Finite Group Databasebeta

← #25153250

Subgroups — #25153250

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2C2×#14583258C211yesmaximal, characteristic, complemented
3#19142891C211yesmaximal, characteristic
4#19135734C212yesmaximal, complemented
5#19135729C212yesmaximal, complemented
6#19135569C211yesmaximal, characteristic, complemented
7#19135568C211yesmaximal, characteristic, complemented
8#19134909C212yesmaximal
9#19134899C212yesmaximal, complemented
10#19134358C211yesmaximal, characteristic, complemented
11C2×C43×#489C211yesmaximal, characteristic, complemented
12C22×Q8×D43—21no—
13C2×#13063325C2211yescharacteristic
14C2×#13063324—21no—
15C2×#13063324C2212yes—
16C2×#13063323—21no—
17C4⋊Q8×D43—24no—
18C4⋊Q8×D43—24no—
19C2×#13063301C2211yescharacteristic
20C2×#13063296C2211yescharacteristic
21C2×C4⋊C4×D43—21no—
22C2×C4⋊C4×D43C2212yes—
23C2×C42×D43C2211yescharacteristic
24#14583258—24no—
25C2×#13063249C2212yes—
26C2×#13063246C2212yes—
27C2×(C2×D43)⋊C8C2212yes—
28C2×#13063236C2211yescharacteristic
29#14582806C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582787—21no—
32#14582787—21no—
33#14582775—21no—
34#14582775—21no—
35#14582765C2211yescharacteristic
36#14582662C2212yes—
37#14582662C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40#14582653C2212yes—
41C2×C4⋊Q8×C43C2211yescharacteristic
42C2×#124×C43C2211yescharacteristic
43C43×#489—24no—
44C2×#103×C43C2212yes—
45C2×#102×C43C2212yes—
46C2×#97×C43C2211yescharacteristic
47C22×Dic86—21no—
48C22×Dic86—22no—
49C2×Q8×D43—28no—
50C2×Q8×D43—44no—
51C2×Q8×D43—44no—
52C22×C22⋊D43—21no—
53C22×C4×D43—22no—
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43C2311yescharacteristic
57C22×C43⋊C8C2312yes—
58#13063325—22no—
59#13063325D414yescomplemented
60#13063324—28no—
61#13063324—24no—
62#13063324—24no—
63#13063323—28no—
64#13063301—24no—
65#13063296—24no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2312yes—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4—21no—
73C4⋊C4×D43—28no—
74C4⋊C4×D43—24no—
75C4⋊C4×D43—24no—
76C2×C22⋊Dic43—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C42×D43—22no—
84C42×D43—22no—
85#13063249—24no—
86#13063246—24no—
87(C2×D43)⋊C8—24no—
88#13063236—22no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C22×Q8×C43—21no—
94C22×Q8×C43C2311yescharacteristic
95C22×D4×C43C2311yescharacteristic
96C22×C8×C43C2312yes—
97C4⋊Q8×C43—22no—
98C4⋊Q8×C43D414yescomplemented
99#124×C43—22no—
100#124×C43—22no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2312yes—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#103×C43—24no—
107#102×C43—24no—
108#97×C43—22no—
109C24×C43—21no—
110C23×D43C2×D411yescharacteristic
111C2×Q8×C43—24no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—42no—
117C2×Q8×C43—42no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—42no—
128C2×C22⋊D43—42no—
129C2×C22⋊D43—42no—
130C22×Dic43—22no—
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136Q8×D43—432no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—28no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—44no—
148C2×C4×D43—44no—
149C2×C4×D43#4114yes—
150C2×Dic86—28no—
151C2×Dic86—24no—
152C2×Dic86—44no—
153C2×Dic86—42no—
154C2×Dic86—42no—
155C2×Dic86—44no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C2×C8×C43—22no—
159C4⋊C4×C43—24no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43C2×D414yes—
162C22⋊C4×C43—42no—
163C22⋊C4×C43—42no—
164C42×C43C2×D412yes—
165C42×C43C2×D412yes—
166C22⋊Dic43—42no—
167C22⋊Dic43—42no—
168C22⋊Dic43—42no—
169(C2×D43)⋊C4—42no—
170C4⋊Dic43—24no—
171C4⋊Dic43—22no—
172C4⋊Dic43—22no—
173C4⋊Dic43—22no—
174C4⋊Dic43C2×D414yes—
175Dic43⋊C4—28no—
176Dic43⋊C4—28no—
177Dic43⋊C4—42no—
178C4×Dic43—22no—
179C4×Dic43—22no—
180C4×Dic43—21no—
