Finite Group Databasebeta

← #25064780

Subgroups — #25064780

Order 11008.

876 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148568C211yesmaximal, characteristic
2#19143612C211yesmaximal, characteristic, complemented
3#19143244C211yesmaximal, characteristic, complemented
4#19133225C212yesmaximal, complemented
5#19133220C212yesmaximal, complemented
6#19133203C211yesmaximal, characteristic, complemented
7#19133201C212yesmaximal, complemented
8#19133195C212yesmaximal, complemented
9#19133190C211yesmaximal, characteristic, complemented
10#19133181C211yesmaximal, characteristic, complemented
11C43×#1531C211yesmaximal, characteristic, complemented
12#14583624C411yescharacteristic
13#14583610C411yescharacteristic
14#14583610C411yescharacteristic
15#14583593C412yes—
16#14583590—22no—
17#14583588C412yes—
18#14583583—21no—
19#14583552C411yescharacteristic
20#14583551—21no—
21#14583507—21no—
22#14583495—22no—
23#14583434C2212yes—
24#14583433C2211yescharacteristic
25#125×D43C2212yes—
26#14583381—21no—
27C4×#10621898C2211yescharacteristic
28#14583023—21no—
29#14582976—21no—
30#14582974—22no—
31#14582961—22no—
32#14582954C2212yes—
33#14582954C2212yes—
34#14582954C2212yes—
35#14582925—21no—
36#14582865—21no—
37C4×#10621877C2211yescharacteristic
38C4×#10621877C2211yescharacteristic
39#14582851C2212yes—
40#14582641C2212yes—
41#14582641C2212yes—
42#14582640C2211yescharacteristic
43#14582640C2212yes—
44#14582640C2211yescharacteristic
45#14582638C2211yescharacteristic
46#14582638C2212yes—
47#14582638C2211yescharacteristic
48C43×#533C2211yescharacteristic
49C43×#432C2211yescharacteristic
50C2×#97×C43C2211yescharacteristic
51C43×#330C2212yes—
52C43×#330C2212yes—
53C2×#10621902—21no—
54C2×#10621898D411yescharacteristic
55C2×#10621877—21no—
56C2×#10621877—21no—
57C2×#10621872—22no—
58#13063323—21no—
59#13063320—22no—
60#13063319—21no—
61#13063319—22no—
62#13063318—22no—
63#13063317—22no—
64#13063317C2311yescharacteristic
65#13063316—21no—
66#13063316C2×C412yes—
67#13063316C2×C412yes—
68#13063315—22no—
69#13063315—22no—
70#13063315—22no—
71#13063313C2311yescharacteristic
72#13063310—22no—
73#13063310—22no—
74#13063308—21no—
75#13063307—22no—
76#13063307—22no—
77#13063305—21no—
78#13063305C2×C412yes—
79#13063304C2×C411yescharacteristic
80#13063301—22no—
81#13063301—21no—
82#13063301—22no—
83#13063300C2×C412yes—
84#13063299C2×C411yescharacteristic
85#13063298—22no—
86Q8×Dic43—21no—
87C4×Dic86C2×C411yescharacteristic
88C4×Dic86C2×C411yescharacteristic
89C4×Dic86D411yescharacteristic
90#13063290C2×C412yes—
91C4×D172—22no—
92C4×D172C2×C411yescharacteristic
93C4×D172C2×C411yescharacteristic
94C4×D172D411yescharacteristic
95#13063287—21no—
96#13063287—22no—
97#13063287C2×C412yes—
98C4×C22⋊D43—21no—
99C4×C22⋊D43C2×C412yes—
100C4×C22⋊D43D412yes—
101#13063284D411yescharacteristic
102#13063283—22no—
103#13063282—21no—
104#13063282—22no—
105#13063282D412yes—
106C4⋊C4×D43—22no—
107C4⋊C4×D43—22no—
108C4⋊C4×D43—21no—
109C4⋊C4×D43C2×C412yes—
110C4⋊C4×D43C2×C412yes—
111C42×D43C2312yes—
112Dic43⋊C8—22no—
