Finite Group Databasebeta

← #25097779

Subgroups — #25097779

Order 11008.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583665C211yesmaximal, characteristic, complemented
2#19147925C211yesmaximal, characteristic
3C2×#14582914C211yesmaximal, characteristic, complemented
4C2×#104×D43C211yesmaximal, characteristic, complemented
5#19137081C211yesmaximal, characteristic, complemented
6#19134898C211yesmaximal, characteristic, complemented
7#19134897C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic, complemented
9#19134896C211yesmaximal, characteristic, complemented
10#19134895C211yesmaximal, characteristic, complemented
11#19134894C211yesmaximal, characteristic, complemented
12#19134894C211yesmaximal, characteristic, complemented
13#19134303C211yesmaximal, characteristic, complemented
14#339×D43C211yesmaximal, characteristic, complemented
15C43×#1871C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#41×D43C2211yescharacteristic
18#14583665—24no—
19#14583665—24no—
20C2×#13063333—21no—
21C2×#13063333—21no—
22C2×#13063331—21no—
23C2×#13063331—21no—
24C22×#10621877C2211yescharacteristic, complemented
25C2×M16×D43C2211yescharacteristic
26C2×M16×D43C2211yescharacteristic
27C2×M16×D43C2211yescharacteristic, complemented
28C2×M16×D43C2211yescharacteristic, complemented
29#14583479C411yescharacteristic, complemented
30#14583479C411yescharacteristic, complemented
31#14583478C411yescharacteristic, complemented
32#14583478C411yescharacteristic, complemented
33#14583472C411yescharacteristic, complemented
34#14583472C411yescharacteristic, complemented
35#14583471—21no—
36#14583465C411yescharacteristic, complemented
37#14583465C411yescharacteristic, complemented
38#14583464—21no—
39#14583460—21no—
40#14583459—21no—
41#14583446—21no—
42#14583446—21no—
43#14583411C2211yescharacteristic
44#14583410C2211yescharacteristic
45#14583408—21no—
46#14583408—21no—
47#14583406C2211yescharacteristic
48C2×#13063282C2211yescharacteristic
49#117×D43C2211yescharacteristic
50C2×C42×D43C2211yescharacteristic
51#14582914—24no—
52C2×#13063253C2211yescharacteristic
53C2×#13063253C2211yescharacteristic
54C2×#13063252C2211yescharacteristic
55C2×#13063252C2211yescharacteristic
56C2×#13063251C2211yescharacteristic
57C2×#13063251C2211yescharacteristic
58#104×D43—24no—
59#14582803—21no—
60#14582799—21no—
61#14582777—21no—
62#14582775—21no—
63C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
64C4×(C2×D43)⋊C4C2211yescharacteristic, complemented
65C4×C22⋊Dic43C2211yescharacteristic, complemented
66#14582660C2211yescharacteristic, complemented
67#14582660C2211yescharacteristic, complemented
68#14582659C2211yescharacteristic, complemented
69#14582659C2211yescharacteristic, complemented
70#14582658C2211yescharacteristic, complemented
71#14582658C2211yescharacteristic, complemented
72C22×M16×C43C2211yescharacteristic, complemented
73C43×#525C2211yescharacteristic
74C2×#104×C43C2211yescharacteristic
75C2×#104×C43C2211yescharacteristic
76C4×C22⋊C4×C43C2211yescharacteristic, complemented
77C43×#339C2211yescharacteristic, complemented
78C43×#339C2211yescharacteristic, complemented
79C2×#10621902C2×C411yescharacteristic
80C2×#10621898—22no—
81C2×#10621898—22no—
82C2×#10621898—21no—
83C2×#10621898—22no—
84C2×#10621898—22no—
85C2×#10621898C2×C411yescharacteristic
86C2×#10621898C2×C411yescharacteristic
87C2×#10621898C2×C411yescharacteristic
88C2×#10621898C2×C411yescharacteristic
89C2×#10621898D411yescharacteristic
90C2×#10621898D411yescharacteristic
91C2×#10621898D411yescharacteristic
92C2×#10621898D411yescharacteristic
93C2×#10621898C2311yescharacteristic
94C2×#10621900—21no—
95C2×#10621900C2×C411yescharacteristic
96#41×D43—22no—
97#41×D43—22no—
98#41×D43—22no—
99#41×D43—22no—
100C22×Dic86D411yescharacteristic
