Finite Group Databasebeta

← #25084366

Subgroups — #25084366

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145177C211yesmaximal, characteristic, complemented
2#19145170C211yesmaximal, characteristic
3#19145155C211yesmaximal, characteristic, complemented
4#19145150C211yesmaximal, characteristic, complemented
5#19144918C211yesmaximal, characteristic, complemented
6#19134256C211yesmaximal, characteristic, complemented
7#19134252C211yesmaximal, characteristic, complemented
8#19134249C211yesmaximal, characteristic, complemented
9#19134245C211yesmaximal, characteristic, complemented
10#19134242C211yesmaximal, characteristic, complemented
11#19134238C211yesmaximal, characteristic, complemented
12#19134235C211yesmaximal, characteristic, complemented
13#19134231C211yesmaximal, characteristic, complemented
14C2×#14582620C211yesmaximal, characteristic, complemented
15C43×#3131C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583278C2211yescharacteristic
23#14583275C2211yescharacteristic
24#14583273C2211yescharacteristic
25#14583271C2211yescharacteristic
26#14583254—22no—
27#14583251C2211yescharacteristic
28#14583251C2211yescharacteristic
29#14583250C2211yescharacteristic
30#14583250C2211yescharacteristic
31#14583249C2211yescharacteristic
32#14583249C2211yescharacteristic
33#14583247C2211yescharacteristic
34#14583247C2211yescharacteristic
35#14583246C2211yescharacteristic
36#14583246C2211yescharacteristic
37#14583245C2211yescharacteristic
38#14583245C2211yescharacteristic
39#14583138—22no—
40#14583133—22no—
41#14583130—22no—
42#14583126—22no—
43C4×#10621885—22no—
44C4×#10621884—22no—
45C4×#10621883—22no—
46C4×#10621882—22no—
47#14582896—22no—
48C2×C4×C43⋊C8C2211yescharacteristic
49C2×C4×C43⋊C8C2211yescharacteristic
50#14582620C2211yescharacteristic
51#14582620C2211yescharacteristic
52#14582620C2211yescharacteristic
53#14582620C2211yescharacteristic
54C43×#533C2211yescharacteristic
55C43×#532C2211yescharacteristic
56C43×#488—22no—
57C43×#487C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#486C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#416—22no—
62C2×C4×C8×C43C2211yescharacteristic
63C2×#10621898—21no—
64C2×#10621885—22no—
65C2×#10621883—22no—
66C2×#10621884—22no—
67C2×#10621882—22no—
68C22×C43⋊C8D412yes—
69C22×C43⋊C8D412yes—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063322C2311yescharacteristic
74#13063317—21no—
75#13063313—21no—
76#13063304—21no—
77#13063304—21no—
78#13063299—21no—
79#13063299—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82C4×D172—21no—
83C4×D172—21no—
84#13063284—21no—
85#13063258—22no—
86#13063258—22no—
87#13063256—22no—
88#13063256—22no—
89#13063250—22no—
90#13063250—22no—
91#13063249—22no—
92#13063249—22no—
93#13063248—22no—
94#13063248—22no—
95#13063247—22no—
96#13063247—22no—
97#13063246—22no—
98#13063246—22no—
99#13063245—22no—
100#13063245—22no—
101C4×C43⋊C8D412yes—
102C4×C43⋊C8D412yes—
103C4×C43⋊C8C2311yescharacteristic
104C4×C43⋊C8C2311yescharacteristic
105C4×C43⋊C8C2311yescharacteristic
106C4×C43⋊C8C2311yescharacteristic
107C2×#41×C43—21no—
108C22×C8×C43D412yes—
109C4⋊Q8×C43C2311yescharacteristic
110C4⋊Q8×C43C2311yescharacteristic
111C4⋊Q8×C43C2311yescharacteristic
112#127×C43C2311yescharacteristic
113#125×C43—21no—
114#124×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117#121×C43—21no—
118#121×C43—21no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123#117×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#103×C43—22no—
126#103×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129C4×C8×C43D412yes—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132#41×C43—44no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—41no—
140C22×C4×C43—41no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C2×C22⋊D43—41no—
