Finite Group Databasebeta

← #25084427

Subgroups — #25084427

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145177C211yesmaximal, characteristic, complemented
2#19145155C211yesmaximal, characteristic
3#19145154C211yesmaximal, characteristic
4#19145105C211yesmaximal, characteristic, complemented
5#19144920C211yesmaximal, characteristic
6#19134273C211yesmaximal, characteristic, complemented
7#19134267C211yesmaximal, characteristic, complemented
8#19134252C211yesmaximal, characteristic, complemented
9#19134249C211yesmaximal, characteristic, complemented
10#19134242C211yesmaximal, characteristic, complemented
11#19134238C211yesmaximal, characteristic, complemented
12#19134226C211yesmaximal, characteristic, complemented
13#19134218C211yesmaximal, characteristic, complemented
14C2×#14582620C211yesmaximal, characteristic, complemented
15C43×#3170C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583298—22no—
22#14583297C2211yescharacteristic
23#14583295C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583295C2211yescharacteristic
26#14583278C2211yescharacteristic
27#14583273C2211yescharacteristic
28#14583272C2211yescharacteristic
29#14583256—22no—
30#14583251C2211yescharacteristic
31#14583251C2211yescharacteristic
32#14583251C2211yescharacteristic
33#14583250C2211yescharacteristic
34#14583249C2211yescharacteristic
35#14583249C2211yescharacteristic
36#14583247C2211yescharacteristic
37#14583247C2211yescharacteristic
38#14583247C2211yescharacteristic
39#14583246C2211yescharacteristic
40#14583138—22no—
41#14583130—22no—
42#14583128—22no—
43C4×#10621885—22no—
44C4×#10621873—22no—
45C4×#10621884—22no—
46#14582935—22no—
47#14582893—22no—
48C2×C4×C43⋊C8C2211yescharacteristic
49C2×C4×C43⋊C8C2211yescharacteristic
50#14582620C2211yescharacteristic
51#14582620C2211yescharacteristic
52#14582620C2211yescharacteristic
53#14582620C2211yescharacteristic
54C43×#533C2211yescharacteristic
55C43×#533C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#494C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#487C2211yescharacteristic
60C43×#467—22no—
61C4×Q16×C43—22no—
62C2×C4×C8×C43C2211yescharacteristic
63C2×#10621898—21no—
64C2×#10621885—22no—
65C2×#10621873—22no—
66C2×#10621884—22no—
67C22×C43⋊C8D412yes—
68C22×C43⋊C8D412yes—
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063322C2311yescharacteristic
73#13063317—21no—
74#13063313—21no—
75#13063304—21no—
76#13063304—21no—
77#13063299—21no—
78#13063299—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×D172—21no—
82C4×D172—21no—
83#13063284—21no—
84#13063258—22no—
85#13063258—22no—
86#13063258—22no—
87#13063257—22no—
88#13063256—22no—
89#13063256—22no—
90#13063256—22no—
91#13063250—22no—
92#13063249—22no—
93#13063249—22no—
94#13063248—22no—
95#13063248—22no—
96#13063248—22no—
97#13063247—22no—
98#13063245—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×Q16×C43—22no—
108C22×C8×C43D412yes—
109C4⋊Q8×C43C2311yescharacteristic
110C4⋊Q8×C43C2311yescharacteristic
111C4⋊Q8×C43C2311yescharacteristic
112C4⋊Q8×C43C2311yescharacteristic
113#125×C43—21no—
114#125×C43—21no—
115C22⋊Q8×C43—21no—
116C22⋊Q8×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119C4×Q8×C43—21no—
120C4×Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43—21no—
123#117×C43—21no—
124#117×C43—21no—
125C2×C42×C43C2311yescharacteristic
126#107×C43—22no—
127#103×C43—22no—
128#103×C43—22no—
129C4×C8×C43D412yes—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
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—
