Finite Group Databasebeta

← #25102511

Subgroups — #25102511

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063371C211yesmaximal, characteristic, complemented
2C2×#14583065C211yesmaximal, characteristic
3C4×#13063351C211yesmaximal, characteristic, complemented
4#19137317C211yesmaximal, characteristic, complemented
5#19134990C211yesmaximal, characteristic, complemented
6#19134973C211yesmaximal, characteristic, complemented
7#19134968C211yesmaximal, characteristic, complemented
8#19134826C211yesmaximal, characteristic, complemented
9#19134825C211yesmaximal, characteristic, complemented
10#19134803C211yesmaximal, characteristic, complemented
11#19134547C211yesmaximal, characteristic, complemented
12#19134408C211yesmaximal, characteristic, complemented
13#19134405C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×AGL(1,ℤ/8)×C43C211yesmaximal, characteristic, complemented
16C2×#13063371C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C2×#13063321C2211yescharacteristic
19#14583382C2211yescharacteristic
20#14583381—21no—
21#14583379—21no—
22#14583379C2211yescharacteristic
23#14583373—21no—
24#14583373C2211yescharacteristic
25#14583371—22no—
26#14583371—21no—
27C4×#10621902—21no—
28C4×#10621898—21no—
29C4×#10621898C2211yescharacteristic
30C2×C4×D172—21no—
31C2×C4×D172C2211yescharacteristic
32C4×D4×D43—22no—
33C4×D4×D43—21no—
34#14583065C418yescomplemented
35#14583009—21no—
36#14582999—21no—
37C4×#10621883—21no—
38C4×#10621882—21no—
39#14582939C2211yescharacteristic, complemented
40C2×#13063252C2211yescharacteristic
41C2×#13063252C2211yescharacteristic
42C2×#13063251C2211yescharacteristic
43C2×#13063251C2211yescharacteristic
44#14582904C2211yescharacteristic, complemented
45#14582898C2211yescharacteristic
46C2×#13063241C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C4×#10621877C2211yescharacteristic, complemented
49#14582802C2211yescharacteristic, complemented
50#14582800C2211yescharacteristic
51#14582778—22no—
52#14582775—22no—
53#14582764C2211yescharacteristic, complemented
54#14582745C2211yescharacteristic, complemented
55#14582667C2211yescharacteristic, complemented
56#14582667C2211yescharacteristic, complemented
57#14582660C2211yescharacteristic, complemented
58#14582660C2211yescharacteristic, complemented
59#14582658C2211yescharacteristic, complemented
60#14582658C2211yescharacteristic, complemented
61C2×AGL(1,ℤ/8)×C43C2211yescharacteristic
62C4×#41×C43C2211yescharacteristic
63C2×C4×D4×C43C2211yescharacteristic, complemented
64C43×#442—21no—
65C43×#440—21no—
66C4×SD16×C43—21no—
67C4×D8×C43—21no—
68C43×#428C2211yescharacteristic, complemented
69C43×#418C2211yescharacteristic, complemented
70C43×#417C2211yescharacteristic
71C4×M16×C43C2211yescharacteristic, complemented
72#13063371—22no—
73#13063371—22no—
74#13063371—22no—
75#13063371C2×C414yescomplemented
76C2×#10621902—21no—
77C2×#10621898—21no—
78C2×#10621898C2311yescharacteristic
79C22×D172—21no—
80C22×D172C2311yescharacteristic
81C22×C22⋊D43—22no—
82C2×D4×D43—22no—
83C2×D4×D43—21no—
84C22×C4×D43—22no—
85C22×C4×D43D412yes—
86#13063351—22no—
