Finite Group Databasebeta

← #25084257

Subgroups — #25084257

Order 11008.

814 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145155C211yesmaximal, characteristic, complemented
2#19145154C211yesmaximal, characteristic, complemented
3#19145150C211yesmaximal, characteristic, complemented
4#19145105C211yesmaximal, characteristic, complemented
5#19145021C211yesmaximal, characteristic
6#19134198C211yesmaximal, characteristic, complemented
7#19134195C211yesmaximal, characteristic, complemented
8#19134191C211yesmaximal, characteristic, complemented
9#19134190C211yesmaximal, characteristic, complemented
10#19134186C211yesmaximal, characteristic, complemented
11#19134185C211yesmaximal, characteristic, complemented
12#19134183C211yesmaximal, characteristic, complemented
13#19134181C211yesmaximal, characteristic, complemented
14C2×C8×C43⋊C8C211yesmaximal, characteristic, complemented
15C43×#3167C211yesmaximal, characteristic, complemented
16C2×#13063345—22no—
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583298—22no—
22#14583297C2211yescharacteristic
23#14583295C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583295C2211yescharacteristic
26#14583295C2211yescharacteristic
27#14583281—22no—
28#14583278C2211yescharacteristic
29#14583275C2211yescharacteristic
30#14583273C2211yescharacteristic
31#14583273C2211yescharacteristic
32#14583272C2211yescharacteristic
33#14583271C2211yescharacteristic
34#14583271C2211yescharacteristic
35#14583251C2211yescharacteristic
36#14583250C2211yescharacteristic
37#14583249C2211yescharacteristic
38#14583247C2211yescharacteristic
39#14583246C2211yescharacteristic
40#14583245C2211yescharacteristic
41#14583130—22no—
42#14583128—22no—
43#14583126—22no—
44C4×#10621873—22no—
45C4×#10621884—22no—
46C4×#10621883—22no—
47#14582935—22no—
48C2×C4×C43⋊C8C2211yescharacteristic
49C2×C4×C43⋊C8C2211yescharacteristic
50C8×C43⋊C8C2211yescharacteristic
51C8×C43⋊C8C2211yescharacteristic
52C8×C43⋊C8C2211yescharacteristic
53C8×C43⋊C8C2211yescharacteristic
54C43×#533C2211yescharacteristic
55C43×#532C2211yescharacteristic
56C43×#498C2211yescharacteristic
57C43×#492C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#486C2211yescharacteristic
60C43×#465—22no—
61C4×SD16×C43—22no—
62C2×C4×C8×C43C2211yescharacteristic
63C2×#10621898—21no—
64#13063345—48no—
65C2×#10621885—22no—
66C2×#10621873—22no—
67C2×#10621883—22no—
68C2×#10621883—22no—
69C2×#10621884—22no—
70C2×#10621884—22no—
71C2×#10621882—22no—
72C22×C43⋊C8D412yes—
73C22×C43⋊C8D412yes—
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—22no—
90#13063258—22no—
91#13063257—22no—
92#13063256—22no—
93#13063256—22no—
94#13063256—22no—
95#13063256—22no—
96#13063250—22no—
97#13063249—22no—
98#13063248—22no—
99#13063247—22no—
100#13063246—22no—
101#13063245—22no—
102C4×C43⋊C8D412yes—
103C4×C43⋊C8D412yes—
104C4×C43⋊C8C2311yescharacteristic
105C4×C43⋊C8C2311yescharacteristic
106C4×C43⋊C8C2311yescharacteristic
107C4×C43⋊C8C2311yescharacteristic
108C2×#41×C43—21no—
109C2×SD16×C43—22no—
110C22×C8×C43D412yes—
111C4⋊Q8×C43C2311yescharacteristic
112C4⋊Q8×C43C2311yescharacteristic
113C4⋊Q8×C43C2311yescharacteristic
114#127×C43C2311yescharacteristic
115#125×C43—21no—
116#124×C43—21no—
117C22⋊Q8×C43—21no—
118C22⋊Q8×C43—21no—
119#121×C43—21no—
120#121×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125#117×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#106×C43—22no—
128#103×C43—22no—
129#102×C43—22no—
130C4×C8×C43D412yes—
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133#41×C43—44no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—41no—
141C22×C4×C43—41no—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C2×C22⋊D43—41no—
146#10621898—44no—
147C2×D172—21no—
148C2×D172—21no—
149C2×D172—21no—
150C2×C4×D43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154SD16×C43—44no—
155C2×C8×C43—24no—
