Finite Group Databasebeta

← #25072735

Subgroups — #25072735

Order 11008.

1200 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144991C211yesmaximal, characteristic, complemented
2#19144686C211yesmaximal, characteristic, complemented
3#19144686C211yesmaximal, characteristic, complemented
4#19133746C214yesmaximal, complemented
5#19133684C214yesmaximal, complemented
6#19133312C211yesmaximal, characteristic, complemented
7#19133038C211yesmaximal, characteristic, complemented
8#19133038C211yesmaximal, characteristic, complemented
9C2×C43×#547C211yesmaximal, characteristic, complemented
10#14583449C2211yescharacteristic
11#14583261—22no—
12#14583251C2212yescomplemented
13#14583247C2212yescomplemented
14#14583217—21no—
15#14583217—21no—
16#14583189C2212yescomplemented
17#14583189C2212yescomplemented
18#14583094C2212yescomplemented
19#14583094C2212yescomplemented
20#14583033—21no—
21#14583033—21no—
22#14583009—22no—
23#14583009—22no—
24#14582956C2211yescharacteristic
25#14582956C2211yescharacteristic
26#14582898—22no—
27C4×#10621877C2211yescharacteristic
28#14582645C2214yescomplemented
29D4⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2214yescomplemented
31C22×#41×C43—21no—
32C43×#547—22no—
33C43×#547—22no—
34C43×#547—22no—
35C43×#547C2214yes—
36C2×C4⋊Q8×C43C2211yescharacteristic
37C2×#123×C43—22no—
38C2×C22⋊Q8×C43—21no—
39C2×#121×C43—21no—
40C2×C4×D4×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic
42C22×C4⋊C4×C43—21no—
43C2×#10621898—21no—
44C2×#10621882—22no—
45C2×#10621882—22no—
46C2×#10621877—21no—
47#13063325C2311yescharacteristic
48#13063322C2311yescharacteristic
49#13063313—21no—
50#13063299—21no—
51#13063299—21no—
52C4×D172—21no—
53C4×D172—21no—
54#13063256—22no—
55#13063256—22no—
56C4⋊(C43⋊C8)C2312yes—
57C4⋊(C43⋊C8)C2312yes—
58#13063248—24no—
59#13063246—22no—
60#13063246—22no—
61#13063245—22no—
62#13063245—22no—
63#13063245—24no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)—21no—
66#13063236—21no—
67#13063236—21no—
68#13063236—21no—
69C4×C43⋊C8C2312yes—
70C2×#41×C43—24no—
71C2×#41×C43—24no—
72C2×#41×C43—48no—
73C22×Q8×C43—21no—
74C22×D4×C43—22no—
75C22×D4×C43D411yescharacteristic
76C22×D4×C43D411yescharacteristic
77C23×C4×C43—22no—
78C23×C4×C43—21no—
79C23×C4×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43D412yes—
83C4⋊Q8×C43C2312yes—
84#123×C43—28no—
85#123×C43—28no—
86C22⋊Q8×C43—24no—
87C22⋊Q8×C43—24no—
88#121×C43—24no—
89#121×C43—24no—
90C4×D4×C43—21no—
91C4×D4×C43—21no—
92C4×D4×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43D412yes—
95C4×D4×C43D412yes—
96C4×D4×C43C2312yes—
97C4×D4×C43C2312yes—
98C2×C4⋊C4×C43—22no—
99C2×C4⋊C4×C43—24no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—24no—
102C2×C4⋊C4×C43D411yescharacteristic
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D412yes—
105C2×C22⋊C4×C43—22no—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C42×C43C2311yescharacteristic
109C24×C43—21no—
110C24×C43—21no—
111#41×C43—416no—
112#41×C43—48no—
113#41×C43—48no—
114C2×Q8×C43—22no—
115C2×Q8×C43—22no—
116C2×Q8×C43—44no—
117C2×D4×C43—24no—
118C2×D4×C43—28no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—48no—
122C2×D4×C43—42no—
123C2×D4×C43C2×D412yes—
124C2×D4×C43C2×D412yes—
125C22×C4×C43—28no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—48no—
134C22×C4×C43—44no—
135C22×C4×C43—44no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C2×C22⋊D43—41no—
140#10621898—44no—
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×C4×D43—41no—
145C2×Dic86—21no—
146C4⋊C4×C43—28no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43C2×D412yes—
