Finite Group Databasebeta

← #25075176

Subgroups — #25075176

Order 11008.

1170 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583554C211yesmaximal, characteristic
2#19145736C211yesmaximal, characteristic, complemented
3#19144388C211yesmaximal, characteristic, complemented
4#19133877C214yesmaximal, complemented
5#19133745C214yesmaximal, complemented
6#19133266C211yesmaximal, characteristic, complemented
7#19133020C211yesmaximal, characteristic, complemented
8#19132985C211yesmaximal, characteristic, complemented
9C43×#3101C211yesmaximal, characteristic, complemented
10C22×#10621898—21no—
11#14583554—22no—
12#14583554—22no—
13#14583554—22no—
14#14583554C2214yes—
15C2×#13063325C2211yescharacteristic
16C2×#13063307—22no—
17C2×#13063304—21no—
18C2×#13063296—21no—
19C2×C4×D172C2211yescharacteristic
20C2×C4⋊C4×D43—21no—
21#14583295C2212yescomplemented
22#14583249C2212yescomplemented
23#14583227—22no—
24#14583196—22no—
25#14583186C2212yescomplemented
26#14583184—22no—
27#14583176C2212yescomplemented
28#14582952C2211yescharacteristic
29#14582942—21no—
30#14582923C2211yescharacteristic
31#14582903—21no—
32#14582644C2214yescomplemented
33D4⋊(C43⋊C8)C2214yescomplemented
34#14582626C2214yescomplemented
35C43×#533C2211yescharacteristic
36C2×C4×D4×C43C2211yescharacteristic
37C43×#483—21no—
38C43×#476C2212yescomplemented
39C43×#461C2212yescomplemented
40C43×#450—21no—
41C4×SD16×C43—22no—
42C43×#431C2211yescharacteristic
43C2×#10621898—24no—
44C2×#10621898—24no—
45C2×#10621898—44no—
46C2×#10621898—44no—
47C22×Dic86—21no—
48C22×D172D411yescharacteristic
49C22×C22⋊D43—22no—
50C22×C4×D43—22no—
51C22×C4×D43—21no—
52C2×#10621877—21no—
53#13063325—21no—
54#13063325—21no—
55#13063325D412yes—
56#13063325C2312yes—
57#13063307—28no—
58#13063307—28no—
59#13063304—24no—
60#13063304—24no—
61#13063296—24no—
62#13063296—24no—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172D412yes—
66C4×D172C2312yes—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43D411yescharacteristic
69C2×C4⋊Dic43D412yes—
70C2×Dic43⋊C4—22no—
71C4⋊C4×D43—24no—
72C4⋊C4×D43—24no—
73C2×C22⋊Dic43—22no—
74C2×(C2×D43)⋊C4—21no—
75#13063258—22no—
76#13063256—24no—
77#13063256—22no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)—21no—
80C4⋊(C43⋊C8)C2312yes—
81#13063249—24no—
82#13063245—22no—
83#13063245—22no—
84C22⋊(C43⋊C8)—21no—
85C4×C43⋊C8C2312yes—
86C22×D4×C43D411yescharacteristic
87C23×C4×C43—21no—
88C2×SD16×C43—22no—
89C4⋊Q8×C43C2311yescharacteristic
90C4⋊Q8×C43C2311yescharacteristic
91#125×C43—21no—
92C22⋊Q8×C43—21no—
93C22⋊Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43D412yes—
99C4×D4×C43C2312yes—
100#117×C43—21no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#106×C43—22no—
105C4⋊C8×C43C2312yes—
106#103×C43—22no—
107#102×C43—22no—
108C22⋊C8×C43—21no—
109C4×C8×C43—21no—
110C24×C43—21no—
111C23×D43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—42no—
116C2×D4×C43C2×D412yes—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C2×C22⋊D43—28no—
126C2×C22⋊D43—48no—
127C22×Dic43—21no—
128C22×Dic43—22no—
129#10621898—48no—
130#10621898—416no—
131#10621898—48no—
132C2×D172—21no—
133C2×D172—22no—
134C2×D172SD1614yescomplemented
135C2×D172C2×D412yes—
136C2×C4×D43—28no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—48no—
140C2×C4×D43—44no—
141C2×Dic86—22no—
142C2×Dic86—22no—
143C2×Dic86—42no—
144C2×Dic86—42no—
145SD16×C43—44no—
146C2×C8×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—41no—
153C4⋊C4×C43—41no—
154C4⋊C4×C43C2×D412yes—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—41no—
158C42×C43—41no—
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2411yescharacteristic
163C22⋊Dic43—28no—
164(C2×D43)⋊C4—22no—
165(C2×D43)⋊C4—22no—
