—
1028C2×C8—1722no—
1029C2×C8—1722no—
1030C2×C8C23×D4311yescharacteristic
1031C2×C8C23×D4311yescharacteristic
1032C2×C8C23×D4312yes—
1033C4⋊C4—22no—
1034C4⋊C4—22no—
1035C4⋊C4—432no—
1036C4⋊C4—432no—
1037C4⋊C4—432no—
1038C4⋊C4—431no—
1039C4⋊C4—431no—
1040C4⋊C4—432no—
1041C4⋊C4—862no—
1042C4⋊C4—861no—
1043C4⋊C4—862no—
1044C4⋊C4—862no—
1045C4⋊C4—862no—
1046C4⋊C4—861no—
1047C4⋊C4—861no—
1048C4⋊C4—862no—
1049C4⋊C4—861no—
1050C4⋊C4—861no—
1051C4⋊C4—862no—
1052C4⋊C4—861no—
1053C4⋊C4—861no—
1054C4⋊C4—861no—
1055C4⋊C4—861no—
1056C4⋊C4—861no—
1057C4⋊C4—862no—
1058C4⋊C4—862no—
1059C4⋊C4C23×D4311yescharacteristic
1060C4⋊C4C23×D4311yescharacteristic
1061C22⋊C4—22no—
1062C22⋊C4—21no—
1063C22⋊C4—22no—
1064C22⋊C4—432no—
1065C22⋊C4—432no—
1066C22⋊C4—432no—
1067C22⋊C4—432no—
1068C22⋊C4—861no—
1069C22⋊C4—861no—
1070C22⋊C4—862no—
1071C22⋊C4—862no—
1072C22⋊C4—862no—
1073C22⋊C4—862no—
1074C22⋊C4—861no—
1075C22⋊C4—862no—
1076C22⋊C4—862no—
1077C22⋊C4—862no—
1078C22⋊C4—861no—
1079C22⋊C4—862no—
1080C22⋊C4—861no—
1081C22⋊C4—862no—
1082C22⋊C4—862no—
1083C42—21no—
1084C42—431no—
1085C42—431no—
1086C42—431no—
1087C42—431no—
1088C42—862no—
1089C42—862no—
1090C42—862no—
1091C42—862no—
1092C42—861no—
1093C23—22no—
1094C23—24no—
1095C23—21no—
1096C23—44no—
1097C23—81no—
1098C23—81no—
1099C23—82no—
1100C23—82no—
1101C23—432no—
1102C23—861no—
1103C23—3442no—
1104C23—3442no—
1105C23—1724no—
1106C23C2×D4×D4312yes—
1107C23C2×D4×D4311yescharacteristic
1108Q8—22no—
1109Q8—22no—
1110Q8—21no—
1111Q8—22no—
1112Q8—21no—
1113Q8—42no—
1114Q8—862no—
1115Q8—861no—
1116Q8—861no—
1117Q8—3441no—
1118Q8—1722no—
1119D4—24no—
1120D4—21no—
1121D4—22no—
1122D4—21no—
1123D4—24no—
1124D4—22no—
1125D4—44no—
1126D4—44no—
1127D4—42no—
1128D4—864no—
1129D4—864no—
1130D4—861no—
1131D4—861no—
1132D4—862no—
1133D4—3441no—
1134D4—3442no—
1135D4—3442no—
1136D4—1722no—
1137D4—1722no—
1138D4—1724no—
1139D4—1724no—
1140D4—1722no—
1141D4C2×#1062190014yes—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—22no—
1147C2×C4—21no—
1148C2×C4—44no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—431no—
1152C2×C4—431no—
1153C2×C4—431no—
1154C2×C4—431no—
1155C2×C4—432no—
1156C2×C4—862no—
1157C2×C4—862no—
1158C2×C4—862no—
1159C2×C4—862no—
1160C2×C4—861no—
1161C2×C4—861no—
1162C2×C4—862no—
1163C2×C4—861no—
1164C2×C4—3442no—
1165C2×C4—3442no—
1166C2×C4—3441no—
1167C2×C4—3441no—
1168C2×C4—3442no—
1169C2×C4—1724no—
1170C2×C4—1721no—
1171C2×C4—1724no—
1172C2×C4—1722no—
1173C2×C4C2×D4×D4312yes—
1174C2×C4C2×D4×D4311yescharacteristic
1175C2×C4C2×#1062190012yes—
1176C2×C4#1306337012yes—
1177C2×C4C24×D4311yescharacteristic
1178C8—21no—
1179C8—21no—
1180C8—22no—
1181C8—861no—
1182C8—861no—
1183C8—862no—
1184C22—21no—
1185C22—21no—
1186C22—22no—
1187C22—24no—
1188C22—22no—
1189C22—22no—
1190C22—42no—
1191C22—42no—
1192C22—41no—
1193C22—41no—
1194C22—41no—
1195C22—84no—
1196C22—164no—
1197C22—862no—
1198C22—862no—
1199C22—862no—
1200C22—1721no—
1201C22—1721no—
1202C22—1721no—
1203C22—6884no—
1204C22#1458353612yes—
1205C22C22×D4×D4311yescharacteristic
1206C4—22no—
1207C4—41no—
1208C4—42no—
1209C4—41no—
1210C4—41no—
1211C4—432no—
1212C4—862no—
1213C4—861no—
1214C4—861no—
1215C4—861no—
1216C4—1721no—
1217C4—1722no—
1218C4—1721no—
1219C4—1722no—
1220C4—1721no—
1221C4#1458353612yes—
1222C4C22×#1062190011yescharacteristic
1223C4C2×#1306337011yescharacteristic
1224C2—22no—
1225C2—42no—
1226C2—44no—
1227C2—81no—
1228C2—3441no—
1229C2—1722no—
1230C2C2×#1458353611yescharacteristic
1231C2#577×D4311yescharacteristic
1232C2#1914936711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3009C2
socleC22×C43C23×D4
prime radical#19148354C2
hypercenter#3009D43
hypocenterC43#61212
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3009