146C2×Dic86—21no—
147C2×Dic86—21no—
148Q16×C43—44no—
149C2×C8×C43—24no—
150C2×C8×C43C2×D412yes—
151C2×C8×C43C2×D412yes—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—41no—
162C4⋊C4×C43—41no—
163C4⋊C4×C43—41no—
164C22⋊C4×C43—41no—
165C22⋊C4×C43—41no—
166C42×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(C2×D43)⋊C4—41no—
176(C2×D43)⋊C4—41no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183Dic43⋊C4—41no—
184Dic43⋊C4—41no—
185C4×Dic43—41no—
186C2×C43⋊C8—24no—
187C2×C43⋊C8—42no—
188C2×C43⋊C8C2×D412yes—
189C2×C43⋊C8C2×D412yes—
190C2×C43⋊C8C2×D412yes—
191C2×C43⋊C8C2×D412yes—
192#10621873—44no—
193C23×C43#12711yescharacteristic
194C22×D43—41no—
195Q8×C43—42no—
196Q8×C43—42no—
197Q8×C43—42no—
198Q8×C43—42no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43#12711yescharacteristic
206C2×C4×C43#12711yescharacteristic
207C2×C4×C43#12711yescharacteristic
208C2×C4×C43#13714yes—
209C2×C4×C43C22×D411yescharacteristic
210C2×C4×C43C22×D411yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C22⋊D43—82no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216D172—42no—
217D172—42no—
218D172—42no—
219C4×D43—82no—
220Dic86—42no—
221Dic86—42no—
222Dic86—42no—
223C8×C43—22no—
224C8×C43#13514yes—
225C43⋊C8—22no—
226C43⋊C8—22no—
227C43⋊C8—22no—
228C43⋊C8—22no—
229#19620—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43#49712yes—
233C22×C43C2×#12711yescharacteristic
234C2×D43—81no—
235C2×D43—81no—
236C2×D43—81no—
237C4×C43—21no—
238C4×C43—21no—
239C4×C43—81no—
240C4×C43—81no—
241C4×C43—81no—
242C4×C43—81no—
243C4×C43#49712yes—
244C4×C43C2×#13512yes—
245C4×C43C2×#13712yes—
246C4×C43#57512yes—
247Dic43—81no—
248Dic43—81no—
249Dic43—81no—
250#3170—431no—
251#3170D4311yescharacteristic, complemented
252#3167—431no—
253#3167—431no—
254#3160—431no—
255#3131—431no—
256#1723—431no—
257#1722—431no—
258#1720—431no—
259#1719—431no—
260#1718—431no—
261#1718—431no—
262#1716—431no—
263#1714—431no—
264C2×#322—431no—
265C2×C43—22no—
266C2×C43#314711yescharacteristic
267C2×C43C2×#49711yescharacteristic
268C2×C43#315011yescharacteristic
269D43—161no—
270#533—431no—
271#533C2×D4311yescharacteristic
272#533C2×D4311yescharacteristic
273#532—431no—
274#500—431no—
275#500—431no—
276#500—431no—
277#500C2×D4311yescharacteristic
278#499—862no—
279#498—431no—
280#498—431no—
281#498—431no—
282#498—431no—
283#494—431no—
284#494C2×D4311yescharacteristic
285#492—431no—
286#492—431no—
287#488—862no—
288#487—431no—
289#487—431no—
290#487—431no—
291#487—431no—
292#487—431no—
293#487—431no—
294#487C2×D4311yescharacteristic
295#487C2×D4311yescharacteristic
296#486—431no—
297#486—431no—
298#486—431no—
299#486—431no—
300#467—22no—
301#467—862no—
302#465—862no—
303#465—862no—
304C4×Q16—22no—
305C4×Q16—862no—
306C4×SD16—862no—
307C4×SD16—862no—
308#427—862no—
309#416—862no—
310C2×C4×C8—431no—
311C2×C4×C8—431no—
312C2×C4×C8C2×D4311yescharacteristic
313#322—431no—
314#322—431no—
315#322—431no—
316#322—431no—
317C43#1962011yescharacteristic, complemented, Sylow
318C2×#41—861no—
319C2×Q16—22no—
320C2×Q16—862no—
321C2×SD16—862no—
322C2×SD16—862no—
323C22×C8—432no—
324C22×C8—432no—
325C22×C8C22⋊D4312yes—
326C4⋊Q8—431no—
327C4⋊Q8—431no—
328C4⋊Q8—431no—
329C4⋊Q8C22×D4311yescharacteristic
330C4⋊Q8C22×D4311yescharacteristic
331C4⋊Q8C22×D4311yescharacteristic
332C4⋊Q8C22×D4311yescharacteristic
333#127—431no—
334#125—21no—
335#125—21no—
336#125—861no—
337#124—861no—
338C22⋊Q8—21no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344#121—861no—
345#121—861no—
346C4×Q8—21no—
347C4×Q8—21no—
