Finite Group Databasebeta

← #25253562

Subgroups — #25253562

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19146282C211yesmaximal, characteristic, complemented
2#19136834C211yesmaximal, characteristic, complemented
3#19136792C211yesmaximal, characteristic, complemented
4#19136780C211yesmaximal, characteristic, complemented
5#19136739C211yesmaximal, characteristic, complemented
6#19136696C211yesmaximal, characteristic, complemented
7#19136689C211yesmaximal, characteristic, complemented
8#19136650C211yesmaximal, characteristic, complemented
9#19136516C211yesmaximal, characteristic, complemented
10#19136506C211yesmaximal, characteristic, complemented
11#19136469C211yesmaximal, characteristic, complemented
12#19136421C211yesmaximal, characteristic, complemented
13#19136305C211yesmaximal, characteristic, complemented
14C2×#14582699C211yesmaximal, characteristic, complemented
15C43×#3334C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583545—21no—
19C2×#13063269C2211yescharacteristic, complemented
20C2×#13063266C2211yescharacteristic
21C2×#13063266C2211yescharacteristic
22C2×#13063265C2211yescharacteristic, complemented
23C22×C43⋊C16C2211yescharacteristic
24#14583283C2211yescharacteristic
25#14583140C2211yescharacteristic
26#14583135C2211yescharacteristic
27#14583115—21no—
28#14583052—21no—
29#14583046—21no—
30C4×D344C2211yescharacteristic
31#14582726C2211yescharacteristic, complemented
32#14582726C2211yescharacteristic, complemented
33#14582726C2211yescharacteristic, complemented
34C4⋊(C43⋊C16)C2211yescharacteristic, complemented
35#14582702C2211yescharacteristic, complemented
36#14582702C2211yescharacteristic, complemented
37#14582702C2211yescharacteristic, complemented
38#14582700C2211yescharacteristic, complemented
39#14582699C2211yescharacteristic
40#14582699C2211yescharacteristic
41#14582699C2211yescharacteristic
42#14582699C2211yescharacteristic
43#14582699C2211yescharacteristic
44#14582699C2211yescharacteristic
45C22⋊(C43⋊C16)C2211yescharacteristic
46C22⋊(C43⋊C16)C2211yescharacteristic, complemented
47#14582675C2211yescharacteristic, complemented
48C43×#547—21no—
49C43×#500C2211yescharacteristic, complemented
50C43×#480—21no—
51C43×#480—21no—
52C43×#474—21no—
53C43×#466C2211yescharacteristic
54C43×#466C2211yescharacteristic, complemented
55C4×D8×C43C2211yescharacteristic, complemented
56C8×D4×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#107×C43C2211yescharacteristic, complemented
59C2×#10621898—21no—
60C22×D172—21no—
61#13063347—22no—
62#13063347—41no—
63C2×Dic172C2311yescharacteristic
64C2×#10621873—21no—
65C2×#10621873—21no—
66C2×D344—22no—
67C2×D344—21no—
68C2×D344—41no—
69C2×D344C2311yescharacteristic
70C2×D344C2311yescharacteristic
71#13063313—21no—
72#13063310—41no—
73#13063304—21no—
74#13063299—21no—
75#13063298—41no—
76#13063293—41no—
77C4×D172—21no—
78C22⋊C4×D43—41no—
79#13063269—41no—
80#13063266—22no—
81#13063266—41no—
82#13063265—41no—
83C2×C43⋊C16—41no—
84C2×C43⋊C16C2311yescharacteristic
85C2×C43⋊C16C2311yescharacteristic
86C2×C43⋊C16C2311yescharacteristic
87C2×C43⋊C16C2311yescharacteristic
88#13063259C2311yescharacteristic
89#13063250—21no—
90#13063247—21no—
91#13063247—21no—
92C2×#41×C43—41no—
93C2×D8×C43C2311yescharacteristic
94C22×C8×C43C2311yescharacteristic
95C22×C8×C43C2311yescharacteristic
96C4⋊Q8×C43—21no—
97#123×C43—41no—
98#123×C43—41no—
99C22⋊Q8×C43—41no—
100#121×C43—21no—
101#121×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43D411yescharacteristic
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43—21no—
106#107×C43—21no—
107#107×C43—21no—
108#107×C43—21no—
109#107×C43C2311yescharacteristic
110#107×C43C2311yescharacteristic
111#107×C43C2311yescharacteristic
112C4⋊C8×C43D411yescharacteristic
113#102×C43—21no—
114#102×C43—21no—
115#102×C43—21no—
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120#41×C43—84no—
121C2×Q8×C43—41no—
122C2×D4×C43—21no—
123C2×D4×C43—41no—
