Finite Group Databasebeta

← #25073868

Subgroups — #25073868

Order 11008.

1004 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#19145540C211yesmaximal, characteristic, complemented
2C2×#14583245C211yesmaximal, characteristic, complemented
3#19144410C211yesmaximal, characteristic, complemented
4#19133788C214yesmaximal, complemented
5#19133781C214yesmaximal, complemented
6#19133263C211yesmaximal, characteristic, complemented
7#19133050C211yesmaximal, characteristic, complemented
8#19132977C211yesmaximal, characteristic, complemented
9C43×#3508C211yesmaximal, characteristic
10C2×#13063325C2211yescharacteristic
11#14583278—21no—
12#14583251—21no—
13#14583245—22no—
14#14583245C2214yes—
15#14583194—21no—
16#14583189—21no—
17#14583184C2212yescomplemented
18#14583179C2212yescomplemented
19#14583109C2214yescomplemented
20#14583054—22no—
21#14582952C2211yescharacteristic
22#14582942—21no—
23#14582923C2211yescharacteristic
24#14582900—21no—
25C2×#13063246—22no—
26C2×C4×C43⋊C8C2211yescharacteristic
27#14582643C2214yes—
28Q8⋊(C43⋊C8)C2212yescomplemented
29Q8⋊(C43⋊C8)C2214yescomplemented
30D4⋊(C43⋊C8)C2212yescomplemented
31C43×#559—21no—
32C43×#559C2212yes—
33C43×#550—21no—
34C43×#550C2212yes—
35C43×#546—22no—
36C43×#546—22no—
37C43×#540—22no—
38C43×#535—21no—
39C43×#533C2211yescharacteristic
40C43×#532—21no—
41C43×#532—21no—
42C2×#127×C43C2211yescharacteristic
43C43×#518—21no—
44C4×#41×C43C2211yescharacteristic
45C22×Dic86—21no—
46C2×#10621885—24no—
47C2×#10621877—21no—
48C22×C43⋊C8—21no—
49#13063325—21no—
50#13063325—21no—
51#13063325—21no—
52#13063325C2312yes—
53C2×C4⋊Dic43—21no—
54C2×C4⋊Dic43—21no—
55#13063258—22no—
56#13063256—22no—
57C4⋊(C43⋊C8)—21no—
58C4⋊(C43⋊C8)C2312yes—
59C4⋊(C43⋊C8)C2312yes—
60#13063249—22no—
61#13063248—24no—
62#13063246—28no—
63#13063246—22no—
64C22⋊(C43⋊C8)—21no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8C2312yes—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43D411yescharacteristic
71C22×D4×C43—21no—
72C22×D4×C43—21no—
73C22×D4×C43D412yes—
74C4⋊Q8×C43D411yescharacteristic
75C4⋊Q8×C43D411yescharacteristic
76#127×C43—22no—
77#127×C43—21no—
78#127×C43—21no—
79#127×C43D412yes—
80#127×C43C2312yes—
81#125×C43—21no—
82#124×C43—22no—
83#124×C43—22no—
84#124×C43—22no—
85#123×C43—24no—
86#123×C43—24no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43D412yes—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43—24no—
93#121×C43—24no—
94#121×C43—22no—
95#120×C43—24no—
96C4×Q8×C43—21no—
97C4×Q8×C43D411yescharacteristic
98C4×Q8×C43C2311yescharacteristic
99C4×Q8×C43C2312yes—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C4×D4×C43—22no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—22no—
106C4×D4×C43—22no—
107C4×D4×C43—22no—
108C4×D4×C43D411yescharacteristic
109C4×D4×C43C2311yescharacteristic
110#117×C43—21no—
111#117×C43—21no—
112#117×C43D411yescharacteristic
113C2×C22⋊C4×C43—24no—
114C2×C42×C43—21no—
115C2×C42×C43C2311yescharacteristic
116C24×C43—22no—
117#41×C43—22no—
118#41×C43—22no—
119#41×C43—84no—
120#41×C43—84no—
121C2×Q8×C43—21no—
122C2×Q8×C43C2×D411yescharacteristic
123C2×Q8×C43C2×D412yes—
124C2×D4×C43—24no—
125C2×D4×C43—24no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—22no—
130C2×D4×C43—22no—
131C2×D4×C43—21no—
132C2×D4×C43—42no—
133C2×D4×C43—42no—
134C2×D4×C43—44no—
135C2×D4×C43—82no—
136C2×D4×C43C2×D411yescharacteristic
137C2×D4×C43C2×D414yes—
138C22×C4×C43—24no—
139C22×C4×C43—24no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×Dic43—41no—
147C2×Dic86—22no—
148C2×Dic86—41no—
149C2×Dic86—82no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43C2×D411yescharacteristic
158C4⋊C4×C43C2×D411yescharacteristic
