Finite Group Databasebeta

← #25079376

Subgroups — #25079376

Order 11008.

760 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145054C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic
3C2×#14583179C211yesmaximal, characteristic, complemented
4#19134084C212yesmaximal, complemented
5#19134060C212yesmaximal, complemented
6#19133960C212yesmaximal, complemented
7#19133936C212yesmaximal, complemented
8#19133347C211yesmaximal, characteristic, complemented
9#19133273C211yesmaximal, characteristic, complemented
10#19133268C211yesmaximal, characteristic, complemented
11D4×M16×C43C211yesmaximal, characteristic, complemented
12C2×#13063358—21no—
13C2×#13063358—21no—
14#14583449C2211yescharacteristic
15C2×#13063325C2211yescharacteristic
16#14583293—22no—
17#14583279C2212yescomplemented
18#14583272C2212yescomplemented
19#14583212—21no—
20#14583179—21no—
21#14583179—21no—
22#14583179C2211yescharacteristic
23#14583179C2212yes—
24#14583179C2212yes—
25#14583179C2211yescharacteristic
26#14583094C2211yescharacteristic
27#14583094C2211yescharacteristic
28#14583033—21no—
29C4×#10621882—21no—
30C4×#10621882—21no—
31#14582952C2211yescharacteristic
32C2×#13063258—21no—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34C2×#13063246—21no—
35#14582652C2212yescomplemented
36#14582650C2212yescomplemented
37#14582646C2212yescomplemented
38#14582646C2212yescomplemented
39#14582646C2212yescomplemented
40#14582642C2212yescomplemented
41C22×M16×C43—21no—
42C2×C4×D4×C43C2211yescharacteristic
43C43×#436C2212yes—
44C43×#435—22no—
45C8×D4×C43C2212yes—
46C43×#423C2211yescharacteristic
47C43×#407—21no—
48C4×M16×C43C2211yescharacteristic
49C2×#10621898—21no—
50C22×Dic86—21no—
51#13063358—44no—
52#13063358—44no—
53C2×Dic172—22no—
54C2×Dic172—22no—
55C2×#10621873—22no—
56C2×#10621873—22no—
57C2×#10621882—21no—
58C2×#10621882—21no—
59C22×C43⋊C8—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325C2312yes—
64#13063325C2311yescharacteristic
65#13063322C2311yescharacteristic
66#13063313—21no—
67#13063299—21no—
68#13063299—21no—
69C4×D172—21no—
70C4×D172—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73#13063258—22no—
74#13063258—22no—
75#13063258—21no—
76#13063258—21no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)C2311yescharacteristic
79C4⋊(C43⋊C8)C2311yescharacteristic
80C4⋊(C43⋊C8)C2312yes—
81#13063246—22no—
82#13063246—22no—
83#13063246—21no—
84#13063246—21no—
85#13063245—21no—
86#13063245—21no—
87C22⋊(C43⋊C8)—21no—
88C4×C43⋊C8—21no—
89C22×D4×C43D411yescharacteristic
90C23×C4×C43—21no—
91C2×M16×C43—21no—
92C2×M16×C43—22no—
93C2×M16×C43—44no—
94C2×M16×C43D411yescharacteristic
95C2×M16×C43D411yescharacteristic
96C22×C8×C43—22no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43D411yescharacteristic
100C4×D4×C43D411yescharacteristic
101C4×D4×C43C2311yescharacteristic
102C4×D4×C43C2311yescharacteristic
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2312yes—
108C22⋊C8×C43—22no—
109C22⋊C8×C43—22no—
110#97×C43D412yes—
111C4×C8×C43C2312yes—
112C24×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—22no—
115C2×D4×C43—41no—
116C2×D4×C43C2×D411yescharacteristic
117C2×D4×C43C2×D411yescharacteristic
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—42no—
124C22×C4×C43—42no—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43#4111yescharacteristic
128C2×C22⋊D43—41no—
129C22×Dic43—41no—
130#10621898—42no—
131#10621898—42no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×C4×D43—41no—
136C2×Dic86—21no—
137C2×Dic86—22no—
138C2×Dic86—42no—
139C2×Dic86—42no—
140C2×Dic86—41no—
141M16×C43—22no—
142M16×C43—42no—
143M16×C43—44no—
144M16×C43D814yescomplemented
145C2×C8×C43—22no—
146C2×C8×C43—44no—
147C2×C8×C43C2×D412yes—
148C2×C8×C43C2×D412yes—
149C4⋊C4×C43—21no—
150C4⋊C4×C43C2×D411yescharacteristic
151C4⋊C4×C43C2×D411yescharacteristic
152C22⋊C4×C43—21no—
153C22⋊C4×C43—21no—
154C22⋊C4×C43—21no—
155C22⋊C4×C43—21no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43#4111yescharacteristic