166C4⋊Dic43—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43C2×D414yes—
171C4⋊Dic43C2×D412yes—
172Dic43⋊C4—28no—
173#10621877—42no—
174C2×C43⋊C8—22no—
175C2×C43⋊C8—22no—
176C23×C43—22no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43#12011yescharacteristic
181C22×D43—22no—
182C22×D43—24no—
183C22×D43—42no—
184C22×D43—42no—
185Q8×C43—42no—
186Q8×C43—42no—
187D4×C43—22no—
188D4×C43—22no—
189D4×C43—42no—
190C2×C4×C43—22no—
191C2×C4×C43—22no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—42no—
196C2×C4×C43—44no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43#12011yescharacteristic
200C2×C4×C43#12011yescharacteristic
201C2×C4×C43#12011yescharacteristic
202C2×C4×C43C2×SD1612yes—
203C2×C4×C43AGL(1,ℤ/8)12yes—
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C22⋊D43—416no—
208C2×Dic43—22no—
209C2×Dic43—24no—
210C2×Dic43—42no—
211C2×Dic43—44no—
212D172—22no—
213D172—24no—
214D172C2×SD1614yes—
215C4×D43—44no—
216C4×D43—416no—
217C4×D43—44no—
218Dic86—42no—
219Dic86—42no—
220Dic86—44no—
221C8×C43—42no—
222C43⋊C8—42no—
223C43⋊C8—42no—
224#18757—431nomaximal, Sylow
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—42no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—84no—
231C22×C43#45012yes—
232C22×C43C2×#12011yescharacteristic
233C2×D43—24no—
234C2×D43—48no—
235C2×D43—42no—
236C2×D43—42no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—42no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43#45012yes—
244C4×C43C22×SD1611yescharacteristic
245C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
246C4×C43#57512yes—
247Dic43—44no—
248Dic43—42no—
249C2×#547—431no—
250#3229—431no—
251#3101D4311yescharacteristic, complemented
252#3077—431no—
253#1654—434no—
254#1635—434no—
255#1546—431no—
256#1486—431no—
257#1478—431no—
258C2×C43—22no—
259C2×C43—82no—
260C2×C43C2×#45011yescharacteristic
261C2×C43#300511yescharacteristic
262C2×C43#302011yescharacteristic
263D43—44no—
264C22×#41—861no—
265#547—434no—
266#547—862no—
267#547—862no—
268#547—862no—
269#533C2×D4311yescharacteristic
270C2×C4⋊Q8—431no—
271C2×#123—862no—
272C2×C22⋊Q8—861no—
273C2×#121—861no—
274C2×C4×D4—431no—
275C2×C4×D4C2×D4311yescharacteristic
276C22×C4⋊C4—861no—
277#498—432no—
278#487—432no—
279#483—21no—
280#483—862no—
281#478—862no—
282#476—432no—
283#476C2×D4312yescomplemented
284#475—862no—
285#474—432no—
286#461C2×D4312yescomplemented
287#450—21no—
288C4×SD16—22no—
289#431—431no—
290#431C2×D4311yescharacteristic
291#428—861no—
292#423—431no—
293#418—861no—
294#332—434no—
295D4⋊C8—434no—
296D4⋊C8—434no—
297C43#1875711yescharacteristic, complemented, Sylow
298C2×#41—864no—
299C2×#41—864no—
300C2×#41—1724no—
301C2×#41—1724no—
302C22×Q8—861no—
303C22×D4—431no—
304C22×D4—862no—
305C22×D4C22⋊D4311yescharacteristic
306C23×C4—21no—
307C23×C4—862no—
308C23×C4—861no—
309C2×SD16—22no—
310C2×M16—861no—
311C4⋊Q8—432no—
312C4⋊Q8—432no—
313C4⋊Q8—861no—
314C4⋊Q8—861no—
315C4⋊Q8C22×D4311yescharacteristic
316C4⋊Q8C22×D4311yescharacteristic
317#125—21no—
318#123—868no—
319#123—868no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—864no—
323C22⋊Q8—864no—
324#121—864no—
325#121—864no—
326C4×Q8—21no—
327C4×Q8—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—432no—
331C4×D4—432no—
332C4×D4—861no—
333C4×D4—861no—
334C4×D4C22⋊D4312yes—
335C4×D4C22×D4312yes—
336#117—21no—
337C2×C4⋊C4—431no—
338C2×C4⋊C4—432no—
339C2×C4⋊C4—864no—
340C2×C4⋊C4—862no—
341C2×C4⋊C4—861no—
342C2×C4⋊C4—864no—
343C2×C4⋊C4C22⋊D4311yescharacteristic
344C2×C22⋊C4—21no—
345C2×C22⋊C4—862no—
346C2×C22⋊C4—861no—
347C2×C42C22×D4311yescharacteristic
348#107—862no—
349#106—22no—
350#106—862no—
351#106—864no—
352C4⋊C8—432no—
353C4⋊C8—861no—
354C4⋊C8—861no—
