Finite Group Databasebeta

← #25960825

Subgroups — #25960825

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583709C211yesmaximal, characteristic
2#19147806C211yesmaximal, characteristic, complemented
3#19147799C211yesmaximal, characteristic, complemented
4#19143477C212yesmaximal, complemented
5#19143476C211yesmaximal, characteristic, complemented
6#19143452C211yesmaximal, characteristic, complemented
7#19143451C212yesmaximal, complemented
8#19143440C211yesmaximal, characteristic, complemented
9#19143431C212yesmaximal, complemented
10#19143420C212yesmaximal, complemented
11#19143417C212yesmaximal, complemented
12#19143413C211yesmaximal, characteristic, complemented
13#19143406C212yesmaximal, complemented
14AGL(1,ℤ/8)×Dic43C211yesmaximal, characteristic, complemented
15#19143363C211yesmaximal, characteristic, complemented
16C4×#13063344C212yesmaximal, complemented
17C2×#14582990C211yesmaximal, characteristic, complemented
18C4×SD16×D43C212yesmaximal, complemented
19#19143189C211yesmaximal, characteristic, complemented
20#19143124C211yesmaximal, characteristic, complemented
21#19143116C211yesmaximal, characteristic, complemented
22#19143017C211yesmaximal, characteristic, complemented
23C43×#2946C211yesmaximal, characteristic, complemented
24C2×#13063372C2211yescharacteristic
25C2×#13063370C2211yescharacteristic
26#14583709C4116yescomplemented
27C2×#13063358C2211yescharacteristic
28C2×#13063354C2212yes—
29C2×#13063349C2212yes—
30C2×#13063345C2211yescharacteristic
31C2×#13063344C2212yes—
32C22×#10621883C2211yescharacteristic
33C2×SD16×D43C2212yes—
34C2×#13063333C2211yescharacteristic
35C2×#13063331C2211yescharacteristic
36#14583380—21no—
37#14583380C2211yescharacteristic
38#14583379C2211yescharacteristic
39#14583379C2211yescharacteristic
40#14583378—21no—
41#14583378—22no—
42#14583378C2212yes—
43#14583378C2212yescomplemented
44#14583376—21no—
45#14583376C2211yescharacteristic, complemented
46#14583375C2212yescomplemented
47#14583372—22no—
48#14583371—21no—
49#14583371C2212yes—
50#41×Dic43C2211yescharacteristic, complemented
51#14583367—21no—
52#14583367C2211yescharacteristic
53#14583367C2211yescharacteristic
54C4×#10621900—21no—
55C4×#10621900—22no—
56C4×#10621900C2212yes—
57C4×#10621900C2212yescomplemented
58C2×#13063290—21no—
59C2×#13063290C2211yescharacteristic, complemented
60C4×Q8×D43C2212yescomplemented
61C2×D4×Dic43C2211yescharacteristic
62C2×(C22⋊D43)⋊C4—22no—
63C4×D4×D43—21no—
64C4×D4×D43C2212yes—
65#14583011C2212yescomplemented
66#14583009C2212yescomplemented
67#14583007C2212yescomplemented
68#14583005C2212yescomplemented
69#14583004C2212yescomplemented
70#14583001C2212yescomplemented
71#14583000C2212yescomplemented
72#14582999C2212yescomplemented
73#14582999C2212yescomplemented
74#14582998C2212yescomplemented
75C4×Dic172C2212yescomplemented
76#14582993C2212yescomplemented
77#14582991C2211yescharacteristic, complemented
78#14582991C2211yescharacteristic, complemented
79#14582990C2212yescomplemented
80#14582990C2212yescomplemented
81#14582990C2211yescharacteristic, complemented
82#14582990C2212yescomplemented
83#14582990C2212yescomplemented
84#14582990C2211yescharacteristic, complemented
85C4×#10621873C2212yescomplemented
86SD16×Dic43C2212yescomplemented
87C4×#10621884C2212yescomplemented
88#14582986C2212yescomplemented
89C4×#10621883C2212yescomplemented
90C4×#10621883C2212yescomplemented
91C4×#10621883C2212yescomplemented
92#14582984C2211yescharacteristic, complemented
93#14582984C2211yescharacteristic, complemented
94D8×Dic43C2212yescomplemented
95#14582979C2211yescharacteristic, complemented
96#14582979C2211yescharacteristic, complemented
97#14582941C2211yescharacteristic, complemented
98#14582940C2212yescomplemented
99#14582938C2212yescomplemented
100#14582936C2212yescomplemented
101#14582935C2211yescharacteristic, complemented
102C2×#13063256C2211yescharacteristic, complemented
103#106×D43C2212yescomplemented
104#14582907C2211yescharacteristic, complemented