153C4⋊C4×C43C2×D412yes—
154C4⋊C4×C43C2×D414yes—
155C22⋊C4×C43—28no—
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C42×C43C2411yescharacteristic
164#10621882—44no—
165#10621882—44no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170#10621877—42no—
171C2×C43⋊C8—22no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—22no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—42no—
178C23×C43—42no—
179C23×C43—42no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43#12011yescharacteristic
183C22×D43—41no—
184Q8×C43—44no—
185Q8×C43—44no—
186D4×C43—24no—
187D4×C43—22no—
188D4×C43—22no—
189D4×C43—22no—
190D4×C43—42no—
191D4×C43—416no—
192D4×C43AGL(1,ℤ/8)14yes—
193C2×C4×C43—22no—
194C2×C4×C43—22no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43—24no—
199C2×C4×C43—44no—
200C2×C4×C43—44no—
201C2×C4×C43—42no—
202C2×C4×C43—42no—
203C2×C4×C43—44no—
204C2×C4×C43—416no—
205C2×C4×C43—44no—
206C2×C4×C43—44no—
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12011yescharacteristic
209C2×C4×C43#12011yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C22⋊D43—82no—
214C2×Dic43—41no—
215D172—42no—
216D172—42no—
217D172—42no—
218C4×D43—82no—
219Dic86—42no—
220C43⋊C8—42no—
221C43⋊C8—42no—
222C43⋊C8—42no—
223#18533—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—24no—
227C22×C43—48no—
228C22×C43—42no—
229C22×C43—42no—
230C22×C43—42no—
231C22×C43—42no—
232C22×C43—42no—
233C22×C43—84no—
234C22×C43#45412yes—
235C22×C43C2×#12011yescharacteristic
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—81no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—21no—
243C4×C43—42no—
244C4×C43—44no—
245C4×C43—42no—
246C4×C43C2×AGL(1,ℤ/8)12yes—
247C4×C43#57512yes—
248Dic43—81no—
249C2×#547D4311yescharacteristic, complemented
250#3141—431no—
251#3109—431no—
252#3109—431no—
253#1635—434no—
254#1625—434no—
255#1556—431no—
256#1490—431no—
257#1490—431no—
258C2×C43—22no—
259C2×C43—44no—
260C2×C43—82no—
261C2×C43#300311yescharacteristic
262C2×C43#300511yescharacteristic
263C2×C43C2×#45411yescharacteristic
264D43—161no—
265C22×#41—21no—
266#547—22no—
267#547—22no—
268#547—22no—
269#547C2×D4314yes—
270#532—431no—
271C2×C4⋊Q8C2×D4311yescharacteristic
272C2×#123—22no—
273C2×C22⋊Q8—21no—
274C2×#121—21no—
275C2×C4×D4C2×D4311yescharacteristic
276C2×C4×D4C2×D4311yescharacteristic
277C22×C4⋊C4—21no—
278#489—862no—
279#487—432no—
280#486—432no—
281#481—861no—
282#481—861no—
283#476—432no—
284#476—432no—
285#459—432no—
286#459—432no—
287#447—861no—
288#447—861no—
289#442—862no—
290#442—862no—
291#432—431no—
292#432—431no—
293#417—862no—
294C4×M16—431no—
295#332—434no—
296D4⋊C8—434no—
297D4⋊C8—434no—
298C43#1853311yescharacteristic, complemented, Sylow
299C2×#41—24no—
300C2×#41—24no—
301C2×#41—48no—
302C2×#41—861no—
303C22×Q8—21no—
304C22×D4—22no—
305C22×D4C22⋊D4311yescharacteristic
306C22×D4C22⋊D4311yescharacteristic
307C23×C4—22no—
308C23×C4—21no—
309C23×C4—21no—
310C2×D8—862no—
311C2×D8—862no—
312C2×M16—861no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—431no—
316C4⋊Q8C22⋊D4312yes—
317C4⋊Q8C22×D4312yes—
318#127—431no—
319#124—861no—
320#123—28no—
321#123—28no—
322C22⋊Q8—24no—
323C22⋊Q8—24no—
324#121—24no—
325#121—24no—
326#121—861no—
327#121—861no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C4×D4—21no—
332C4×D4—861no—
333C4×D4—861no—
334C4×D4C22⋊D4312yes—
335C4×D4C22⋊D4312yes—
336C4×D4C22×D4312yes—
337C4×D4C22×D4312yes—
338C2×C4⋊C4—22no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—24no—
342C2×C4⋊C4C22⋊D4311yescharacteristic
343C2×C4⋊C4C22⋊D4311yescharacteristic
