Finite Group Databasebeta

← #25079056

Subgroups — #25079056

Order 11008.

642 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145154C211yesmaximal, characteristic, complemented
2#19144666C211yesmaximal, characteristic, complemented
3#19144655C211yesmaximal, characteristic
4#19134053C211yesmaximal, characteristic, complemented
5#19134046C211yesmaximal, characteristic, complemented
6#19134039C211yesmaximal, characteristic, complemented
7#19134032C211yesmaximal, characteristic, complemented
8#19133977C211yesmaximal, characteristic, complemented
9#19133970C211yesmaximal, characteristic, complemented
10#19133943C211yesmaximal, characteristic, complemented
11#19133936C211yesmaximal, characteristic, complemented
12#19133343C211yesmaximal, characteristic, complemented
13#19133259C211yesmaximal, characteristic, complemented
14#19133255C211yesmaximal, characteristic, complemented
15C8×#41×C43C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583297C2211yescharacteristic
19#14583272C2211yescharacteristic
20#14583250C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583240—21no—
23#14583223—21no—
24#14583194C2211yescharacteristic
25#14583189C2211yescharacteristic
26#14583184C2211yescharacteristic
27#14583179C2211yescharacteristic
28#14583128—21no—
29#14583128—21no—
30#14583109C2211yescharacteristic
31#14583104C2211yescharacteristic
32#14583099C2211yescharacteristic
33#14583094C2211yescharacteristic
34#14583061—21no—
35#14583044—21no—
36C4×#10621885—21no—
37C4×#10621873—21no—
38C4×#10621873—21no—
39C4×#10621884—21no—
40C4×#10621883—21no—
41C4×#10621882—21no—
42#14582952C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582646C2211yescharacteristic
51#14582646C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4×C8×C43—21no—
66C2×C4×C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621873—21no—
70C2×#10621873—21no—
71C2×#10621883—21no—
72C2×#10621884—21no—
73C2×#10621882—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063322C2311yescharacteristic
78#13063317—21no—
79#13063313—21no—
80#13063304—21no—
81#13063304—21no—
82#13063299—21no—
83#13063299—21no—
84C4×Dic86—21no—
85C4×Dic86—21no—
86C4×D172—21no—
87C4×D172—21no—
88#13063284—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063250—21no—
100#13063250—21no—
101#13063249—21no—
102#13063249—21no—
103#13063248—21no—
104#13063248—21no—
105#13063247—21no—
106#13063247—21no—
107#13063246—21no—
108#13063246—21no—
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113C4×C43⋊C8—21no—
114C4×C43⋊C8—21no—
115C2×#41×C43D411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43D411yescharacteristic
119C22×C8×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—
137C4×C8×C43—21no—
138C4×C8×C43—21no—
139C4×C8×C43—21no—
140C4×C8×C43D411yescharacteristic
141C4×C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
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—
164C2×C8×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—41no—
168C2×C8×C43—42no—
169C2×C8×C43—42no—
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#10621885—42no—
190#10621884—42no—
191#10621883—42no—
192#10621882—42no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—41no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201Dic43⋊C4—41no—
202Dic43⋊C4—41no—
203C4×Dic43—41no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208#10621873—42no—
209#10621873—42no—
210C23×C43—21no—
211C23×C43#12111yescharacteristic
212C22×D43—41no—
213Q8×C43—21no—
214Q8×C43#13512yes—
215D4×C43—24no—
216D4×C43—21no—
217D4×C43#13512yes—
218C2×C4×C43—24no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—42no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—82no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240D172—41no—