101C2×Q8×D43C2×C411yescharacteristic
102C22×D172D411yescharacteristic
103C22×C22⋊D43D411yescharacteristic
104C22×C22⋊D43D411yescharacteristic
105C2×D4×D43—21no—
106C2×D4×D43C2×C411yescharacteristic
107C22×C4×D43—21no—
108C22×C4×D43—21no—
109C22×C4×D43C2311yescharacteristic
110C22×C4×D43C2311yescharacteristic
111#13063333—28no—
112#13063333—28no—
113#13063331—28no—
114#13063331—28no—
115C2×#10621877—21no—
116C2×#10621877—22no—
117C2×#10621877—22no—
118C2×#10621877C2311yescharacteristic
119C2×#10621877C2311yescharacteristic
120C2×#10621872—21no—
121C2×#10621872—21no—
122C2×#10621872—21no—
123C2×#10621872—21no—
124M16×D43—22no—
125M16×D43—22no—
126M16×D43—22no—
127M16×D43—22no—
128M16×D43—22no—
129M16×D43—22no—
130M16×D43D414yescomplemented
131M16×D43D414yescomplemented
132C22×C43⋊C8—21no—
133C2×C8×D43—21no—
134C2×C8×D43—21no—
135C2×C8×D43—21no—
136C2×C8×D43—21no—
137#13063324—21no—
138#13063324—21no—
139#13063321—21no—
140#13063321—21no—
141#13063311—21no—
142#13063311—21no—
143#13063311—21no—
144#13063311—21no—
145#13063310—21no—
146#13063310—21no—
147#13063309—21no—
148#13063308—21no—
149#13063307—21no—
150#13063307—21no—
151#13063306—21no—
152#13063305C2×C411yescharacteristic, complemented
153#13063305C2×C411yescharacteristic, complemented
154#13063304C2×C411yescharacteristic, complemented
155#13063304C2×C411yescharacteristic, complemented
156#13063303—21no—
157#13063303—21no—
158#13063302—21no—
159#13063302—21no—
160#13063301C2×C411yescharacteristic, complemented
161#13063301C2×C411yescharacteristic, complemented
162#13063300—21no—
163#13063300—21no—
164#13063300C2×C411yescharacteristic, complemented
165#13063300C2×C411yescharacteristic, complemented
166#13063299C2×C411yescharacteristic, complemented
167#13063299C2×C411yescharacteristic, complemented
168#13063298—21no—
169#13063298—21no—
170#13063298—21no—
171#13063298—21no—
172#13063298—21no—
173#13063298—21no—
174#13063297—21no—
175#13063297—21no—
176#13063296—21no—
177#13063296—21no—
178#13063296C2×C411yescharacteristic, complemented
179#13063296C2×C411yescharacteristic, complemented
180#13063295—21no—
181#13063295—21no—
182#13063295—21no—
183#13063294—21no—
184#13063293—21no—
185#13063293—21no—
186#13063293—21no—
187C4×D172—21no—
188C4×D172—21no—
189C4×C22⋊D43—21no—
190C4×C22⋊D43—21no—
191C4×C22⋊D43—21no—
192C4×C22⋊D43—21no—
193#13063284C2311yescharacteristic
194#13063283C2×C411yescharacteristic
195#13063283C2×C411yescharacteristic
196#13063282—21no—
197#13063282—22no—
198#13063282—22no—
199#13063281—21no—
200C2×Dic43⋊C4—21no—
201C4⋊C4×D43C2×C411yescharacteristic
202C4⋊C4×D43C2×C411yescharacteristic
203C2×C22⋊Dic43—21no—
204C2×(C2×D43)⋊C4—21no—
205C2×(C2×D43)⋊C4—21no—
206C2×(C2×D43)⋊C4—21no—
207C22⋊C4×D43—21no—
208C2×C4×Dic43—21no—
209C2×C4×Dic43C2311yescharacteristic
210C2×C4×Dic43C2311yescharacteristic
211C42×D43—21no—
212C42×D43—22no—
213C42×D43—22no—
214#13063253—22no—
215#13063253—22no—
216#13063252—22no—
217#13063252—22no—
218#13063251—22no—
219#13063251—22no—
220C43⋊#95—21no—
221C43⋊#95—21no—
222C43⋊#95—21no—
223C2×#41×C43C2311yescharacteristic
224C23×C4×C43C2311yescharacteristic
225C2×M16×C43—21no—
226C2×M16×C43—22no—
227C2×M16×C43—22no—
228C2×M16×C43C2311yescharacteristic
229C2×M16×C43C2311yescharacteristic
230C22×C8×C43—21no—
231#123×C43—21no—
232C22⋊Q8×C43C2×C411yescharacteristic, complemented
233C22⋊Q8×C43C2×C411yescharacteristic, complemented
234#121×C43C2×C411yescharacteristic, complemented
235#121×C43C2×C411yescharacteristic, complemented
236#120×C43—21no—
237C4×D4×C43—21no—
238C4×D4×C43—21no—
239#117×C43C2311yescharacteristic
240C2×C22⋊C4×C43—21no—
241C2×C42×C43C2311yescharacteristic
242C2×C42×C43C2311yescharacteristic
243#104×C43—22no—
244#104×C43—22no—
245#95×C43—21no—