124C2×D4×C43—41no—
125C2×D4×C43D811yescharacteristic
126C22×C4×C43—41no—
127C22×C4×C43—41no—
128C22×C4×C43—41no—
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C2×C22⋊D43—41no—
132C2×C22⋊D43—41no—
133#10621898—42no—
134#10621898—81no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172—41no—
138C2×D172—42no—
139C2×D172—81no—
140C2×C4×D43—41no—
141C2×C4×D43—41no—
142C2×Dic86—21no—
143D8×C43—21no—
144D8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43C2×D411yescharacteristic
150C2×C8×C43C2×D411yescharacteristic
151C2×C8×C43C2×D411yescharacteristic
152C2×C8×C43C2411yescharacteristic
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—41no—
157C4⋊C4×C43—41no—
158C4⋊C4×C43—41no—
159C4⋊C4×C43D811yescharacteristic
160C22⋊C4×C43—41no—
161C22⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43D811yescharacteristic
164C22⋊C4×C43D811yescharacteristic
165C42×C43C2×D411yescharacteristic
166C22⋊Dic43—41no—
167(C2×D43)⋊C4—41no—
168(C2×D43)⋊C4—41no—
169(C2×D43)⋊C4—41no—
170(C2×D43)⋊C4—41no—
171C4⋊Dic43—21no—
172Dic43⋊C4—41no—
173Dic172—21no—
174Dic172—21no—
175D344—21no—
176D344—21no—
177D344—21no—
178D344—42no—
179D344#4112yescomplemented
180#10621873—42no—
181#10621873—81no—
182C43⋊C16—21no—
183C43⋊C16—21no—
184C43⋊C16—21no—
185C43⋊C16—21no—
186C23×C43—41no—
187C23×C43C2×D811yescharacteristic
188C23×C43C2×D811yescharacteristic
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—82no—
192C22×D43—82no—
193C22×D43—161no—
194Q8×C43—82no—
195D4×C43—22no—
196D4×C43—41no—
197D4×C43—41no—
198D4×C43—82no—
199D4×C43—82no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—82no—
208C2×C4×C43—82no—
209C2×C4×C43—82no—
210C2×C4×C43C2×D811yescharacteristic
211C2×C4×C43C2×D811yescharacteristic
212C2×C4×C43C2×D811yescharacteristic
213C2×C4×C43C2×D811yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C22⋊D43—82no—
216C22⋊D43—161no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219D172—22no—
220D172—41no—
221D172—41no—
222D172—41no—
223D172—82no—
224C4×D43—82no—
225C4×D43—161no—
226Dic86—41no—
227Dic86—41no—
228C8×C43—21no—
229C8×C43—21no—
230C8×C43—21no—
231C8×C43C2×#4111yescharacteristic
232C8×C43H(5,𝔽2)11yescharacteristic
233#33873—431nomaximal, Sylow
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—81no—
240C22×C43—81no—
241C22×C43—81no—
242C22×C43#50912yes—
243C22×C43C22×D811yescharacteristic
244C2×D43—42no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C2×D43—164no—
251C4×C43—21no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—81no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43#54611yescharacteristic
259C4×C43#57711yescharacteristic
260Dic43—81no—
261Dic43—81no—
262#3334D4311yescharacteristic, complemented
263#3280—431no—
264#2243—431no—
265#2235—431no—
266#2233—431no—
267#2226—431no—
268#2218—431no—
269#2217—431no—
270#2210—431no—
271#2186—431no—
272#2184—431no—
273#2177—431no—
274#2168—431no—
275#2139—431no—
276C2×#357—431no—
277C2×C43—22no—
278C2×C43—41no—
279C2×C43—161no—
280C2×C43#329411yescharacteristic
281C2×C43C2×#50911yescharacteristic
282C2×C43#341611yescharacteristic
283D43—82no—
284D43—161no—
285C2×#135—431no—
286C22×D8—431no—
287#547—21no—
288#546—861no—
289C2×SD32—431no—
290C2×D16—431no—
291C2×D16—431no—
292C2×M32—431no—
293C22×C16—431no—
294#500C2×D4311yescharacteristic, complemented
295#495—431no—
296#480—21no—
297#480—21no—
298#474—21no—
299#467—431no—
300#466—431no—
301#466C2×D4311yescharacteristic
302#466C2×D4311yescharacteristic, complemented
303#463—861no—
304#450—861no—
305#449—861no—
306C4×D8—431no—
307C4×D8C2×D4311yescharacteristic, complemented
308C8×D4C2×D4311yescharacteristic
309C2×#107C2×D4311yescharacteristic
310C2×#107C2×D4311yescharacteristic, complemented
311#367—431no—
312#367—431no—
313#367—431no—
314C4⋊C16—431no—
315#358—431no—
316#358—431no—
317#358—431no—
318#357—431no—
319#357—431no—
320#357—431no—
321#357—431no—
322#357—431no—
323#357—431no—
324#357—431no—
325C22⋊C16—431no—
