Finite Group Databasebeta

← #25079640

Subgroups — #25079640

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144660C211yesmaximal, characteristic
2#19144377C211yesmaximal, characteristic
3#19143613C211yesmaximal, characteristic
4#19134167C211yesmaximal, characteristic, complemented
5#19134139C211yesmaximal, characteristic, complemented
6#19134091C211yesmaximal, characteristic, complemented
7#19134081C211yesmaximal, characteristic, complemented
8#19134050C211yesmaximal, characteristic, complemented
9#19134022C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133962C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133295C211yesmaximal, characteristic, complemented
15C43×#3185C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237—21no—
18#14583203—21no—
19#14583196—21no—
20#14583191C2211yescharacteristic
21#14583186C2211yescharacteristic
22#14583181C2211yescharacteristic
23#14583181C2211yescharacteristic
24#14583176C2211yescharacteristic
25#14583176C2211yescharacteristic
26#14583106C2211yescharacteristic
27#14583101C2211yescharacteristic
28#14583059—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31C4×#10621885—21no—
32C4×#10621884—21no—
33#14582978C2211yescharacteristic
34#14582978C2211yescharacteristic
35#14582975—21no—
36#14582975—21no—
37#14582956C2211yescharacteristic
38#14582954—21no—
39#14582952C2211yescharacteristic
40#14582935—21no—
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582893—21no—
43#14582851—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582645C2211yescharacteristic
55#14582645C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#533C2211yescharacteristic
58C43×#498C2211yescharacteristic
59C43×#494C2211yescharacteristic
60C43×#487C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#470—21no—
63C43×#470—21no—
64C43×#441—21no—
65C43×#441—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621884—21no—
70C2×#10621872—21no—
71C2×#10621872—21no—
72C22×C43⋊C8—21no—
73C4×Dic86D411yescharacteristic
74C4×Dic86C2311yescharacteristic
75C4×D172D411yescharacteristic
76C4×D172C2311yescharacteristic
77C4×C22⋊D43—21no—
78C4×C22⋊D43—21no—
79#13063284D411yescharacteristic
80#13063282—21no—
81C42×D43—21no—
82#13063258—21no—
83#13063258—21no—
84#13063258—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063245—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—21no—
112C8×Dic43—21no—
113C2×Q16×C43—21no—
114C2×Q16×C43—21no—
115C2×M16×C43D411yescharacteristic
116C2×M16×C43D411yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126C22⋊Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43—21no—
130C4×Q8×C43—21no—
131#117×C43—21no—
132#117×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#97×C43D411yescharacteristic
141#97×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43#4111yescharacteristic
151C2×C22⋊D43—21no—
152#10621898—22no—
153#10621898—41no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×Dic86C2×D411yescharacteristic
159Q16×C43—42no—
160Q16×C43—42no—
161M16×C43—22no—
162M16×C43—41no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43—41no—
177C4⋊C4×C43—41no—
178C4⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C22⋊C4×C43—41no—
181C42×C43—41no—
182C42×C43—41no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—21no—
188#10621885—42no—
189#10621884—42no—
190(C2×D43)⋊C4—21no—
191(C2×D43)⋊C4—21no—
192C4⋊Dic43C2×D411yescharacteristic
193C4⋊Dic43C2×D411yescharacteristic
194Dic43⋊C4—21no—
195Dic43⋊C4—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—42no—
206#10621872—42no—
207#10621872—42no—
208C23×C43#12111yescharacteristic
209C22×D43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—81no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C22⋊D43—42no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236D172—21no—
237D172—21no—
238C4×D43—42no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—81no—
242Dic86—21no—
243Dic86#13712yes—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43#13512yes—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19185—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43C2×#12111yescharacteristic
259C2×D43—41no—
260C2×D43—41no—
261C2×D43—41no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—81no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13711yescharacteristic
272C4×C43#57511yescharacteristic
273C4×C43#57511yescharacteristic
274Dic43—22no—
275Dic43—41no—
276Dic43—41no—
277#3185D4311yescharacteristic, complemented
278#3107—431no—
279#3076—431no—
280#2971—431no—
281#1703—431no—
282#1699—431no—
283#1691—431no—
284#1689—431no—
285#1684—431no—
286#1680—431no—
287#1672—431no—
288#1670—431no—
289#1565—431no—
290#1554—431no—
291#1552—431no—