246C24×C43C2×D411yescharacteristic
247C23×D43—21no—
248C23×D43C2×D411yescharacteristic
249C23×D43C2×D411yescharacteristic
250#41×C43—21no—
251#41×C43—21no—
252#41×C43—21no—
253#41×C43—21no—
254C2×Q8×C43C22×C411yescharacteristic
255C2×D4×C43—21no—
256C2×D4×C43—21no—
257C2×D4×C43—21no—
258C2×D4×C43C22×C411yescharacteristic
259C22×C4×C43—21no—
260C22×C4×C43—21no—
261C22×C4×C43—21no—
262C22×C4×C43—21no—
263C22×C4×C43—21no—
264C22×C4×C43—21no—
265C22×C4×C43—21no—
266C22×C4×C43C22×C411yescharacteristic
267C22×C4×C43C22×C411yescharacteristic
268C22×C4×C43C2×D411yescharacteristic
269C22×C4×C43C2×D411yescharacteristic
270C22×C4×C43C2×D411yescharacteristic
271C22×C4×C43C2411yescharacteristic
272C2×C22⋊D43—21no—
273C2×C22⋊D43—22no—
274C2×C22⋊D43—22no—
275C2×C22⋊D43—21no—
276C2×C22⋊D43—21no—
277C2×C22⋊D43—21no—
278C2×C22⋊D43—21no—
279C2×C22⋊D43—21no—
280C2×C22⋊D43—21no—
281C2×C22⋊D43—22no—
282C2×C22⋊D43—22no—
283C2×C22⋊D43C22⋊C411yescharacteristic
284C2×C22⋊D43C22⋊C411yescharacteristic
285C2×C22⋊D43C22⋊C411yescharacteristic
286C2×C22⋊D43C22⋊C411yescharacteristic
287C2×C22⋊D43C22⋊C411yescharacteristic
288C2×C22⋊D43C22⋊C411yescharacteristic
289C2×C22⋊D43C22⋊C411yescharacteristic
290C2×C22⋊D43C22⋊C411yescharacteristic
291C22×Dic43—21no—
292C22×Dic43—21no—
293C22×Dic43—21no—
294C22×Dic43C2×D411yescharacteristic
295C22×Dic43C2×D411yescharacteristic
296#10621902—22no—
297#10621902—22no—
298Q8×D43—22no—
299Q8×D43—22no—
300#10621900—22no—
301#10621900—22no—
302#10621900—42no—
303#10621900—42no—
304D4×D43—22no—
305D4×D43—22no—
306D4×D43—42no—
307D4×D43—42no—
308#10621898—22no—
309#10621898—22no—
310#10621898—22no—
311#10621898—22no—
312#10621898—22no—
313#10621898—22no—
314#10621898—22no—
315#10621898—22no—
316#10621898—22no—
317#10621898—22no—
318#10621898—22no—
319#10621898—22no—
320#10621898—22no—
321#10621898—22no—
322#10621898—22no—
323#10621898—22no—
324#10621898—21no—
325#10621898—21no—
326#10621898—21no—
327#10621898—21no—
328#10621898—42no—
329#10621898—42no—
330C2×D172—21no—
331C2×D172—21no—
332C2×D172—21no—
333C2×D172—22no—
334C2×D172—22no—
335C2×D172C22⋊C411yescharacteristic
336C2×D172C22⋊C411yescharacteristic
337C2×D172C22⋊C411yescharacteristic
338C2×D172C22⋊C411yescharacteristic
339C2×D172C22×C411yescharacteristic
340C2×C4×D43—21no—
341C2×C4×D43—21no—
342C2×C4×D43—21no—
343C2×C4×D43—21no—
344C2×C4×D43—21no—
345C2×C4×D43—21no—
346C2×C4×D43—21no—
347C2×C4×D43—21no—
348C2×C4×D43—21no—
349C2×C4×D43—42no—
350C2×C4×D43—42no—
351C2×C4×D43—42no—
352C2×C4×D43—42no—
353C2×C4×D43—42no—
354C2×C4×D43C22×C411yescharacteristic
355C2×C4×D43C22×C411yescharacteristic
356C2×C4×D43C22×C411yescharacteristic
357C2×C4×D43C22×C411yescharacteristic
358C2×C4×D43C2×D411yescharacteristic
359C2×C4×D43C2×D411yescharacteristic
360C2×C4×D43C2×D411yescharacteristic
361C2×C4×D43C2×D411yescharacteristic
362C2×C4×D43C2×D412yes—
363C2×C4×D43C2×D412yes—
364C2×C4×D43#4112yes—
365C2×C4×D43#4112yes—
366C2×Dic86—22no—
367C2×Dic86—22no—
368C2×Dic86—21no—
369C2×Dic86C22⋊C411yescharacteristic
370C2×Dic86C22⋊C411yescharacteristic
371C2×Dic86C22⋊C411yescharacteristic
372C2×Dic86C22⋊C411yescharacteristic
373C2×Dic86C22×C411yescharacteristic
374M16×C43—24no—
375M16×C43—21no—
376M16×C43—21no—
377M16×C43C2×D412yes—
378M16×C43C2×D412yes—
379C2×C8×C43—24no—
380C2×C8×C43—21no—
381C2×C8×C43—21no—
382C4⋊C4×C43—21no—
383C4⋊C4×C43—21no—
384C4⋊C4×C43C22×C411yescharacteristic
385C4⋊C4×C43C22×C411yescharacteristic
386C22⋊C4×C43—21no—
387C22⋊C4×C43—21no—
388C22⋊C4×C43—21no—
389C22⋊C4×C43—21no—
390C22⋊C4×C43—21no—
391C22⋊C4×C43—42no—
392C42×C43—21no—
393C42×C43—21no—
394C42×C43—21no—
395C42×C43—21no—
396C42×C43—21no—
397C22⋊Dic43—21no—
398C22⋊Dic43—21no—
399C22⋊Dic43—21no—
400C22⋊Dic43—21no—
401C22⋊Dic43—21no—
402C22⋊Dic43—42no—