87#13063351C2×C414yescomplemented
88C2×#10621883—21no—
89C2×#10621882—21no—
90C2×#10621877C2311yescharacteristic
91C2×#10621877C2311yescharacteristic
92#13063321—22no—
93#13063321C2×C414yescomplemented
94Q8×Dic43—21no—
95C4×Dic86—21no—
96C4×Dic86D411yescharacteristic, complemented
97C4×Dic86D411yescharacteristic, complemented
98C4×D172—22no—
99C4×D172—22no—
100C4×D172—21no—
101C4×D172—21no—
102C4×D172—21no—
103C4×D172—21no—
104C4×D172—21no—
105C4×D172—21no—
106C4×D172—21no—
107C4×D172D411yescharacteristic, complemented
108C4×D172D411yescharacteristic, complemented
109D4×Dic43—21no—
110D4×Dic43—22no—
111#13063287—22no—
112#13063287—22no—
113#13063287—21no—
114#13063287—21no—
115C4×C22⋊D43—22no—
116C4×C22⋊D43—22no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—22no—
120(C22⋊D43)⋊C4—22no—
121(C22⋊D43)⋊C4—22no—
122#13063284—21no—
123#13063284C2311yescharacteristic
124#13063283—22no—
125#13063283—21no—
126#13063282—22no—
127#13063282—21no—
128C2×C4⋊Dic43—21no—
129C2×C4⋊Dic43C2311yescharacteristic
130C4⋊C4×D43—22no—
131C4⋊C4×D43—21no—
132C2×C22⋊Dic43—22no—
133C2×(C2×D43)⋊C4—22no—
134C2×(C2×D43)⋊C4—22no—
135C2×(C2×D43)⋊C4D412yes—
136C22⋊C4×D43—22no—
137C22⋊C4×D43—22no—
138C22⋊C4×D43—22no—
139C2×C4×Dic43C2311yescharacteristic
140C2×C4×Dic43C2311yescharacteristic
141C42×D43—22no—
142C42×D43—21no—
143#13063258—21no—
144#13063256—21no—
145#13063252—22no—
146#13063252C2×C414yescomplemented
147#13063251—22no—
148#13063251C2×C414yescomplemented
149#13063248—21no—
150#13063246—21no—
151#13063246—21no—
152#13063245—21no—
153#13063241—22no—
154#13063241C2×C414yescomplemented
155#13063236—21no—
156C4×C43⋊C8—21no—
157C43⋊#95—21no—
158C43⋊#95—21no—
159C43⋊#95—22no—
160C2×#41×C43C2311yescharacteristic
161C22×D4×C43C2311yescharacteristic
162C23×C4×C43—21no—
163AGL(1,ℤ/8)×C43—22no—
164AGL(1,ℤ/8)×C43C2×C414yescomplemented
165C2×SD16×C43—21no—
166C2×D8×C43—21no—
167C2×M16×C43C2311yescharacteristic
168C2×M16×C43C2311yescharacteristic
169C4×Q8×C43D411yescharacteristic, complemented
170C4×Q8×C43D411yescharacteristic, complemented
171C4×D4×C43—21no—
172C4×D4×C43—21no—
173C4×D4×C43—21no—
174C4×D4×C43—21no—
175C4×D4×C43—21no—
176C4×D4×C43—21no—
177C4×D4×C43D411yescharacteristic, complemented
178C4×D4×C43D411yescharacteristic, complemented
179#117×C43—21no—
180#117×C43C2311yescharacteristic
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C22⋊C4×C43—21no—
183C2×C42×C43—21no—
184C2×C42×C43C2311yescharacteristic
185#107×C43—21no—
186#106×C43—21no—
187#103×C43—21no—
188#102×C43—21no—
189#102×C43—21no—
190#102×C43—21no—
191#97×C43—21no—
192C4×C8×C43—21no—
193C24×C43—21no—
194C23×D43—22no—
195C23×D43C2×D412yes—
196#41×C43—21no—
197#41×C43—21no—
198#41×C43C22×C412yes—
199#41×C43#4112yes—
200C2×Q8×C43C2×D411yescharacteristic
201C2×D4×C43—21no—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—21no—
205C2×D4×C43—21no—
206C2×D4×C43—21no—
207C2×D4×C43C22×C412yescomplemented
208C2×D4×C43C2×D411yescharacteristic
209C22×C4×C43—21no—
210C22×C4×C43—21no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—41no—
214C22×C4×C43—41no—
215C22×C4×C43—82no—