159C4⋊C4×C43C2×D412yes—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—24no—
164C22⋊C4×C43—21no—
165C22⋊C4×C43—21no—
166C22⋊C4×C43—21no—
167C22⋊C4×C43—22no—
168C42×C43—21no—
169C42×C43—21no—
170C42×C43—21no—
171C42×C43—22no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2411yescharacteristic
176#10621885—84no—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179C4⋊Dic43—41no—
180C4⋊Dic43—41no—
181#10621877—42no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—42no—
186C23×C43—24no—
187C23×C43—21no—
188C23×C43—44no—
189C23×C43—82no—
190C23×C43—82no—
191C23×C43#12011yescharacteristic
192Q8×C43—21no—
193Q8×C43—21no—
194Q8×C43—24no—
195Q8×C43—42no—
196D4×C43—21no—
197D4×C43—21no—
198D4×C43—44no—
199D4×C43—42no—
200D4×C43—42no—
201D4×C43—42no—
202D4×C43—44no—
203D4×C43—44no—
204D4×C43—44no—
205D4×C43—82no—
206D4×C43—84no—
207D4×C43—84no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—84no—
219C2×C4×C43—84no—
220C2×C4×C43#12011yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12011yescharacteristic
223C2×C4×C43#13512yes—
224C2×C4×C43#13712yes—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×Dic43—42no—
229C2×Dic43—82no—
230Dic86—44no—
231Dic86—82no—
232C43⋊C8—42no—
233C43⋊C8—42no—
234C43⋊C8—42no—
235#18635—431nomaximal, Sylow
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—44no—
239C22×C43—41no—
240C22×C43—44no—
241C22×C43—41no—
242C22×C43—44no—
243C22×C43—41no—
244C22×C43—164no—
245C22×C43#45212yes—
246C22×C43C2×#12011yescharacteristic
247C4×C43—21no—
248C4×C43—21no—
249C4×C43—41no—
250C4×C43—41no—
251C4×C43—42no—
252C4×C43—41no—
253C4×C43—42no—
254C4×C43#45212yes—
255C4×C43#45512yes—
256C4×C43C2×#13511yescharacteristic
257C4×C43C2×#13711yescharacteristic
258C4×C43#57612yes—
259Dic43—82no—
260#3508D4311yescharacteristic
261#3209—431no—
262C2×#486—431no—
263#3079—431no—
264#1641—434no—
265#1640—434no—
266#1545—431no—
267#1493—431no—
268#1476—431no—
269C2×C43—22no—
270C2×C43—81no—
271C2×C43—84no—
272C2×C43C2×#45211yescharacteristic
273C2×C43#300811yescharacteristic
274C2×C43C2×#45511yescharacteristic
275#559—21no—
276#559C2×D4312yes—
277#550—21no—
278#550C2×D4312yes—
279#546—22no—
280#546—22no—
281#540—22no—
282#535—21no—
283#533C2×D4311yescharacteristic
284#532—21no—
285#532—21no—
286C2×C4⋊Q8—431no—
287C2×#127C2×D4311yescharacteristic
288#518—21no—
289C4×#41C2×D4311yescharacteristic
290#494—861no—
291#487—861no—
292#486—434no—
293#486—862no—
294#477—861no—
295#476—861no—
296#475—432no—
297#474—432no—
298#462—434no—
299#451—862no—
300#431—431no—
301#428—861no—
302#423—431no—
303#417—861no—
304C2×#102—862no—
305C2×C4×C8—431no—
306#331—434no—
307Q8⋊C8—432no—
308Q8⋊C8—434no—
309D4⋊C8—432no—
310C43#1863511yescharacteristic, complemented, Sylow
311C2×#41—22no—
312C2×#41—22no—
313C2×#41C22⋊D4311yescharacteristic
314C22×Q8—861no—
315C22×D4—21no—
316C22×D4—21no—
317C22×D4C22⋊D4312yes—
318C2×Q16—864no—
319C2×M16—861no—
320C22×C8—861no—
321C4⋊Q8—432no—
322C4⋊Q8—861no—
323C4⋊Q8—861no—
324C4⋊Q8—861no—
325C4⋊Q8C22⋊D4311yescharacteristic
326C4⋊Q8C22⋊D4311yescharacteristic
327#127—22no—
328#127—21no—
329#127—21no—
330#127C22⋊D4312yes—
331#127C22×D4312yes—
332#125—21no—
333#124—22no—
334#124—22no—
335#124—22no—
336#123—24no—
337#123—24no—
338C22⋊Q8—21no—
339C22⋊Q8C22⋊D4312yes—
340#121—22no—
341#121—22no—
342#121—22no—
343#121—24no—
344#121—24no—
345#121—22no—
346#120—24no—
347C4×Q8—21no—
348C4×Q8C22⋊D4311yescharacteristic
349C4×Q8C22×D4311yescharacteristic
350C4×Q8C22×D4312yes—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—22no—
354C4×D4—21no—
355C4×D4—21no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—22no—