292C2×C43—41no—
293C2×C43#303511yescharacteristic
294C2×C43#305611yescharacteristic
295C2×C43#306911yescharacteristic
296D43—81no—
297#533C2×D4311yescharacteristic
298#533C2×D4311yescharacteristic
299C4×#41—431no—
300#498C2×D4311yescharacteristic
301#494C2×D4311yescharacteristic
302#487C2×D4311yescharacteristic
303#487C2×D4311yescharacteristic
304#485—861no—
305#479—861no—
306#478—861no—
307#477—431no—
308#476—431no—
309#475—431no—
310#475—431no—
311#474—431no—
312#474—431no—
313#470—21no—
314#470—21no—
315#462—431no—
316#461—431no—
317#452—861no—
318C8×Q8—431no—
319C8×Q8—431no—
320#441—21no—
321#441—21no—
322C4×Q16—861no—
323C4×SD16—861no—
324#436—431no—
325#436—431no—
326#436—861no—
327#436—861no—
328#432—431no—
329#432—861no—
330#431—431no—
331#427—861no—
332C2×C4⋊C8—431no—
333#416—861no—
334C4×M16—861no—
335C4×M16C2×D4311yescharacteristic
336#335—431no—
337#335—431no—
338#334—431no—
339#334—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348C43#1918511yescharacteristic, complemented, Sylow
349C2×#41—431no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16—861no—
353C2×SD16—861no—
354C2×M16—861no—
355C2×M16—861no—
356C2×M16C22⋊D4311yescharacteristic
357C2×M16C22⋊D4311yescharacteristic
358C22×C8—861no—
359C4⋊Q8C22×D4311yescharacteristic
360C4⋊Q8C22×D4311yescharacteristic
361C4⋊Q8C22×D4311yescharacteristic
362C4⋊Q8C22×D4311yescharacteristic
363#125—21no—
364#125—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—431no—
374C4×Q8—431no—
375C4×D4—431no—
376C4×D4—431no—
377C4×D4—861no—
378C4×D4—861no—
379#117—21no—
380#117—21no—
381#117—431no—
382#117—861no—
383C2×C42—861no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#106—21no—
389#106—21no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—861no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—861no—
419#97C22⋊D4311yescharacteristic
420#97C22⋊D4311yescharacteristic
421C4×C8—861no—
422C4×C8—861no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C4×C8C22×D4311yescharacteristic
426#41—862no—
427#41—1721no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—431no—
433C2×D4—431no—
434C2×D4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4D4×D4311yescharacteristic
439C22×C4#1062190011yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441Q16—42no—
442Q16—42no—
443Q16—1722no—
444SD16—1722no—
445M16—22no—
446M16—41no—
447M16—1722no—
448M16—1722no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1722no—
456C2×C8C2×C22⋊D4311yescharacteristic
457C2×C8C2×C22⋊D4311yescharacteristic
458C2×C8C2×C22⋊D4311yescharacteristic
459C2×C8C2×C22⋊D4311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—431no—
473C4⋊C4—431no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C42—41no—
482C42—41no—
483C42—861no—
484C42—861no—
485C42—861no—
486C42D4×D4311yescharacteristic
487C42#1062190011yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—861no—
491C23#1306329611yescharacteristic
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—432no—
500Q8—861no—
501D4—861no—
502D4—861no—
503D4—1722no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—3441no—
517C2×C4—1722no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306329611yescharacteristic
521C2×C4#1306329611yescharacteristic
522C2×C4#1306329611yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C2×#1062190011yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8#1306334512yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22C2×#1306329611yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—862no—
552C4—1721no—
553C4—1721no—
554C4C2×#1306334511yescharacteristic
555C4#137×D4311yescharacteristic
556C4#1458369711yescharacteristic
557C4#1458369811yescharacteristic
558C2—41no—
559C2—3441no—
560C2#1914404411yescharacteristic
561C2#1914421911yescharacteristic
562C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3185C2
socleC22×C43C2×#121
prime radicalC2×#10621898D4
hypercenter#3185D43
hypocenterC43#19185
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3185

Complements

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

NH ≅ G/Ntype
4. #19134167C2semidirect
5. #19134139C2semidirect
6. #19134091C2semidirect
7. #19134081C2semidirect
8. #19134050C2semidirect
9. #19134022C2semidirect
10. #19133974C2semidirect
11. #19133962C2semidirect
12. #19133347C2semidirect
13. #19133305C2semidirect
14. #19133295C2semidirect
15. C43×#3185C2semidirect
277. #3185D43semidirect
348. C43#19185semidirect

Maximal subgroups

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

subgroupindex
#191446602
#191443772
#191436132
#191341672
#191341392
#191340912
#191340812
#191340502
#191340222
#191339742
#191339622
#191333472
#191333052
#191332952
C43×#31852
#1918543