Finite Group Databasebeta

← #25129859

Subgroups — #25129859

Order 11008.

1424 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583447C211yesmaximal, characteristic
2C2×#14583211C212yesmaximal, complemented
3#389×D43C211yesmaximal, characteristic, complemented
4#19135924C211yesmaximal, characteristic, complemented
5#19135923C211yesmaximal, characteristic, complemented
6#19135826C211yesmaximal, characteristic, complemented
7#19134909C212yesmaximal, complemented
8#19134844C212yesmaximal, complemented
9#19134840C212yesmaximal, complemented
10#19134662C211yesmaximal, characteristic, complemented
11C43×#2041C211yesmaximal, characteristic, complemented
12C22×#10621900—21no—
13#14583447—28no—
14C2×#13063325C2211yescharacteristic
15C2×#13063312—21no—
16C2×#13063296—21no—
17C2×#13063296C2212yes—
18C2×D4×Dic43—21no—
19C2×D4×Dic43C2212yes—
20C2×C4⋊C4×D43—21no—
21C2×C4⋊C4×D43C2211yescharacteristic
22C2×C4⋊C4×D43C2211yescharacteristic
23C2×C42×D43C2211yescharacteristic
24#14583211—28no—
25C2×#13063259C2212yes—
26C2×#13063258C2212yes—
27C2×#13063246C2212yes—
28C2×#13063246C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30#14582798C2211yescharacteristic
31#14582797C2211yescharacteristic
32#14582796—21no—
33#14582795C2211yescharacteristic
34#14582794—21no—
35#95×D43—21no—
36#14582662C2212yes—
37#14582661C2212yes—
38#14582654C2211yescharacteristic
39#14582653C2212yes—
40C2×#127×C43C2211yescharacteristic
41C2×#102×C43C2212yes—
42C2×#102×C43C2212yes—
43C43×#389C2211yescharacteristic
44C43×#336C2211yescharacteristic
45C2×#10621900—28no—
46C2×#10621900—44no—
47C2×#10621900—44no—
48C22×Dic86—21no—
49C22×C22⋊D43—22no—
50C23×Dic43—22no—
51C22×C4×D43—21no—
52C22×C4×D43—21no—
53C22×C4×D43D411yescharacteristic
54C22×C4×D43D411yescharacteristic
55C22×C4×D43C2311yescharacteristic
56C22×C43⋊C8C2312yes—
57#13063325—24no—
58#13063312—28no—
59#13063296—28no—
60#13063296—24no—
61#13063296D418yes—
62D4×Dic43—28no—
63D4×Dic43—24no—
64D4×Dic43—24no—
65C2×C4⋊Dic43—21no—
66C2×C4⋊Dic43—21no—
67C2×C4⋊Dic43C2311yescharacteristic
68C2×C4⋊Dic43C2312yes—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×Dic43⋊C4—21no—
71C2×Dic43⋊C4—21no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C4⋊C4×D43—22no—
75C4⋊C4×D43—22no—
76C4⋊C4×D43—24no—
77C4⋊C4×D43—44no—
78C2×C22⋊Dic43—22no—
79C2×C22⋊Dic43—22no—
80C2×C4×Dic43D411yescharacteristic
81C2×C4×Dic43D411yescharacteristic
82C2×C4×Dic43C2311yescharacteristic
83C42×D43—24no—
84#13063259—24no—
85#13063258—24no—
86#13063246—24no—
87#13063246—24no—
88(C2×D43)⋊C8—24no—
89C43⋊#95—21no—
90C43⋊#95—21no—
91C43⋊#95—21no—
92C22×D4×C43—21no—
93C22×D4×C43—21no—
94C22×D4×C43C2312yes—
95C22×C8×C43C2312yes—
96#127×C43—24no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2311yescharacteristic
100C2×C42×C43C2311yescharacteristic
101#102×C43—24no—
102#102×C43—24no—
103#95×C43—21no—
104C24×C43—22no—
105C23×D43C2×D411yescharacteristic
106C2×D4×C43—24no—
107C2×D4×C43—24no—
108C2×D4×C43—22no—
109C2×D4×C43—22no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—42no—
114C2×D4×C43—42no—
115C2×D4×C43—42no—
116C2×D4×C43—42no—
117C2×D4×C43C2×D414yes—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2411yescharacteristic
123C2×C22⋊D43—28no—
124C2×C22⋊D43—44no—
125C2×C22⋊D43—44no—
126C22×Dic43—28no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129C22×Dic43—21no—
130C22×Dic43—44no—
131C22×Dic43—44no—
132C22×Dic43C2×D411yescharacteristic
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135#10621900—432no—
136C2×C4×D43—21no—
137C2×C4×D43—21no—
138C2×C4×D43—22no—
139C2×C4×D43—24no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—22no—
143C2×C4×D43—22no—
144C2×C4×D43—41no—
145C2×C4×D43—42no—
146C2×C4×D43—42no—
147C2×C4×D43—42no—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43D814yes—
151C2×C4×D43C2×D414yes—
152C2×Dic86—24no—
153C2×Dic86—42no—
154C2×Dic86—42no—
155C2×C8×C43—22no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43#4112yescomplemented
162C42×C43—22no—
163C22⋊Dic43—28no—
164C22⋊Dic43—28no—