403(C2×D43)⋊C4—21no—
404(C2×D43)⋊C4—21no—
405(C2×D43)⋊C4—21no—
406(C2×D43)⋊C4—21no—
407(C2×D43)⋊C4—21no—
408(C2×D43)⋊C4—21no—
409(C2×D43)⋊C4—21no—
410(C2×D43)⋊C4—21no—
411(C2×D43)⋊C4—21no—
412(C2×D43)⋊C4—21no—
413(C2×D43)⋊C4—42no—
414(C2×D43)⋊C4—42no—
415(C2×D43)⋊C4—42no—
416C4⋊Dic43—21no—
417C4⋊Dic43—21no—
418C4⋊Dic43C22×C411yescharacteristic
419C4⋊Dic43C22×C411yescharacteristic
420Dic43⋊C4—21no—
421Dic43⋊C4—21no—
422Dic43⋊C4—21no—
423Dic43⋊C4—21no—
424Dic43⋊C4—21no—
425Dic43⋊C4—21no—
426Dic43⋊C4—42no—
427C4×Dic43—21no—
428C4×Dic43—21no—
429C4×Dic43—21no—
430C4×Dic43—21no—
431C4×Dic43—21no—
432C4×Dic43—21no—
433C4×Dic43—21no—
434C4×Dic43—42no—
435#10621877—24no—
436#10621877—21no—
437#10621877—21no—
438#10621877C2×D412yes—
439#10621877C2×D412yes—
440C2×C43⋊C8—24no—
441C2×C43⋊C8—21no—
442C2×C43⋊C8—21no—
443#10621872—24no—
444#10621872—24no—
445#10621872—24no—
446#10621872—24no—
447C8×D43—24no—
448C8×D43—24no—
449C8×D43—24no—
450C8×D43—24no—
451C23×C43—21no—
452C23×C43—21no—
453C23×C43—21no—
454C23×C43—41no—
455C23×C43—41no—
456C23×C43C2×C22⋊C411yescharacteristic
457C23×C43C2×C22⋊C411yescharacteristic
458C23×C43C22×D411yescharacteristic
459C22×D43—21no—
460C22×D43—21no—
461C22×D43—21no—
462C22×D43—41no—
463C22×D43—41no—
464C22×D43—41no—
465C22×D43—41no—
466C22×D43—42no—
467C22×D43—81no—
468C22×D43—81no—
469C22×D43C2×C22⋊C411yescharacteristic
470C22×D43C2×C22⋊C411yescharacteristic
471C22×D43C2×C22⋊C411yescharacteristic
472C22×D43C2×C22⋊C411yescharacteristic
473C22×D43#12112yes—
474C22×D43#12112yes—
475Q8×C43—21no—
476Q8×C43—21no—
477D4×C43—21no—
478D4×C43—21no—
479D4×C43—41no—
480D4×C43—41no—
481D4×C43—81no—
482D4×C43—81no—
483C2×C4×C43—21no—
484C2×C4×C43—21no—
485C2×C4×C43—21no—
486C2×C4×C43—21no—
487C2×C4×C43—21no—
488C2×C4×C43—21no—
489C2×C4×C43—21no—
490C2×C4×C43—21no—
491C2×C4×C43—21no—
492C2×C4×C43—21no—
493C2×C4×C43—22no—
494C2×C4×C43—21no—
495C2×C4×C43—21no—
496C2×C4×C43—21no—
497C2×C4×C43—41no—
498C2×C4×C43—41no—
499C2×C4×C43—41no—
500C2×C4×C43—41no—
501C2×C4×C43—41no—
502C2×C4×C43—41no—
503C2×C4×C43—41no—
504C2×C4×C43C2×C22⋊C411yescharacteristic
505C2×C4×C43C2×C22⋊C411yescharacteristic
506C2×C4×C43C23×C411yescharacteristic
507C2×C4×C43C22×D411yescharacteristic
508C2×C4×C43C22×D411yescharacteristic
509C2×C4×C43C22×D411yescharacteristic
510C2×C4×C43C2×#4111yescharacteristic
511C2×C4×C43C2×#4111yescharacteristic
512C22⋊D43—22no—
513C22⋊D43—22no—
514C22⋊D43—22no—
515C22⋊D43—22no—
516C22⋊D43—22no—
517C22⋊D43—22no—
518C22⋊D43—22no—
519C22⋊D43—22no—
520C22⋊D43—41no—
521C22⋊D43—41no—
522C22⋊D43—42no—
523C22⋊D43—42no—
524C22⋊D43—81no—
525C22⋊D43—81no—
526C22⋊D43—81no—
527C22⋊D43—81no—
528C2×Dic43—21no—
529C2×Dic43—21no—
530C2×Dic43—22no—
531C2×Dic43—21no—
532C2×Dic43—21no—
533C2×Dic43—21no—
534C2×Dic43—41no—
535C2×Dic43—41no—
536C2×Dic43—42no—
537C2×Dic43—41no—
538C2×Dic43—41no—
539C2×Dic43—41no—
540C2×Dic43C2×C22⋊C411yescharacteristic
541C2×Dic43C2×C22⋊C411yescharacteristic
542C2×Dic43C2×C22⋊C411yescharacteristic
543C2×Dic43C2×C22⋊C411yescharacteristic
544C2×Dic43#12112yes—
545C2×Dic43#12112yes—
546D172—22no—
547D172—22no—
548D172—22no—
549D172—22no—
550D172—21no—
551D172—21no—
552D172—42no—
553D172—81no—
554D172—81no—
555C4×D43—21no—
556C4×D43—21no—
557C4×D43—21no—
558C4×D43—21no—
559C4×D43—21no—
560C4×D43—21no—
561C4×D43—21no—
562C4×D43—21no—
563C4×D43—48no—
564C4×D43—42no—
565C4×D43—41no—
566C4×D43—41no—
567C4×D43—42no—
568C4×D43—81no—
569C4×D43—81no—
570C4×D43C4×D412yes—
571C4×D43C4×D412yes—
572C4×D43C4×D412yes—
573C4×D43C4×D412yes—
574C4×D43#12012yes—
575C4×D43#12012yes—
576C4×D43#12312yes—
577C4×D43#12312yes—
578Dic86—22no—
579Dic86—22no—
580Dic86—22no—
581Dic86—22no—
582Dic86—21no—
583Dic86—21no—
584Dic86—42no—
585C8×C43—22no—
586C8×C43—22no—
587C43⋊C8—22no—
