Finite Group Databasebeta

← #25082015

Subgroups — #25082015

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145513C211yesmaximal, characteristic, complemented
2#19144050C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134037C212yesmaximal, complemented
5#19134030C212yesmaximal, complemented
6#19133953C212yesmaximal, complemented
7#19133948C212yesmaximal, complemented
8#19133371C211yesmaximal, characteristic, complemented
9#19133273C211yesmaximal, characteristic, complemented
10C2×#14582643C211yesmaximal, characteristic, complemented
11C43×#3038C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13#14583449C2211yescharacteristic
14#14583275C2212yes—
15#14583245C2212yes—
16#14583121—21no—
17#14583114—21no—
18#14583109C2211yescharacteristic, complemented
19#14583104C2211yescharacteristic, complemented
20#14583099C2211yescharacteristic, complemented
21#14583094C2211yescharacteristic, complemented
22#14583091—21no—
23#14583091—21no—
24#14583033—22no—
25Q8×C43⋊C8C2212yescomplemented
26D4×C43⋊C8—22no—
27D4×C43⋊C8C2212yescomplemented
28#14582952—21no—
29#14582952C2211yescharacteristic
30C2×C4⋊(C43⋊C8)—21no—
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C2×C4⋊(C43⋊C8)C2211yescharacteristic
33#14582893—21no—
34#14582651C2212yescomplemented
35#14582651C2212yescomplemented
36#14582646C2212yescomplemented
37#14582643C2212yes—
38#14582643C2212yes—
39#14582642C2212yescomplemented
40C2×AGL(1,ℤ/8)×C43—21no—
41C2×#127×C43C2211yescharacteristic
42C4×#41×C43C2211yescharacteristic
43C43×#460—21no—
44C43×#460C2212yes—
45C43×#459—21no—
46C43×#459C2212yes—
47C43×#423C2211yescharacteristic
48C43×#418—21no—
49C2×#10621898—21no—
50#13063345—44no—
51C2×#10621885—21no—
52C2×#10621883—21no—
53C2×#10621884—21no—
54C2×#10621882—21no—
55C2×#10621882—22no—
56C2×#10621882—22no—
57C22×C43⋊C8—21no—
58C22×C43⋊C8—21no—
59C22×C43⋊C8—22no—
60#13063325C2311yescharacteristic
61#13063322C2311yescharacteristic
62#13063313—21no—
63#13063299—21no—
64#13063299—21no—
65C4×D172—21no—
66C4×D172—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)—21no—
69C4⋊(C43⋊C8)—22no—
70C4⋊(C43⋊C8)D411yescharacteristic
71C4⋊(C43⋊C8)D411yescharacteristic
72C4⋊(C43⋊C8)C2311yescharacteristic
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2312yes—
75#13063248—21no—
76#13063248—21no—
77#13063246—22no—
78#13063246—22no—
79#13063245—21no—
80#13063245—21no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)D412yes—
83C4×C43⋊C8—22no—
84C4×C43⋊C8C2312yes—
85C2×#41×C43D411yescharacteristic
86C22×D4×C43—21no—
87C22×D4×C43—21no—
88C22×D4×C43—21no—
89AGL(1,ℤ/8)×C43—44no—
90C2×SD16×C43—22no—
91C2×D8×C43—22no—
92C2×M16×C43—21no—
93#127×C43—21no—
94#127×C43—21no—
95#127×C43—21no—
96#127×C43C2312yes—
97C4×Q8×C43D411yescharacteristic
98C4×Q8×C43C2311yescharacteristic
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43D411yescharacteristic
102C4×D4×C43C2311yescharacteristic
103#117×C43—21no—
104#117×C43D411yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109#102×C43—22no—
110#102×C43—22no—
111C24×C43—41no—
112#41×C43—22no—
113#41×C43D814yescomplemented
114C2×Q8×C43C2×D411yescharacteristic
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43—22no—
119C2×D4×C43—41no—
120C2×D4×C43—41no—
121C2×D4×C43—41no—
122C2×D4×C43—42no—
123C2×D4×C43—42no—
124C2×D4×C43—81no—
125C2×D4×C43—81no—
126C2×D4×C43—82no—
127C2×D4×C43C2×D411yescharacteristic
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43#4111yescharacteristic
134C2×C22⋊D43—41no—
135#10621898—42no—
136#10621898—42no—
137C2×D172—21no—
138C2×D172—21no—
139C2×D172—21no—
140C2×C4×D43—41no—
141C2×Dic86—21no—
142SD16×C43—44no—
143D8×C43—44no—
144M16×C43—42no—
145C2×C8×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43C2×D411yescharacteristic
149C4⋊C4×C43C2×D411yescharacteristic
150C22⋊C4×C43—21no—
151C22⋊C4×C43—21no—
152C22⋊C4×C43—21no—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43—21no—
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43#4111yescharacteristic