165C4⋊Dic43—24no—
166C4⋊Dic43—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—22no—
169C4⋊Dic43—42no—
170C4⋊Dic43C2×D414yes—
171C4⋊Dic43#4112yescomplemented
172Dic43⋊C4—24no—
173Dic43⋊C4—42no—
174Dic43⋊C4—42no—
175Dic43⋊C4—42no—
176C4×Dic43—22no—
177C4×Dic43—22no—
178C4×Dic43—22no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C23×C43—24no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—42no—
188C23×C43—42no—
189C23×C43C22×D411yescharacteristic
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43#12012yes—
195C22×D43C2×D812yes—
196C22×D43AGL(1,ℤ/8)12yes—
197D4×C43—24no—
198D4×C43—24no—
199D4×C43—48no—
200D4×C43—48no—
201D4×C43—42no—
202D4×C43—42no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—22no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43C2×D812yes—
214C2×C4×C43#13712yes—
215C2×C4×C43C22×D412yes—
216C2×C4×C43C2×#4111yescharacteristic
217C2×C4×C43C2×#4111yescharacteristic
218C2×C4×C432−1+412yes—
219C22⋊D43—416no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—24no—
226C2×Dic43—22no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—416no—
230C2×Dic43—41no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43#12012yes—
238C2×Dic43C2×D812yes—
239C4×D43—28no—
240C4×D43—24no—
241C4×D43—24no—
242C4×D43—44no—
243C4×D43—48no—
244C4×D43—84no—
245Dic86—48no—
246C8×C43—42no—
247C43⋊C8—42no—
248#24060—431nomaximal, Sylow
249C22×C43—44no—
250C22×C43—44no—
251C22×C43—44no—
252C22×C43—82no—
253C22×C43—82no—
254C22×C43—82no—
255C22×C43—82no—
256C22×C43C2×#12011yescharacteristic
257C22×C43#52511yescharacteristic
258C22×C43#53611yescharacteristic
259C22×C43C22×D811yescharacteristic
260C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C43C2×#13711yescharacteristic
262C22×C43#57511yescharacteristic
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43#44714yes—
270C4×C43—22no—
271C4×C43—22no—
272C4×C43—42no—
273C4×C43—81no—
274C4×C43#54712yes—
275C4×C43#54712yes—
276Dic43—22no—
277Dic43—22no—
278Dic43—42no—
279Dic43—44no—
280Dic43—41no—
281Dic43—81no—
282C2×#532—431no—
283C2×#480—432no—
284C2×#389—431no—
285#2057—431no—
286#2057—431no—
287#2041—431no—
288#2041D4311yescharacteristic, complemented
289#1874—432no—
290#1862—432no—
291#1862—432no—
292#1817—431no—
293C2×C43—84no—
294C2×C43#240611yescharacteristic
295C2×C43C2×#44711yescharacteristic
296C2×C43#300711yescharacteristic
297C2×C43#310011yescharacteristic
298C2×C43#311211yescharacteristic
299C2×C43#322611yescharacteristic
300C2×C43#323411yescharacteristic
301D43—24no—
302C22×#41—861no—
303#532—868no—
304C2×C4⋊Q8—431no—
305C2×#127C2×D4311yescharacteristic
306C2×#124—861no—
307C2×#121—432no—
308C2×#121—861no—
309C2×C4×D4—432no—
310C2×C4×D4—861no—
311C22×C4⋊C4—431no—
312C22×C4⋊C4—431no—
313C22×C4⋊C4—861no—
314C22×C42—431no—
315#480—868no—
316C2×#107—432no—
317C2×#107—432no—
318C2×#102—432no—
319C2×#102—432no—
320C2×#102C2×D4312yes—
321C2×#102C2×D4312yes—
322C2×C22⋊C8—432no—
323#389—431no—
324#389—431no—
325#389—431no—
326#389—861no—
327#389—861no—
328#389C2×D4311yescharacteristic
329C2×#95—861no—
330#340—432no—
331#340—432no—
332#336—432no—
333#336—431no—
334#336C2×D4311yescharacteristic
335C43#2406011yescharacteristic, complemented, Sylow
336C2×#41—868no—
337C2×#41—1724no—
338C2×#41—1724no—
339C22×Q8—861no—
340C22×D4—21no—
341C22×D4—21no—
342C22×D4—862no—
343C22×D4C22×D4312yes—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—861no—
348C23×C4—861no—
349C23×C4—862no—
350C22×C8—432no—
351C22×C8C22×D4312yes—
352C4⋊Q8—864no—
353#127—24no—
354#124—868no—
355#121—438no—
356#121—864no—
357#121—868no—
358C4×D4—864no—
359C4×D4—868no—
360C4×D4—864no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—431no—
365C2×C4⋊C4—862no—
366C2×C4⋊C4—864no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—1724no—
375C2×C4⋊C4C22×D4311yescharacteristic
376C2×C4⋊C4C22×D4311yescharacteristic
377C2×C22⋊C4—862no—
378C2×C22⋊C4—862no—
379C2×C42—431no—
380C2×C42—431no—
381C2×C42—431no—
382C2×C42—864no—
383C2×C42C22×D4311yescharacteristic
384#107—864no—