181C4×Dic43—21no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43C22×D411yescharacteristic
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43#12412yes—
198C22×D43AGL(1,ℤ/8)12yes—
199C22×D43#13712yes—
200Q8×C43—48no—
201Q8×C43—42no—
202Q8×C43—42no—
203D4×C43—42no—
204D4×C43—42no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—24no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43#12012yes—
216C2×C4×C43#12012yes—
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C2×#4112yes—
220C2×C4×C432−1+412yes—
221C22⋊D43—84no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—24no—
229C2×Dic43—42no—
230C2×Dic43—42no—
231C2×Dic43—41no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43#12412yes—
238C2×Dic43AGL(1,ℤ/8)12yes—
239C2×Dic43#13712yes—
240C4×D43—28no—
241C4×D43—28no—
242C4×D43—24no—
243C4×D43—24no—
244C4×D43—416no—
245Dic86—416no—
246Dic86—48no—
247C8×C43—42no—
248C43⋊C8—42no—
249#25908—431nomaximal, Sylow
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—81no—
254C22×C43—81no—
255C22×C43—81no—
256C22×C43—81no—
257C22×C43C2×#12011yescharacteristic
258C22×C43C2×#12411yescharacteristic
259C22×C43#53611yescharacteristic
260C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C43C2×#13711yescharacteristic
263C22×C43C2×#13711yescharacteristic
264C2×D43—22no—
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43#48914yescomplemented
271C4×C43—22no—
272C4×C43—22no—
273C4×C43—44no—
274C4×C43—81no—
275C4×C43#54812yes—
276C4×C43#54812yes—
277Dic43—22no—
278Dic43—22no—
279Dic43—22no—
280Dic43—44no—
281Dic43—81no—
282Dic43—81no—
283C22×C4⋊Q8—431no—
284C2×#489—431no—
285C2×#489D4311yescharacteristic, complemented
286#2850—431no—
287#2024—432no—
288#2023—432no—
289#1993—431no—
290#1993—431no—
291#1874—432no—
292#1872—432no—
293#1749—431no—
294C2×C43—161no—
295C2×C43#243611yescharacteristic
296C2×C43#300311yescharacteristic
297C2×C43#300411yescharacteristic
298C2×C43C2×#48911yescharacteristic
299C2×C43#314111yescharacteristic
300C2×C43#323811yescharacteristic
301C2×C43#323911yescharacteristic
302D43—24no—
303C23×Q8—861no—
304C2×C4⋊Q8—432no—
305C2×C4⋊Q8—431no—
306C2×C4⋊Q8—861no—
307C2×C4⋊Q8—861no—
308C2×C4⋊Q8—864no—
309C2×C4⋊Q8—864no—
310C2×C4⋊Q8C2×D4311yescharacteristic
311C2×#124C2×D4311yescharacteristic
312C2×C22⋊Q8—431no—
313C2×#121—431no—
314C22×C4⋊C4—432no—
315C22×C4⋊C4—861no—
316C22×C42—431no—
317#489—24no—
318#489—864no—
319C2×#103—432no—
320C2×#103C2×D4312yes—
321C2×#102—432no—
322C2×#102C2×D4312yes—
323C2×C22⋊C8—432no—
324C2×#97—431no—
325C2×#97C2×D4311yescharacteristic
326#391—431no—
327#390—431no—
328#388—861no—
329#388—861no—
330#386—861no—
331#386—861no—
332#382—431no—
333#340—432no—
334#340—432no—
335#340—432no—
336#340—432no—
337#336—432no—
338C43#2590811yescharacteristic, complemented, Sylow
339C22×Q8—21no—
340C22×Q8—862no—
341C22×Q8—868no—
342C22×Q8—861no—
343C22×Q8—1724no—
344C22×Q8—1724no—
345C22×Q8C22×D4311yescharacteristic
346C22×D4—861no—
347C22×D4C22×D4311yescharacteristic
348C23×C4—431no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—862no—
352C22×C8—432no—
353C22×C8C22×D4312yes—
354C4⋊Q8—22no—
355C4⋊Q8—434no—
356C4⋊Q8—864no—
357C4⋊Q8—868no—
358C4⋊Q8—868no—
359C4⋊Q8—864no—
360C4⋊Q8—862no—
361C4⋊Q8C22⋊D4314yescomplemented
362#124—22no—
363#124—22no—
364C22⋊Q8—864no—
365#121—864no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—432no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—864no—
371C2×C4⋊C4—868no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—864no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4C22×D4312yes—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C42—431no—
385C2×C42—431no—
386C2×C42—431no—
387C2×C42—862no—
388C2×C42—862no—
389C2×C42C22×D4311yescharacteristic
390#103—24no—