159C42×C43C2411yescharacteristic
160#10621882—42no—
161#10621882—42no—
162(C2×D43)⋊C4—41no—
163(C2×D43)⋊C4—41no—
164C4⋊Dic43—22no—
165C4⋊Dic43—21no—
166C4⋊Dic43—22no—
167C4⋊Dic43—21no—
168C4⋊Dic43—41no—
169C4⋊Dic43—41no—
170C2×C43⋊C8—21no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—22no—
173C2×C43⋊C8—42no—
174Dic172—44no—
175Dic172—44no—
176#10621873—44no—
177#10621873—44no—
178C23×C43—21no—
179C23×C43—21no—
180C23×C43—42no—
181C23×C43—42no—
182C23×C43—81no—
183C23×C43#12111yescharacteristic
184C22×D43—41no—
185D4×C43—21no—
186D4×C43—21no—
187D4×C43—21no—
188D4×C43—42no—
189D4×C43#13712yescomplemented
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—41no—
195C2×C4×C43—42no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—42no—
201C2×C4×C43—42no—
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43C2×D812yes—
206C2×C4×C43AGL(1,ℤ/8)12yes—
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C2×#4111yescharacteristic
210C22⋊D43—82no—
211C2×Dic43—42no—
212C2×Dic43—41no—
213C2×Dic43—82no—
214D172—41no—
215D172—41no—
216D172—41no—
217D172—41no—
218D172—81no—
219C4×D43—82no—
220Dic86—42no—
221Dic86—41no—
222Dic86—42no—
223Dic86—41no—
224Dic86—82no—
225C8×C43—22no—
226C8×C43—42no—
227C8×C43C2×D814yes—
228C43⋊C8—41no—
229C43⋊C8—42no—
230C43⋊C8—41no—
231#19163—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—22no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—84no—
241C22×C43#45912yes—
242C22×C43C2×#12111yescharacteristic
243C2×D43—81no—
244C2×D43—81no—
245C2×D43—81no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—41no—
250C4×C43—41no—
251C4×C43#45912yes—
252C4×C43C22×D811yescharacteristic
253C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
254C4×C43C2×#13711yescharacteristic
255C4×C43#57511yescharacteristic
256Dic43—82no—
257Dic43—81no—
258#3152—431no—
259#3100—431no—
260C2×#474—431no—
261D4×M16D4311yescharacteristic, complemented
262#1689—432no—
263#1685—432no—
264#1669—432no—
265#1665—432no—
266#1565—431no—
267#1547—431no—
268#1546—431no—
269C2×C43—22no—
270C2×C43—42no—
271C2×C43—81no—
272C2×C43C2×#45911yescharacteristic
273C2×C43#305611yescharacteristic
274C2×C43#306911yescharacteristic
275D43—161no—
276C2×#137—861no—
277C2×#137—861no—
278C22×M16—21no—
279#532—431no—
280C2×C4⋊Q8—431no—
281C2×C4×D4C2×D4311yescharacteristic
282#497—862no—
283#494—432no—
284#492—432no—
285#480—861no—
286#474—431no—
287#474—431no—
288#474—432no—
289#474—432no—
290#474—861no—
291#474—861no—
292#459—431no—
293#459—431no—
294#447—861no—
295C4×D8—861no—
296C4×D8—861no—
297#436C2×D4312yes—
298#435—22no—
299C8×D4C2×D4312yes—
300#431—431no—
301C2×#107—861no—
302#423C2×D4311yescharacteristic
303C2×C4⋊C8—431no—
304C2×#102—861no—
305#407—21no—
306C4×M16C2×D4311yescharacteristic
307#335—432no—
308#334—432no—
309#332—432no—
310#332—432no—
311#332—432no—
312#331—432no—
313C43#1916311yescharacteristic, complemented, Sylow
314C2×#41—861no—
315C22×Q8—861no—
316C22×D4D17211yescharacteristic
317C23×C4—21no—
318#137—1724no—
319#137—1724no—
320C2×Q16—862no—
321C2×Q16—862no—
322C2×SD16—862no—
323C2×SD16—862no—
324C2×D8—861no—
325C2×D8—861no—
326C2×M16—21no—
327C2×M16—22no—
328C2×M16—44no—
329C2×M16C22⋊D4311yescharacteristic
330C2×M16C22⋊D4311yescharacteristic
331C22×C8—22no—
332C22×C8—861no—
333C4⋊Q8—432no—
334C4⋊Q8—431no—
335C4⋊Q8—861no—
336C4⋊Q8—861no—
337C4⋊Q8—861no—
338#127—431no—
339#124—861no—
340#121—861no—
341#121—861no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—861no—
345C4×D4—861no—
346C4×D4D17211yescharacteristic
347C4×D4D17211yescharacteristic
348C4×D4C22×D4311yescharacteristic
349C4×D4C22×D4311yescharacteristic
350C2×C4⋊C4—861no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4D17211yescharacteristic
353C2×C22⋊C4—21no—
354C2×C42C22×D4311yescharacteristic
355#107—862no—
356#107—862no—
357#107—861no—
358#107—861no—
359C4⋊C8—21no—
360C4⋊C8—432no—
361C4⋊C8—431no—