105#14582906C2212yescomplemented
106#14582904C2211yescharacteristic
107#14582902C2212yes—
108#14582900C2211yescharacteristic, complemented
109#14582898C2211yescharacteristic
110#14582897C2212yes—
111#14582897C2212yescomplemented
112#14582896C2211yescharacteristic
113#14582892C2212yes—
114#14582892C2212yescomplemented
115C2×#13063250C2211yescharacteristic, complemented
116#103×D43C2212yescomplemented
117#102×D43C2212yes—
118#14582856C2212yescomplemented
119#14582855C2211yescharacteristic, complemented
120#14582853C2212yescomplemented
121#14582851C2212yescomplemented
122M16×Dic43C2211yescharacteristic, complemented
123C2×C8×Dic43C2211yescharacteristic, complemented
124C4×C8×D43C2212yescomplemented
125C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
126C43×#520C2211yescharacteristic, complemented
127C43×#518C2211yescharacteristic
128C43×#442C2212yescomplemented
129C43×#440C2212yescomplemented
130C4×SD16×C43C2212yescomplemented
131C4×D8×C43C2212yescomplemented
132C43×#428C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C2×#102×C43C2211yescharacteristic
135C43×#405C2211yescharacteristic, complemented
136#13063372—24no—
137#13063372C2×C418yescomplemented
138#13063370—24no—
139#13063370C2×C418yescomplemented
140C2×#10621898—21no—
141C2×#10621898C2311yescharacteristic
142C2×#10621898C2311yescharacteristic
143C2×#10621900—22no—
144C2×#10621900—21no—
145C2×#10621900C2312yes—
146C2×#10621900C2312yes—
147C22×Dic86—21no—
148C22×Dic86C2311yescharacteristic
149C2×Q8×D43C2312yes—
150C22×C22⋊D43—22no—
151C2×D4×D43—21no—
152C2×D4×D43C2312yes—
153C23×Dic43—21no—
154C22×C4×D43—22no—
155#13063358C2×C418yescomplemented
156#13063354C2×C4116yescomplemented
157#13063349C2×C4116yescomplemented
158#13063345C2×C418yescomplemented
159#13063344C2×C4116yescomplemented
160C2×Dic172C2312yes—
161C2×#10621885C2311yescharacteristic
162C2×#10621873C2312yes—
163C2×#10621883C2×C418yescomplemented
164C2×#10621883C2312yes—
165C2×#10621883C2312yes—
166C2×#10621883C2311yescharacteristic
167C2×#10621884C2311yescharacteristic
168SD16×D43C2×C4116yescomplemented
169C2×#10621882C2311yescharacteristic
170#13063333C2×C418yescomplemented
171#13063331—24no—
172C2×#10621877C2311yescharacteristic
173C2×#10621872C2312yes—
174C2×#10621872C2312yes—
175C22×C43⋊C8C2311yescharacteristic
176C2×C8×D43C2312yes—
177C2×C8×D43C2312yes—
178Q8×Dic43C2311yescharacteristic
179Q8×Dic43C2311yescharacteristic
180C4×Dic86—21no—
181C4×Dic86—22no—
182C4×Dic86—22no—
183C4×Dic86C2312yes—
184C4×Dic86C2312yes—
185C4×Dic86C2312yes—
186#13063290—21no—
187#13063290—21no—
188#13063290—21no—
189#13063290—22no—
190#13063290—22no—
191#13063290—21no—
192#13063290—21no—
193#13063290D411yescharacteristic
194#13063290D411yescharacteristic
195#13063290C2312yes—
196#13063290C2312yes—
197#13063290C2311yescharacteristic
198#13063290C2311yescharacteristic
199C4×D172—21no—
200C4×D172C2312yes—
201D4×Dic43—21no—
202D4×Dic43—21no—
203D4×Dic43—21no—
204D4×Dic43—21no—
205D4×Dic43C2312yes—
206D4×Dic43C2312yes—
207D4×Dic43C2311yescharacteristic
208D4×Dic43C2311yescharacteristic
209#13063287—21no—
210#13063287D411yescharacteristic
211#13063287D411yescharacteristic
212#13063287C2311yescharacteristic
213#13063287C2311yescharacteristic
214C4×C22⋊D43—22no—
215C4×C22⋊D43—22no—
216C4×C22⋊D43—22no—
217C4×C22⋊D43—22no—
218C4×C22⋊D43—22no—
219C4×C22⋊D43—22no—
220C4×C22⋊D43—22no—
221(C22⋊D43)⋊C4—22no—
222(C22⋊D43)⋊C4—21no—
223(C22⋊D43)⋊C4—21no—
224(C22⋊D43)⋊C4—22no—
225(C22⋊D43)⋊C4—22no—
226(C22⋊D43)⋊C4—22no—
227(C22⋊D43)⋊C4—22no—
228(C22⋊D43)⋊C4—22no—
229(C22⋊D43)⋊C4—22no—
230(C22⋊D43)⋊C4—22no—
231(C22⋊D43)⋊C4D412yes—
232(C22⋊D43)⋊C4D412yes—
233#13063284—21no—
234#13063284C2311yescharacteristic
235#13063283—21no—
236#13063283—22no—
237#13063283C2312yes—
238#13063283C2312yes—
239#13063282—22no—
240#13063282—21no—
241#13063282C2312yes—
242#13063281—22no—
243#13063281—22no—
244#13063281—22no—
245#13063281—22no—
246#13063281—22no—
247C2×C4⋊Dic43C2311yescharacteristic
248C2×Dic43⋊C4—21no—
