Finite Group Databasebeta

← #25079616

Subgroups — #25079616

Order 11008.

614 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#19145313C211yesmaximal, characteristic, complemented
2#19144655C211yesmaximal, characteristic
3#19144383C211yesmaximal, characteristic, complemented
4#19134170C211yesmaximal, characteristic, complemented
5#19134128C211yesmaximal, characteristic, complemented
6#19134118C211yesmaximal, characteristic, complemented
7#19134060C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19134011C211yesmaximal, characteristic, complemented
10#19133999C211yesmaximal, characteristic, complemented
11#19133943C211yesmaximal, characteristic, complemented
12#19133347C211yesmaximal, characteristic, complemented
13#19133306C211yesmaximal, characteristic, complemented
14#19133291C211yesmaximal, characteristic, complemented
15C43×#2971C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583272C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583223—21no—
23#14583206—21no—
24#14583199—21no—
25#14583194C2211yescharacteristic
26#14583194C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583189C2211yescharacteristic
29#14583184C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583145—21no—
32#14583145—21no—
33#14583099C2211yescharacteristic
34#14583094C2211yescharacteristic
35#14583044—21no—
36#14583001—21no—
37#14583001—21no—
38C4×#10621884—21no—
39C4×#10621882—21no—
40#14582952C2211yescharacteristic
41#14582935—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43#14582895—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582646C2211yescharacteristic
53#14582646C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C43×#436—21no—
60C43×#436—21no—
61C43×#436C2211yescharacteristic
62C43×#436C2211yescharacteristic
63C43×#432—21no—
64C43×#432C2211yescharacteristic
65C4×M16×C43—21no—
66C4×M16×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621873—21no—
69C2×#10621873—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063322C2311yescharacteristic
77#13063317—21no—
78#13063313—21no—
79#13063304—21no—
80#13063304—21no—
81#13063299—21no—
82#13063299—21no—
83C4×Dic86—21no—
84C4×Dic86—21no—
85C4×D172—21no—
86C4×D172—21no—
87#13063284—21no—
88#13063259—21no—
89#13063259—21no—
90#13063258—21no—
91#13063258—21no—
92#13063258—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256—21no—
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063250—21no—
102#13063250—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249—21no—
106#13063247—21no—
107#13063247—21no—
108#13063246—21no—
109#13063246—21no—
110#13063246—21no—
111#13063245—21no—
112#13063245—21no—
113C22⋊(C43⋊C8)—21no—
114C4×C43⋊C8—21no—
115C2×#41×C43D411yescharacteristic
116C2×M16×C43—21no—
117C2×M16×C43—21no—
118C2×M16×C43D411yescharacteristic
119C2×M16×C43D411yescharacteristic
120C4×Q8×C43D411yescharacteristic
121C4×Q8×C43C2311yescharacteristic
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43D411yescharacteristic
125C4×D4×C43C2311yescharacteristic
126#117×C43—21no—
127#117×C43D411yescharacteristic
128C2×C42×C43—21no—
129C2×C42×C43C2311yescharacteristic
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43C2311yescharacteristic
133C4⋊C8×C43C2311yescharacteristic
134C22⋊C8×C43—21no—
135C22⋊C8×C43—21no—
136C22⋊C8×C43—21no—
137#97×C43—21no—
138#97×C43D411yescharacteristic
139#97×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—41no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—41no—
156#10621898—82no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164M16×C43—22no—
165M16×C43—41no—
166M16×C43—42no—
167M16×C43—42no—
168C2×C8×C43—21no—
169C2×C8×C43—21no—
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C2×C8×C43C2×D411yescharacteristic
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188C22⋊Dic43—41no—
189#10621884—42no—
190#10621882—42no—
191(C2×D43)⋊C4—41no—
192(C2×D43)⋊C4—41no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199Dic43⋊C4—41no—
200Dic43⋊C4—41no—
201C4×Dic43—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—42no—
207#10621873—42no—
208#10621873—42no—
209C23×C43—21no—
210C23×C43#12111yescharacteristic
211C22×D43—41no—
212Q8×C43—21no—
213Q8×C43#13712yes—
214D4×C43—21no—
215D4×C43—21no—
216D4×C43—42no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—81no—
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—82no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—81no—
244C4×D43—82no—
245Dic86—41no—
246Dic86—41no—
247Dic86—81no—
248Dic86—81no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—21no—
252C8×C43—41no—
253C8×C43—41no—
254C8×C43#13512yes—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8—41no—
259#19183—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C2×#12111yescharacteristic
267C2×D43—81no—
268C2×D43—81no—
269C2×D43—81no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43C2×#13511yescharacteristic
278C4×C43C2×#13711yescharacteristic
279C4×C43#57511yescharacteristic
280C4×C43#57511yescharacteristic
281Dic43—81no—
282Dic43—81no—
283Dic43—81no—
284#3182—431no—
285#3106—431no—
286#3076—431no—
287#2971D4311yescharacteristic, complemented
288#1703—431no—
289#1697—431no—
290#1695—431no—
291#1685—431no—
292#1684—431no—
293#1678—431no—
294#1676—431no—
295#1666—431no—
296#1565—431no—
297#1554—431no—
298#1551—431no—
299C2×C43—41no—