588C43⋊C8—22no—
589#20903—431nomaximal, Sylow
590C22×C43—21no—
591C22×C43—21no—
592C22×C43—21no—
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—41no—
601C22×C43—81no—
602C22×C43—81no—
603C22×C43C22×C22⋊C411yescharacteristic
604C22×C43C2×#12111yescharacteristic
605C22×C43C2×#12111yescharacteristic
606C2×D43—21no—
607C2×D43—21no—
608C2×D43—21no—
609C2×D43—21no—
610C2×D43—21no—
611C2×D43—21no—
612C2×D43—21no—
613C2×D43—21no—
614C2×D43—21no—
615C2×D43—21no—
616C2×D43—42no—
617C2×D43—42no—
618C2×D43—41no—
619C2×D43—41no—
620C2×D43—41no—
621C2×D43—84no—
622C2×D43—81no—
623C2×D43—81no—
624C2×D43#38612yes—
625C2×D43#38612yes—
626C4×C43—21no—
627C4×C43—21no—
628C4×C43—42no—
629C4×C43—41no—
630C4×C43—41no—
631C4×C43—41no—
632C4×C43—81no—
633C4×C43C2×C4×D411yescharacteristic
634C4×C43C2×C4×D411yescharacteristic
635C4×C43C2×#12011yescharacteristic
636C4×C43C2×#12311yescharacteristic
637Dic43—21no—
638Dic43—21no—
639Dic43—42no—
640Dic43—41no—
641Dic43—41no—
642Dic43—41no—
643Dic43—81no—
644Dic43#38612yes—
645Dic43#38612yes—
646C2×#568—431no—
647#3449—431no—
648C2×#421—431no—
649C22×#104—431no—
650#2297—431no—
651#1871—431no—
652#1871—431no—
653#1871—431no—
654#1871—431no—
655#1871—431no—
656#1871—431no—
657#1871—431no—
658#1871D4311yescharacteristic, complemented
659#1733—431no—
660C2×#339—431no—
661C2×C43—21no—
662C2×C43—21no—
663C2×C43—41no—
664C2×C43—41no—
665C2×C43—81no—
666C2×C43C2×#38611yescharacteristic
667C2×C43#290111yescharacteristic
668C2×C43#290111yescharacteristic
669D43—22no—
670D43—22no—
671D43—41no—
672D43—41no—
673D43—81no—
674C22×#41—431no—
675C22×#41—431no—
676#568—864no—
677#568—864no—
678C2×#131—861no—
679C2×#131—861no—
680C2×#131—861no—
681C2×#131—861no—
682C22×M16—431no—
683C22×M16—431no—
684C22×M16—431no—
685C22×M16—431no—
686C22×M16—431no—
687C22×M16C2×D4311yescharacteristic, complemented
688#537—431no—
689#537—431no—
690#537—431no—
691#537—431no—
692#536—431no—
693#536—431no—
694#536—861no—
695#535—431no—
696#535—431no—
697#535—861no—
698#534—861no—
699#534—861no—
700#532—861no—
701#532—861no—
702#525—431no—
703#525—431no—
704#525—431no—
705#525—861no—
706#525—861no—
707#525C2×D4311yescharacteristic
708C2×#117—431no—
709C2×#117—431no—
710C22×C42—431no—
711#421—864no—
712C2×#104—431no—
713C2×#104—431no—
714C2×#104—431no—
715C2×#104—431no—
716C2×#104—431no—
717C2×#104—431no—
718C2×#104—864no—
719C2×#104C2×D4311yescharacteristic
720C2×#104C2×D4311yescharacteristic
721#391—861no—
722#390—861no—
723#386—861no—
724#386—861no—
725C4×C22⋊C4—431no—
726C4×C22⋊C4—431no—
727C4×C22⋊C4—431no—
728C4×C22⋊C4C2×D4311yescharacteristic, complemented
729#339—431no—
730#339—431no—
731#339—431no—
732#339—431no—
733#339—431no—
734#339—431no—
735#339C2×D4311yescharacteristic, complemented
736#339C2×D4311yescharacteristic, complemented
737C43#2090311yescharacteristic, complemented, Sylow
738C2×#41—431no—
739C2×#41—431no—
740C2×#41—431no—
741C2×#41—431no—
742C2×#41—431no—
743C2×#41—431no—
744C2×#41—431no—
745C2×#41—431no—
746C2×#41—431no—
747C2×#41—431no—
748C2×#41—431no—
749C2×#41—862no—
750C2×#41—862no—
751C2×#41—862no—
752C2×#41—862no—
753C2×#41—861no—
754C2×#41—861no—
755C2×#41—862no—
756C2×#41—862no—
757C2×#41—862no—
758C2×#41—862no—
759C2×#41C22×D4311yescharacteristic
760C22×Q8—431no—
761C22×Q8—431no—
762C22×D4—431no—
763C22×D4—431no—
764C22×D4—431no—
765C22×D4—431no—
766C22×D4—861no—
767C23×C4—431no—
768C23×C4—431no—
769C23×C4—861no—
770C23×C4—861no—
771C23×C4C22×D4311yescharacteristic
772#131—868no—
773#131—868no—
774#131—868no—
775#131—868no—
776C2×M16—21no—
777C2×M16—22no—
778C2×M16—22no—
779C2×M16—431no—
780C2×M16—431no—
781C2×M16—434no—
782C2×M16—434no—
783C2×M16—861no—
784C2×M16—861no—
785C2×M16—861no—
786C2×M16—861no—
787C2×M16—862no—
788C2×M16—862no—