249C2×Dic43⋊C4—22no—
250C2×Dic43⋊C4—22no—
251C4⋊C4×D43—22no—
252C4⋊C4×D43—21no—
253C4⋊C4×D43C2312yes—
254C4⋊C4×D43C2312yes—
255C2×C22⋊Dic43—21no—
256C2×(C2×D43)⋊C4—22no—
257C22⋊C4×D43—22no—
258C22⋊C4×D43—22no—
259C2×C4×Dic43—21no—
260C2×C4×Dic43—22no—
261C2×C4×Dic43—22no—
262C2×C4×Dic43—21no—
263C2×C4×Dic43C2311yescharacteristic
264C42×D43—22no—
265C42×D43—21no—
266C42×D43C2312yes—
267#13063259C2312yes—
268#13063258C2311yescharacteristic
269#13063258C2311yescharacteristic
270#13063257C2312yes—
271#13063256C2311yescharacteristic
272#13063256C2312yes—
273#13063256C2312yes—
274#13063256C2311yescharacteristic
275#13063250C2312yes—
276#13063250C2312yes—
277#13063250C2311yescharacteristic
278#13063250C2311yescharacteristic
279#13063249C2312yes—
280#13063248C2312yes—
281#13063248C2312yes—
282#13063248C2312yes—
283#13063247C2311yescharacteristic
284#13063247C2311yescharacteristic
285#13063246C2312yes—
286#13063246C2312yes—
287#13063246C2312yes—
288#13063245C2312yes—
289#13063236C2312yes—
290#13063235C2312yes—
291C4×C43⋊C8C2312yes—
292C8×Dic43C2311yescharacteristic
293C8×Dic43C2312yes—
294C8×Dic43C2311yescharacteristic
295C8×Dic43C2311yescharacteristic
296C8×Dic43C2311yescharacteristic
297C2×#41×C43C2311yescharacteristic
298C22×D4×C43C2311yescharacteristic
299AGL(1,ℤ/8)×C43C2×C418yescomplemented
300C2×SD16×C43C2312yes—
301C2×D8×C43C2312yes—
302C2×M16×C43C2311yescharacteristic
303C22×C8×C43C2311yescharacteristic
304C4×Q8×C43C2312yes—
305C4×D4×C43—21no—
306C4×D4×C43—21no—
307C4×D4×C43—22no—
308C4×D4×C43C2312yes—
309C4×D4×C43C2312yes—
310C4×D4×C43C2312yes—
311#117×C43—21no—
312#117×C43C2311yescharacteristic
313#117×C43C2311yescharacteristic
314C2×C4⋊C4×C43—21no—
315C2×C4⋊C4×C43C2311yescharacteristic
316C2×C22⋊C4×C43—22no—
317#107×C43C2312yes—
318#106×C43C2312yes—
319#103×C43C2311yescharacteristic
320#103×C43C2311yescharacteristic
321#102×C43C2312yes—
322#102×C43C2311yescharacteristic
323#102×C43C2312yes—
324#102×C43C2311yescharacteristic
325#97×C43C2312yes—
326C4×C8×C43C2312yes—
327C24×C43—21no—
328C23×D43—22no—
329#41×C43—22no—
330#41×C43C22×C414yescomplemented
331C2×Q8×C43C2411yescharacteristic
332C2×D4×C43—21no—
333C2×D4×C43—22no—
334C2×D4×C43—21no—
335C2×D4×C43C22×C414yes—
336C2×D4×C43C2411yescharacteristic
337C2×D4×C43C2412yes—
338C22×C4×C43—21no—
339C22×C4×C43—22no—
340C22×C4×C43—22no—
341C22×C4×C43—22no—
342C22×C4×C43—21no—
343C22×C4×C43C2411yescharacteristic
344C2×C22⋊D43—216no—
345C2×C22⋊D43—22no—
346C2×C22⋊D43—21no—
347C2×C22⋊D43—22no—
348C2×C22⋊D43—22no—
349C2×C22⋊D43C2×D412yes—
350C22×Dic43—22no—
351C22×Dic43—22no—
352C22×Dic43—21no—
353C22×Dic43—22no—
354C22×Dic43—21no—
355C22×Dic43—22no—
356C22×Dic43—21no—
357C22×Dic43—21no—
358C22×Dic43—82no—
359C22×Dic43C2×D411yescharacteristic
360C22×Dic43C2×D411yescharacteristic
361Q8×D43—24no—
362Q8×D43C22×C418yescomplemented
363#10621900—216no—
364#10621900—24no—
365#10621900—24no—
366#10621900—28no—
367#10621900C22×C418yes—
368#10621900C22×C418yescomplemented
369D4×D43—28no—
370D4×D43—24no—
371D4×D43C22×C418yes—
372#10621898—22no—
373#10621898—28no—
374#10621898C22×C414yes—
375#10621898C22×C414yes—
376#10621898#4114yes—
377C2×D172C2×D411yescharacteristic
378C2×D172C2411yescharacteristic
379C2×C4×D43—21no—
380C2×C4×D43—21no—
381C2×C4×D43—22no—
382C2×C4×D43—21no—
383C2×C4×D43—22no—
384C2×C4×D43—22no—
385C2×C4×D43—22no—
386C2×C4×D43—84no—
387C2×C4×D43C2×D412yes—
388C2×C4×D43C2×D412yes—
389C2×C4×D43C2412yes—
390C2×Dic86—21no—
391C2×Dic86—22no—
392C2×Dic86—22no—
393C2×Dic86—28no—
394C2×Dic86C22×C414yescomplemented
395C2×Dic86C2×D411yescharacteristic
396C2×Dic86C2412yes—
397C2×Dic86C2411yescharacteristic
398SD16×C43C22×C418yescomplemented
399D8×C43C22×C418yescomplemented
400M16×C43C22×C414yescomplemented
401C2×C8×C43—22no—
402C2×C8×C43C2411yescharacteristic
403C2×C8×C43C2411yescharacteristic
404C2×C8×C43C2412yes—
405C4⋊C4×C43—21no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43C2×D411yescharacteristic
408C4⋊C4×C43C2×D411yescharacteristic
