Finite Group Databasebeta

← #25150916

Subgroups — #25150916

Order 11008.

1318 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583447C211yesmaximal, characteristic
2C2×#14583308C211yesmaximal, characteristic, complemented
3C2×#14583263C211yesmaximal, characteristic, complemented
4#19142906C211yesmaximal, characteristic, complemented
5#19135783C212yesmaximal, complemented
6#19135776C212yesmaximal, complemented
7#19135567C211yesmaximal, characteristic, complemented
8#19134858C212yesmaximal, complemented
9#19134844C212yesmaximal, complemented
10#19134358C211yesmaximal, characteristic, complemented
11C43×#1961C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13#14583447—24no—
14#14583447—24no—
15C2×#13063325C2211yescharacteristic
16C2×#13063317C2211yescharacteristic
17C2×#13063312—21no—
18C2×#13063296—21no—
19C2×#13063296C2212yes—
20C2×D4×Dic43—21no—
21C2×D4×Dic43C2212yes—
22C2×C42×D43C2211yescharacteristic
23#14583308—24no—
24#14583263—24no—
25C2×#13063259C2212yes—
26C2×#13063257C2212yes—
27C2×#13063246C2212yes—
28C2×#13063246C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30C2×#13063236C2211yescharacteristic
31#14582798C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582784—21no—
34#14582784—21no—
35#14582773—21no—
36#14582773—21no—
37#14582756C2211yescharacteristic
38#14582756C2211yescharacteristic
39#14582661C2212yes—
40#14582661C2212yes—
41#14582653C2212yes—
42C2×#127×C43C2211yescharacteristic
43C2×#102×C43C2212yes—
44C2×#102×C43C2212yes—
45C2×#97×C43C2211yescharacteristic
46C43×#382C2211yescharacteristic
47C2×#10621900—28no—
48C2×#10621900—44no—
49C2×#10621900—44no—
50C22×Dic86—21no—
51C22×C22⋊D43—22no—
52C23×Dic43—22no—
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C22×C43⋊C8C2312yes—
57#13063325—22no—
58#13063325D414yes—
59#13063317—22no—
60#13063317—22no—
61#13063312—28no—
62#13063296—28no—
63#13063296—24no—
64#13063296—24no—
65D4×Dic43—28no—
66D4×Dic43—24no—
67D4×Dic43—24no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2312yes—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×C22⋊Dic43—22no—
77C2×C22⋊Dic43—22no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C42×D43—22no—
84C42×D43—22no—
85#13063259—24no—
86#13063257—24no—
87#13063246—24no—
88#13063246—24no—
89(C2×D43)⋊C8—24no—
90#13063236—22no—
91C43⋊#95—21no—
92C43⋊#95—21no—
93C43⋊#95—21no—
94C43⋊#95—21no—
95C22×D4×C43—21no—
96C22×D4×C43—21no—
97C22×D4×C43C2312yes—
98C22×C8×C43C2312yes—
99#127×C43—22no—
100#127×C43D414yes—
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C42×C43C2311yescharacteristic
104#102×C43—24no—
105#102×C43—24no—
106#97×C43—22no—
107#95×C43—21no—
108#95×C43—21no—
109C24×C43—22no—
110C23×D43C2×D411yescharacteristic
111C2×D4×C43—24no—
112C2×D4×C43—24no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—42no—
119C2×D4×C43—42no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C2×D4×C43C2×D414yes—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2411yescharacteristic
128C2×C22⋊D43—28no—
129C2×C22⋊D43—44no—
130C2×C22⋊D43—44no—
131C22×Dic43—28no—
132C22×Dic43—22no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43—44no—
136C22×Dic43—44no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140#10621900—432no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—41no—
150C2×C4×D43—41no—
151C2×Dic86—24no—
152C2×Dic86—42no—
153C2×Dic86—42no—
154C2×C8×C43—22no—
155C2×C8×C43—22no—
156C2×C8×C43#4114yescomplemented
157C4⋊C4×C43—22no—
158C4⋊C4×C43—22no—
159C42×C43C2×D412yes—
160C42×C43C2×D412yes—
161C22⋊Dic43—28no—
162C22⋊Dic43—28no—
163(C2×D43)⋊C4—42no—
164(C2×D43)⋊C4—42no—
165C4⋊Dic43—24no—
166C4⋊Dic43—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—42no—
172C4⋊Dic43—42no—
173C4⋊Dic43C2×D414yes—
174Dic43⋊C4—42no—
175Dic43⋊C4—42no—
176C4×Dic43—22no—
177C4×Dic43—22no—