385#107—864no—
386#102—24no—
387#102—24no—
388#102—864no—
389#102—864no—
390C22⋊C8—864no—
391#95—21no—
392#95—861no—
393#95—861no—
394#95—861no—
395C24—22no—
396C24—431no—
397#41—17232no—
398C2×Q8—864no—
399C2×Q8—1722no—
400C2×Q8—1722no—
401C2×D4—24no—
402C2×D4—24no—
403C2×D4—22no—
404C2×D4—22no—
405C2×D4—22no—
406C2×D4—22no—
407C2×D4—22no—
408C2×D4—42no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—42no—
412C2×D4—868no—
413C2×D4—1724no—
414C2×D4—1724no—
415C2×D4D4×D4314yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—431no—
419C22×C4—431no—
420C22×C4—434no—
421C22×C4—434no—
422C22×C4—431no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—862no—
426C22×C4—864no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—862no—
430C22×C4—868no—
431C22×C4—861no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—861no—
435C22×C4—1721no—
436C22×C4—1722no—
437C22×C4—1722no—
438C22×C4—1722no—
439C22×C4—1722no—
440C22×C4—1722no—
441C22×C4—1724no—
442C22×C4—1724no—
443C22×C4D4×D4311yescharacteristic
444C22×C4D4×D4311yescharacteristic
445C22×C4C23×D4311yescharacteristic
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—862no—
450C2×C8—862no—
451C2×C8—862no—
452C4⋊C4—21no—
453C4⋊C4—22no—
454C4⋊C4—42no—
455C4⋊C4—434no—
456C4⋊C4—432no—
457C4⋊C4—864no—
458C4⋊C4—864no—
459C4⋊C4—862no—
460C4⋊C4—861no—
461C4⋊C4—862no—
462C4⋊C4—1722no—
463C4⋊C4—1722no—
464C4⋊C4—1722no—
465C4⋊C4—1722no—
466C4⋊C4#1062190012yescomplemented
467C22⋊C4—868no—
468C22⋊C4—868no—
469C42—22no—
470C42—862no—
471C42—862no—
472C42—862no—
473C23—24no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—432no—
481C23—432no—
482C23—432no—
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—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—868no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—864no—
514C2×C4—864no—
515C2×C4—861no—
516C2×C4—864no—
517C2×C4—862no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—3444no—
521C2×C4—1724no—
522C2×C4—1728no—
523C2×C4—17216no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4—1721no—
531C2×C4D8×D4312yes—
532C2×C4#1306335412yes—
533C2×C4C2×D4×D4312yes—
534C2×C4#41×D4311yescharacteristic
535C2×C4C2×#1062190011yescharacteristic
536C2×C4#1306337212yes—
537C8—42no—
538C8—1722no—
539C22—44no—
540C22—44no—
541C22—44no—
542C22—82no—
543C22—82no—
544C22—82no—
545C22—82no—
546C22—434no—
547C22—862no—
548C22—862no—
549C22—862no—
550C22—862no—
551C22—862no—
552C22—862no—
553C22#120×D4311yescharacteristic
554C22#1458340911yescharacteristic
555C22#1458346911yescharacteristic
556C22C2×D8×D4311yescharacteristic
557C22AGL(1,ℤ/8)×D4311yescharacteristic
558C22C2×#1306335411yescharacteristic
559C22#1458369511yescharacteristic
560C4—22no—
561C4—22no—
562C4—42no—
563C4—81no—
564C4—862no—
565C4—862no—
566C4—3441no—
567C4—1724no—
568C4—1722no—
569C4—1721no—
570C4#1458354712yes—
571C4#1458354912yes—
572C2—84no—
573C2—864no—
574C2#1913792511yescharacteristic
575C2#447×D4311yescharacteristic
576C2#1914385011yescharacteristic
577C2#1914459411yescharacteristic
578C2#1914471611yescharacteristic
579C2#1914571211yescharacteristic
580C2#1914578011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2041C2
socleC23×C43C22×D4
prime radicalC2×#14583447C2
hypercenter#2041D43
hypocenterC43#24060
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2041

Complements

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

NH ≅ G/Ntype
2. C2×#14583211C2semidirect
3. #389×D43C2semidirect
4. #19135924C2semidirect
5. #19135923C2semidirect
6. #19135826C2semidirect
7. #19134909C2semidirect
8. #19134844C2semidirect
9. #19134840C2semidirect
10. #19134662C2semidirect
11. C43×#2041C2semidirect
161. C4⋊C4×C43#41semidirect
171. C4⋊Dic43#41semidirect
288. #2041D43semidirect
335. C43#24060semidirect
466. C4⋊C4#10621900semidirect

Maximal subgroups

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

subgroupindex
C2×#145834472
C2×#145832112
#389×D432
#191359242
#191359232
#191358262
#191349092
#191348442
#191348402
#191346622
C43×#20412
#2406043