326C22⋊C16—431no—
327#346—431no—
328C43#3387311yescharacteristic, complemented, Sylow
329C2×#41—41no—
330C2×#41—861no—
331C22×D4—861no—
332#135—862no—
333#135—1721no—
334C2×Q16—431no—
335C2×SD16—861no—
336C2×SD16—861no—
337C2×D8—431no—
338C2×D8—431no—
339C2×D8—862no—
340C2×D8—861no—
341C2×D8—1721no—
342C2×D8C22×D4311yescharacteristic
343C22×C8C22×D4311yescharacteristic
344C22×C8C22×D4311yescharacteristic
345C4⋊Q8—21no—
346#124—861no—
347#123—41no—
348#123—41no—
349#123—1721no—
350C22⋊Q8—41no—
351C22⋊Q8—861no—
352#121—21no—
353#121—21no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357C4×D4—21no—
358C4×D4—861no—
359C4×D4C22⋊D4311yescharacteristic
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C22⋊C4—1721no—
363SD32—1721no—
364D16—862no—
365D16—1721no—
366M32—1721no—
367C2×C16—431no—
368C2×C16—431no—
369C2×C16—431no—
370C2×C16—431no—
371C2×C16—1721no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—431no—
376#107C22×D4311yescharacteristic
377#107C22×D4311yescharacteristic
378#107C22×D4311yescharacteristic
379C4⋊C8C22⋊D4311yescharacteristic
380#103—861no—
381#102—21no—
382#102—21no—
383#102—21no—
384#102—861no—
385#102—861no—
386C22⋊C8C22⋊D4311yescharacteristic
387C22⋊C8C22⋊D4311yescharacteristic
388C4×C8C22×D4311yescharacteristic
389C24—1721no—
390#41—84no—
391#41—3441no—
392#41—1722no—
393C2×Q8—41no—
394C2×Q8—861no—
395C2×D4—21no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—861no—
399C2×D4—861no—
400C2×D4—3441no—
401C2×D4—1722no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1721no—
405C2×D4#1062188211yescharacteristic
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4C2×C22⋊D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413Q16—861no—
414Q16—861no—
415SD16—3441no—
416SD16—1722no—
417D8—21no—
418D8—21no—
419D8—432no—
420D8—861no—
421D8—861no—
422D8—861no—
423D8—1722no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×C22⋊D4311yescharacteristic
429C2×C8C2×C22⋊D4311yescharacteristic
430C2×C8C2×C22⋊D4311yescharacteristic
431C2×C8C23×D4311yescharacteristic
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—861no—
439C4⋊C4—1721no—
440C4⋊C4#1062188211yescharacteristic
441C22⋊C4—41no—
442C22⋊C4—41no—
443C22⋊C4—41no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4#1062188211yescharacteristic
450C22⋊C4#1062188211yescharacteristic
451C42C2×C22⋊D4311yescharacteristic
452C16—861no—
453C16—861no—
454C16—861no—
455C16—861no—
456C23—41no—
457C23—3442no—
458C23—3442no—
459C23—1721no—
460C23—1721no—
461C23—6881no—
462C23C2×#1062188211yescharacteristic
463C23C2×#1062188211yescharacteristic
464Q8—82no—
465Q8—1721no—
466Q8—1721no—
467D4—22no—
468D4—41no—
469D4—41no—
470D4—82no—
471D4—82no—
472D4—862no—
473D4—3442no—
474D4—3442no—
475D4—1721no—
476D4—1721no—
477D4—1721no—
478D4—6881no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—82no—
487C2×C4—82no—
488C2×C4—82no—
489C2×C4—3442no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—6881no—
493C2×C4C2×#1062188211yescharacteristic
494C2×C4C2×#1062188211yescharacteristic
495C2×C4C2×#1062188211yescharacteristic
496C2×C4C2×#1062188211yescharacteristic
497C2×C4C22×C22⋊D4311yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D4311yescharacteristic
502C8#1306337111yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—3441no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—1722no—
517C22—6884no—
518C22#1458333512yes—
519C22C22×#1062188211yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—3441no—
528C4—3441no—
529C4#1458353711yescharacteristic
530C4#1458370711yescharacteristic
531C2—22no—
532C2—41no—
533C2—161no—
534C2—3442no—
535C2—6881no—
536C2#1914640211yescharacteristic
537C2C2×#1458333511yescharacteristic
538C2#1914773911yescharacteristic
subgroupG/H
centerC22C22×#10621882
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3334C2
socleC22×C43C22×D8
hypercenter#3334D43
hypocenterC43#33873
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #3334