300C2×C43—81no—
301C2×C43#303511yescharacteristic
302C2×C43#305611yescharacteristic
303C2×C43#306811yescharacteristic
304D43—161no—
305#533—431no—
306#532—431no—
307C4×#41C2×D4311yescharacteristic
308#500—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#482—861no—
313#479—861no—
314#478—861no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#475—431no—
320#474—431no—
321#468—861no—
322#468—861no—
323#460—431no—
324#459—431no—
325#449—861no—
326C8×Q8C2×D4311yescharacteristic
327C8×Q8C2×D4311yescharacteristic
328#440—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332#436—21no—
333#436—21no—
334#436C2×D4311yescharacteristic
335#436C2×D4311yescharacteristic
336#432—21no—
337#432C2×D4311yescharacteristic
338#431—431no—
339#427—861no—
340C2×C4⋊C8—431no—
341#416—861no—
342C4×M16—21no—
343C4×M16C2×D4311yescharacteristic
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348#333—431no—
349#333—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1918311yescharacteristic, complemented, Sylow
357C2×#41—861no—
358C2×#41D17211yescharacteristic
359C2×SD16—861no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—861no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16C22⋊D4311yescharacteristic
366C2×M16C22⋊D4311yescharacteristic
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8—431no—
371#127—431no—
372#125—861no—
373#124—861no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—861no—
377#121—861no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8D17211yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—861no—
385C4×D4—861no—
386C4×D4D17211yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—861no—
390#117D17211yescharacteristic
391C2×C42—21no—
392C2×C42C22×D4311yescharacteristic
393#107—861no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—21no—
425C22⋊C8—861no—
426#97—21no—
427#97C22⋊D4311yescharacteristic
428#97C22⋊D4311yescharacteristic
429C4×C8—21no—
430C4×C8—21no—
431C4×C8—861no—
432C4×C8C22×D4311yescharacteristic
433C4×C8C22×D4311yescharacteristic
434#41—22no—
435#41—41no—
436#41—3442no—
437C2×Q8—861no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8C2×D17211yescharacteristic
441C2×D4—21no—
442C2×D4—861no—
443C2×D4—861no—
444C2×D4—861no—
445C2×D4—1721no—
446C2×D4C2×D17211yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—1721no—
451C22×C4C2×D17211yescharacteristic
452C22×C4#1062189811yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454SD16—1722no—
455SD16—1722no—
456SD16—1722no—
457D8—1722no—
458M16—22no—
459M16—41no—
460M16—42no—
461M16—42no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—861no—
468C2×C8—1722no—
469C2×C8C2×C22⋊D4311yescharacteristic
470C2×C8C2×C22⋊D4311yescharacteristic
471C2×C8C2×C22⋊D4311yescharacteristic
472C2×C8C2×C22⋊D4311yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4C2×D17211yescharacteristic
484C4⋊C4C2×D17211yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—1721no—
489C22⋊C4—1721no—
490C22⋊C4—1721no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1721no—
495C42C2×D17211yescharacteristic
496C42#1062189811yescharacteristic
497C42C2×C22⋊D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—1721no—
501C23#1306329911yescharacteristic
502Q8—21no—
503Q8—3441no—
504Q8—3441no—
505Q8—1721no—
506Q8—1721no—
507Q8#1306335812yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—3441no—
512D4—3442no—
513D4—1721no—
514D4—1721no—
515D4—1721no—
516D4—1721no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—81no—
529C2×C4—3442no—
530C2×C4—1721no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329911yescharacteristic
534C2×C4#1306329911yescharacteristic
535C2×C4#1306329911yescharacteristic
536C2×C4C22×C22⋊D4311yescharacteristic
537C2×C4C22×D17211yescharacteristic
538C2×C4C2×#1062189811yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—1721no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8#1306334512yes—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—3441no—
556C22—3441no—
557C22—3441no—
558C22C2×#1306329911yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—3441no—
567C4—3441no—
568C4—3441no—
569C4C2×#1306334511yescharacteristic
570C4C2×#1306335811yescharacteristic
571C4#1458369711yescharacteristic
572C4#1458369911yescharacteristic
573C2—41no—
574C2—81no—
575C2—6881no—
576C2#1914405011yescharacteristic
577C2#1914422511yescharacteristic
578C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2971C2
socleC22×C43C2×#121
prime radical#19144655C2
hypercenter#2971D43
hypocenterC43#19183
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2971

Complements

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

NH ≅ G/Ntype
1. #19145313C2semidirect
3. #19144383C2semidirect
4. #19134170C2semidirect
5. #19134128C2semidirect
6. #19134118C2semidirect
7. #19134060C2semidirect
8. #19134053C2semidirect
9. #19134011C2semidirect
10. #19133999C2semidirect
11. #19133943C2semidirect
12. #19133347C2semidirect
13. #19133306C2semidirect
14. #19133291C2semidirect
15. C43×#2971C2semidirect
287. #2971D43semidirect
356. C43#19183semidirect

Maximal subgroups

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

subgroupindex
#191453132
#191446552
#191443832
#191341702
#191341282
#191341182
#191340602
#191340532
#191340112
#191339992
#191339432
#191333472
#191333062
#191332912
C43×#29712
#1918343