344C2×C4⋊C4C22⋊D4312yes—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C42C22×D4311yescharacteristic
349#106—862no—
350#106—862no—
351C4⋊C8—432no—
352C4⋊C8—432no—
353#103—864no—
354#102—862no—
355#102—862no—
356#102—864no—
357#102—862no—
358#102—862no—
359C22⋊C8—861no—
360C22⋊C8—861no—
361#97—861no—
362#97—861no—
363#97—861no—
364C4×C8—432no—
365C24—21no—
366C24—21no—
367#41—416no—
368#41—48no—
369#41—48no—
370#41—1724no—
371C2×Q8—22no—
372C2×Q8—22no—
373C2×Q8—44no—
374C2×Q8—861no—
375C2×D4—24no—
376C2×D4—28no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—42no—
380C2×D4—48no—
381C2×D4—861no—
382C2×D4—861no—
383C2×D4—861no—
384C2×D4—1721no—
385C2×D4C2×C22⋊D4312yes—
386C2×D4C2×C22⋊D4312yes—
387C22×C4—28no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—44no—
396C22×C4—44no—
397C22×C4—48no—
398C22×C4—1721no—
399C22×C4C2×C22⋊D4311yescharacteristic
400C22×C4C2×C22⋊D4311yescharacteristic
401C22×C4C2×C22⋊D4311yescharacteristic
402D8—1724no—
403D8—1724no—
404M16—1722no—
405C2×C8—862no—
406C2×C8—862no—
407C2×C8—862no—
408C4⋊C4—28no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4C2×C22⋊D4314yes—
417C4⋊C4C2×C22⋊D4312yes—
418C4⋊C4C2×C22⋊D4312yes—
419C22⋊C4—28no—
420C22⋊C4—22no—
421C22⋊C4—22no—
422C22⋊C4—22no—
423C22⋊C4—22no—
424C22⋊C4—1721no—
425C22⋊C4—1721no—
426C42C2×C22⋊D4311yescharacteristic
427C42C2×C22⋊D4311yescharacteristic
428C42C2×C22⋊D4311yescharacteristic
429C42C23×D4311yescharacteristic
430C23—24no—
431C23—22no—
432C23—22no—
433C23—42no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—1721no—
439C23#1306329411yescharacteristic
440Q8—44no—
441Q8—44no—
442Q8—1722no—
443D4—24no—
444D4—22no—
445D4—22no—
446D4—22no—
447D4—42no—
448D4—416no—
449D4—3442no—
450D4—1722no—
451D4—1722no—
452D4—1722no—
453D4#1306335114yes—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—416no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—3442no—
469C2×C4—1721no—
470C2×C4#1306329411yescharacteristic
471C2×C4#1306329411yescharacteristic
472C2×C4#1306329411yescharacteristic
473C2×C4C22×C22⋊D4311yescharacteristic
474C2×C4C22×C22⋊D4311yescharacteristic
475C2×C4C22×C22⋊D4311yescharacteristic
476C8—1722no—
477C8—1722no—
478C8—1722no—
479C22—21no—
480C22—21no—
481C22—24no—
482C22—48no—
483C22—42no—
484C22—42no—
485C22—42no—
486C22—42no—
487C22—42no—
488C22—84no—
489C22—3441no—
490C22—3441no—
491C22—3441no—
492C22#1458307212yes—
493C22C2×#1306329411yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—42no—
499C4—44no—
500C4—42no—
501C4—3441no—
502C4C2×#1306335112yes—
503C4#1458369712yes—
504C2—22no—
505C2—44no—
506C2—82no—
507C2—6881no—
508C2#1914382211yescharacteristic
509C2#1914383711yescharacteristic
510C2C2×#1458307211yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#547C2
socleC22×C43C2×#120
hypercenterC2×#547D43
hypocenterC43#18533
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #19144991C2semidirect
2. #19144686C2semidirect
3. #19144686C2semidirect
4. #19133746C2semidirect
5. #19133684C2semidirect
6. #19133312C2semidirect
7. #19133038C2semidirect
8. #19133038C2semidirect
9. C2×C43×#547C2semidirect
12. #14583251C22semidirect
13. #14583247C22semidirect
16. #14583189C22semidirect
17. #14583189C22semidirect
18. #14583094C22semidirect
19. #14583094C22semidirect
28. #14582645C22semidirect
29. D4⋊(C43⋊C8)C22semidirect
30. D4⋊(C43⋊C8)C22semidirect
249. C2×#547D43semidirect
298. C43#18533semidirect

Maximal subgroups

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

subgroupindex
#191449912
#191446862
#191337462
#191336842
#191333122
#191330382
C2×C43×#5472
#1853343