216C22×C4×C43C2×D411yescharacteristic
217C22×C4×C43C2×D411yescharacteristic
218C22×C4×C43C2411yescharacteristic
219C2×C22⋊D43—22no—
220C2×C22⋊D43—21no—
221C2×C22⋊D43—28no—
222C2×C22⋊D43—82no—
223C2×C22⋊D43—82no—
224C22×Dic43—22no—
225C22×Dic43—21no—
226C22×Dic43—21no—
227C22×Dic43C2×D412yes—
228#10621902—24no—
229#10621902—24no—
230D4×D43—24no—
231D4×D43—28no—
232D4×D43—24no—
233D4×D43—28no—
234#10621898—24no—
235#10621898—21no—
236#10621898—21no—
237#10621898—24no—
238#10621898C22×C412yes—
239#10621898#4112yes—
240C2×D172—22no—
241C2×D172—24no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—21no—
245C2×D172—21no—
246C2×D172—24no—
247C2×D172C22×C412yes—
248C2×D172C2×D411yescharacteristic
249C2×D172#4112yes—
250C2×C4×D43—22no—
251C2×C4×D43—21no—
252C2×C4×D43—22no—
253C2×C4×D43—21no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—21no—
258C2×C4×D43—22no—
259C2×C4×D43—82no—
260C2×C4×D43—84no—
261C2×Dic86C2×D411yescharacteristic
262SD16×C43—24no—
263D8×C43—24no—
264M16×C43—21no—
265M16×C43—21no—
266M16×C43—21no—
267M16×C43C22×C412yescomplemented
268C2×C8×C43—21no—
269C2×C8×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2×D411yescharacteristic
275C4⋊C4×C43C2×D411yescharacteristic
276C22⋊C4×C43—21no—
277C22⋊C4×C43—21no—
278C22⋊C4×C43—21no—
279C22⋊C4×C43—41no—
280C22⋊C4×C43—41no—
281C42×C43—21no—
282C42×C43—21no—
283C42×C43—21no—
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C42×C43C2×D411yescharacteristic
287C42×C43C2×D411yescharacteristic
288C22⋊Dic43—22no—
289C22⋊Dic43—21no—
290C22⋊Dic43—82no—
291#10621883—24no—
292#10621882—24no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—22no—
296(C2×D43)⋊C4—21no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—21no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—82no—
301C4⋊Dic43—22no—
302C4⋊Dic43—21no—
303C4⋊Dic43—21no—
304C4⋊Dic43C2×D411yescharacteristic
305C4⋊Dic43C2×D411yescharacteristic
306Dic43⋊C4—22no—
307Dic43⋊C4—21no—
308Dic43⋊C4—21no—
309C4×Dic43—22no—
310C4×Dic43—22no—
311C4×Dic43—21no—
312C4×Dic43—21no—
313C4×Dic43—21no—
314C4×Dic43—21no—
315C4×Dic43—21no—
316C4×Dic43—21no—
317C4×Dic43C22×C412yescomplemented
318#10621877—21no—
319#10621877—21no—
320#10621877—21no—
321#10621877C22×C412yescomplemented
322C2×C43⋊C8—21no—
323C2×C43⋊C8—21no—
324C23×C43—21no—
325C23×C43—22no—
326C23×C43—42no—
327C23×C43—42no—
328C23×C43—41no—
329C23×C43—41no—
330C23×C43C22×D411yescharacteristic
331C22×D43—22no—
332C22×D43—21no—
333C22×D43—28no—
334C22×D43—22no—
335C22×D43—42no—
336C22×D43—42no—
337C22×D43—82no—
338C22×D43—82no—
339C22×D43C4×D414yes—
340Q8×C43—21no—
341Q8×C43C4×D412yes—
342D4×C43—22no—
343D4×C43—22no—
344D4×C43—22no—
345D4×C43—22no—
346D4×C43—21no—
347D4×C43—41no—
348D4×C43—41no—
349D4×C43C4×D412yes—
350C2×C4×C43—21no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—21no—
354C2×C4×C43—21no—
355C2×C4×C43—41no—
356C2×C4×C43—41no—
357C2×C4×C43—42no—
358C2×C4×C43—42no—
359C2×C4×C43—41no—
360C2×C4×C43—81no—
361C2×C4×C43—82no—
362C2×C4×C43—82no—
363C2×C4×C43#12011yescharacteristic
364C2×C4×C43#12011yescharacteristic
365C2×C4×C43#12011yescharacteristic