409C4⋊C4×C43C2412yes—
410C4⋊C4×C43C2411yescharacteristic
411C4⋊C4×C43C2411yescharacteristic
412C22⋊C4×C43—22no—
413C22⋊C4×C43—22no—
414C22⋊C4×C43—22no—
415C22⋊C4×C43—21no—
416C22⋊C4×C43C2×D412yes—
417C42×C43—22no—
418C42×C43—21no—
419C42×C43C2412yes—
420C22⋊Dic43—22no—
421C22⋊Dic43—22no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425#10621885C22×C414yescomplemented
426#10621884C22×C414yescomplemented
427#10621883C22×C418yescomplemented
428#10621883C22×C418yescomplemented
429#10621883C22×C414yescomplemented
430#10621882C22×C414yescomplemented
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4C2×D412yes—
437(C2×D43)⋊C4C2×D412yes—
438C4⋊Dic43—21no—
439C4⋊Dic43—21no—
440C4⋊Dic43—21no—
441C4⋊Dic43C2411yescharacteristic
442C4⋊Dic43C2411yescharacteristic
443C4⋊Dic43C2412yes—
444Dic43⋊C4—22no—
445Dic43⋊C4—22no—
446Dic43⋊C4—22no—
447Dic43⋊C4—22no—
448Dic43⋊C4—22no—
449Dic43⋊C4—22no—
450Dic43⋊C4—21no—
451Dic43⋊C4—22no—
452Dic43⋊C4—21no—
453Dic43⋊C4C2×D412yes—
454Dic43⋊C4C2×D412yes—
455C4×Dic43—22no—
456C4×Dic43—22no—
457C4×Dic43—22no—
458C4×Dic43—21no—
459C4×Dic43—21no—
460C4×Dic43—21no—
461C4×Dic43—22no—
462C4×Dic43—21no—
463C4×Dic43—22no—
464C4×Dic43—22no—
465C4×Dic43—22no—
466C4×Dic43—21no—
467C4×Dic43C2×D411yescharacteristic
468C4×Dic43C2×D412yes—
469C4×Dic43C2×D412yes—
470C4×Dic43C2×D411yescharacteristic
471C4×Dic43C2411yescharacteristic
472C4×Dic43C2411yescharacteristic
473#10621877—22no—
474C2×C43⋊C8C22×C414yescomplemented
475C2×C43⋊C8C2412yes—
476C2×C43⋊C8C2411yescharacteristic
477C2×C43⋊C8C2411yescharacteristic
478Dic172C22×C418yescomplemented
479#10621873C22×C418yescomplemented
480#10621872—24no—
481#10621872C22×C418yescomplemented
482C8×D43—24no—
483C8×D43C22×C418yescomplemented
484C23×C43—21no—
485C23×C43—22no—
486C23×C43—24no—
487C23×C43—81no—
488C23×C43—81no—
489C23×C43C22×D411yescharacteristic
490C22×D43—21no—
491C22×D43—28no—
492C22×D43—82no—
493C22×D43—82no—
494C22×D43C22×D412yes—
495Q8×C43—21no—
496Q8×C43C23×C412yes—
497D4×C43—24no—
498D4×C43—24no—
499D4×C43—22no—
500D4×C43—21no—
501D4×C43C23×C412yes—
502D4×C43C23×C414yes—
503C2×C4×C43—21no—
504C2×C4×C43—24no—
505C2×C4×C43—22no—
506C2×C4×C43—21no—
507C2×C4×C43—21no—
508C2×C4×C43—82no—
509C2×C4×C43—82no—
510C2×C4×C43—82no—
511C2×C4×C43—81no—
512C2×C4×C43C23×C412yes—
513C2×C4×C43C22×D412yes—
514C2×C4×C43C22×D412yes—
515C2×C4×C43C22×D411yescharacteristic
516C2×C4×C43C2×#4112yes—
517C2×C4×C43C2511yescharacteristic
518C22⋊D43—24no—
519C22⋊D43—28no—
520C22⋊D43—28no—
521C22⋊D43—28no—
522C22⋊D43C4×D418yes—
523C2×Dic43—24no—
524C2×Dic43—22no—
525C2×Dic43—21no—
526C2×Dic43—28no—
527C2×Dic43—28no—
528C2×Dic43—22no—
529C2×Dic43—21no—
530C2×Dic43—21no—
531C2×Dic43—22no—
532C2×Dic43—41no—
533C2×Dic43—44no—
534C2×Dic43—42no—
535C2×Dic43—81no—
536C2×Dic43—82no—
537C2×Dic43—81no—
538C2×Dic43C22×D411yescharacteristic
539C2×Dic43C22×D411yescharacteristic
540C2×Dic43C22×D411yescharacteristic
541C2×Dic43C22×D412yes—
542C2×Dic43C22×D411yescharacteristic
543D172—21no—
544D172C4×D414yes—
545D172C23×C412yes—
546C4×D43—28no—
547C4×D43—24no—
548C4×D43—24no—
549C4×D43—42no—
550C4×D43—42no—
551C4×D43—81no—
552C4×D43—82no—
553C4×D43—82no—
554C4×D43—82no—
555C4×D43C23×C414yes—
556C4×D43C2×#4114yes—
557Dic86—24no—
558Dic86—22no—
559Dic86—21no—
560Dic86—28no—
561Dic86C4×D414yes—
562Dic86C23×C414yes—
563Dic86C23×C412yes—
564C8×C43—21no—
565C8×C43—21no—
566C8×C43C23×C414yes—
567C43⋊C8—22no—
568C43⋊C8C23×C412yes—
569C43⋊C8C23×C412yes—
570C4×#577—431nomaximal, Sylow
571C22×C43—21no—
572C22×C43—21no—
573C22×C43—24no—
574C22×C43—22no—
575C22×C43—42no—
576C22×C43—41no—
577C22×C43—42no—
578C22×C43—41no—
579C22×C43—84no—
580C22×C43C2×C4×D412yes—
581C22×C43C23×D411yescharacteristic
582C2×D43—22no—
583C2×D43—22no—
584C2×D43—22no—
585C2×D43—41no—
586C2×D43—41no—
587C2×D43—88no—
588C2×D43C2×C4×D414yes—
589C4×C43—22no—
590C4×C43—22no—
591C4×C43—22no—
592C4×C43—41no—
593C4×C43—42no—
594C4×C43—41no—
595C4×C43C2×C4×D412yes—
596C4×C43C24×C411yescharacteristic