156C2×C8×C43C2×D412yes—
157C2×C8×C43C2×D412yes—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—41no—
165C4⋊C4×C43—41no—
166C22⋊C4×C43—41no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C42×C43—41no—
170C42×C43C2×D411yescharacteristic
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2411yescharacteristic
174C22⋊Dic43—41no—
175#10621885—44no—
176#10621884—44no—
177#10621884—44no—
178#10621883—44no—
179#10621883—44no—
180#10621882—44no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—41no—
192C2×C43⋊C8—24no—
193C2×C43⋊C8SD1618yescomplemented
194C2×C43⋊C8C2×D412yes—
195C2×C43⋊C8C2×D412yes—
196C2×C43⋊C8C2×D412yes—
197C2×C43⋊C8C2×D412yes—
198#10621873—44no—
199C23×C43—41no—
200C23×C43#12711yescharacteristic
201C22×D43—41no—
202Q8×C43—42no—
203Q8×C43—42no—
204Q8×C43—42no—
205D4×C43—42no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—82no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—82no—
215C2×C4×C43#12711yescharacteristic
216C2×C4×C43#12711yescharacteristic
217C2×C4×C43#12711yescharacteristic
218C2×C4×C43C2×SD1614yes—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C22⋊D43—82no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226D172—42no—
227D172—42no—
228D172—42no—
229C4×D43—82no—
230Dic86—42no—
231Dic86—42no—
232Dic86—42no—
233C8×C43—22no—
234C8×C43#13514yescomplemented
235C43⋊C8—22no—
236C43⋊C8C2×SD1614yes—
237C43⋊C8C2×SD1614yes—
238C43⋊C8#13514yescomplemented
239#19596—431nomaximal, Sylow
240C22×C43—21no—
241C22×C43—21no—
242C22×C43—81no—
243C22×C43—81no—
244C22×C43—81no—
245C22×C43#49212yes—
246C22×C43C2×#12711yescharacteristic
247C2×D43—81no—
248C2×D43—81no—
249C2×D43—81no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—81no—
253C4×C43—81no—
254C4×C43—81no—
255C4×C43#49212yes—
256C4×C43C22×SD1612yes—
257C4×C43C2×#13512yes—
258C4×C43C2×#13512yes—
259Dic43—81no—
260Dic43—81no—
261Dic43—81no—
262#3167—431no—
263#3167—431no—
264#3167—431no—
265#3167D4311yescharacteristic, complemented
266#3160—431no—
267#3147—431no—
268#1708—431no—
269#1708—431no—
270#1707—431no—
271#1707—431no—
272#1706—431no—
273#1706—431no—
274#1705—431no—
275#1705—431no—
276C2×C82—431no—
277C2×C43—22no—
278C2×C43—161no—
279C2×C43C2×#49211yescharacteristic
280C2×C43#314711yescharacteristic
281C2×C43#314711yescharacteristic
282D43—161no—
283C2×#135—862no—
284#533—431no—
285#533C2×D4311yescharacteristic
286#532—431no—
287#532C2×D4311yescharacteristic
288#500—431no—
289#500—431no—
290#499—862no—
291#498—431no—
292#498—431no—
293#498—431no—
294#498—431no—
295#498—431no—
296#498C2×D4311yescharacteristic
297#495—862no—
298#494—431no—
299#493—431no—
300#492—431no—
301#492—431no—
302#492—431no—
303#492—431no—
304#492—431no—
305#492C2×D4311yescharacteristic
306#487—431no—
307#487—431no—
308#487—431no—
309#487C2×D4311yescharacteristic
310#486—431no—
311#486—431no—
312#486—431no—
313#486C2×D4311yescharacteristic
314#465—22no—
315#465—862no—
316#465—862no—
317#465—862no—
318C4×SD16—22no—
319C4×SD16—862no—
320C4×SD16—862no—
321C4×SD16—862no—
322#427—862no—
323C2×C4×C8—431no—
324C2×C4×C8—431no—
325C2×C4×C8C2×D4311yescharacteristic
326C82—431no—
327C82—431no—
328C82—431no—
329C82—431no—
330C43#1959611yescharacteristic, complemented, Sylow
331C2×#41—21no—
332C2×#41—861no—
333#135—1728no—
334C2×Q16—862no—
335C2×SD16—22no—
336C2×SD16—862no—
337C2×SD16—862no—
338C2×SD16—862no—
339C2×SD16—862no—
340C2×SD16—862no—
341C2×D8—862no—
342C22×C8—432no—
343C22×C8—432no—
344C22×C8C22⋊D4312yes—
345C4⋊Q8—431no—
346C4⋊Q8—431no—
347C4⋊Q8—431no—
348C4⋊Q8C22×D4311yescharacteristic
349C4⋊Q8C22×D4311yescharacteristic
350C4⋊Q8C22×D4311yescharacteristic
351#127—431no—
352#127C22×D4311yescharacteristic
353#125—21no—
354#125—861no—
355#124—21no—
356#124—861no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359C22⋊Q8—861no—
360C22⋊Q8—861no—
361#121—21no—
362#121—21no—
363#121—861no—