Complements

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

NH ≅ G/Ntype
1. #19148459C2semidirect
3. #19146904C2semidirect
4. #19146819C2semidirect
5. #19146815C2semidirect
6. #19146804C2semidirect
7. #19146505C2semidirect
8. #19146434C2semidirect
9. #19146423C2semidirect
10. #19146412C2semidirect
11. #19144915C2semidirect
12. #19144586C2semidirect
13. #19144582C2semidirect
14. #19144389C2semidirect
15. #19144282C2semidirect
16. #19144280C2semidirect
17. #19144064C2semidirect
18. #19143868C2semidirect
19. C2×SD16×Dic43C2semidirect
20. #19143303C2semidirect
21. #19143121C2semidirect
22. #19143120C2semidirect
23. C43×#3009C2semidirect
25. C2×#13063356C22semidirect
26. C2×#13063333C22semidirect
27. C2×#13063332C22semidirect
31. #14583620C22semidirect
33. #14583607C22semidirect
34. #14583591C22semidirect
35. #14583583C22semidirect
47. #14583473C22semidirect
49. #14583452C22semidirect
54. #14583382C22semidirect
55. #14583379C22semidirect
56. C2×Q8×Dic43C22semidirect
58. #14583255C22semidirect
59. #14583255C22semidirect
60. #14583252C22semidirect
61. #14583252C22semidirect
62. #14583248C22semidirect
63. #14583248C22semidirect
64. #14583244C22semidirect
65. #14583244C22semidirect
66. #14583241C22semidirect
67. #14583238C22semidirect
68. #14583230C22semidirect
69. #14583228C22semidirect
70. #14583224C22semidirect
71. #14583222C22semidirect
72. #14583218C22semidirect
73. #14583216C22semidirect
74. #14583201C22semidirect
75. #14583197C22semidirect
76. #14583187C22semidirect
77. #14583177C22semidirect
78. #14583155C22semidirect
79. #14583154C22semidirect
80. #14583147C22semidirect
81. #14583142C22semidirect
82. #14583138C22semidirect
83. #14583137C22semidirect
84. #14583130C22semidirect
85. #14583125C22semidirect
86. #14583123C22semidirect
87. #14583119C22semidirect
88. #14583107C22semidirect
89. #14583097C22semidirect
90. #14583058C22semidirect
91. #14583058C22semidirect
92. #14583048C22semidirect
93. #14583048C22semidirect
94. SD16×Dic43C22semidirect
95. SD16×Dic43C22semidirect
96. SD16×Dic43C22semidirect
97. SD16×Dic43C22semidirect
98. #14582974C22semidirect
99. #14582974C22semidirect
100. (C22⋊D43)⋊C8C22semidirect
101. (C22⋊D43)⋊C8C22semidirect
102. #14582942C22semidirect
103. #14582941C22semidirect
104. C2×#13063257C22semidirect
105. #14582922C22semidirect
107. #14582904C22semidirect
108. #14582902C22semidirect
109. #14582901C22semidirect
110. #14582900C22semidirect
111. #14582900C22semidirect
112. #14582897C22semidirect
113. #14582896C22semidirect
114. #14582895C22semidirect
115. #14582895C22semidirect
116. #14582893C22semidirect
117. #14582892C22semidirect
118. C2×#13063249C22semidirect
120. C2×#13063246C22semidirect
121. #102×D43C22semidirect
122. #14582865C22semidirect
123. C2×C8×Dic43C22semidirect
125. C2×#137×C43C22semidirect
127. C43×#536C22semidirect
128. C43×#452C22semidirect
129. C43×#452C22semidirect
130. C43×#450C22semidirect
131. C43×#450C22semidirect
133. C43×#416C22semidirect
134. C43×#408C22semidirect
626. #3009D43semidirect
643. C2×#137C2×D43semidirect
667. #536C2×D43semidirect
712. #452C2×D43semidirect
713. #452C2×D43semidirect
716. #450C2×D43semidirect
717. #450C2×D43semidirect
743. #416C2×D43semidirect
749. #408C2×D43semidirect
751. C43#61212semidirect

Maximal subgroups

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

subgroupindex
#191484592
#191483542
#191469042
#191468192
#191468152
#191468042
#191465052
#191464342
#191464232
#191464122
#191449152
#191445862
#191445822
#191443892
#191442822
#191442802
#191440642
#191438682
C2×SD16×Dic432
#191433032
#191431212
#191431202
C43×#30092
#6121243