597C4×C43C22×#4111yescharacteristic
598Dic43—21no—
599Dic43—21no—
600Dic43—24no—
601Dic43—22no—
602Dic43—21no—
603Dic43—41no—
604Dic43—42no—
605Dic43—41no—
606Dic43C2×C4×D414yes—
607Dic43#57712yescomplemented
608C2×#577—431no—
609C4×2−1+4—431no—
610C4×H(5,𝔽2)—431no—
611#2952—432no—
612#2952—431no—
613#2949—432no—
614#2949—431no—
615#2947—432no—
616#2947—431no—
617#2946—432no—
618#2946D4311yescharacteristic, complemented
619C4×#137—432no—
620C4×#137—431no—
621C4×AGL(1,ℤ/8)—432no—
622C4×AGL(1,ℤ/8)—431no—
623C4×#135—432no—
624C4×#135—431no—
625C2×C4×SD16—432no—
626C2×C4×SD16—431no—
627#2912—431no—
628#2898—431no—
629#2897—431no—
630C4×#131—431no—
631C2×C43—22no—
632C2×C43—44no—
633C2×C43—42no—
634C2×C43C22×C4×D411yescharacteristic
635C2×C43C2×#57711yescharacteristic
636C2×C43#358411yescharacteristic
637D43—24no—
638D43—42no—
639C2×2−1+4—431no—
640C2×H(5,𝔽2)—431no—
641#577—4316no—
642C2×#137—432no—
643C2×#137—431no—
644C2×AGL(1,ℤ/8)—432no—
645C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
646C2×#135—431no—
647C2×#135—432no—
648C22×SD16—431no—
649C22×SD16—432no—
650C2×#131—431no—
651C2×#131—431no—
652#520—431no—
653#520—431no—
654#520—432no—
655#520—432no—
656#520—431no—
657#520—861no—
658#520—862no—
659#520—861no—
660#520C2×D4311yescharacteristic, complemented
661#519—432no—
662#519—431no—
663#519—861no—
664#518—432no—
665#518—862no—
666#518—861no—
667#518C2×D4311yescharacteristic
668C4×#41—431no—
669C4×#41—431no—
670C4×#41—432no—
671C4×#41—432no—
672C4×#41—431no—
673C4×#41—861no—
674C4×#41—862no—
675C4×#41—861no—
676C2×C4×Q8—432no—
677C2×C4×Q8—431no—
678C2×C4×Q8—861no—
679C2×C4×D4—431no—
680C2×C4×D4—432no—
681C2×C4×D4—862no—
682C2×C4×D4—861no—
683#442—432no—
684#442—432no—
685#442C2×D4312yescomplemented
686#441—432no—
687#441—432no—
688#441—432no—
689#440—432no—
690#440—432no—
691#440—432no—
692#440—432no—
693#440—432no—
694#440C2×D4312yescomplemented
695C4×Q16—432no—
696C4×Q16—431no—
697C4×Q16—431no—
698C4×Q16—432no—
699C4×SD16—432no—
700C4×SD16—432no—
701C4×SD16—432no—
702C4×SD16—432no—
703C4×SD16—432no—
704C4×SD16—432no—
705C4×SD16—431no—
706C4×SD16—431no—
707C4×SD16—432no—
708C4×SD16—432no—
709C4×SD16—432no—
710C4×SD16—432no—
711C4×SD16—431no—
712C4×SD16—431no—
713C4×SD16—432no—
714C4×SD16C2×D4312yescomplemented
715C4×D8—432no—
716C4×D8—431no—
717C4×D8—431no—
718C4×D8C2×D4312yescomplemented
719#428—431no—
720#428—432no—
721#428—432no—
722#428C2×D4311yescharacteristic, complemented
723#427—431no—
724#427—432no—
725C2×#106—431no—
726C2×#106—432no—
727#419—431no—
728#419—432no—
729#418—431no—
730#418—432no—
731#417—431no—
732#417—431no—
733#417—432no—
734#417—432no—
735#416—431no—
736#416—432no—
737#416—432no—
738#416C2×D4311yescharacteristic, complemented
739C2×#103—431no—
740C2×#103—432no—
741C2×#102—432no—
742C2×#102C2×D4311yescharacteristic
743#405—431no—
744#405—432no—
745#405—432no—
746#405C2×D4311yescharacteristic, complemented
747C4×M16—431no—
748C4×M16—432no—
749C2×C4×C8—431no—
750C2×C4×C8—432no—
751C43C4×#57711yescharacteristic, complemented, Sylow
7522−1+4—438no—
7532−1+4—864no—
754H(5,𝔽2)—438no—
755H(5,𝔽2)—864no—
756C2×#41—431no—
757C2×#41—432no—
758C2×#41—432no—
759C2×#41—431no—
760C2×#41—861no—
761C2×#41—862no—
762C2×#41—861no—
763C2×#41C22×D4311yescharacteristic
764C22×Q8—432no—
765C22×Q8—431no—
766C22×Q8—861no—
767C22×D4—432no—
768C22×D4—861no—
769C22×D4—862no—
770C22×D4C22×D4311yescharacteristic
771C23×C4—862no—
772C23×C4—861no—
773#137—4316no—
774#137—438no—
775AGL(1,ℤ/8)—4316no—
776AGL(1,ℤ/8)C4×D4318yescomplemented
777#135—438no—
778#135—4316no—
779C2×Q16—431no—
780C2×Q16—432no—
781C2×SD16—431no—
782C2×SD16—438no—
783C2×SD16—432no—
784C2×SD16—432no—
785C2×SD16—431no—
786C2×SD16—4316no—
787C2×SD16—432no—
788C2×SD16C22×D4312yes—
789C2×D8—431no—
790C2×D8C22×D4312yes—
791#131—438no—
792#131—864no—
793C2×M16—431no—
794C2×M16—432no—
795C2×M16—432no—
796C2×M16C22×D4311yescharacteristic
797C22×C8—431no—
798C22×C8—432no—
799C22×C8—432no—
800C22×C8C22×D4311yescharacteristic
