Finite Group Databasebeta

← #25253570

Subgroups — #25253570

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#19146943C211yesmaximal, characteristic, complemented
2#19146282C211yesmaximal, characteristic, complemented
3#19136832C211yesmaximal, characteristic, complemented
4#19136793C211yesmaximal, characteristic, complemented
5#19136781C211yesmaximal, characteristic, complemented
6#19136743C211yesmaximal, characteristic, complemented
7#19136698C211yesmaximal, characteristic, complemented
8#19136691C211yesmaximal, characteristic, complemented
9#19136651C211yesmaximal, characteristic, complemented
10#19136520C211yesmaximal, characteristic, complemented
11#19136509C211yesmaximal, characteristic, complemented
12#19136472C211yesmaximal, characteristic, complemented
13#19136308C211yesmaximal, characteristic, complemented
14C2×#14582701C211yesmaximal, characteristic, complemented
15C43×#2168C211yesmaximal, characteristic, complemented
16C2×#13063347C2211yescharacteristic
17C22×D344C2211yescharacteristic
18#14583553—21no—
19#14583545—21no—
20C2×#13063270C2211yescharacteristic, complemented
21C2×D688C2211yescharacteristic
22C2×D688C2211yescharacteristic
23#14583304C2211yescharacteristic, complemented
24#14583283C2211yescharacteristic
25#14583213—21no—
26#14583213—21no—
27#14583180—21no—
28#14583140C2211yescharacteristic
29#14583135C2211yescharacteristic
30#14583135C2211yescharacteristic
31#14583135C2211yescharacteristic, complemented
32#14583115—21no—
33#14583052—21no—
34#14583046—21no—
35C4×D344C2211yescharacteristic
36C4×D344C2211yescharacteristic, complemented
37C2×#13063259C2211yescharacteristic
38C2×#13063259C2211yescharacteristic, complemented
39#14582727C2211yescharacteristic, complemented
40#14582727C2211yescharacteristic, complemented
41#14582727C2211yescharacteristic, complemented
42#14582704C2211yescharacteristic, complemented
43#14582704C2211yescharacteristic, complemented
44#14582704C2211yescharacteristic, complemented
45#14582701C2211yescharacteristic
46#14582701C2211yescharacteristic
47#14582701C2211yescharacteristic
48#14582701C2211yescharacteristic
49#14582701C2211yescharacteristic
50#14582701C2211yescharacteristic
51#14582701C2211yescharacteristic, complemented
52C2×M32×C43C2211yescharacteristic, complemented
53C22×C16×C43C2211yescharacteristic
54C8×D4×C43C2211yescharacteristic
55C43×C4⋊C16C2211yescharacteristic, complemented
56C43×C22⋊C16C2211yescharacteristic
57C43×C22⋊C16C2211yescharacteristic, complemented
58C43×#346C2211yescharacteristic, complemented
59C2×#10621898—21no—
60C2×#10621900—41no—
61C22×D172—21no—
62#13063347—22no—
63#13063347—41no—
64C2×Dic172C2311yescharacteristic
65C2×#10621873—21no—
66C2×#10621873—21no—
67C2×D344—22no—
68C2×D344—21no—
69C2×D344—41no—
70C2×D344C2311yescharacteristic
71C2×D344C2311yescharacteristic
72C2×D344C2311yescharacteristic
73#13063325—21no—
74#13063313—21no—
75#13063310—41no—
76#13063309—41no—
77#13063309—41no—
78#13063305—41no—
79#13063304—21no—
80#13063299—21no—
81#13063299—21no—
82#13063299—21no—
83#13063298—41no—
84#13063293—41no—
85C4×D172—21no—
86C4×D172—21no—
87C2×C4⋊Dic43—21no—
88C2×C4⋊Dic43—21no—
89C22⋊C4×D43—41no—
90#13063270—41no—
91D688—22no—
92D688—41no—
93#13063259—21no—
94#13063259—21no—
95#13063259—21no—
96#13063259C2311yescharacteristic
97#13063259C2311yescharacteristic
98#13063259C2311yescharacteristic
99#13063259C2311yescharacteristic
100#13063250—21no—
101#13063247—21no—
102#13063247—21no—
103#13063247—21no—
104#13063247—21no—
105#13063247—21no—
106C22×C8×C43C2311yescharacteristic
107C22×C8×C43C2311yescharacteristic
108C4×D4×C43D411yescharacteristic
109M32×C43—41no—
110C2×C16×C43—41no—
111C2×C16×C43C2311yescharacteristic
112C2×C16×C43C2311yescharacteristic
113C2×C16×C43C2311yescharacteristic
114C2×C16×C43C2311yescharacteristic
115C4⋊C8×C43D411yescharacteristic