241D172—41no—
242D172—41no—
243D172—41no—
244D172—81no—
245C4×D43—82no—
246Dic86—41no—
247Dic86—41no—
248Dic86—41no—
249Dic86—41no—
250Dic86—81no—
251C8×C43—21no—
252C8×C43—21no—
253C8×C43—21no—
254C8×C43—41no—
255C8×C43—41no—
256C8×C43#13512yes—
257C43⋊C8—41no—
258C43⋊C8—41no—
259C43⋊C8—41no—
260C43⋊C8—41no—
261#19127—431nomaximal, Sylow
262C22×C43—21no—
263C22×C43—22no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—41no—
267C22×C43—41no—
268C22×C43C2×#12111yescharacteristic
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—21no—
273C4×C43—21no—
274C4×C43—22no—
275C4×C43—21no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43#47112yes—
279C4×C43C2×#13511yescharacteristic
280C4×C43C2×#13511yescharacteristic
281C4×C43C2×#13511yescharacteristic
282C4×C43#57511yescharacteristic
283Dic43—81no—
284Dic43—81no—
285Dic43—81no—
286#3167—431no—
287#3107—431no—
288#3106—431no—
289C8×#41D4311yescharacteristic, complemented
290#1684—431no—
291#1683—431no—
292#1682—431no—
293#1681—431no—
294#1672—431no—
295#1671—431no—
296#1666—431no—
297#1665—431no—
298#1564—431no—
299#1544—431no—
300#1543—431no—
301C2×C43—41no—
302C2×C43—42no—
303C2×C43#303511yescharacteristic
304C2×C43#305011yescharacteristic
305C2×C43C2×#47111yescharacteristic
306D43—161no—
307#533—431no—
308#532—431no—
309C4×#41C2×D4311yescharacteristic
310#498—431no—
311#492—431no—
312#487—431no—
313#486—431no—
314#485—861no—
315#482—861no—
316#477—431no—
317#476—431no—
318#475—431no—
319#474—431no—
320#465—861no—
321#465—861no—
322#462—431no—
323#461—431no—
324#460—431no—
325#459—431no—
326#452—861no—
327#449—861no—
328C8×Q8C2×D4311yescharacteristic
329C8×Q8C2×D4311yescharacteristic
330C4×Q16—861no—
331C4×SD16—861no—
332C4×SD16—861no—
333C4×SD16—861no—
334C4×SD16—861no—
335C4×D8—861no—
336C8×D4—21no—
337C8×D4—21no—
338C8×D4C2×D4311yescharacteristic
339C8×D4C2×D4311yescharacteristic
340#431—21no—
341#431—431no—
342#431—431no—
343#431C2×D4311yescharacteristic
344C2×C4×C8—21no—
345C2×C4×C8C2×D4311yescharacteristic
346#335—431no—
347#335—431no—
348#334—431no—
349#334—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#332—431no—
355#332—431no—
356#331—431no—
357#331—431no—
358C43#1912711yescharacteristic, complemented, Sylow
359C2×#41—861no—
360C2×#41D17211yescharacteristic
361C2×Q16—861no—
362C2×SD16—861no—
363C2×SD16—861no—
364C2×SD16—861no—
365C2×SD16—861no—
366C2×D8—861no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8C22⋊D4311yescharacteristic
370C22×C8C22⋊D4311yescharacteristic
371C4⋊Q8—431no—
372C4⋊Q8—431no—
373C4⋊Q8—431no—
374#127—431no—
375#125—861no—
376#124—861no—
377C22⋊Q8—861no—
378C22⋊Q8—861no—
379#121—861no—
380#121—861no—
381C4×Q8—861no—
382C4×Q8—861no—
383C4×Q8D17211yescharacteristic
384C4×Q8C22×D4311yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—861no—
388C4×D4—861no—
389C4×D4D17211yescharacteristic
390C4×D4C22×D4311yescharacteristic
391#117—21no—
392#117—861no—
393#117D17211yescharacteristic
394C2×C42—21no—
395C2×C42C22×D4311yescharacteristic
396#107—861no—
397#107—861no—
398#106—861no—
399#106—861no—
400#106—861no—
401#106—861no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—431no—
405C4⋊C8—431no—
406C4⋊C8—431no—
407C4⋊C8—431no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—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—
426C22⋊C8—861no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—21no—
430C4×C8—861no—
431C4×C8—861no—
432C4×C8C22⋊D4311yescharacteristic
433C4×C8C22⋊D4311yescharacteristic
434C4×C8C22×D4311yescharacteristic
435C4×C8C22×D4311yescharacteristic
436#41—22no—
437#41—22no—
438#41—3442no—
439C2×Q8—861no—
440C2×Q8—861no—