362C4⋊C8—431no—
363C4⋊C8—861no—
364C4⋊C8C22×D4312yes—
365#102—862no—
366#102—862no—
367#102—861no—
368#102—861no—
369#102—861no—
370#102—861no—
371C22⋊C8—22no—
372C22⋊C8—22no—
373C22⋊C8—861no—
374#97C22⋊D4312yes—
375C4×C8—861no—
376C4×C8C22×D4312yes—
377C24—21no—
378#41—1722no—
379#41—1722no—
380C2×Q8—861no—
381C2×Q8—862no—
382C2×Q8—1722no—
383C2×Q8—1722no—
384C2×Q8—1721no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—41no—
388C2×D4—861no—
389C2×D4—861no—
390C2×D4—861no—
391C2×D4—1721no—
392C2×D4C2×D17211yescharacteristic
393C2×D4C2×D17211yescharacteristic
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—42no—
400C22×C4—42no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4C2×D17211yescharacteristic
404C22×C4#1062189811yescharacteristic
405C22×C4C2×C22⋊D4311yescharacteristic
406Q16—1724no—
407Q16—1724no—
408SD16—1724no—
409SD16—1724no—
410D8—1722no—
411D8—1722no—
412M16—22no—
413M16—42no—
414M16—44no—
415M16#1062188214yescomplemented
416C2×C8—22no—
417C2×C8—44no—
418C2×C8—861no—
419C2×C8—861no—
420C2×C8—862no—
421C2×C8—1722no—
422C2×C8C2×C22⋊D4312yes—
423C2×C8C2×C22⋊D4312yes—
424C4⋊C4—21no—
425C4⋊C4—862no—
426C4⋊C4—861no—
427C4⋊C4—862no—
428C4⋊C4—861no—
429C4⋊C4—1721no—
430C4⋊C4—1721no—
431C4⋊C4C2×D17211yescharacteristic
432C4⋊C4C2×D17211yescharacteristic
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42C2×D17211yescharacteristic
440C42#1062189811yescharacteristic
441C42C2×C22⋊D4311yescharacteristic
442C42C23×D4311yescharacteristic
443C23—21no—
444C23—21no—
445C23—42no—
446C23—42no—
447C23—81no—
448C23—1721no—
449C23#1306329911yescharacteristic
450Q8—3442no—
451Q8—1722no—
452Q8—1721no—
453Q8—1722no—
454Q8—1721no—
455D4—21no—
456D4—21no—
457D4—21no—
458D4—42no—
459D4—3441no—
460D4—3442no—
461D4—1721no—
462D4—1721no—
463D4—1721no—
464D4—1721no—
465D4#1306335812yescomplemented
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—1721no—
481C2×C4—1722no—
482C2×C4#1306329911yescharacteristic
483C2×C4#1306329911yescharacteristic
484C2×C4#1306329911yescharacteristic
485C2×C4C2×#1062188212yes—
486C2×C4#1306335012yes—
487C2×C4C22×C22⋊D4311yescharacteristic
488C2×C4C22×D17211yescharacteristic
489C2×C4C2×#1062189811yescharacteristic
490C8—22no—
491C8—42no—
492C8—1721no—
493C8—1722no—
494C8—1721no—
495C8C2×#1062188214yes—
496C22—21no—
497C22—21no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—84no—
505C22—3441no—
506C22—3441no—
507C22—3441no—
508C22#1458309412yes—
509C22C2×#1306329911yescharacteristic
510C4—21no—
511C4—21no—
512C4—21no—
513C4—41no—
514C4—41no—
515C4—3441no—
516C4—3442no—
517C4#1458309412yes—
518C4C22×#1062188211yescharacteristic
519C4C2×#1306335011yescharacteristic
520C4C2×#1306335811yescharacteristic
521C4#1458369911yescharacteristic
522C2—22no—
523C2—42no—
524C2—81no—
525C2—6881no—
526C2C2×#1458309411yescharacteristic
527C2#1914422511yescharacteristic
528C2#1914433211yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingD4×M16×C43C2
socleC22×C43C2×#121
prime radical#19144595C2
hypercenterD4×M16D43
hypocenterC43#19163
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
1. #19145054C2semidirect
3. C2×#14583179C2semidirect
4. #19134084C2semidirect
5. #19134060C2semidirect
6. #19133960C2semidirect
7. #19133936C2semidirect
8. #19133347C2semidirect
9. #19133273C2semidirect
10. #19133268C2semidirect
11. D4×M16×C43C2semidirect
17. #14583279C22semidirect
18. #14583272C22semidirect
35. #14582652C22semidirect
36. #14582650C22semidirect
37. #14582646C22semidirect
38. #14582646C22semidirect
39. #14582646C22semidirect
40. #14582642C22semidirect
144. M16×C43D8semidirect
189. D4×C43#137semidirect
261. D4×M16D43semidirect
313. C43#19163semidirect
415. M16#10621882semidirect
465. D4#13063358semidirect

Maximal subgroups

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

subgroupindex
#191450542
#191445952
C2×#145831792
#191340842
#191340602
#191339602
#191339362
#191333472
#191332732
#191332682
D4×M16×C432
#1916343