391#103—864no—
392#102—24no—
393#102—864no—
394C22⋊C8—864no—
395#97—22no—
396#97—862no—
397#95—861no—
398#95—861no—
399#95—861no—
400#95—861no—
401C24—21no—
402C24—431no—
403C2×Q8—24no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—42no—
409C2×Q8—42no—
410C2×Q8—868no—
411C2×Q8—864no—
412C2×Q8—1722no—
413C2×Q8—1722no—
414C2×Q8—1724no—
415C2×Q8—1724no—
416C2×Q8—17232no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—1722no—
422C2×D4—1722no—
423C2×D4—1722no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—434no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—868no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—861no—
442C22×C4—861no—
443C22×C4—1724no—
444C22×C4—1724no—
445C22×C4D4×D4311yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4C23×D4311yescharacteristic
448C2×C8—22no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—862no—
452C2×C8—862no—
453C2×C8—862no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—434no—
457C4⋊C4—868no—
458C4⋊C4—868no—
459C4⋊C4—864no—
460C4⋊C4—862no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—1722no—
464C4⋊C4C2×C22⋊D4314yes—
465C22⋊C4—42no—
466C22⋊C4—42no—
467C22⋊C4—1722no—
468C22⋊C4—1722no—
469C22⋊C4—1722no—
470C22⋊C4—1722no—
471C42—862no—
472C42—862no—
473C42—861no—
474C42—861no—
475C42D4×D4312yes—
476C42C2×C22⋊D4312yes—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—432no—
485C23—432no—
486C23—432no—
487C23—861no—
488C23—861no—
489C23—861no—
490C23—861no—
491C23C2×D4×D4311yescharacteristic
492Q8—48no—
493Q8—42no—
494Q8—42no—
495Q8—1728no—
496Q8—17216no—
497D4—42no—
498D4—42no—
499D4—3444no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—432no—
513C2×C4—868no—
514C2×C4—868no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—864no—
522C2×C4—864no—
523C2×C4—864no—
524C2×C4—17216no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4—1721no—
531C2×C4—1722no—
532C2×C4—1722no—
533C2×C4#1306329312yes—
534C2×C4#1306329312yes—
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4C22×C22⋊D4311yescharacteristic
537C2×C4#41×D4312yes—
538C2×C4#1306337212yes—
539C8—42no—
540C8—1722no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22—81no—
547C22—81no—
548C22—434no—
549C22—862no—
550C22—862no—
551C22—862no—
552C22—862no—
553C22—862no—
554C22—862no—
555C22C2×#1306329311yescharacteristic
556C22#124×D4311yescharacteristic
557C22#1458346911yescharacteristic
558C22AGL(1,ℤ/8)×D4311yescharacteristic
559C22AGL(1,ℤ/8)×D4311yescharacteristic
560C22#137×D4311yescharacteristic
561C22#137×D4311yescharacteristic
562C4—22no—
563C4—22no—
564C4—44no—
565C4—81no—
566C4—862no—
567C4—862no—
568C4—862no—
569C4—3441no—
570C4—3441no—
571C4—1724no—
572C4#1458355612yes—
573C4#1458355712yes—
574C2—161no—
575C2—864no—
576C2#1913825011yescharacteristic
577C2#1914382011yescharacteristic
578C2#1914382711yescharacteristic
579C2#489×D4311yescharacteristic
580C2#1914498711yescharacteristic
581C2#1914581211yescharacteristic
582C2#1914582111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#489C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#489D43
hypocenterC43#25908
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#489

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D43C2semidirect
2. C2×#14583258C2semidirect
4. #19135734C2semidirect
5. #19135729C2semidirect
6. #19135569C2semidirect
7. #19135568C2semidirect
9. #19134899C2semidirect
10. #19134358C2semidirect
11. C2×C43×#489C2semidirect
59. #13063325D4semidirect
98. C4⋊Q8×C43D4semidirect
270. C2×D43#489semidirect
285. C2×#489D43semidirect
338. C43#25908semidirect
361. C4⋊Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
C2×#145832582
#191428912
#191357342
#191357292
#191355692
#191355682
#191349092
#191348992
#191343582
C2×C43×#4892
#2590843