441C2×Q8—861no—
442C2×Q8C2×D17211yescharacteristic
443C2×D4—21no—
444C2×D4—861no—
445C2×D4—861no—
446C2×D4—861no—
447C2×D4—1721no—
448C2×D4C2×D17211yescharacteristic
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—1721no—
453C22×C4C2×D17211yescharacteristic
454C22×C4#1062189811yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456Q16—1722no—
457SD16—1722no—
458SD16—1722no—
459SD16—1722no—
460SD16—1722no—
461D8—1722no—
462C2×C8—22no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—41no—
466C2×C8—42no—
467C2×C8—42no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8C2×C22⋊D4311yescharacteristic
473C2×C8C2×C22⋊D4311yescharacteristic
474C2×C8C2×C22⋊D4311yescharacteristic
475C2×C8C2×C22⋊D4311yescharacteristic
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—861no—
482C4⋊C4—861no—
483C4⋊C4—861no—
484C4⋊C4—1721no—
485C4⋊C4—1721no—
486C4⋊C4C2×D17211yescharacteristic
487C4⋊C4C2×D17211yescharacteristic
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—21no—
491C22⋊C4—1721no—
492C22⋊C4—1721no—
493C22⋊C4—1721no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—1721no—
498C42C2×D17211yescharacteristic
499C42#1062189811yescharacteristic
500C42C2×C22⋊D4311yescharacteristic
501C42C23×D4311yescharacteristic
502C23—21no—
503C23—1721no—
504C23#1306329911yescharacteristic
505Q8—21no—
506Q8—3441no—
507Q8—1721no—
508Q8—1721no—
509Q8—1721no—
510Q8—1721no—
511Q8#1306334712yes—
512D4—24no—
513D4—21no—
514D4—3441no—
515D4—3442no—
516D4—1721no—
517D4—1721no—
518D4—1721no—
519D4—1721no—
520D4#1306334712yes—
521C2×C4—24no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—42no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—3442no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4#1306329911yescharacteristic
538C2×C4#1306329911yescharacteristic
539C2×C4#1306329911yescharacteristic
540C2×C4C22×C22⋊D4311yescharacteristic
541C2×C4C22×D17211yescharacteristic
542C2×C4C2×#1062189811yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—1721no—
549C8—1721no—
550C8—1721no—
551C8—1721no—
552C8#1306334512yes—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—22no—
557C22—41no—
558C22—41no—
559C22—3441no—
560C22—3441no—
561C22—3441no—
562C22C2×#1306329911yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—22no—
567C4—41no—
568C4—41no—
569C4—3441no—
570C4—3441no—
571C4—3441no—
572C4#1458316212yes—
573C4C2×#1306334511yescharacteristic
574C4C2×#1306334711yescharacteristic
575C4C2×#1306334711yescharacteristic
576C4#1458369711yescharacteristic
577C2—41no—
578C2—42no—
579C2—6881no—
580C2#1914405011yescharacteristic
581C2#1914417611yescharacteristic
582C2C2×#1458316211yescharacteristic
subgroupG/H
centerC2×C4#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC8×#41×C43C2
socleC22×C43C2×#121
prime radical#19144655C2
hypercenterC8×#41D43
hypocenterC43#19127
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C8×#41

Complements

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

NH ≅ G/Ntype
1. #19145154C2semidirect
2. #19144666C2semidirect
4. #19134053C2semidirect
5. #19134046C2semidirect
6. #19134039C2semidirect
7. #19134032C2semidirect
8. #19133977C2semidirect
9. #19133970C2semidirect
10. #19133943C2semidirect
11. #19133936C2semidirect
12. #19133343C2semidirect
13. #19133259C2semidirect
14. #19133255C2semidirect
15. C8×#41×C43C2semidirect
289. C8×#41D43semidirect
358. C43#19127semidirect

Maximal subgroups

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

subgroupindex
#191451542
#191446662
#191446552
#191340532
#191340462
#191340392
#191340322
#191339772
#191339702
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#191332592
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#1912743