366C2×C4×C43#12011yescharacteristic
367C2×C4×C43C23×C411yescharacteristic
368C2×C4×C43C22×D411yescharacteristic
369C2×C4×C43C22×D411yescharacteristic
370C2×C4×C43C2×#4111yescharacteristic
371C2×C4×C43C2×#4111yescharacteristic
372C2×C4×C43C2×#4111yescharacteristic
373C22⋊D43—28no—
374C22⋊D43—22no—
375C22⋊D43—22no—
376C22⋊D43—88no—
377C2×Dic43—21no—
378C2×Dic43—22no—
379C2×Dic43—21no—
380C2×Dic43—22no—
381C2×Dic43—21no—
382C2×Dic43—41no—
383C2×Dic43—41no—
384C2×Dic43—42no—
385C2×Dic43—41no—
386C2×Dic43—41no—
387C2×Dic43—41no—
388C2×Dic43—82no—
389D172—28no—
390D172—22no—
391D172—22no—
392D172—21no—
393D172—22no—
394D172—22no—
395D172C4×D412yes—
396C4×D43—28no—
397C4×D43—22no—
398C4×D43—22no—
399C4×D43—44no—
400C4×D43—42no—
401C4×D43—81no—
402C4×D43—82no—
403C4×D43—82no—
404C4×D43—82no—
405C4×D43—82no—
406Dic86—21no—
407Dic86C4×D412yes—
408C8×C43—22no—
409C8×C43—41no—
410C43⋊C8—22no—
411C43⋊C8—41no—
412#21473—431nomaximal, Sylow
413C22×C43—21no—
414C22×C43—21no—
415C22×C43—22no—
416C22×C43—44no—
417C22×C43—41no—
418C22×C43—41no—
419C22×C43—42no—
420C22×C43—82no—
421C22×C43—81no—
422C22×C43—81no—
423C22×C43C2×C4×D411yescharacteristic
424C22×C43C2×#12011yescharacteristic
425C22×C43#52511yescharacteristic
426C2×D43—22no—
427C2×D43—24no—
428C2×D43—42no—
429C2×D43—41no—
430C2×D43—42no—
431C2×D43—41no—
432C2×D43—44no—
433C2×D43—82no—
434C2×D43—88no—
435C4×C43—21no—
436C4×C43—21no—
437C4×C43—21no—
438C4×C43—21no—
439C4×C43—22no—
440C4×C43—41no—
441C4×C43—41no—
442C4×C43—81no—
443C4×C43C2×C4×D411yescharacteristic
444C4×C43C2×C4×D411yescharacteristic
445C4×C43#52511yescharacteristic
446C4×C43#52511yescharacteristic
447Dic43—22no—
448Dic43—42no—
449Dic43—42no—
450Dic43—41no—
451Dic43—41no—
452Dic43—81no—
453C4×H(5,𝔽2)—431no—
454C2×#453—431no—
455C4×AGL(1,ℤ/8)—431no—
456C4×AGL(1,ℤ/8)D4311yescharacteristic, complemented
457#2328—431no—
458#1887—431no—
459#1883—431no—
460#1883—431no—
461#1860—431no—
462#1860—431no—
463#1856—431no—
464#1792—431no—
465#1759—431no—
466#1759—431no—
467C4×#100—431no—
468C2×C43—21no—
469C2×C43—21no—
470C2×C43—42no—
471C2×C43—82no—
472C2×C43C4×#12011yescharacteristic
473C2×C43#301911yescharacteristic
474C2×C43#302111yescharacteristic
475D43—44no—
476D43—42no—
477C2×H(5,𝔽2)—431no—
478C2×AGL(1,ℤ/8)—431no—
479C2×AGL(1,ℤ/8)C2×D4311yescharacteristic
480C2×#127—431no—
481#520—431no—
482#520—431no—
483#520—861no—
484#520—861no—
485#518—431no—
486#518—862no—
487#518—861no—
488#518—861no—
489C4×#41—431no—
490C4×#41—861no—
491C4×#41—861no—
492C4×#41C2×D4311yescharacteristic
493C2×C4×D4—431no—
494C2×C4×D4—861no—
495C2×C4×D4—862no—
496C2×C4×D4—861no—
497C2×C4×D4C2×D4311yescharacteristic, complemented
498#453—438no—
499#442—21no—
500#442—861no—
501#440—21no—
502#440—861no—
503C4×SD16—21no—
504C4×SD16—861no—
505C4×D8—21no—
506C4×D8—861no—
507#428—431no—
508#428C2×D4311yescharacteristic, complemented
509C2×#104—431no—
510C2×#104—431no—
511C2×#104—431no—
512C2×#104—431no—
513#418—431no—
514#418C2×D4311yescharacteristic, complemented
515#417—431no—
516#417C2×D4311yescharacteristic
517C2×#100—431no—
518C2×#100—431no—
519C4×M16—431no—
