Finite Group Databasebeta

← #25087280

Subgroups — #25087280

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q16×Dic86C211yesmaximal, characteristic, complemented
2#19147331C211yesmaximal, characteristic, complemented
3#19147262C211yesmaximal, characteristic
4#19134247C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134051C211yesmaximal, characteristic, complemented
7#19134036C211yesmaximal, characteristic, complemented
8#19133994C211yesmaximal, characteristic, complemented
9#19133815C211yesmaximal, characteristic, complemented
10#19133767C211yesmaximal, characteristic, complemented
11#19133722C211yesmaximal, characteristic
12#19133672C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3304C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17Q8×Dic86C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583303—21no—
20#14583271C2211yescharacteristic
21#14583258—21no—
22#14583251C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583245—21no—
25#14583245C2211yescharacteristic
26#14583194C2211yescharacteristic
27#14583194C2211yescharacteristic
28#14583192—21no—
29#14583192—21no—
30#14583189—21no—
31#14583189C2211yescharacteristic
32#14583189C2211yescharacteristic
33#14583184—21no—
34#14583118—21no—
35#14583106C2211yescharacteristic
36#14583096—21no—
37#14583096C2211yescharacteristic
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C8×Dic86C2211yescharacteristic
41#14583004—21no—
42Q16×Dic43—21no—
43C4×#10621883—21no—
44C4×#10621883C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582643C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#550C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#482—21no—
60C43×#475C2211yescharacteristic
61C43×#465—21no—
62C43×#460C2211yescharacteristic
63C43×#452—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#416—21no—
67C2×#10621885—21no—
68C2×#10621883—21no—
69C2×#10621883—41no—
70C2×#10621883D411yescharacteristic
71#13063325—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063324—21no—
77#13063324—41no—
78#13063324—41no—
79Q8×Dic43—21no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84#13063259—21no—
85#13063259—21no—
86#13063258—21no—
87#13063258—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256D411yescharacteristic
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063248—41no—
103#13063248D411yescharacteristic
104#13063246—21no—
105#13063246—21no—
106#13063246—21no—
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110#13063236—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×Q16×C43D411yescharacteristic
117C2×SD16×C43—21no—
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120#127×C43—21no—
121#127×C43C2311yescharacteristic
122#126×C43—41no—
123#124×C43—21no—
124C22⋊Q8×C43—21no—
125#121×C43—21no—
126#121×C43—41no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#107×C43D411yescharacteristic
134#106×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43D411yescharacteristic
138#103×C43D411yescharacteristic
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—41no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—41no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—41no—
160C2×Dic86—41no—
161C2×Dic86C2×D411yescharacteristic
162Q16×C43—22no—
163SD16×C43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—81no—
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184#10621885—42no—
185#10621883—22no—
186#10621883—42no—
187#10621883—82no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194C4⋊Dic43C2×D411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—21no—
199C4×Dic43—41no—
200C4×Dic43—41no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43—41no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43#13712yes—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—41no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—82no—
222D4×C43—81no—
223D4×C43—161no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240Dic86—21no—
241Dic86—81no—
242Dic86—81no—
243Dic86—161no—
244Dic86—161no—
245Dic86#13512yes—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255#19844—431nomaximal, Sylow
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—81no—
260C22×C43—81no—
261C22×C43—81no—
262C22×C43D4211yescharacteristic
263C4×C43—22no—
264C4×C43—21no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13711yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278Q8×Q16—431no—
279#3369—431no—
280#3362—431no—
281#3304D4311yescharacteristic
282#1719—431no—
283#1698—431no—
284#1684—431no—
285#1682—431no—
286#1675—431no—
287#1645—431no—
288#1638—431no—
289#1631—431no—
290#1623—431no—
291#1584—431no—
292SD16⋊C8—431no—
293C2×C43—81no—
294C2×C43—161no—