801C4×Q8—431no—
802C4×Q8—431no—
803C4×Q8—431no—
804C4×Q8—431no—
805C4×Q8—432no—
806C4×Q8—432no—
807C4×Q8—431no—
808C4×Q8—431no—
809C4×Q8—432no—
810C4×Q8—432no—
811C4×Q8—432no—
812C4×Q8—862no—
813C4×Q8—862no—
814C4×Q8—861no—
815C4×Q8—862no—
816C4×Q8—861no—
817C4×Q8—861no—
818C4×Q8—862no—
819C4×Q8—861no—
820C4×Q8—861no—
821C4×Q8—861no—
822C4×Q8C22×D4312yes—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—22no—
826C4×D4—431no—
827C4×D4—431no—
828C4×D4—432no—
829C4×D4—432no—
830C4×D4—432no—
831C4×D4—432no—
832C4×D4—431no—
833C4×D4—431no—
834C4×D4—431no—
835C4×D4—431no—
836C4×D4—432no—
837C4×D4—861no—
838C4×D4—862no—
839C4×D4—862no—
840C4×D4—861no—
841C4×D4—861no—
842C4×D4—862no—
843C4×D4—862no—
844C4×D4—862no—
845C4×D4—861no—
846C4×D4—862no—
847C4×D4—862no—
848C4×D4—861no—
849C4×D4—862no—
850C4×D4—862no—
851C4×D4—862no—
852C4×D4—861no—
853C4×D4—862no—
854C4×D4—862no—
855C4×D4—862no—
856C4×D4—862no—
857C4×D4—861no—
858C4×D4—861no—
859C4×D4—862no—
860C4×D4C22×D4312yes—
861C4×D4C22×D4312yes—
862C4×D4C22×D4312yes—
863#117—21no—
864#117—432no—
865#117—431no—
866#117—432no—
867#117—432no—
868#117—861no—
869#117—862no—
870#117—862no—
871#117—862no—
872#117—861no—
873#117—862no—
874#117—862no—
875#117—862no—
876#117—861no—
877#117—862no—
878#117C22×D4311yescharacteristic
879#117C22×D4311yescharacteristic
880C2×C4⋊C4—21no—
881C2×C4⋊C4—431no—
882C2×C4⋊C4—432no—
883C2×C4⋊C4—432no—
884C2×C4⋊C4—862no—
885C2×C4⋊C4—862no—
886C2×C4⋊C4—862no—
887C2×C4⋊C4—861no—
888C2×C4⋊C4—861no—
889C2×C4⋊C4C22×D4311yescharacteristic
890C2×C22⋊C4—22no—
891C2×C22⋊C4—862no—
892C2×C22⋊C4—862no—
893C2×C22⋊C4—862no—
894C2×C22⋊C4—861no—
895C2×C42—431no—
896C2×C42—432no—
897C2×C42—861no—
898C2×C42—862no—
899C2×C42—862no—
900C2×C42—862no—
901C2×C42—861no—
902C2×C42—861no—
903#107—432no—
904#107—431no—
905#107—431no—
906#107C22×D4312yes—
907#106—432no—
908#106—431no—
909#106—432no—
910#106—432no—
911#106—431no—
912#106C22×D4312yes—
913#103—432no—
914#103—432no—
915#103—432no—
916#103—431no—
917#103—431no—
918#103—432no—
919#103—432no—
920#103—432no—
921#103C22×D4311yescharacteristic
922#103C22×D4311yescharacteristic
923#102—432no—
924#102—432no—
925#102—432no—
926#102—431no—
927#102—431no—
928#102—432no—
929#102C22×D4312yes—
930#102C22×D4312yes—
931#102C22×D4311yescharacteristic
932#102C22×D4311yescharacteristic
933#97—432no—
934#97—432no—
935#97C22×D4312yes—
936C4×C8—431no—
937C4×C8—431no—
938C4×C8—432no—
939C4×C8—431no—
940C4×C8—431no—
941C4×C8—432no—
942C4×C8C22×D4312yes—
943C24—21no—
944C24—862no—
945#41—22no—
946#41—434no—
947#41—434no—
948#41—438no—
949#41—438no—
950#41—434no—
951#41—868no—
952#41—864no—
953#41—864no—
954#41—8616no—
955#41—868no—
956#41—862no—
957#41C2×C4×D4314yescomplemented
958C2×Q8—431no—
959C2×Q8—438no—
960C2×Q8—434no—
961C2×Q8—432no—
962C2×Q8—431no—
963C2×Q8—862no—
964C2×Q8—868no—
965C2×Q8—864no—
966C2×Q8—861no—
967C2×Q8—862no—
968C2×Q8C23×D4311yescharacteristic
969C2×D4—21no—
970C2×D4—21no—
971C2×D4—22no—
972C2×D4—432no—
973C2×D4—438no—
974C2×D4—431no—
975C2×D4—431no—
976C2×D4—864no—
977C2×D4—862no—
978C2×D4—868no—
979C2×D4—8616no—
980C2×D4—862no—
981C2×D4—862no—
982C2×D4—861no—
983C2×D4C2×C4×D4314yes—
984C2×D4C23×D4311yescharacteristic
985C2×D4C23×D4312yes—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—22no—
990C22×C4—22no—
991C22×C4—432no—
992C22×C4—431no—
993C22×C4—431no—
994C22×C4—432no—
995C22×C4—432no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—862no—
999C22×C4—862no—
1000C22×C4—862no—
1001C22×C4—862no—
1002C22×C4—862no—
1003C22×C4—861no—
1004C22×C4—862no—
1005C22×C4—861no—
1006C22×C4—862no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—861no—
1010C22×C4—862no—
1011C22×C4—3444no—
1012C22×C4—3442no—
1013C22×C4C23×D4311yescharacteristic
1014Q16—434no—
1015Q16—438no—
1016SD16—434no—
1017SD16—438no—
1018SD16—438no—
1019SD16—434no—
1020SD16—438no—
1021SD16C2×C4×D4318yescomplemented
1022D8—434no—
1023D8C2×C4×D4318yescomplemented
1024M16—438no—
1025M16—864no—