520C4×M16C2×D4311yescharacteristic, complemented
521#390—431no—
522#390—431no—
523#386—862no—
524#386—862no—
525#382—431no—
526#376—431no—
527#343—431no—
528#343—431no—
529#339—431no—
530#339—431no—
531#339—431no—
532#339—431no—
533C43#2147311yescharacteristic, complemented, Sylow
534H(5,𝔽2)—434no—
535H(5,𝔽2)—862no—
536H(5,𝔽2)—862no—
537H(5,𝔽2)—862no—
538C2×#41—431no—
539C2×#41—861no—
540C2×#41—861no—
541C2×#41C22×D4311yescharacteristic
542C22×D4—431no—
543C22×D4—861no—
544C22×D4—862no—
545C22×D4—861no—
546C22×D4—862no—
547C22×D4C22×D4311yescharacteristic
548C23×C4—21no—
549C23×C4—432no—
550C23×C4—862no—
551AGL(1,ℤ/8)—22no—
552AGL(1,ℤ/8)—434no—
553AGL(1,ℤ/8)—862no—
554AGL(1,ℤ/8)C4×D4314yescomplemented
555C2×SD16—21no—
556C2×SD16—861no—
557C2×D8—21no—
558C2×D8—861no—
559C2×M16—431no—
560C2×M16—431no—
561C2×M16C22×D4311yescharacteristic
562C2×M16C22×D4311yescharacteristic
563#127—434no—
564#127—862no—
565C4×Q8—431no—
566C4×Q8—431no—
567C4×Q8—861no—
568C4×Q8—861no—
569C4×Q8C22⋊D4311yescharacteristic, complemented
570C4×Q8C22⋊D4311yescharacteristic, complemented
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4—431no—
578C4×D4—431no—
579C4×D4—861no—
580C4×D4—861no—
581C4×D4—861no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585C4×D4—862no—
586C4×D4—862no—
587C4×D4—862no—
588C4×D4—862no—
589C4×D4—862no—
590C4×D4—862no—
591C4×D4—862no—
592C4×D4—861no—
593C4×D4—861no—
594C4×D4—861no—
595C4×D4—861no—
596C4×D4—861no—
597C4×D4—861no—
598C4×D4—861no—
599C4×D4—861no—
600C4×D4—861no—
601C4×D4C22⋊D4311yescharacteristic, complemented
602C4×D4C22⋊D4311yescharacteristic, complemented
603#117—21no—
604#117—431no—
605#117—862no—
606#117—862no—
607#117—861no—
608#117—861no—
609#117—861no—
610#117C22×D4311yescharacteristic
611C2×C4⋊C4—431no—
612C2×C4⋊C4—862no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4C22×D4311yescharacteristic
616C2×C22⋊C4—21no—
617C2×C22⋊C4—432no—
618C2×C22⋊C4—862no—
619C2×C22⋊C4—862no—
620C2×C22⋊C4—862no—
621C2×C22⋊C4—862no—
622C2×C22⋊C4—862no—
623C2×C22⋊C4—862no—
624C2×C42—21no—
625C2×C42—431no—
626C2×C42—431no—
627C2×C42—862no—
628C2×C42—861no—
629C2×C42C22×D4311yescharacteristic
630#107—21no—
631#107—861no—
632#106—21no—
633#106—861no—
634#104—434no—
635#104—434no—
636#104—862no—
637#104—862no—
638#103—21no—
639#103—861no—
640#102—21no—
641#102—21no—
642#102—21no—
643#102—861no—
644#102—861no—
645#102—861no—
646#100—434no—
647#100—862no—
648#97—21no—
649#97—861no—
650C4×C8—21no—
651C4×C8—861no—
652#95—862no—
653#95—861no—
654#95—861no—
655C24—21no—
656C24—432no—
657C24—862no—
658#41—21no—
659#41—21no—
660#41—432no—
661#41—432no—
662#41—864no—
663#41—864no—
664#41—864no—
665#41—864no—
666#41—861no—
667#41—861no—
668#41C2×C4×D4312yes—
669#41#1062189812yes—
670C2×Q8—431no—
671C2×Q8C2×C22⋊D4311yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—432no—
679C2×D4—431no—
680C2×D4—432no—
681C2×D4—864no—
682C2×D4—862no—
683C2×D4—864no—
684C2×D4—868no—
685C2×D4—868no—
686C2×D4—864no—
687C2×D4—862no—
688C2×D4—861no—
689C2×D4—864no—
690C2×D4—868no—
691C2×D4—861no—
692C2×D4—861no—
693C2×D4—861no—