178C4×Dic43—21no—
179C4×Dic43—21no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C23×C43—24no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43C22×D411yescharacteristic
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43—21no—
197C22×D43AGL(1,ℤ/8)12yes—
198D4×C43—24no—
199D4×C43—24no—
200D4×C43—48no—
201D4×C43—48no—
202D4×C43—42no—
203D4×C43—42no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43#12012yes—
215C2×C4×C43#12012yes—
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43C22×D411yescharacteristic
218C2×C4×C43C2×#4112yes—
219C2×C4×C432−1+412yes—
220C22⋊D43—416no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—24no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—416no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43AGL(1,ℤ/8)12yes—
240C4×D43—28no—
241C4×D43—44no—
242C4×D43—42no—
243C4×D43—42no—
244Dic86—48no—
245C8×C43—24no—
246C43⋊C8—42no—
247#25676—431nomaximal, Sylow
248C22×C43—44no—
249C22×C43—44no—
250C22×C43—44no—
251C22×C43—82no—
252C22×C43—82no—
253C22×C43—82no—
254C22×C43—82no—
255C22×C43C2×#12011yescharacteristic
256C22×C43#53211yescharacteristic
257C22×C43#53611yescharacteristic
258C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
259C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
260C22×C43#57511yescharacteristic
261C22×C43#57511yescharacteristic
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C4×C43—22no—
270C4×C43—22no—
271C4×C43—81no—
272C4×C43—81no—
273C4×C43#54712yes—
274C4×C43#54812yes—
275Dic43—22no—
276Dic43—41no—
277Dic43—44no—
278Dic43—41no—
279Dic43—81no—
280Dic43—81no—
281C2×#532—431no—
282C2×#501—431no—
283C2×#490—431no—
284#2851—431no—
285#2034—432no—
286#2033—432no—
287#1993—431no—
288#1961D4311yescharacteristic, complemented
289#1864—432no—
290#1862—432no—
291#1749—431no—
292C2×C43—84no—
293C2×C43#243211yescharacteristic
294C2×C43#300311yescharacteristic
295C2×C43#300511yescharacteristic
296C2×C43#317111yescharacteristic
297C2×C43#318011yescharacteristic
298C2×C43#323411yescharacteristic
299C2×C43#323511yescharacteristic
300D43—42no—
301C22×#41—861no—
302#532—864no—
303#532—864no—
304C2×C4⋊Q8—431no—
305C2×#127C2×D4311yescharacteristic
306C2×#125—431no—
307C2×#124—861no—
308C2×#121—432no—
309C2×#121—861no—
310C2×C4×D4—432no—
311C2×C4×D4—861no—
312C22×C42—431no—
313#501—864no—
314#490—864no—
315C2×#107—432no—
316C2×#106—432no—
317C2×#102—432no—
318C2×#102—432no—
319C2×#102C2×D4312yes—
320C2×#102C2×D4312yes—
321C2×C22⋊C8—432no—
322C2×#97—431no—
323C2×#97C2×D4311yescharacteristic
324#389—431no—
325#389—431no—
326#387—861no—
327#387—861no—
328#385—861no—
329#385—861no—
330#382C2×D4311yescharacteristic
331#380—431no—
332#380—431no—
333#340—432no—
334#340—432no—
335#336—432no—
336C43#2567611yescharacteristic, complemented, Sylow
337C2×#41—868no—
338C2×#41—1724no—
339C2×#41—1724no—
340C22×Q8—861no—
341C22×D4—21no—
342C22×D4—21no—
343C22×D4—862no—
344C22×D4C22×D4312yes—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—431no—
348C23×C4—862no—
349C22×C8—432no—
350C22×C8C22×D4312yes—
351C4⋊Q8—434no—
352C4⋊Q8—862no—
353#127—22no—
354#127D17214yes—
355#125—862no—
356#125—862no—
357#124—868no—
358#121—864no—
359#121—868no—
360#121—864no—
361C4×D4—864no—
362C4×D4—868no—
363C4×D4—864no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—431no—
366C2×C4⋊C4—431no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4C22×D4311yescharacteristic
373C2×C4⋊C4C22×D4311yescharacteristic
374C2×C22⋊C4—862no—
375C2×C22⋊C4—862no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—861no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42—431no—
381C2×C42—862no—
382C2×C42—862no—
383C2×C42C22×D4311yescharacteristic
384#107—864no—
385#106—864no—
386#102—24no—
387#102—24no—
388#102—864no—
389#102—864no—
390C22⋊C8—864no—