1026M16—862no—
1027M16C2×C4×D4314yescomplemented
1028C2×C8—22no—
1029C2×C8—434no—
1030C2×C8—431no—
1031C2×C8—431no—
1032C2×C8—438no—
1033C2×C8—432no—
1034C2×C8—864no—
1035C2×C8C23×D4311yescharacteristic
1036C2×C8C23×D4311yescharacteristic
1037C2×C8C23×D4312yes—
1038C4⋊C4—22no—
1039C4⋊C4—21no—
1040C4⋊C4—432no—
1041C4⋊C4—432no—
1042C4⋊C4—431no—
1043C4⋊C4—431no—
1044C4⋊C4—432no—
1045C4⋊C4—862no—
1046C4⋊C4—862no—
1047C4⋊C4—861no—
1048C4⋊C4—862no—
1049C4⋊C4—862no—
1050C4⋊C4—861no—
1051C4⋊C4—861no—
1052C4⋊C4—861no—
1053C4⋊C4—861no—
1054C4⋊C4—862no—
1055C4⋊C4—862no—
1056C4⋊C4—862no—
1057C4⋊C4D4×D4311yescharacteristic
1058C4⋊C4D4×D4311yescharacteristic
1059C4⋊C4C23×D4312yes—
1060C4⋊C4C23×D4311yescharacteristic
1061C4⋊C4C23×D4311yescharacteristic
1062C22⋊C4—21no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
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—861no—
1076C22⋊C4—861no—
1077C22⋊C4—862no—
1078C22⋊C4D4×D4312yes—
1079C42—22no—
1080C42—21no—
1081C42—432no—
1082C42—431no—
1083C42—432no—
1084C42—431no—
1085C42—431no—
1086C42—431no—
1087C42—861no—
1088C42—861no—
1089C42—862no—
1090C42—862no—
1091C42—862no—
1092C42—861no—
1093C42—861no—
1094C42—862no—
1095C42—861no—
1096C42—862no—
1097C42—862no—
1098C42—862no—
1099C42C23×D4312yes—
1100C23—21no—
1101C23—22no—
1102C23—24no—
1103C23—81no—
1104C23—81no—
1105C23—432no—
1106C23—868no—
1107C23—861no—
1108C23—3442no—
1109C23—3442no—
1110C23C2×D4×D4311yescharacteristic
1111Q8—21no—
1112Q8—434no—
1113Q8—434no—
1114Q8—432no—
1115Q8—868no—
1116Q8—864no—
1117Q8—862no—
1118Q8—861no—
1119Q8C22×C4×D4312yes—
1120D4—24no—
1121D4—24no—
1122D4—22no—
1123D4—21no—
1124D4—438no—
1125D4—434no—
1126D4—432no—
1127D4—868no—
1128D4—868no—
1129D4—868no—
1130D4—864no—
1131D4—861no—
1132D4C22×C4×D4312yes—
1133D4C22×C4×D4314yes—
1134C2×C4—21no—
1135C2×C4—24no—
1136C2×C4—21no—
1137C2×C4—22no—
1138C2×C4—21no—
1139C2×C4—82no—
1140C2×C4—82no—
1141C2×C4—82no—
1142C2×C4—81no—
1143C2×C4—431no—
1144C2×C4—432no—
1145C2×C4—434no—
1146C2×C4—434no—
1147C2×C4—431no—
1148C2×C4—431no—
1149C2×C4—431no—
1150C2×C4—864no—
1151C2×C4—868no—
1152C2×C4—862no—
1153C2×C4—868no—
1154C2×C4—868no—
1155C2×C4—864no—
1156C2×C4—861no—
1157C2×C4—862no—
1158C2×C4—864no—
1159C2×C4—861no—
1160C2×C4—861no—
1161C2×C4—862no—
1162C2×C4—3442no—
1163C2×C4—3441no—
1164C2×C4—3442no—
1165C2×C4—3442no—
1166C2×C4—3442no—
1167C2×C4—3441no—
1168C2×C4—3441no—
1169C2×C4—1722no—
1170C2×C4—1722no—
1171C2×C4—1724no—
1172C2×C4—1722no—
1173C2×C4—1721no—
1174C2×C4C22×C4×D4312yes—
1175C2×C4C2×D4×D4312yes—
1176C2×C4C2×D4×D4312yes—
1177C2×C4C2×D4×D4311yescharacteristic
1178C2×C4#41×D4312yes—
1179C2×C4C24×D4311yescharacteristic
1180C8—21no—
1181C8—21no—
1182C8—432no—
1183C8—432no—
1184C8—862no—
1185C8C22×C4×D4314yes—
1186C22—21no—
1187C22—21no—
1188C22—22no—
1189C22—24no—
1190C22—42no—
1191C22—41no—
1192C22—41no—
1193C22—42no—
1194C22—84no—
1195C22—434no—
1196C22—862no—
1197C22—862no—
1198C22—862no—
1199C22—3448no—
1200C22—1721no—
1201C22—1721no—
1202C22C4×D4×D4312yes—
1203C22C22×D4×D4311yescharacteristic
1204C4—22no—
1205C4—22no—
1206C4—22no—
1207C4—41no—
1208C4—41no—
1209C4—42no—
1210C4—432no—
1211C4—434no—
1212C4—861no—
1213C4—861no—
1214C4—861no—
1215C4—862no—
1216C4—864no—
1217C4—1722no—
1218C4—1721no—
1219C4—1721no—
1220C4C4×D4×D4312yes—
1221C4C23×C4×D4311yescharacteristic
1222C4C2×#41×D4311yescharacteristic
1223C2—22no—
1224C2—44no—
1225C2—42no—
1226C2—864no—
1227C2—1722no—
1228C2C2×C4×D4×D4311yescharacteristic
1229C2#577×D4311yescharacteristic
1230C2#1914936311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2946C2
socleC22×C43C23×D4
prime radicalC2×#14583709C2
cosocleC2×C4×C43C25
hypercenter#2946D43
hypocenterC43C4×#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #2946

Complements

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

NH ≅ G/Ntype
2. #19147806C2semidirect
3. #19147799C2semidirect
4. #19143477C2semidirect
5. #19143476C2semidirect
6. #19143452C2semidirect
7. #19143451C2semidirect