295C2×C43#326611yescharacteristic
296C2×C43#328511yescharacteristic
297C2×C43#328811yescharacteristic
298Q82—431no—
299Q82—431no—
300#556C2×D4311yescharacteristic
301#550C2×D4311yescharacteristic
302#500—431no—
303#500—861no—
304#492—431no—
305#489—861no—
306#487—431no—
307#487—431no—
308#486—431no—
309#486—861no—
310#486C2×D4311yescharacteristic
311#482—21no—
312#477—431no—
313#477—431no—
314#477—861no—
315#477—861no—
316#476—431no—
317#476—431no—
318#476—861no—
319#475—861no—
320#475C2×D4311yescharacteristic
321#465—21no—
322#464—861no—
323#462—431no—
324#460—431no—
325#460—861no—
326#460C2×D4311yescharacteristic
327#452—21no—
328#446—431no—
329C8×Q8—431no—
330C8×Q8—431no—
331#441—861no—
332C4×Q16—861no—
333C4×Q16C2×D4311yescharacteristic
334C4×SD16—431no—
335C4×SD16—861no—
336C8×D4C2×D4311yescharacteristic
337#416—21no—
338#335—431no—
339#335—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343#331—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346Q8⋊C8—431no—
347D4⋊C8—431no—
348#322—431no—
349C43#1984411yescharacteristic, complemented, Sylow
350C2×#41—21no—
351C2×Q16—861no—
352C2×Q16C22⋊D4311yescharacteristic
353C2×SD16—21no—
354C2×SD16—431no—
355C2×SD16—861no—
356C2×SD16—1721no—
357C22×C8—21no—
358C4⋊Q8—431no—
359C4⋊Q8—431no—
360C4⋊Q8—861no—
361C4⋊Q8—861no—
362C4⋊Q8—861no—
363C4⋊Q8—861no—
364C4⋊Q8—1721no—
365C4⋊Q8—1721no—
366C4⋊Q8C22×D4311yescharacteristic
367#127—21no—
368#127C22×D4311yescharacteristic
369#126—41no—
370#124—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8C22×D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4C22×D4311yescharacteristic
384#117—21no—
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107C22⋊D4311yescharacteristic
390#106—21no—
391#106—431no—
392#106—861no—
393#106—861no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401#103—21no—
402#103—431no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—1721no—
409#103C22⋊D4311yescharacteristic
410#103C22⋊D4311yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—431no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421#97—861no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427#41—42no—
428#41—81no—
429C2×Q8—21no—
430C2×Q8—431no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—1721no—
434C2×Q8—1721no—
435C2×Q8C2×C22⋊D4311yescharacteristic
436C2×Q8C2×C22⋊D4311yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4D4×D4311yescharacteristic
443C22×C4—21no—
444C22×C4—41no—
445Q16—22no—
446Q16—1722no—
447SD16—81no—
448SD16—862no—
449SD16—3442no—
450SD16—1722no—
451C2×C8—21no—
452C2×C8—81no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8C2×C22⋊D4311yescharacteristic
460C2×C8C2×C22⋊D4311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—431no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4D4×D4311yescharacteristic
477C4⋊C4C2×C22⋊D4311yescharacteristic
478C4⋊C4C2×C22⋊D4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42—861no—
487C42—1721no—
488C42—1721no—
489C42C23×D4311yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—41no—
497Q8—432no—
498Q8—861no—
499Q8—3441no—
500Q8—3441no—
501Q8—6881no—
502Q8—6881no—
503Q8#1306335512yes—
504D4—21no—
505D4—21no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—82no—
511D4—81no—
512D4—161no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4#1306337011yescharacteristic
529C8—21no—
530C8—21no—
531C8—41no—
532C8—861no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D4×C22⋊D4311yescharacteristic
545C4—22no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—81no—
552C4—862no—
553C4—3441no—
554C4—3441no—
555C4—1721no—
556C4#135×D4311yescharacteristic
557C4C2×#1306335511yescharacteristic
558C4#1458371011yescharacteristic
559C4#1458371311yescharacteristic
560C2—81no—
561C2—161no—
562C2#1914610111yescharacteristic
563C2#1914633011yescharacteristic
564C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3304C2
socleC22×C43D42
prime radicalC43×#550C22
hypercenter#3304D43
hypocenterC43#19844
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3304

Complements

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

NH ≅ G/Ntype
1. Q16×Dic86C2semidirect
2. #19147331C2semidirect
4. #19134247C2semidirect
5. #19134133C2semidirect
6. #19134051C2semidirect
7. #19134036C2semidirect
8. #19133994C2semidirect
9. #19133815C2semidirect
10. #19133767C2semidirect
12. #19133672C2semidirect
13. #19133446C2semidirect
14. #19133407C2semidirect
349. C43#19844semidirect

Maximal subgroups

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

subgroupindex
Q16×Dic862
#191473312
#191472622
#191342472
#191341332
#191340512
#191340362
#191339942
#191338152
#191337672
#191337222
#191336722
#191334462
#191334072
C43×#33042
#1984443