694C2×D4—861no—
695C2×D4—3442no—
696C2×D4—3442no—
697C2×D4C2×C4×D4312yescomplemented
698C2×D4C2×C22⋊D4311yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—41no—
704C22×C4—41no—
705C22×C4—82no—
706C22×C4—432no—
707C22×C4—862no—
708C22×C4—862no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—862no—
713C22×C4—861no—
714C22×C4—861no—
715C22×C4—862no—
716C22×C4—861no—
717C22×C4—862no—
718C22×C4—861no—
719C22×C4—3444no—
720C22×C4—3442no—
721C22×C4D4×D4311yescharacteristic
722C22×C4D4×D4311yescharacteristic
723C22×C4C23×D4311yescharacteristic
724SD16—24no—
725SD16—864no—
726D8—24no—
727D8—864no—
728M16—21no—
729M16—21no—
730M16—21no—
731M16—432no—
732M16—861no—
733M16—861no—
734M16—861no—
735M16C2×C4×D4312yescomplemented
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—861no—
739C2×C8—861no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—21no—
743C4⋊C4—21no—
744C4⋊C4—431no—
745C4⋊C4—431no—
746C4⋊C4—862no—
747C4⋊C4—862no—
748C4⋊C4—861no—
749C4⋊C4—861no—
750C4⋊C4—861no—
751C4⋊C4—861no—
752C4⋊C4C2×C22⋊D4311yescharacteristic
753C4⋊C4C2×C22⋊D4311yescharacteristic
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—41no—
758C22⋊C4—41no—
759C22⋊C4—862no—
760C22⋊C4—862no—
761C22⋊C4—862no—
762C22⋊C4—862no—
763C22⋊C4—861no—
764C22⋊C4—862no—
765C22⋊C4—862no—
766C22⋊C4—861no—
767C22⋊C4—861no—
768C22⋊C4—3442no—
769C22⋊C4—3442no—
770C42—21no—
771C42—21no—
772C42—21no—
773C42—432no—
774C42—862no—
775C42—862no—
776C42—861no—
777C42—861no—
778C42—861no—
779C42—861no—
780C42—861no—
781C42—861no—
782C42D4×D4311yescharacteristic
783C42D4×D4311yescharacteristic
784C42C2×C22⋊D4311yescharacteristic
785C42C2×C22⋊D4311yescharacteristic
786C23—21no—
787C23—22no—
788C23—42no—
789C23—42no—
790C23—41no—
791C23—41no—
792C23—434no—
793C23—868no—
794C23—862no—
795C23—861no—
796C23—862no—
797C23—3442no—
798C23—3442no—
799C23—1722no—
800C23—1722no—
801C23C2×D4×D4311yescharacteristic
802Q8—21no—
803Q8—432no—
804Q8—861no—
805Q8C4×C22⋊D4312yes—
806D4—22no—
807D4—22no—
808D4—22no—
809D4—22no—
810D4—21no—
811D4—41no—
812D4—41no—
813D4—432no—
814D4—868no—
815D4—868no—
816D4—862no—
817D4—862no—
818D4—862no—
819D4—862no—
820D4—862no—
821D4—861no—
822D4—862no—
823D4—3448no—
824D4C4×C22⋊D4312yes—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—81no—
836C2×C4—82no—
837C2×C4—82no—
838C2×C4—868no—
839C2×C4—861no—
840C2×C4—862no—
841C2×C4—862no—
842C2×C4—862no—
843C2×C4—861no—
844C2×C4—861no—
845C2×C4—862no—
846C2×C4—3442no—
847C2×C4—3441no—
848C2×C4—3442no—
849C2×C4—3442no—
850C2×C4—3442no—
851C2×C4—3442no—
852C2×C4—1722no—
853C2×C4—1724no—
854C2×C4—1721no—
855C2×C4—1721no—
856C2×C4—1721no—
857C2×C4—1721no—
858C2×C4—1721no—
859C2×C4—1722no—
860C2×C4#1306329311yescharacteristic
861C2×C4#1306329311yescharacteristic
862C2×C4#1306329311yescharacteristic
863C2×C4#1306329311yescharacteristic
864C2×C4C22×C4×D4311yescharacteristic
865C2×C4C2×D4×D4311yescharacteristic
866C2×C4C22×C22⋊D4311yescharacteristic
867C2×C4#41×D4311yescharacteristic
868C2×C4#41×D4311yescharacteristic
869C2×C4C2×#1062189811yescharacteristic
870C8—22no—
871C8—41no—
872C8—862no—
873C8—1721no—