145#10621898—44no—
146C2×D172—21no—
147C2×D172—21no—
148C2×D172—21no—
149C2×C4×D43—41no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×C8×C43—24no—
154C2×C8×C43C2×D412yes—
155C2×C8×C43C2×D412yes—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C42×C43—41no—
168C42×C43C2×D411yescharacteristic
169C42×C43C2×D411yescharacteristic
170C42×C43C2×D411yescharacteristic
171C42×C43C2411yescharacteristic
172C22⋊Dic43—41no—
173#10621885—44no—
174#10621884—44no—
175#10621883—44no—
176#10621882—44no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—41no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187C4×Dic43—41no—
188C2×C43⋊C8—42no—
189C2×C43⋊C8—42no—
190C2×C43⋊C8C2×D412yes—
191C2×C43⋊C8C2×D412yes—
192C2×C43⋊C8C2×D412yes—
193C2×C43⋊C8C2×D412yes—
194C23×C43—41no—
195C23×C43#12711yescharacteristic
196C22×D43—41no—
197Q8×C43—42no—
198Q8×C43—42no—
199Q8×C43—42no—
200D4×C43—42no—
201D4×C43—42no—
202D4×C43—42no—
203D4×C43—82no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—82no—
210C2×C4×C43#12711yescharacteristic
211C2×C4×C43#12711yescharacteristic
212C2×C4×C43#12711yescharacteristic
213C2×C4×C43#13514yes—
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C22⋊D43—82no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221D172—42no—
222D172—42no—
223D172—42no—
224C4×D43—82no—
225Dic86—42no—
226Dic86—42no—
227Dic86—42no—
228C8×C43—22no—
229C8×C43—22no—
230C43⋊C8—22no—
231C43⋊C8—22no—
232C43⋊C8—22no—
233C43⋊C8—22no—
234#19613—431nomaximal, Sylow
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43#49512yes—
241C22×C43C2×#12711yescharacteristic
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—81no—
248C4×C43—81no—
249C4×C43—81no—
250C4×C43#49512yes—
251C4×C43C2×#13512yes—
252C4×C43#57512yes—
253C4×C43#57512yes—
254Dic43—81no—
255Dic43—81no—
256Dic43—81no—
257#3170—431no—
258#3169—431no—
259#3167—431no—
260#3167—431no—
261#3131—431no—
262#3131D4311yescharacteristic, complemented
263#1720—431no—
264#1720—431no—
265#1719—431no—
266#1719—431no—
267#1718—431no—
268#1718—431no—
269#1717—431no—
270#1717—431no—
271C2×#322—431no—
272C2×C43—22no—
273C2×C43—161no—
274C2×C43C2×#49511yescharacteristic
275C2×C43#315011yescharacteristic
276C2×C43#315011yescharacteristic
277D43—161no—
278#533—431no—
279#533C2×D4311yescharacteristic
280#532—431no—
281#532C2×D4311yescharacteristic
282#500—431no—
283#500—431no—
284#498—431no—
285#498—431no—
286#494—431no—
287#493—431no—
288#492—431no—
289#492—431no—
290#488—22no—
291#488—862no—
292#487—431no—
293#487—431no—
294#487—431no—
295#487—431no—
296#487—431no—
297#487—431no—
298#487C2×D4311yescharacteristic
299#487C2×D4311yescharacteristic
300#486—431no—
301#486—431no—
302#486—431no—
303#486—431no—
304#486—431no—
305#486—431no—
306#486C2×D4311yescharacteristic
307#486C2×D4311yescharacteristic
308#467—862no—
309#466—862no—
310#465—862no—
311#465—862no—
312C4×Q16—862no—
313C4×SD16—862no—
314C4×SD16—862no—
315C4×D8—862no—
316#416—22no—
317#416—862no—
318C2×C4×C8—431no—
319C2×C4×C8—431no—
320C2×C4×C8C2×D4311yescharacteristic
321#322—431no—
322#322—431no—
323#322—431no—
324#322—431no—
325C43#1961311yescharacteristic, complemented, Sylow
326C2×#41—21no—
327C2×#41—861no—
328C2×Q16—862no—
329C2×SD16—862no—
330C2×SD16—862no—
331C2×D8—862no—
332C22×C8—432no—
333C22×C8—432no—
334C22×C8C22⋊D4312yes—
335C4⋊Q8—431no—
336C4⋊Q8—431no—
337C4⋊Q8—431no—
338C4⋊Q8C22×D4311yescharacteristic
339C4⋊Q8C22×D4311yescharacteristic
340C4⋊Q8C22×D4311yescharacteristic
341#127—431no—
342#127C22×D4311yescharacteristic
343#125—21no—
344#125—861no—
345#124—21no—
346#124—861no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—861no—
350C22⋊Q8—861no—
351#121—21no—
352#121—21no—
353#121—861no—
354#121—861no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—861no—