116C22⋊C8×C43D411yescharacteristic
117C22⋊C8×C43D411yescharacteristic
118C4×C8×C43C2311yescharacteristic
119C23×D43—41no—
120C2×D4×C43D811yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C2×C22⋊D43—41no—
124C2×C22⋊D43—41no—
125C2×C22⋊D43—41no—
126C2×C22⋊D43—41no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129#10621900—84no—
130#10621898—42no—
131#10621898—81no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—41no—
136C2×D172—42no—
137C2×D172—81no—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43—41no—
141C2×Dic86—21no—
142C2×Dic86—41no—
143C2×C8×C43—21no—
144C2×C8×C43—21no—
145C2×C8×C43—21no—
146C2×C8×C43—21no—
147C2×C8×C43C2×D411yescharacteristic
148C2×C8×C43C2×D411yescharacteristic
149C2×C8×C43C2×D411yescharacteristic
150C2×C8×C43C2411yescharacteristic
151C4⋊C4×C43D811yescharacteristic
152C22⋊C4×C43D811yescharacteristic
153C22⋊C4×C43D811yescharacteristic
154C42×C43C2×D411yescharacteristic
155C22⋊Dic43—41no—
156(C2×D43)⋊C4—41no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159(C2×D43)⋊C4—41no—
160(C2×D43)⋊C4—41no—
161(C2×D43)⋊C4—41no—
162(C2×D43)⋊C4—41no—
163C4⋊Dic43—21no—
164C4⋊Dic43—21no—
165C4⋊Dic43—21no—
166C4⋊Dic43—21no—
167C4⋊Dic43—41no—
168C4⋊Dic43—41no—
169C4⋊Dic43—41no—
170Dic43⋊C4—41no—
171Dic172—21no—
172Dic172—21no—
173D344—21no—
174D344—21no—
175D344—21no—
176D344—21no—
177D344—21no—
178D344—42no—
179D344#4112yescomplemented
180#10621873—42no—
181#10621873—81no—
182C16×C43—21no—
183C16×C43—21no—
184C16×C43—21no—
185C16×C43—21no—
186C23×C43C2×D811yescharacteristic
187C23×C43C2×D811yescharacteristic
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—82no—
192C22×D43—82no—
193C22×D43—161no—
194D4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43C2×D811yescharacteristic
200C2×C4×C43C2×D811yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×D811yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—82no—
205C22⋊D43—82no—
206C22⋊D43—82no—
207C22⋊D43—161no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—82no—
214C2×Dic43—82no—
215D172—22no—
216D172—41no—
217D172—41no—
218D172—41no—
219D172—41no—
220D172—41no—
221D172—82no—
222C4×D43—82no—
223C4×D43—82no—
224C4×D43—161no—
225Dic86—41no—
226Dic86—41no—
227Dic86—82no—
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#50912yes—
240C22×C43C22×D811yescharacteristic
241C2×D43—42no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
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#54611yescharacteristic
256C4×C43#57711yescharacteristic
257Dic43—81no—
258Dic43—81no—
259Dic43—81no—
260Dic43—81no—
261Dic43—81no—
262#3334—431no—
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#2168D4311yescharacteristic, complemented
275#2139—431no—
276C2×#357—431no—
277C2×C43—22no—
278C2×C43—41no—
279C2×C43#329411yescharacteristic
280C2×C43C2×#50911yescharacteristic
281C2×C43#341611yescharacteristic
282D43—82no—
283D43—161no—
284D43—161no—
285C2×#135—431no—
286C22×D8—431no—
287#547—861no—
288#546—861no—
289C2×SD32—431no—
290C2×D16—431no—
291C2×D16—431no—
292C2×M32C2×D4311yescharacteristic, complemented
293C22×C16C2×D4311yescharacteristic
294#500—431no—
295#495—431no—
296#480—861no—
297#480—861no—
298#474—861no—
299#467—431no—
300#466—431no—
301#466—431no—
302#466—431no—
303#463—861no—
304#450—861no—
305#449—861no—
306C4×D8—431no—
307C4×D8—431no—
308C8×D4C2×D4311yescharacteristic
309C2×#107—431no—
310C2×#107—431no—
311#367—431no—
312#367—431no—
313#367—431no—
314C4⋊C16C2×D4311yescharacteristic, complemented
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⋊C16C2×D4311yescharacteristic
326C22⋊C16C2×D4311yescharacteristic, complemented
327#346C2×D4311yescharacteristic, complemented
328C43#3387311yescharacteristic, complemented, Sylow
329C2×#41—861no—
330C2×#41—1721no—
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—431no—
340C2×D8—862no—
341C2×D8—861no—
342C2×D8—1721no—