789C2×M16—862no—
790C2×M16—862no—
791C2×M16—862no—
792C2×M16—862no—
793C2×M16—861no—
794C2×M16—862no—
795C2×M16—862no—
796C2×M16C22×D4311yescharacteristic
797C2×M16C22×D4311yescharacteristic
798C22×C8—21no—
799C22×C8—861no—
800C22×C8—861no—
801C22×C8—861no—
802C22×C8—861no—
803C22×C8—861no—
804C4⋊Q8—861no—
805C4⋊Q8—861no—
806#127—861no—
807#127—861no—
808#124—861no—
809#124—861no—
810#124—861no—
811#124—861no—
812#123—21no—
813#123—861no—
814#123—861no—
815#123—861no—
816#123—861no—
817#123—861no—
818#123—861no—
819#123—861no—
820C22⋊Q8—431no—
821C22⋊Q8—431no—
822C22⋊Q8—431no—
823C22⋊Q8—431no—
824C22⋊Q8—431no—
825C22⋊Q8—431no—
826C22⋊Q8—861no—
827C22⋊Q8—861no—
828C22⋊Q8—861no—
829C22⋊Q8—861no—
830C22⋊Q8C4×D4311yescharacteristic, complemented
831C22⋊Q8C4×D4311yescharacteristic, complemented
832#121—431no—
833#121—431no—
834#121—431no—
835#121—431no—
836#121—431no—
837#121—431no—
838#121—861no—
839#121—861no—
840#121—861no—
841#121—861no—
842#121—861no—
843#121—861no—
844#121—861no—
845#121—861no—
846#121—861no—
847#121—861no—
848#121—861no—
849#121—861no—
850#121C4×D4311yescharacteristic, complemented
851#121C4×D4311yescharacteristic, complemented
852#120—21no—
853#120—861no—
854#120—861no—
855#120—861no—
856#120—861no—
857#120—861no—
858#120—861no—
859#120—861no—
860C4×D4—21no—
861C4×D4—21no—
862C4×D4—861no—
863C4×D4—861no—
864C4×D4—861no—
865C4×D4—861no—
866C4×D4—861no—
867C4×D4—861no—
868#117—431no—
869#117—431no—
870#117—431no—
871#117—861no—
872#117—862no—
873#117—862no—
874#117—861no—
875#117C22×D4311yescharacteristic
876C2×C4⋊C4—431no—
877C2×C4⋊C4—431no—
878C2×C4⋊C4—861no—
879C2×C22⋊C4—21no—
880C2×C22⋊C4—861no—
881C2×C22⋊C4—861no—
882C2×C22⋊C4—861no—
883C2×C22⋊C4—861no—
884C2×C22⋊C4—861no—
885C2×C42—431no—
886C2×C42—431no—
887C2×C42—861no—
888C2×C42—862no—
889C2×C42—862no—
890C2×C42—861no—
891C2×C42C22×D4311yescharacteristic
892C2×C42C22×D4311yescharacteristic
893#104—22no—
894#104—22no—
895#104—862no—
896#104—862no—
897#104—862no—
898#104—862no—
899#104—862no—
900#104—862no—
901#95—21no—
902#95—861no—
903#95—861no—
904#95—861no—
905C24—431no—
906C24—431no—
907C24—861no—
908C24D4×D4311yescharacteristic
909#41—21no—
910#41—21no—
911#41—21no—
912#41—21no—
913#41—862no—
914#41—862no—
915#41—862no—
916#41—862no—
917#41—862no—
918#41—862no—
919#41—862no—
920#41—862no—
921#41—862no—
922#41—862no—
923#41—862no—
924#41—862no—
925#41—862no—
926#41—862no—
927#41—862no—
928#41—862no—
929#41—862no—
930#41—862no—
931#41—862no—
932#41—862no—
933#41—861no—
934#41—861no—
935#41—861no—
936#41—861no—
937#41—1722no—
938#41—1722no—
939#41—1722no—
940#41—1722no—
941C2×Q8—431no—
942C2×Q8—431no—
943C2×Q8—431no—
944C2×Q8—431no—
945C2×Q8—431no—
946C2×Q8—862no—
947C2×Q8—862no—
948C2×Q8—861no—
949C2×Q8—862no—
950C2×Q8—862no—
951C2×Q8C2×C4×D4311yescharacteristic
952C2×D4—21no—
953C2×D4—21no—
954C2×D4—21no—
955C2×D4—431no—
956C2×D4—431no—
957C2×D4—431no—
958C2×D4—431no—
959C2×D4—431no—
960C2×D4—431no—
961C2×D4—431no—
962C2×D4—431no—
963C2×D4—431no—
964C2×D4—431no—
965C2×D4—431no—
966C2×D4—431no—
967C2×D4—431no—
968C2×D4—862no—
969C2×D4—862no—
970C2×D4—861no—
971C2×D4—861no—
972C2×D4—861no—
973C2×D4—862no—
974C2×D4—862no—
975C2×D4—862no—
976C2×D4—862no—
977C2×D4—861no—
978C2×D4—862no—
979C2×D4—862no—
980C2×D4—861no—
981C2×D4—861no—
982C2×D4—861no—
983C2×D4—861no—
984C2×D4—861no—
985C2×D4—861no—
986C2×D4—1722no—
987C2×D4—1722no—
988C2×D4C2×C4×D4311yescharacteristic
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—431no—
997C22×C4—431no—
998C22×C4—431no—
999C22×C4—432no—
1000C22×C4—432no—
1001C22×C4—431no—
1002C22×C4—431no—
1003C22×C4—432no—
1004C22×C4—432no—
1005C22×C4—431no—
1006C22×C4—431no—
1007C22×C4—431no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—861no—