113Dic43⋊C8—22no—
114Dic43⋊C8—22no—
115(C2×D43)⋊C8—22no—
116(C2×D43)⋊C8—22no—
117(C2×D43)⋊C8—22no—
118#13063236C2311yescharacteristic
119#13063236C2312yes—
120#13063236C2311yescharacteristic
121C4×C43⋊C8—21no—
122C4×C43⋊C8—21no—
123C8×Dic43—22no—
124C22×C8×C43—21no—
125C4⋊Q8×C43C2×C411yescharacteristic
126C4⋊Q8×C43C2×C411yescharacteristic
127#125×C43C2312yes—
128C22⋊Q8×C43—21no—
129C22⋊Q8×C43—21no—
130C4×Q8×C43—21no—
131C4×Q8×C43—21no—
132#117×C43C2×C412yes—
133C2×C42×C43C2311yescharacteristic
134C4⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136#97×C43—21no—
137#97×C43C2312yes—
138#97×C43C2311yescharacteristic
139#97×C43C2311yescharacteristic
140C2×Q8×C43—21no—
141C2×Q8×C43—21no—
142C22×C4×C43C22×C411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—21no—
146C2×C22⋊D43C22⋊C412yes—
147#10621902—44no—
148#10621898—42no—
149C2×D172—22no—
150C2×D172C22⋊C411yescharacteristic
151C2×D172C22×C411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43C22×C412yes—
157C2×C4×D43C2×D412yes—
158C2×C4×D43C2×D412yes—
159C2×Dic86C22⋊C411yescharacteristic
160C2×Dic86C22×C411yescharacteristic
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—22no—
164C2×C8×C43—42no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C4⋊C4×C43C22×C412yes—
170C4⋊C4×C43C22×C412yes—
171C22⋊C4×C43—22no—
172C42×C43—22no—
173C42×C43C22×C411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43C22⋊C412yes—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183(C2×D43)⋊C4—22no—
184(C2×D43)⋊C4—22no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4C22⋊C412yes—
187(C2×D43)⋊C4C22⋊C412yes—
188C4⋊Dic43—22no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43C22⋊C411yescharacteristic
192C4⋊Dic43C22⋊C411yescharacteristic
193C4⋊Dic43C22×C411yescharacteristic
194C4⋊Dic43C22×C411yescharacteristic
195Dic43⋊C4—21no—
196Dic43⋊C4—21no—
197Dic43⋊C4—21no—
198Dic43⋊C4—21no—
199Dic43⋊C4—22no—
200Dic43⋊C4—22no—
201Dic43⋊C4—22no—
202Dic43⋊C4—22no—
203Dic43⋊C4—22no—
204Dic43⋊C4C22⋊C412yes—
205Dic43⋊C4C22⋊C412yes—
206C4×Dic43—21no—
207C4×Dic43—22no—
208C4×Dic43C22×C412yes—
209C4×Dic43C2×D412yes—
210C4×Dic43C2×D412yes—
211#10621877—42no—
212#10621877—42no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—22no—
215C2×C43⋊C8—21no—
216#10621872—44no—
217C23×C43C2×C22⋊C411yescharacteristic
218C22×D43—21no—
219C22×D43C2×C22⋊C412yes—
220Q8×C43—42no—
221Q8×C43—81no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43C2×C22⋊C411yescharacteristic
228C2×C4×C43C2×C22⋊C411yescharacteristic
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×C4×C43C23×C411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C22⋊D43—42no—
234C22⋊D43—81no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43C2×C22⋊C412yes—
239C2×Dic43C2×C22⋊C412yes—
240C2×Dic43C2×C22⋊C412yes—
241D172—22no—
242D172—41no—
243D172—44no—
244C4×D43—42no—
245C4×D43—42no—
246C4×D43—42no—
247C4×D43—44no—
248C4×D43—42no—
249C4×D43—82no—
250C4×D43—82no—
251Dic86—22no—
252Dic86—41no—
253C8×C43—42no—
254C8×C43—41no—
255C8×C43—41no—
256C43⋊C8—22no—
257C43⋊C8—42no—
258C43⋊C8—41no—