358C4×Q8—861no—
359C4×D4—21no—
360C4×D4—21no—
361C4×D4—861no—
362C4×D4—861no—
363#117—21no—
364#117—861no—
365C2×C42C22×D4311yescharacteristic
366#107—862no—
367#107—862no—
368#106—862no—
369#106—862no—
370#103—22no—
371#103—22no—
372#103—862no—
373#103—862no—
374#103—862no—
375#103—862no—
376#103—862no—
377#103—862no—
378#102—22no—
379#102—22no—
380#102—862no—
381#102—862no—
382#102—862no—
383#102—862no—
384#102—862no—
385#102—862no—
386C4×C8—432no—
387C4×C8—432no—
388C4×C8—431no—
389C4×C8—431no—
390C4×C8—431no—
391C4×C8—431no—
392C4×C8C22⋊D4312yes—
393C4×C8C22×D4311yescharacteristic
394C4×C8C22×D4311yescharacteristic
395#41—44no—
396#41—1724no—
397C2×Q8—21no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—861no—
401C2×Q8—861no—
402C2×Q8—861no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—41no—
407C2×D4—861no—
408C2×D4—861no—
409C2×D4—861no—
410C2×D4—1721no—
411C22×C4—41no—
412C22×C4—1721no—
413C22×C4D4×D4311yescharacteristic
414C22×C4D4×D4311yescharacteristic
415C22×C4C2×C22⋊D4311yescharacteristic
416Q16—1724no—
417SD16—1724no—
418SD16—1724no—
419D8—1724no—
420C2×C8—24no—
421C2×C8—432no—
422C2×C8—432no—
423C2×C8—432no—
424C2×C8—432no—
425C2×C8—1722no—
426C2×C8—1722no—
427C2×C8C2×C22⋊D4312yes—
428C2×C8C2×C22⋊D4312yes—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—861no—
438C4⋊C4—861no—
439C4⋊C4—861no—
440C4⋊C4—861no—
441C4⋊C4—861no—
442C4⋊C4—861no—
443C4⋊C4—1721no—
444C4⋊C4—1721no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—1721no—
449C22⋊C4—1721no—
450C22⋊C4—1721no—
451C42—41no—
452C42—1721no—
453C42D4×D4311yescharacteristic
454C42D4×D4311yescharacteristic
455C42C2×C22⋊D4311yescharacteristic
456C42C23×D4311yescharacteristic
457C23—41no—
458C23—1721no—
459C23#1306332111yescharacteristic
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—1722no—
464Q8—1722no—
465Q8—1722no—
466D4—42no—
467D4—42no—
468D4—42no—
469D4—82no—
470D4—3442no—
471D4—1722no—
472D4—1722no—
473D4—1722no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—82no—
480C2×C4—3442no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4#1306332111yescharacteristic
485C2×C4#1306332111yescharacteristic
486C2×C4#1306332111yescharacteristic
487C2×C4#1306334514yes—
488C2×C4C2×D4×D4311yescharacteristic
489C2×C4C2×D4×D4311yescharacteristic
490C2×C4C22×C22⋊D4311yescharacteristic
491C8—22no—
492C8—22no—
493C8—862no—
494C8—862no—
495C8—862no—
496C8—862no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—3441no—
503C22—3441no—
504C22—3441no—
505C22#1458328112yes—
506C22C2×#1306332111yescharacteristic
507C4—21no—
508C4—21no—
509C4—81no—
510C4—81no—
511C4—81no—
512C4—3441no—
513C4—3441no—
514C4—3441no—
515C4#1458328112yes—
516C4C2×#1306334512yes—
517C4#1458369612yes—
518C4#1458369612yes—
519C2—22no—
520C2—161no—
521C2—6881no—
522C2C2×#1458328111yescharacteristic
523C2#1914503811yescharacteristic
524C2#1914503811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3131C2
socleC22×C43C2×#127
prime radical#19145170C2
hypercenter#3131D43
hypocenterC43#19613
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #19145177C2semidirect
3. #19145155C2semidirect
4. #19145150C2semidirect
5. #19144918C2semidirect
6. #19134256C2semidirect
7. #19134252C2semidirect
8. #19134249C2semidirect
9. #19134245C2semidirect
10. #19134242C2semidirect
11. #19134238C2semidirect
12. #19134235C2semidirect
13. #19134231C2semidirect
14. C2×#14582620C2semidirect
15. C43×#3131C2semidirect
262. #3131D43semidirect
325. C43#19613semidirect

Maximal subgroups

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

subgroupindex
#191451772
#191451702
#191451552
#191451502
#191449182
#191342562
#191342522
#191342492
#191342452
#191342422
#191342382
#191342352
#191342312
C2×#145826202
C43×#31312
#1961343