343C22×C8C22×D4311yescharacteristic
344C22×C8C22×D4311yescharacteristic
345C4⋊Q8—861no—
346#124—861no—
347#123—1721no—
348#123—1721no—
349#123—1721no—
350C22⋊Q8—861no—
351C22⋊Q8—1721no—
352#121—861no—
353#121—861no—
354#121—861no—
355#121—1721no—
356#120—1721no—
357C4×D4—861no—
358C4×D4—861no—
359C4×D4D17211yescharacteristic
360C2×C4⋊C4—861no—
361C2×C4⋊C4—861no—
362C2×C22⋊C4—1721no—
363SD32—1721no—
364D16—862no—
365D16—1721no—
366M32—41no—
367C2×C16—41no—
368C2×C16C22×D4311yescharacteristic
369C2×C16C22×D4311yescharacteristic
370C2×C16C22×D4311yescharacteristic
371C2×C16C22×D4311yescharacteristic
372#107—431no—
373#107—431no—
374#107—431no—
375#107—431no—
376#107—861no—
377#107—861no—
378#107—861no—
379C4⋊C8D17211yescharacteristic
380#103—861no—
381#102—861no—
382#102—861no—
383#102—861no—
384#102—861no—
385#102—861no—
386C22⋊C8D17211yescharacteristic
387C22⋊C8D17211yescharacteristic
388C4×C8C22×D4311yescharacteristic
389C24—1721no—
390#41—3441no—
391#41—3444no—
392#41—1722no—
393C2×Q8—861no—
394C2×Q8—1721no—
395C2×D4—861no—
396C2×D4—861no—
397C2×D4—861no—
398C2×D4—3441no—
399C2×D4—1722no—
400C2×D4—1721no—
401C2×D4—1721no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4—1721no—
405C2×D4D34411yescharacteristic
406C22×C4—1721no—
407C22×C4—1721no—
408C22×C4—1721no—
409C22×C4—1721no—
410C22×C4—1721no—
411C22×C4C2×D17211yescharacteristic
412C22×C4C2×D17211yescharacteristic
413Q16—861no—
414Q16—861no—
415SD16—3441no—
416SD16—1722no—
417D8—432no—
418D8—861no—
419D8—861no—
420D8—861no—
421D8—861no—
422D8—861no—
423D8—1722no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8C2×D17211yescharacteristic
429C2×C8C2×D17211yescharacteristic
430C2×C8C2×D17211yescharacteristic
431C2×C8C23×D4311yescharacteristic
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—861no—
435C4⋊C4—861no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C4⋊C4D34411yescharacteristic
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C22⋊C4—1721no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C22⋊C4—1721no—
449C22⋊C4D34411yescharacteristic
450C22⋊C4D34411yescharacteristic
451C42C2×D17211yescharacteristic
452C16—21no—
453C16—21no—
454C16—21no—
455C16—21no—
456C23—3442no—
457C23—3442no—
458C23—1721no—
459C23—1721no—
460C23—1721no—
461C23—6881no—
462C23C2×D34411yescharacteristic
463C23C2×D34411yescharacteristic
464Q8—3442no—
465Q8—1721no—
466Q8—1721no—
467D4—22no—
468D4—862no—
469D4—3442no—
470D4—3442no—
471D4—3442no—
472D4—3442no—
473D4—1721no—
474D4—1721no—
475D4—1721no—
476D4—1721no—
477D4—1721no—
478D4—6881no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—3442no—
484C2×C4—3442no—
485C2×C4—3442no—
486C2×C4—3442no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4—1721no—
492C2×C4—6881no—
493C2×C4C2×D34411yescharacteristic
494C2×C4C2×D34411yescharacteristic
495C2×C4C2×D34411yescharacteristic
496C2×C4C2×D34411yescharacteristic
497C2×C4C22×D17211yescharacteristic
498C8—21no—
499C8—21no—
500C8—21no—
501C8#41×D4311yescharacteristic
502C8#1306337011yescharacteristic
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—3441no—
509C22—3441no—
510C22—3441no—
511C22—3441no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22—3441no—
516C22—1722no—
517C22—6884no—
518C22#1458333712yes—
519C22C22×D34411yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—3441no—
525C4—3441no—
526C4—3441no—
527C4—3441no—
528C4—3441no—
529C4#1458354411yescharacteristic
530C4#1458371111yescharacteristic
531C2—22no—
532C2—41no—
533C2—3442no—
534C2—6881no—
535C2—6881no—
536C2#1914640911yescharacteristic
537C2C2×#1458333711yescharacteristic
538C2#1914774311yescharacteristic
subgroupG/H
centerC22C22×D344
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#2168C2
socleC22×C43C22×D8
hypercenter#2168D43
hypocenterC43#33873
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4 ◁ #2168