355C4⋊C8C22×D4312yes—
356#103—22no—
357#103—864no—
358#102—22no—
359#102—862no—
360#102—862no—
361C22⋊C8—21no—
362C22⋊C8—861no—
363C4×C8—21no—
364C4×C8—432no—
365C24—21no—
366C24—861no—
367#41—1728no—
368#41—17216no—
369#41—1728no—
370C2×Q8—21no—
371C2×Q8—21no—
372C2×Q8—862no—
373C2×Q8—862no—
374C2×Q8—1722no—
375C2×Q8—1722no—
376C2×D4—21no—
377C2×D4—42no—
378C2×D4—434no—
379C2×D4—432no—
380C2×D4—868no—
381C2×D4—861no—
382C2×D4—862no—
383C2×D4—1728no—
384C2×D4C2×C22⋊D4312yes—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—868no—
391C22×C4—861no—
392C22×C4—862no—
393C22×C4—862no—
394C22×C4—862no—
395C22×C4—1724no—
396C22×C4—1728no—
397C22×C4D4×D4311yescharacteristic
398C22×C4D4×D4311yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400SD16—44no—
401M16—1722no—
402C2×C8—22no—
403C2×C8—862no—
404C2×C8—862no—
405C4⋊C4—21no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—434no—
413C4⋊C4—432no—
414C4⋊C4—868no—
415C4⋊C4—861no—
416C4⋊C4—862no—
417C4⋊C4—862no—
418C4⋊C4—862no—
419C4⋊C4C2×C22⋊D4312yes—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—41no—
423C22⋊C4—868no—
424C22⋊C4—862no—
425C22⋊C4—862no—
426C42—41no—
427C42D4×D4311yescharacteristic
428C42D4×D4311yescharacteristic
429C42C2×C22⋊D4311yescharacteristic
430C42C23×D4311yescharacteristic
431C23—22no—
432C23—42no—
433C23—42no—
434C23—42no—
435C23—864no—
436C23—862no—
437C23—1722no—
438C23—1722no—
439C23#1306329311yescharacteristic
440Q8—42no—
441Q8—42no—
442Q8—1724no—
443Q8—1722no—
444Q8—1722no—
445D4—22no—
446D4—22no—
447D4—42no—
448D4—434no—
449D4—864no—
450D4—862no—
451D4—17216no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—862no—
462C2×C4—864no—
463C2×C4—1724no—
464C2×C4—17216no—
465C2×C4—1722no—
466C2×C4—1724no—
467C2×C4—1724no—
468C2×C4#1306329311yescharacteristic
469C2×C4#1306329311yescharacteristic
470C2×C4#1306329311yescharacteristic
471C2×C4SD16×D4312yes—
472C2×C4#1306335212yes—
473C2×C4C2×D4×D4311yescharacteristic
474C2×C4C2×D4×D4311yescharacteristic
475C2×C4C22×C22⋊D4311yescharacteristic
476C8—42no—
477C8—1722no—
478C8—1722no—
479C22—21no—
480C22—21no—
481C22—42no—
482C22—42no—
483C22—42no—
484C22—84no—
485C22—864no—
486C22—1728no—
487C22—1722no—
488C22—1722no—
489C22#1458304812yes—
490C22C2×#1306329311yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—42no—
495C4—81no—
496C4—81no—
497C4—1724no—
498C4—1722no—
499C4#1458304812yes—
500C4C2×SD16×D4311yescharacteristic
501C4C2×#1306335211yescharacteristic
502C4#1458369712yes—
503C2—22no—
504C2—82no—
505C2—1724no—
506C2C2×#1458304811yescharacteristic
507C2#1914383511yescharacteristic
508C2#1914395711yescharacteristic
subgroupG/H
centerC22C2×#13063293
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3101C2
socleC22×C43C2×#120
prime radicalC2×#14583554C2
hypercenter#3101D43
hypocenterC43#18757
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3101

Complements

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

NH ≅ G/Ntype
2. #19145736C2semidirect
3. #19144388C2semidirect
4. #19133877C2semidirect
5. #19133745C2semidirect
6. #19133266C2semidirect
7. #19133020C2semidirect
8. #19132985C2semidirect
9. C43×#3101C2semidirect
21. #14583295C22semidirect
22. #14583249C22semidirect
25. #14583186C22semidirect
27. #14583176C22semidirect
32. #14582644C22semidirect
33. D4⋊(C43⋊C8)C22semidirect
34. #14582626C22semidirect
38. C43×#476C22semidirect
39. C43×#461C22semidirect
134. C2×D172SD16semidirect
251. #3101D43semidirect
283. #476C2×D43semidirect
286. #461C2×D43semidirect
297. C43#18757semidirect

Maximal subgroups

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

subgroupindex
C2×#145835542
#191457362
#191443882
#191338772
#191337452
#191332662
#191330202
#191329852
C43×#31012
#1875743