Complements

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

NH ≅ G/Ntype
1. #19146282C2semidirect
2. #19136834C2semidirect
3. #19136792C2semidirect
4. #19136780C2semidirect
5. #19136739C2semidirect
6. #19136696C2semidirect
7. #19136689C2semidirect
8. #19136650C2semidirect
9. #19136516C2semidirect
10. #19136506C2semidirect
11. #19136469C2semidirect
12. #19136421C2semidirect
13. #19136305C2semidirect
14. C2×#14582699C2semidirect
15. C43×#3334C2semidirect
19. C2×#13063269C22semidirect
22. C2×#13063265C22semidirect
31. #14582726C22semidirect
32. #14582726C22semidirect
33. #14582726C22semidirect
34. C4⋊(C43⋊C16)C22semidirect
35. #14582702C22semidirect
36. #14582702C22semidirect
37. #14582702C22semidirect
38. #14582700C22semidirect
46. C22⋊(C43⋊C16)C22semidirect
47. #14582675C22semidirect
49. C43×#500C22semidirect
54. C43×#466C22semidirect
55. C4×D8×C43C22semidirect
58. C2×#107×C43C22semidirect
179. D344#41semidirect
262. #3334D43semidirect
294. #500C2×D43semidirect
302. #466C2×D43semidirect
307. C4×D8C2×D43semidirect
310. C2×#107C2×D43semidirect
328. C43#33873semidirect

Maximal subgroups

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

subgroupindex
#191462822
#191368342
#191367922
#191367802
#191367392
#191366962
#191366892
#191366502
#191365162
#191365062
#191364692
#191364212
#191363052
C2×#145826992
C43×#33342
#3387343