874C22—21no—
875C22—21no—
876C22—22no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—42no—
881C22—82no—
882C22—81no—
883C22—81no—
884C22—862no—
885C22—864no—
886C22—3442no—
887C22—3448no—
888C22—1724no—
889C22—1721no—
890C22—1722no—
891C22—1721no—
892C22—1722no—
893C22C4×D4×D4311yescharacteristic
894C22C2×#1306329311yescharacteristic
895C22#1458340811yescharacteristic
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—22no—
901C4—41no—
902C4—41no—
903C4—81no—
904C4—862no—
905C4—3441no—
906C4—1722no—
907C4—1721no—
908C4—1722no—
909C4—1721no—
910C4C4×D4×D4311yescharacteristic
911C4C2×C4×C22⋊D4311yescharacteristic
912C4#1458340611yescharacteristic
913C4#1458340811yescharacteristic
914C2—21no—
915C2—21no—
916C2—42no—
917C2—82no—
918C2—1722no—
919C2—1724no—
920C2C4×#1306329311yescharacteristic
921C2#1914395011yescharacteristic
922C2#1914396411yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×AGL(1,ℤ/8)×C43C2
socleC22×C43C2×#120
prime radicalC2×#14583065C2
cosocleC22×C4×C43C24
hypercenterC4×AGL(1,ℤ/8)D43
hypocenterC43#21473
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C4×#13063371C2semidirect
3. C4×#13063351C2semidirect
4. #19137317C2semidirect
5. #19134990C2semidirect
6. #19134973C2semidirect
7. #19134968C2semidirect
8. #19134826C2semidirect
9. #19134825C2semidirect
10. #19134803C2semidirect
11. #19134547C2semidirect
12. #19134408C2semidirect
13. #19134405C2semidirect
14. C4×#13063241C2semidirect
15. C4×AGL(1,ℤ/8)×C43C2semidirect
34. #14583065C4semidirect
39. #14582939C22semidirect
44. #14582904C22semidirect
48. C4×#10621877C22semidirect
49. #14582802C22semidirect
53. #14582764C22semidirect
54. #14582745C22semidirect
55. #14582667C22semidirect
56. #14582667C22semidirect
57. #14582660C22semidirect
58. #14582660C22semidirect
59. #14582658C22semidirect
60. #14582658C22semidirect
63. C2×C4×D4×C43C22semidirect
68. C43×#428C22semidirect
69. C43×#418C22semidirect
71. C4×M16×C43C22semidirect
75. #13063371C2×C4semidirect
87. #13063351C2×C4semidirect
93. #13063321C2×C4semidirect
96. C4×Dic86D4semidirect
97. C4×Dic86D4semidirect
107. C4×D172D4semidirect
108. C4×D172D4semidirect
146. #13063252C2×C4semidirect
148. #13063251C2×C4semidirect
154. #13063241C2×C4semidirect
164. AGL(1,ℤ/8)×C43C2×C4semidirect
169. C4×Q8×C43D4semidirect
170. C4×Q8×C43D4semidirect
177. C4×D4×C43D4semidirect
178. C4×D4×C43D4semidirect
207. C2×D4×C43C22×C4semidirect
267. M16×C43C22×C4semidirect
317. C4×Dic43C22×C4semidirect
321. #10621877C22×C4semidirect
456. C4×AGL(1,ℤ/8)D43semidirect
497. C2×C4×D4C2×D43semidirect
508. #428C2×D43semidirect
514. #418C2×D43semidirect
520. C4×M16C2×D43semidirect
533. C43#21473semidirect
554. AGL(1,ℤ/8)C4×D43semidirect
569. C4×Q8C22⋊D43semidirect
570. C4×Q8C22⋊D43semidirect
601. C4×D4C22⋊D43semidirect
602. C4×D4C22⋊D43semidirect
697. C2×D4C2×C4×D43semidirect
735. M16C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C4×#130633712
C2×#145830652
C4×#130633512
#191373172
#191349902
#191349732
#191349682
#191348262
#191348252
#191348032
#191345472
#191344082
#191344052
C4×#130632412
C4×AGL(1,ℤ/8)×C432
#2147343