259#17682—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43C22×C22⋊C411yescharacteristic
264C2×D43—22no—
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—42no—
276C4×C43—42no—
277C4×C43#42112yes—
278Dic43—22no—
279Dic43—22no—
280Dic43—22no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#3515—431no—
285#2971—431no—
286#2923—431no—
287#1535—432no—
288#1534—432no—
289#1531D4311yescharacteristic, complemented
290#1529—431no—
291#1529—432no—
292#1528—432no—
293#1526—431no—
294#1524—431no—
295C2×C43—41no—
296C2×C43#288911yescharacteristic
297C2×C43C2×#42111yescharacteristic
298C2×C43#290111yescharacteristic
299D43—42no—
300D43—81no—
301#557—431no—
302#554—431no—
303#554—431no—
304#553—432no—
305#552—432no—
306#552—862no—
307#552—861no—
308#547—431no—
309#547—861no—
310#541—861no—
311#539—862no—
312#533C2×D4311yescharacteristic
313#529—432no—
314#529—431no—
315C2×#125—432no—
316#520—861no—
317C4×#41—431no—
318C8×Q8—861no—
319#436—862no—
320#436—861no—
321#433—862no—
322#432—432no—
323#432—432no—
324#432—432no—
325#432C2×D4311yescharacteristic
326#424—861no—
327#408—861no—
328C4×M16—431no—
329C4×M16—431no—
330C4×M16—432no—
331C2×#97C2×D4311yescharacteristic
332#330—432no—
333#330—432no—
334#330—431no—
335#330—431no—
336#330—432no—
337#330C2×D4312yes—
338#330C2×D4312yes—
339#329—431no—
340#329—431no—
341#329—432no—
342C43#1768211yescharacteristic, complemented, Sylow
343C2×#41—431no—
344C2×#41—861no—
345C2×M16—862no—
346C2×M16—861no—
347C2×M16—861no—
348C22×C8—21no—
349C4⋊Q8—861no—
350C4⋊Q8C4×D4311yescharacteristic
351C4⋊Q8C4×D4311yescharacteristic
352#126—862no—
353#126—862no—
354#126—862no—
355#126—861no—
356#125—432no—
357#125—432no—
358#125—431no—
359#125—862no—
360#125—862no—
361#125—862no—
362#125—862no—
363#125—861no—
364#125C22×D4312yes—
365#124—431no—
366#123—862no—
367#123—862no—
368#123—862no—
369#123—862no—
370#123—861no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—431no—
374C22⋊Q8—432no—
375C22⋊Q8—862no—
376C22⋊Q8—861no—
377C22⋊Q8—862no—
378C22⋊Q8—861no—
379#121—431no—
380#121—432no—
381#121—862no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—431no—
385C4×Q8—431no—
386C4×Q8—432no—
387C4×Q8—431no—
388C4×Q8—861no—
389C4×D4—432no—
390C4×D4—432no—
391C4×D4—432no—
392C4×D4—431no—
393C4×D4—431no—
394C4×D4—431no—
395C4×D4—862no—
396C4×D4—862no—
397C4×D4—861no—
398C4×D4—861no—
399#117—431no—
400#117—432no—
401#117—862no—
402#117—862no—
403#117—861no—
404#117C4×D4312yes—
405C2×C4⋊C4—432no—
406C2×C4⋊C4—432no—
407C2×C4⋊C4—861no—
408C2×C4⋊C4—862no—
409C2×C4⋊C4—862no—
410C2×C42—432no—
411C2×C42C22×D4311yescharacteristic
412C4⋊C8—21no—
413C4⋊C8—862no—
414C4⋊C8—862no—
415C4⋊C8—862no—
416C22⋊C8—21no—
417C22⋊C8—862no—
418C22⋊C8—862no—
419C22⋊C8—862no—
420#97—21no—
421#97—431no—
422#97—431no—
423#97—432no—
424#97C22×D4311yescharacteristic
425#97C22×D4311yescharacteristic
426#97C22×D4312yes—
427C4×C8—862no—
428C4×C8—861no—
429C4×C8—861no—
430#41—1722no—
431#41—1724no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—431no—
435C2×Q8—431no—
436C2×D4—432no—