359C4×D4C22⋊D4311yescharacteristic
360C4×D4C22×D4311yescharacteristic
361#117—21no—
362#117—21no—
363#117C22⋊D4311yescharacteristic
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C22⋊C4—24no—
367C2×C42—21no—
368C2×C42C22×D4311yescharacteristic
369#107—862no—
370#106—862no—
371C4⋊C8—432no—
372C4⋊C8—432no—
373C4⋊C8—861no—
374#103—862no—
375#103—864no—
376#102—868no—
377#102—862no—
378C22⋊C8—861no—
379C4×C8—432no—
380C4×C8—861no—
381C4×C8—861no—
382C24—22no—
383#41—22no—
384#41—22no—
385#41—84no—
386#41—84no—
387C2×Q8—21no—
388C2×Q8—862no—
389C2×Q8—3442no—
390C2×Q8—1721no—
391C2×Q8C2×C22⋊D4311yescharacteristic
392C2×Q8C2×C22⋊D4312yes—
393C2×D4—21no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—44no—
402C2×D4—42no—
403C2×D4—42no—
404C2×D4—82no—
405C2×D4C2×C22⋊D4311yescharacteristic
406C2×D4C2×C22⋊D4314yes—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—1721no—
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416Q16—3444no—
417M16—1722no—
418C2×C8—862no—
419C2×C8—862no—
420C2×C8—862no—
421C2×C8—1722no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—862no—
430C4⋊C4—862no—
431C4⋊C4—1721no—
432C4⋊C4—1721no—
433C4⋊C4C2×C22⋊D4312yes—
434C4⋊C4C2×C22⋊D4311yescharacteristic
435C4⋊C4C2×C22⋊D4311yescharacteristic
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—24no—
439C22⋊C4—24no—
440C22⋊C4—21no—
441C22⋊C4—22no—
442C22⋊C4—21no—
443C22⋊C4—21no—
444C42—21no—
445C42—21no—
446C42—21no—
447C42—22no—
448C42C2×C22⋊D4311yescharacteristic
449C42C2×C22⋊D4311yescharacteristic
450C42C2×C22⋊D4311yescharacteristic
451C42C23×D4311yescharacteristic
452C23—24no—
453C23—21no—
454C23—44no—
455C23—82no—
456C23—82no—
457C23#1306329411yescharacteristic
458Q8—21no—
459Q8—21no—
460Q8—24no—
461Q8—42no—
462Q8—3442no—
463Q8—1724no—
464D4—21no—
465D4—21no—
466D4—44no—
467D4—42no—
468D4—44no—
469D4—44no—
470D4—42no—
471D4—42no—
472D4—44no—
473D4—82no—
474D4—84no—
475D4—84no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—84no—
487C2×C4—84no—
488C2×C4—3442no—
489C2×C4—1722no—
490C2×C4#1306329411yescharacteristic
491C2×C4#1306329411yescharacteristic
492C2×C4#1306329411yescharacteristic
493C2×C4#1306334512yes—
494C2×C4#1306335512yes—
495C2×C4C22×C22⋊D4311yescharacteristic
496C2×C4C22×C22⋊D4311yescharacteristic
497C2×C4C22×C22⋊D4311yescharacteristic
498C8—1722no—
499C8—1722no—
500C8—1722no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—44no—
505C22—41no—
506C22—44no—
507C22—41no—
508C22—44no—
509C22—164no—
510C22#1458306112yes—
511C22C2×#1306329411yescharacteristic
512C4—21no—
513C4—21no—
514C4—41no—
515C4—41no—
516C4—42no—
517C4—41no—
518C4—42no—
519C4—3442no—
520C4#1458306112yes—
521C4#1458307712yes—
522C4C2×#1306334511yescharacteristic
523C4C2×#1306335511yescharacteristic
524C4#1458370212yes—
525C2—22no—
526C2—84no—
527C2—81no—
528C2C2×#1458306111yescharacteristic
529C2#1914386311yescharacteristic
530C2C2×#1458307711yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3508C2
socleC22×C43C2×#120
hypercenter#3508D43
hypocenterC43#18635
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #19145540C2semidirect
2. C2×#14583245C2semidirect
3. #19144410C2semidirect
4. #19133788C2semidirect
5. #19133781C2semidirect
6. #19133263C2semidirect
7. #19133050C2semidirect
8. #19132977C2semidirect
17. #14583184C22semidirect
18. #14583179C22semidirect
19. #14583109C22semidirect
28. Q8⋊(C43⋊C8)C22semidirect
29. Q8⋊(C43⋊C8)C22semidirect
30. D4⋊(C43⋊C8)C22semidirect
310. C43#18635semidirect

Maximal subgroups

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

subgroupindex
#191455402
C2×#145832452
#191444102
#191337882
#191337812
#191332632
#191330502
#191329772
C43×#35082
#1863543