1011C22×C4—861no—
1012C22×C4—861no—
1013C22×C4—861no—
1014C22×C4—861no—
1015C22×C4—861no—
1016C22×C4—861no—
1017C22×C4—861no—
1018C22×C4—861no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4—861no—
1022C22×C4—1722no—
1023C22×C4—1722no—
1024C22×C4—1722no—
1025C22×C4—1722no—
1026C22×C4—1722no—
1027C22×C4C2×C4×D4311yescharacteristic
1028C22×C4C2×C4×D4311yescharacteristic
1029C22×C4D4×D4311yescharacteristic
1030C22×C4D4×D4311yescharacteristic
1031C22×C4D4×D4311yescharacteristic
1032C22×C4C23×D4311yescharacteristic
1033M16—24no—
1034M16—21no—
1035M16—21no—
1036M16—432no—
1037M16—432no—
1038M16—864no—
1039M16—864no—
1040M16—864no—
1041M16—864no—
1042M16—864no—
1043M16—861no—
1044M16—861no—
1045M16D4×D4312yes—
1046M16D4×D4312yes—
1047C2×C8—24no—
1048C2×C8—21no—
1049C2×C8—21no—
1050C2×C8—864no—
1051C2×C8—864no—
1052C2×C8—864no—
1053C2×C8—864no—
1054C2×C8—864no—
1055C2×C8—861no—
1056C2×C8—861no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—431no—
1060C4⋊C4—431no—
1061C4⋊C4—861no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4—861no—
1065C4⋊C4—861no—
1066C4⋊C4—861no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—1722no—
1070C4⋊C4C2×C4×D4311yescharacteristic
1071C4⋊C4C2×C4×D4311yescharacteristic
1072C22⋊C4—21no—
1073C22⋊C4—21no—
1074C22⋊C4—21no—
1075C22⋊C4—21no—
1076C22⋊C4—21no—
1077C22⋊C4—42no—
1078C22⋊C4—861no—
1079C22⋊C4—861no—
1080C22⋊C4—861no—
1081C22⋊C4—861no—
1082C22⋊C4—861no—
1083C22⋊C4—861no—
1084C22⋊C4—861no—
1085C22⋊C4—861no—
1086C22⋊C4—861no—
1087C22⋊C4—861no—
1088C22⋊C4—861no—
1089C22⋊C4—861no—
1090C22⋊C4—861no—
1091C22⋊C4—861no—
1092C22⋊C4—861no—
1093C22⋊C4—1722no—
1094C22⋊C4—1722no—
1095C22⋊C4—1722no—
1096C22⋊C4—1722no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—861no—
1103C42—861no—
1104C42—861no—
1105C42—861no—
1106C42—861no—
1107C42—861no—
1108C42—861no—
1109C42—1722no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—41no—
1114C23—41no—
1115C23—431no—
1116C23—431no—
1117C23—432no—
1118C23—432no—
1119C23—431no—
1120C23—431no—
1121C23—861no—
1122C23—861no—
1123C23—861no—
1124C23—3441no—
1125C23—3441no—
1126C23—1721no—
1127C23—1721no—
1128C23—1721no—
1129C23—1721no—
1130C23—1722no—
1131C23C22⋊C4×D4311yescharacteristic
1132C23C22⋊C4×D4311yescharacteristic
1133C23C2×D4×D4311yescharacteristic
1134Q8—21no—
1135Q8—21no—
1136Q8—862no—
1137Q8—862no—
1138Q8—862no—
1139Q8—862no—
1140Q8—861no—
1141Q8—861no—
1142Q8—1722no—
1143D4—21no—
1144D4—21no—
1145D4—41no—
1146D4—41no—
1147D4—81no—
1148D4—81no—
1149D4—862no—
1150D4—862no—
1151D4—862no—
1152D4—862no—
1153D4—862no—
1154D4—862no—
1155D4—862no—
1156D4—862no—
1157D4—862no—
1158D4—862no—
1159D4—862no—
1160D4—862no—
1161D4—861no—
1162D4—861no—
1163D4—3441no—
1164D4—3441no—
1165D4—3441no—
1166D4—3441no—
1167D4—3441no—
1168D4—3441no—
1169D4—1722no—
1170D4—1722no—
1171D4—1722no—
1172D4—1721no—
1173D4—1721no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—22no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—431no—
1196C2×C4—431no—
1197C2×C4—432no—
1198C2×C4—432no—
1199C2×C4—432no—
1200C2×C4—432no—
1201C2×C4—432no—
1202C2×C4—432no—
1203C2×C4—432no—
1204C2×C4—432no—
1205C2×C4—432no—
1206C2×C4—432no—
1207C2×C4—431no—
1208C2×C4—431no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—861no—
1216C2×C4—861no—
1217C2×C4—861no—
1218C2×C4—861no—
1219C2×C4—862no—
1220C2×C4—861no—
1221C2×C4—861no—
1222C2×C4—861no—
1223C2×C4—3441no—
1224C2×C4—3441no—
1225C2×C4—1722no—
1226C2×C4—1722no—
1227C2×C4—1728no—
1228C2×C4—1722no—
1229C2×C4—1721no—
1230C2×C4—1721no—
1231C2×C4—1721no—
1232C2×C4—1721no—
1233C2×C4—1721no—
1234C2×C4—1721no—
1235C2×C4—1721no—
1236C2×C4C22⋊C4×D4311yescharacteristic
1237C2×C4C22⋊C4×D4311yescharacteristic
1238C2×C4C22×C4×D4311yescharacteristic
1239C2×C4C2×D4×D4311yescharacteristic