437C2×D4—431no—
438C2×D4—431no—
439C2×D4—862no—
440C2×D4—861no—
441C22×C4—432no—
442C22×C4—432no—
443C22×C4—432no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—861no—
448C22×C4C2×C4×D4311yescharacteristic
449C22×C4D4×D4311yescharacteristic
450C22×C4D4×D4311yescharacteristic
451M16—1724no—
452M16—1722no—
453M16—1722no—
454C2×C8—22no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—42no—
458C2×C8—861no—
459C2×C8—862no—
460C2×C8—861no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—431no—
466C4⋊C4—432no—
467C4⋊C4—431no—
468C4⋊C4—432no—
469C4⋊C4—431no—
470C4⋊C4—431no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4C2×C4×D4312yes—
484C4⋊C4C2×C4×D4312yes—
485C22⋊C4—22no—
486C22⋊C4—432no—
487C22⋊C4—432no—
488C22⋊C4—432no—
489C22⋊C4—862no—
490C22⋊C4—862no—
491C22⋊C4—862no—
492C22⋊C4—861no—
493C22⋊C4—861no—
494C22⋊C4—861no—
495C22⋊C4—861no—
496C22⋊C4—861no—
497C42—22no—
498C42—432no—
499C42—432no—
500C42—432no—
501C42—862no—
502C42—861no—
503C42C2×C4×D4311yescharacteristic
504C42D4×D4311yescharacteristic
505C42D4×D4311yescharacteristic
506C42C23×D4311yescharacteristic
507C23—432no—
508C23—861no—
509C23C22⋊C4×D4311yescharacteristic
510Q8—42no—
511Q8—81no—
512Q8—862no—
513Q8—1721no—
514D4—862no—
515D4—3441no—
516D4—1721no—
517D4—1724no—
518D4—1722no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—432no—
525C2×C4—432no—
526C2×C4—432no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—3442no—
531C2×C4—3442no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1724no—
536C2×C4—1722no—
537C2×C4C22⋊C4×D4311yescharacteristic
538C2×C4C22⋊C4×D4311yescharacteristic
539C2×C4C22⋊C4×D4311yescharacteristic
540C2×C4C22×C4×D4311yescharacteristic
541C2×C4C2×D4×D4311yescharacteristic
542C2×C4C2×D4×D4311yescharacteristic
543C8—41no—
544C8—41no—
545C8—42no—
546C8—862no—
547C8—1722no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—862no—
553C22—862no—
554C22—862no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22C2×C22⋊C4×D4311yescharacteristic
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—42no—
565C4—42no—
566C4—862no—
567C4—862no—
568C4—862no—
569C4—1721no—
570C4—1721no—
571C4—1721no—
572C4#1458291412yes—
573C2—41no—
574C2—3441no—
575C2—1722no—
576C2#1914307511yescharacteristic
577C2C2×#1458291411yescharacteristic
578C2#1914314111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1531C2
socleC22×C43C22×C22⋊C4
prime radical#19148568C2
cosocleC42×C43C24
hypercenter#1531D43
hypocenterC43#17682
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
2. #19143612C2semidirect
3. #19143244C2semidirect
4. #19133225C2semidirect
5. #19133220C2semidirect
6. #19133203C2semidirect
7. #19133201C2semidirect
8. #19133195C2semidirect
9. #19133190C2semidirect
10. #19133181C2semidirect
11. C43×#1531C2semidirect
289. #1531D43semidirect
342. C43#17682semidirect

Maximal subgroups

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

subgroupindex
#191485682
#191436122
#191432442
#191332252
#191332202
#191332032
#191332012
#191331952
#191331902
#191331812
C43×#15312
#1768243