364#121—861no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—861no—
368C4×Q8—861no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—861no—
372C4×D4—861no—
373#117—21no—
374#117—861no—
375C2×C42C22×D4311yescharacteristic
376#107—862no—
377#107—862no—
378#106—22no—
379#106—862no—
380#106—862no—
381#106—862no—
382#106—862no—
383#106—862no—
384#103—22no—
385#103—862no—
386#103—862no—
387#103—862no—
388#102—22no—
389#102—862no—
390#102—862no—
391#102—862no—
392C4×C8—432no—
393C4×C8—432no—
394C4×C8—431no—
395C4×C8—431no—
396C4×C8—431no—
397C4×C8—431no—
398C4×C8C22⋊D4312yes—
399C4×C8C22×D4311yescharacteristic
400C4×C8C22×D4311yescharacteristic
401#41—44no—
402#41—1724no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—861no—
407C2×Q8—861no—
408C2×Q8—861no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—861no—
414C2×D4—861no—
415C2×D4—861no—
416C2×D4—1721no—
417C22×C4—41no—
418C22×C4—1721no—
419C22×C4D4×D4311yescharacteristic
420C22×C4D4×D4311yescharacteristic
421C22×C4C2×C22⋊D4311yescharacteristic
422Q16—1724no—
423SD16—44no—
424SD16—1724no—
425SD16—1724no—
426SD16—1724no—
427SD16—1724no—
428SD16—1724no—
429D8—1724no—
430C2×C8—24no—
431C2×C8—438no—
432C2×C8—432no—
433C2×C8—432no—
434C2×C8—432no—
435C2×C8—432no—
436C2×C8—864no—
437C2×C8C2×C22⋊D4312yes—
438C2×C8C2×C22⋊D4312yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—861no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—1721no—
454C4⋊C4—1721no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—1721no—
459C22⋊C4—1721no—
460C22⋊C4—1721no—
461C42—41no—
462C42—1721no—
463C42D4×D4311yescharacteristic
464C42D4×D4311yescharacteristic
465C42C2×C22⋊D4311yescharacteristic
466C42C23×D4311yescharacteristic
467C23—41no—
468C23—1721no—
469C23#1306332111yescharacteristic
470Q8—42no—
471Q8—42no—
472Q8—42no—
473Q8—1722no—
474Q8—1722no—
475Q8—1722no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—82no—
480D4—3442no—
481D4—1722no—
482D4—1722no—
483D4—1722no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—82no—
490C2×C4—3442no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4#1306332111yescharacteristic
495C2×C4#1306332111yescharacteristic
496C2×C4#1306332111yescharacteristic
497C2×C4SD16×D4314yes—
498C2×C4C2×D4×D4311yescharacteristic
499C2×C4C2×D4×D4311yescharacteristic
500C2×C4C22×C22⋊D4311yescharacteristic
501C8—22no—
502C8—434no—
503C8—434no—
504C8—434no—
505C8—862no—
506C8#1306334514yescomplemented
507C22—21no—
508C22—21no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—3441no—
513C22—3441no—
514C22—3441no—
515C22#1458327012yes—
516C22C2×#1306332111yescharacteristic
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—3441no—
523C4—3441no—
524C4—3441no—
525C4#1458327012yes—
526C4C2×SD16×D4312yes—
527C4#135×D4312yes—
528C4C2×#1306334512yes—
529C2—22no—
530C2—161no—
531C2—6881no—
532C2C2×#1458327011yescharacteristic
533C2#1914501911yescharacteristic
534C2#1914502111yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3167C2
socleC22×C43C2×#127
prime radical#19145021C2
hypercenter#3167D43
hypocenterC43#19596
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19145155C2semidirect
2. #19145154C2semidirect
3. #19145150C2semidirect
4. #19145105C2semidirect
6. #19134198C2semidirect
7. #19134195C2semidirect
8. #19134191C2semidirect
9. #19134190C2semidirect
10. #19134186C2semidirect
11. #19134185C2semidirect
12. #19134183C2semidirect
13. #19134181C2semidirect
14. C2×C8×C43⋊C8C2semidirect
15. C43×#3167C2semidirect
193. C2×C43⋊C8SD16semidirect
234. C8×C43#135semidirect
238. C43⋊C8#135semidirect
265. #3167D43semidirect
330. C43#19596semidirect
506. C8#13063345semidirect

Maximal subgroups

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

subgroupindex
#191451552
#191451542
#191451502
#191451052
#191450212
#191341982
#191341952
#191341912
#191341902
#191341862
#191341852
#191341832
#191341812
C2×C8×C43⋊C82
C43×#31672
#1959643