159C42×C43C2411yescharacteristic
160#10621885—42no—
161#10621884—42no—
162#10621883—42no—
163#10621882—42no—
164#10621882—82no—
165#10621882—82no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—42no—
174C2×C43⋊C8—82no—
175C2×C43⋊C8—81no—
176C2×C43⋊C8C2×D412yes—
177C2×C43⋊C8C2×D412yes—
178C23×C43—21no—
179C23×C43—42no—
180C23×C43—82no—
181C23×C43—82no—
182C23×C43—82no—
183C23×C43#12111yescharacteristic
184C22×D43—41no—
185Q8×C43—21no—
186Q8×C43C2×D812yes—
187D4×C43—24no—
188D4×C43—21no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—42no—
193D4×C43—82no—
194D4×C43—82no—
195D4×C43—82no—
196D4×C43—82no—
197D4×C43C2×D812yes—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—24no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—81no—
208C2×C4×C43#12111yescharacteristic
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43C2×D812yes—
212C2×C4×C43#13512yes—
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C22⋊D43—82no—
217C2×Dic43—41no—
218D172—41no—
219D172—41no—
220D172—41no—
221D172—41no—
222D172—81no—
223C4×D43—82no—
224Dic86—41no—
225Dic86—41no—
226C8×C43—42no—
227C43⋊C8—22no—
228C43⋊C8—22no—
229C43⋊C8—41no—
230C43⋊C8—41no—
231C43⋊C8—42no—
232#19410—431nomaximal, Sylow
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—22no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—82no—
239C22×C43—82no—
240C22×C43—82no—
241C22×C43—164no—
242C22×C43#46612yes—
243C22×C43C2×#12111yescharacteristic
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C4×C43—21no—
248C4×C43—22no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—41no—
252C4×C43—41no—
253C4×C43#46612yes—
254C4×C43C22×D811yescharacteristic
255C4×C43C2×#13511yescharacteristic
256C4×C43#57611yescharacteristic
257C4×C43#57711yescharacteristic
258Dic43—81no—
259#3205—431no—
260#3038D4311yescharacteristic, complemented
261#3035—431no—
262#2988—431no—
263#1682—432no—
264#1681—432no—
265#1668—432no—
266#1667—432no—
267#1571—431no—
268#1547—431no—
269C2×#331—431no—
270C2×C43—22no—
271C2×C43—42no—
272C2×C43—162no—
273C2×C43#304511yescharacteristic
274C2×C43C2×#46611yescharacteristic
275C2×C43#306811yescharacteristic
276D43—161no—
277C2×AGL(1,ℤ/8)—21no—
278C2×#135—861no—
279#532—431no—
280C2×#127C2×D4311yescharacteristic
281C4×#41C2×D4311yescharacteristic
282#493—432no—
283#486—432no—
284#464—861no—
285#463—861no—
286#462—431no—
287#461—431no—
288#460—21no—
289#460—431no—
290#460C2×D4312yes—
291#459—21no—
292#459—431no—
293#459—861no—
294#459—861no—
295#459C2×D4312yes—
296#447—862no—
297C8×Q8—432no—
298C8×D4—432no—
299C8×D4—862no—
300#431—431no—
301#431—861no—
302#423C2×D4311yescharacteristic
303C2×C4⋊C8—431no—
304C2×C4⋊C8—431no—
305C2×C4⋊C8—861no—
306#418—21no—
307#416—861no—
308#335—432no—
309#335—432no—
310#332—432no—
311#331—432no—
312#331—432no—
313#331—432no—
314C43#1941011yescharacteristic, complemented, Sylow
315C2×#41—861no—
316C2×#41C22⋊D4311yescharacteristic
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320AGL(1,ℤ/8)—44no—
321#135—1724no—
322C2×Q16—861no—
323C2×SD16—22no—
324C2×SD16—861no—
325C2×SD16—861no—
326C2×D8—22no—
327C2×D8—862no—
328C2×D8—862no—
329C2×D8—861no—
330C2×M16—21no—
331C22×C8—862no—
332C22×C8—861no—
333C22×C8—861no—
334C4⋊Q8—431no—
335#127—21no—
336#127—21no—
337#127—21no—
338#127—431no—
339#127C22×D4312yes—
340#124—861no—
341#121—861no—
342#121—861no—
343C4×Q8C22⋊D4311yescharacteristic
344C4×Q8C22×D4311yescharacteristic
345C4×D4—21no—
346C4×D4—21no—
347C4×D4—861no—
348C4×D4—861no—
349C4×D4C22⋊D4311yescharacteristic
350C4×D4C22×D4311yescharacteristic
351#117—21no—
352#117C22⋊D4311yescharacteristic
353C2×C42—21no—
354C2×C42C22×D4311yescharacteristic
355C4⋊C8—21no—
356C4⋊C8—431no—
357C4⋊C8—431no—
358C4⋊C8—432no—
359C4⋊C8—431no—
360C4⋊C8—431no—
361C4⋊C8—862no—
362C4⋊C8—861no—
363C4⋊C8—861no—
364C4⋊C8C22×D4312yes—
365#103—861no—
366#103—861no—
367#102—22no—
368#102—22no—
369#102—862no—
370#102—862no—
371#102—861no—