Complements

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

NH ≅ G/Ntype
1. #19146943C2semidirect
2. #19146282C2semidirect
3. #19136832C2semidirect
4. #19136793C2semidirect
5. #19136781C2semidirect
6. #19136743C2semidirect
7. #19136698C2semidirect
8. #19136691C2semidirect
9. #19136651C2semidirect
10. #19136520C2semidirect
11. #19136509C2semidirect
12. #19136472C2semidirect
13. #19136308C2semidirect
14. C2×#14582701C2semidirect
15. C43×#2168C2semidirect
20. C2×#13063270C22semidirect
23. #14583304C22semidirect
31. #14583135C22semidirect
36. C4×D344C22semidirect
38. C2×#13063259C22semidirect
39. #14582727C22semidirect
40. #14582727C22semidirect
41. #14582727C22semidirect
42. #14582704C22semidirect
43. #14582704C22semidirect
44. #14582704C22semidirect
51. #14582701C22semidirect
52. C2×M32×C43C22semidirect
55. C43×C4⋊C16C22semidirect
57. C43×C22⋊C16C22semidirect
58. C43×#346C22semidirect
179. D344#41semidirect
274. #2168D43semidirect
292. C2×M32C2×D43semidirect
314. C4⋊C16C2×D43semidirect
326. C22⋊C16C2×D43semidirect
327. #346C2×D43semidirect
328. C43#33873semidirect

Maximal subgroups

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

subgroupindex
#191469432
#191462822
#191368322
#191367932
#191367812
#191367432
#191366982
#191366912
#191366512
#191365202
#191365092
#191364722
#191363082
C2×#145827012
C43×#21682
#3387343