348C4×Q8—21no—
349C4×Q8—21no—
350C4×Q8—861no—
351C4×Q8—861no—
352C4×D4—861no—
353C4×D4—861no—
354#117—21no—
355#117—21no—
356#117—861no—
357C2×C42C22×D4311yescharacteristic
358#107—22no—
359#107—862no—
360#107—862no—
361#107—862no—
362#106—862no—
363#106—862no—
364#106—862no—
365#106—862no—
366#103—22no—
367#103—22no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372#103—862no—
373#103—862no—
374#102—862no—
375#102—862no—
376#102—862no—
377#102—862no—
378C4×C8—432no—
379C4×C8—432no—
380C4×C8—431no—
381C4×C8—431no—
382C4×C8—431no—
383C4×C8—431no—
384C4×C8C22⋊D4312yes—
385C4×C8C22×D4311yescharacteristic
386C4×C8C22×D4311yescharacteristic
387#41—1724no—
388C2×Q8—21no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—861no—
393C2×Q8—861no—
394C2×Q8—861no—
395C2×D4—861no—
396C2×D4—861no—
397C2×D4—861no—
398C2×D4—1721no—
399C22×C4—1721no—
400C22×C4D4×D4311yescharacteristic
401C22×C4D4×D4311yescharacteristic
402C22×C4C2×C22⋊D4311yescharacteristic
403Q16—44no—
404Q16—1724no—
405SD16—1724no—
406SD16—1724no—
407C2×C8—24no—
408C2×C8—432no—
409C2×C8—432no—
410C2×C8—432no—
411C2×C8—432no—
412C2×C8—864no—
413C2×C8—1722no—
414C2×C8C2×C22⋊D4312yes—
415C2×C8C2×C22⋊D4312yes—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—1721no—
435C4⋊C4—1721no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4—1721no—
441C42—41no—
442C42—41no—
443C42—1721no—
444C42D4×D4311yescharacteristic
445C42D4×D4311yescharacteristic
446C42C2×C22⋊D4311yescharacteristic
447C42C23×D4311yescharacteristic
448C23—1721no—
449C23#1306332111yescharacteristic
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—1722no—
455Q8—1722no—
456Q8—1722no—
457D4—3442no—
458D4—1722no—
459D4—1722no—
460D4—1722no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—3442no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4—1721no—
471C2×C4#1306332111yescharacteristic
472C2×C4#1306332111yescharacteristic
473C2×C4#1306332111yescharacteristic
474C2×C4#1306335714yes—
475C2×C4C2×D4×D4311yescharacteristic
476C2×C4C2×D4×D4311yescharacteristic
477C2×C4C22×C22⋊D4311yescharacteristic
478C8—22no—
479C8—862no—
480C8—862no—
481C8—862no—
482C8—862no—
483C8#1306334514yes—
484C22—21no—
485C22—21no—
486C22—3441no—
487C22—3441no—
488C22—3441no—
489C22#1458329212yes—
490C22C2×#1306332111yescharacteristic
491C4—21no—
492C4—21no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—3441no—
498C4—3441no—
499C4—3441no—
500C4#1458329212yes—
501C4C2×#1306334512yes—
502C4C2×#1306335712yes—
503C4#1458369612yes—
504C2—22no—
505C2—6881no—
506C2#1914502111yescharacteristic
507C2C2×#1458329211yescharacteristic
508C2#1914503811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3170C2
socleC22×C43C2×#127
prime radical#14583449C22
hypercenter#3170D43
hypocenterC43#19620
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3170

Complements

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

NH ≅ G/Ntype
1. #19145177C2semidirect
4. #19145105C2semidirect
6. #19134273C2semidirect
7. #19134267C2semidirect
8. #19134252C2semidirect
9. #19134249C2semidirect
10. #19134242C2semidirect
11. #19134238C2semidirect
12. #19134226C2semidirect
13. #19134218C2semidirect
14. C2×#14582620C2semidirect
15. C43×#3170C2semidirect
251. #3170D43semidirect
317. C43#19620semidirect

Maximal subgroups

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

subgroupindex
#191451772
#191451552
#191451542
#191451052
#191449202
#191342732
#191342672
#191342522
#191342492
#191342422
#191342382
#191342262
#191342182
C2×#145826202
C43×#31702
#1962043