391#97—22no—
392#97—862no—
393#95—21no—
394#95—21no—
395#95—861no—
396#95—861no—
397#95—861no—
398#95—861no—
399C24—22no—
400C24—431no—
401#41—17232no—
402C2×Q8—864no—
403C2×Q8—1722no—
404C2×Q8—1722no—
405C2×D4—24no—
406C2×D4—24no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—42no—
413C2×D4—42no—
414C2×D4—42no—
415C2×D4—42no—
416C2×D4—868no—
417C2×D4—1724no—
418C2×D4—1724no—
419C2×D4C2×D17214yes—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—431no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—862no—
426C22×C4—862no—
427C22×C4—862no—
428C22×C4—868no—
429C22×C4—862no—
430C22×C4—862no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—1721no—
438C22×C4—1721no—
439C22×C4—1724no—
440C22×C4—1724no—
441C22×C4D4×D4311yescharacteristic
442C22×C4D4×D4311yescharacteristic
443C22×C4C23×D4311yescharacteristic
444C2×C8—22no—
445C2×C8—22no—
446C2×C8—862no—
447C2×C8—862no—
448C2×C8—862no—
449C2×C8#1062190014yescomplemented
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—434no—
453C4⋊C4—864no—
454C4⋊C4—862no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—1722no—
460C4⋊C4—1722no—
461C4⋊C4—1722no—
462C4⋊C4—1722no—
463C22⋊C4—868no—
464C22⋊C4—868no—
465C22⋊C4—1722no—
466C22⋊C4—1722no—
467C42—862no—
468C42—862no—
469C42—861no—
470C42—861no—
471C42C2×D17212yes—
472C42D4×D4312yes—
473C23—24no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—432no—
481C23—861no—
482C23—861no—
483C23—861no—
484C23—861no—
485C23—861no—
486C23—861no—
487C23C2×D4×D4311yescharacteristic
488Q8—1728no—
489D4—24no—
490D4—24no—
491D4—48no—
492D4—48no—
493D4—42no—
494D4—42no—
495D4—17216no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—432no—
507C2×C4—868no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—864no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—1724no—
518C2×C4—17216no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1722no—
526C2×C4—1722no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4#1306329512yes—
530C2×C4#1306329512yes—
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4C22×D17211yescharacteristic
533C2×C4C2×#1062190012yes—
534C2×C4#1306337212yes—
535C8—24no—
536C8—1722no—
537C22—44no—
538C22—44no—
539C22—44no—
540C22—82no—
541C22—82no—
542C22—82no—
543C22—82no—
544C22—862no—
545C22—862no—
546C22—862no—
547C22—1721no—
548C22—1721no—
549C22—1721no—
550C22—1721no—
551C22C2×#1306329511yescharacteristic
552C22#1458344711yescharacteristic
553C22#1458346911yescharacteristic
554C22AGL(1,ℤ/8)×D4311yescharacteristic
555C22AGL(1,ℤ/8)×D4311yescharacteristic
556C22#1458369511yescharacteristic
557C22#1458369511yescharacteristic
558C4—22no—
559C4—22no—
560C4—81no—
561C4—81no—
562C4—862no—
563C4—3441no—
564C4—3441no—
565C4—1724no—
566C4—1721no—
567C4—1721no—
568C4#1458355312yes—
569C4#1458355512yes—
570C2—84no—
571C2—1722no—
572C2#1913822511yescharacteristic
573C2#1914382411yescharacteristic
574C2#1914383911yescharacteristic
575C2#1914518711yescharacteristic
576C2#1914529011yescharacteristic
577C2#1914578011yescharacteristic
578C2#1914578811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1961C2
socleC23×C43C22×D4
prime radicalC2×#14583447C2
hypercenter#1961D43
hypocenterC43#25676
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. C2×#14583308C2semidirect
3. C2×#14583263C2semidirect
4. #19142906C2semidirect
5. #19135783C2semidirect
6. #19135776C2semidirect
7. #19135567C2semidirect
8. #19134858C2semidirect
9. #19134844C2semidirect
10. #19134358C2semidirect
11. C43×#1961C2semidirect
156. C2×C8×C43#41semidirect
288. #1961D43semidirect
336. C43#25676semidirect
449. C2×C8#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145834472
C2×#145833082
C2×#145832632
#191429062
#191357832
#191357762
#191355672
#191348582
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