8. #19143440C2semidirect
9. #19143431C2semidirect
10. #19143420C2semidirect
11. #19143417C2semidirect
12. #19143413C2semidirect
13. #19143406C2semidirect
14. AGL(1,ℤ/8)×Dic43C2semidirect
15. #19143363C2semidirect
16. C4×#13063344C2semidirect
17. C2×#14582990C2semidirect
18. C4×SD16×D43C2semidirect
19. #19143189C2semidirect
20. #19143124C2semidirect
21. #19143116C2semidirect
22. #19143017C2semidirect
23. C43×#2946C2semidirect
26. #14583709C4semidirect
43. #14583378C22semidirect
45. #14583376C22semidirect
46. #14583375C22semidirect
50. #41×Dic43C22semidirect
57. C4×#10621900C22semidirect
59. C2×#13063290C22semidirect
60. C4×Q8×D43C22semidirect
65. #14583011C22semidirect
66. #14583009C22semidirect
67. #14583007C22semidirect
68. #14583005C22semidirect
69. #14583004C22semidirect
70. #14583001C22semidirect
71. #14583000C22semidirect
72. #14582999C22semidirect
73. #14582999C22semidirect
74. #14582998C22semidirect
75. C4×Dic172C22semidirect
76. #14582993C22semidirect
77. #14582991C22semidirect
78. #14582991C22semidirect
79. #14582990C22semidirect
80. #14582990C22semidirect
81. #14582990C22semidirect
82. #14582990C22semidirect
83. #14582990C22semidirect
84. #14582990C22semidirect
85. C4×#10621873C22semidirect
86. SD16×Dic43C22semidirect
87. C4×#10621884C22semidirect
88. #14582986C22semidirect
89. C4×#10621883C22semidirect
90. C4×#10621883C22semidirect
91. C4×#10621883C22semidirect
92. #14582984C22semidirect
93. #14582984C22semidirect
94. D8×Dic43C22semidirect
95. #14582979C22semidirect
96. #14582979C22semidirect
97. #14582941C22semidirect
98. #14582940C22semidirect
99. #14582938C22semidirect
100. #14582936C22semidirect
101. #14582935C22semidirect
102. C2×#13063256C22semidirect
103. #106×D43C22semidirect
104. #14582907C22semidirect
105. #14582906C22semidirect
108. #14582900C22semidirect
111. #14582897C22semidirect
114. #14582892C22semidirect
115. C2×#13063250C22semidirect
116. #103×D43C22semidirect
118. #14582856C22semidirect
119. #14582855C22semidirect
120. #14582853C22semidirect
121. #14582851C22semidirect
122. M16×Dic43C22semidirect
123. C2×C8×Dic43C22semidirect
124. C4×C8×D43C22semidirect
126. C43×#520C22semidirect
128. C43×#442C22semidirect
129. C43×#440C22semidirect
130. C4×SD16×C43C22semidirect
131. C4×D8×C43C22semidirect
132. C43×#428C22semidirect
133. C43×#416C22semidirect
135. C43×#405C22semidirect
137. #13063372C2×C4semidirect
139. #13063370C2×C4semidirect
155. #13063358C2×C4semidirect
156. #13063354C2×C4semidirect
157. #13063349C2×C4semidirect
158. #13063345C2×C4semidirect
159. #13063344C2×C4semidirect
163. C2×#10621883C2×C4semidirect
168. SD16×D43C2×C4semidirect
170. #13063333C2×C4semidirect
299. AGL(1,ℤ/8)×C43C2×C4semidirect
330. #41×C43C22×C4semidirect
362. Q8×D43C22×C4semidirect
368. #10621900C22×C4semidirect
394. C2×Dic86C22×C4semidirect
398. SD16×C43C22×C4semidirect
399. D8×C43C22×C4semidirect
400. M16×C43C22×C4semidirect
425. #10621885C22×C4semidirect
426. #10621884C22×C4semidirect
427. #10621883C22×C4semidirect
428. #10621883C22×C4semidirect
429. #10621883C22×C4semidirect
430. #10621882C22×C4semidirect
474. C2×C43⋊C8C22×C4semidirect
478. Dic172C22×C4semidirect
479. #10621873C22×C4semidirect
481. #10621872C22×C4semidirect
483. C8×D43C22×C4semidirect
607. Dic43#577semidirect
618. #2946D43semidirect
660. #520C2×D43semidirect
685. #442C2×D43semidirect
694. #440C2×D43semidirect
714. C4×SD16C2×D43semidirect
718. C4×D8C2×D43semidirect
722. #428C2×D43semidirect
738. #416C2×D43semidirect
746. #405C2×D43semidirect
751. C43C4×#577semidirect
776. AGL(1,ℤ/8)C4×D43semidirect
957. #41C2×C4×D43semidirect
1021. SD16C2×C4×D43semidirect
1023. D8C2×C4×D43semidirect
1027. M16C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837092
#191478062
#191477992
#191434772
#191434762
#191434522
#191434512
#191434402
#191434312
#191434202
#191434172
#191434132
#191434062
AGL(1,ℤ/8)×Dic432
#191433632
C4×#130633442
C2×#145829902
C4×SD16×D432
#191431892
#191431242
#191431162
#191430172
C43×#29462
C4×#57743