372#102—861no—
373C22⋊C8—432no—
374C22⋊C8—862no—
375C4×C8—432no—
376C4×C8—862no—
377C24—41no—
378#41—22no—
379#41—1722no—
380#41—1722no—
381#41#1062188214yescomplemented
382C2×Q8—861no—
383C2×Q8C2×C22⋊D4311yescharacteristic
384C2×D4—21no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—41no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4—81no—
394C2×D4—81no—
395C2×D4—82no—
396C2×D4—861no—
397C2×D4—861no—
398C2×D4—861no—
399C2×D4—1721no—
400C2×D4C2×C22⋊D4311yescharacteristic
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—1721no—
405C22×C4D4×D4311yescharacteristic
406C22×C4#1062190011yescharacteristic
407C22×C4C2×C22⋊D4311yescharacteristic
408Q16—1722no—
409SD16—44no—
410SD16—1722no—
411SD16—1722no—
412D8—44no—
413D8—3442no—
414D8—3442no—
415D8—1722no—
416M16—42no—
417C2×C8—22no—
418C2×C8—432no—
419C2×C8—432no—
420C2×C8—862no—
421C2×C8—861no—
422C2×C8—861no—
423C2×C8—3442no—
424C2×C8—3441no—
425C2×C8—1722no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4C2×C22⋊D4311yescharacteristic
431C4⋊C4C2×C22⋊D4311yescharacteristic
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—1721no—
436C22⋊C4—1721no—
437C42—21no—
438C42—21no—
439C42—21no—
440C42D4×D4311yescharacteristic
441C42#1062190011yescharacteristic
442C42C2×C22⋊D4311yescharacteristic
443C42C23×D4311yescharacteristic
444C23—21no—
445C23—42no—
446C23—82no—
447C23—82no—
448C23—82no—
449C23—1721no—
450C23#1306329711yescharacteristic
451Q8—21no—
452Q8—1721no—
453Q8—1721no—
454Q8C2×#1062188212yes—
455D4—24no—
456D4—21no—
457D4—42no—
458D4—42no—
459D4—42no—
460D4—42no—
461D4—82no—
462D4—82no—
463D4—82no—
464D4—82no—
465D4—3441no—
466D4—3442no—
467D4—1721no—
468D4—1721no—
469D4—1721no—
470D4—1721no—
471D4C2×#1062188212yes—
472C2×C4—21no—
473C2×C4—24no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—81no—
482C2×C4—3442no—
483C2×C4—1721no—
484C2×C4#1306329711yescharacteristic
485C2×C4#1306329711yescharacteristic
486C2×C4#1306329711yescharacteristic
487C2×C4C2×#1062188212yes—
488C2×C4#1306334512yes—
489C2×C4C2×D4×D4311yescharacteristic
490C2×C4C22×C22⋊D4311yescharacteristic
491C2×C4C2×#1062190011yescharacteristic
492C8—42no—
493C8—862no—
494C8—862no—
495C8—1721no—
496C8—1721no—
497C8—1722no—
498C22—21no—
499C22—21no—
500C22—22no—
501C22—41no—
502C22—41no—
503C22—82no—
504C22—82no—
505C22—82no—
506C22—164no—
507C22—3441no—
508C22—3441no—
509C22—3441no—
510C22#1458313312yes—
511C22C2×#1306329711yescharacteristic
512C4—21no—
513C4—21no—
514C4—21no—
515C4—22no—
516C4—41no—
517C4—41no—
518C4—3441no—
519C4#1458313312yes—
520C4C22×#1062188211yescharacteristic
521C4C2×#1306334511yescharacteristic
522C4#1458370311yescharacteristic
523C4#1458370911yescharacteristic
524C2—22no—
525C2—42no—
526C2—162no—
527C2—6881no—
528C2#1914413811yescharacteristic
529C2C2×#1458313311yescharacteristic
530C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3038C2
socleC22×C43C2×#121
hypercenter#3038D43
hypocenterC43#19410
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3038

Complements

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

NH ≅ G/Ntype
1. #19145513C2semidirect
2. #19144050C2semidirect
3. #19143706C2semidirect
4. #19134037C2semidirect
5. #19134030C2semidirect
6. #19133953C2semidirect
7. #19133948C2semidirect
8. #19133371C2semidirect
9. #19133273C2semidirect
10. C2×#14582643C2semidirect
11. C43×#3038C2semidirect
18. #14583109C22semidirect
19. #14583104C22semidirect
20. #14583099C22semidirect
21. #14583094C22semidirect
25. Q8×C43⋊C8C22semidirect
27. D4×C43⋊C8C22semidirect
34. #14582651C22semidirect
35. #14582651C22semidirect
36. #14582646C22semidirect
39. #14582642C22semidirect
113. #41×C43D8semidirect
260. #3038D43semidirect
314. C43#19410semidirect
381. #41#10621882semidirect

Maximal subgroups

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

subgroupindex
#191455132
#191440502
#191437062
#191340372
#191340302
#191339532
#191339482
#191333712
#191332732
C2×#145826432
C43×#30382
#1941043