1240C2×C4C2×D4×D4311yescharacteristic
1241C2×C4C2×D4×D4311yescharacteristic
1242C2×C4#41×D4311yescharacteristic
1243C2×C4#41×D4311yescharacteristic
1244C8—22no—
1245C8—22no—
1246C8—862no—
1247C8—862no—
1248C22—21no—
1249C22—21no—
1250C22—21no—
1251C22—21no—
1252C22—21no—
1253C22—21no—
1254C22—21no—
1255C22—21no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—81no—
1260C22—81no—
1261C22—432no—
1262C22—432no—
1263C22—861no—
1264C22—861no—
1265C22—861no—
1266C22—861no—
1267C22—861no—
1268C22—861no—
1269C22—861no—
1270C22—861no—
1271C22—861no—
1272C22—861no—
1273C22—3441no—
1274C22—3441no—
1275C22—3444no—
1276C22—1722no—
1277C22—1722no—
1278C22—1721no—
1279C22—1721no—
1280C22—1721no—
1281C22C2×C22⋊C4×D4311yescharacteristic
1282C22#121×D4311yescharacteristic
1283C22#121×D4311yescharacteristic
1284C4—21no—
1285C4—21no—
1286C4—42no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—81no—
1291C4—432no—
1292C4—432no—
1293C4—861no—
1294C4—861no—
1295C4—3441no—
1296C4—1722no—
1297C4—1721no—
1298C4—1721no—
1299C4—1721no—
1300C4C4×D4×D4311yescharacteristic
1301C4C4×D4×D4311yescharacteristic
1302C4#120×D4311yescharacteristic
1303C4#123×D4311yescharacteristic
1304C2—21no—
1305C2—21no—
1306C2—41no—
1307C2—41no—
1308C2—81no—
1309C2—862no—
1310C2—862no—
1311C2—3441no—
1312C2—1721no—
1313C2—1721no—
1314C2#386×D4311yescharacteristic
1315C2#1914313911yescharacteristic
1316C2#1914314111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1871C2
socleC22×C43C22×C22⋊C4
prime radical#19147925C2
cosocleC22×C4×C43C24
hypercenter#1871D43
hypocenterC43#20903
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1871

Complements

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

NH ≅ G/Ntype
1. C2×#14583665C2semidirect
3. C2×#14582914C2semidirect
4. C2×#104×D43C2semidirect
5. #19137081C2semidirect
6. #19134898C2semidirect
7. #19134897C2semidirect
8. #19134896C2semidirect
9. #19134896C2semidirect
10. #19134895C2semidirect
11. #19134894C2semidirect
12. #19134894C2semidirect
13. #19134303C2semidirect
14. #339×D43C2semidirect
15. C43×#1871C2semidirect
24. C22×#10621877C22semidirect
27. C2×M16×D43C22semidirect
28. C2×M16×D43C22semidirect
29. #14583479C4semidirect
30. #14583479C4semidirect
31. #14583478C4semidirect
32. #14583478C4semidirect
33. #14583472C4semidirect
34. #14583472C4semidirect
36. #14583465C4semidirect
37. #14583465C4semidirect
63. C4×(C2×D43)⋊C4C22semidirect
64. C4×(C2×D43)⋊C4C22semidirect
65. C4×C22⋊Dic43C22semidirect
66. #14582660C22semidirect
67. #14582660C22semidirect
68. #14582659C22semidirect
69. #14582659C22semidirect
70. #14582658C22semidirect
71. #14582658C22semidirect
72. C22×M16×C43C22semidirect
76. C4×C22⋊C4×C43C22semidirect
77. C43×#339C22semidirect
78. C43×#339C22semidirect
130. M16×D43D4semidirect
131. M16×D43D4semidirect
152. #13063305C2×C4semidirect
153. #13063305C2×C4semidirect
154. #13063304C2×C4semidirect
155. #13063304C2×C4semidirect
160. #13063301C2×C4semidirect
161. #13063301C2×C4semidirect
164. #13063300C2×C4semidirect
165. #13063300C2×C4semidirect
166. #13063299C2×C4semidirect
167. #13063299C2×C4semidirect
178. #13063296C2×C4semidirect
179. #13063296C2×C4semidirect
232. C22⋊Q8×C43C2×C4semidirect
233. C22⋊Q8×C43C2×C4semidirect
234. #121×C43C2×C4semidirect
235. #121×C43C2×C4semidirect
658. #1871D43semidirect
687. C22×M16C2×D43semidirect
728. C4×C22⋊C4C2×D43semidirect
735. #339C2×D43semidirect
736. #339C2×D43semidirect
737. C43#20903semidirect
830. C22⋊Q8C4×D43semidirect
831. C22⋊Q8C4×D43semidirect
850. #121C4×D43semidirect
851. #121C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145836652
#191479252
C2×#145829142
C2×#104×D432
#191370812
#191348982
#191348972
#191348962
#191348952
#191348942
#191343032
#339×D432
C43×#18712
#2090343