Finite Group Databasebeta

← #25084408

Subgroups — #25084408

Order 11008.

820 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic, complemented
2#19145154C211yesmaximal, characteristic, complemented
3#19145150C211yesmaximal, characteristic, complemented
4#19145021C211yesmaximal, characteristic, complemented
5#19144917C211yesmaximal, characteristic, complemented
6#19134271C211yesmaximal, characteristic, complemented
7#19134260C211yesmaximal, characteristic, complemented
8#19134257C211yesmaximal, characteristic, complemented
9#19134251C211yesmaximal, characteristic, complemented
10#19134236C211yesmaximal, characteristic, complemented
11#19134233C211yesmaximal, characteristic, complemented
12#19134225C211yesmaximal, characteristic, complemented
13#19134216C211yesmaximal, characteristic, complemented
14C2×#14582621C211yesmaximal, characteristic, complemented
15C43×#3169C211yesmaximal, characteristic, complemented
16C2×#13063345—22no—
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583297C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583281—22no—
23#14583278C2211yescharacteristic
24#14583275C2211yescharacteristic
25#14583275C2211yescharacteristic
26#14583273C2211yescharacteristic
27#14583272C2211yescharacteristic
28#14583271C2211yescharacteristic
29#14583271C2211yescharacteristic
30#14583253—22no—
31#14583251C2211yescharacteristic
32#14583250C2211yescharacteristic
33#14583249C2211yescharacteristic
34#14583249C2211yescharacteristic
35#14583247C2211yescharacteristic
36#14583246C2211yescharacteristic
37#14583245C2211yescharacteristic
38#14583245C2211yescharacteristic
39#14583245C2211yescharacteristic
40#14583245C2211yescharacteristic
41#14583133—22no—
42#14583128—22no—
43#14583126—22no—
44C4×#10621873—22no—
45C4×#10621883—22no—
46C4×#10621882—22no—
47#14582895—22no—
48C2×C4×C43⋊C8C2211yescharacteristic
49C2×C4×C43⋊C8C2211yescharacteristic
50#14582621C2211yescharacteristic
51#14582621C2211yescharacteristic
52#14582621C2211yescharacteristic
53#14582621C2211yescharacteristic
54C43×#532C2211yescharacteristic
55C43×#532C2211yescharacteristic
56C43×#500C2211yescharacteristic
57C43×#493C2211yescharacteristic
58C43×#486C2211yescharacteristic
59C43×#486C2211yescharacteristic
60C43×#466—22no—
61C4×D8×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×#10621882—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#13063257—22no—
91#13063256—22no—
92#13063250—22no—
93#13063249—22no—
94#13063249—22no—
95#13063248—22no—
96#13063247—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—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×#41×C43—21no—
110C2×D8×C43—22no—
111C22×C8×C43D412yes—
112C4⋊Q8×C43C2311yescharacteristic
113C4⋊Q8×C43C2311yescharacteristic
114#127×C43C2311yescharacteristic
115#127×C43C2311yescharacteristic
116#124×C43—21no—
117#124×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43—21no—
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C2×C42×C43C2311yescharacteristic
127#107×C43—22no—
128#102×C43—22no—
129#102×C43—22no—
130C4×C8×C43D412yes—
131C4×C8×C43C2311yescharacteristic
132C4×C8×C43C2311yescharacteristic
133#41×C43—44no—
134#41×C43—44no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—21no—
142C2×D4×C43—21no—
143C2×D4×C43—41no—
144C2×D4×C43—41no—
145C22×C4×C43—41no—
146C22×C4×C43—41no—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D411yescharacteristic
150C2×C22⋊D43—41no—
151#10621898—44no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×C4×D43—41no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159D8×C43—44no—
160C2×C8×C43—42no—
161C2×C8×C43C2×D412yes—
162C2×C8×C43C2×D412yes—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C22⋊C4×C43—41no—
168C22⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C22⋊C4×C43—41no—
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—41no—
176#10621885—44no—
177#10621884—44no—
178#10621883—44no—
179#10621883—44no—
180#10621882—44no—
181#10621882—44no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—41no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192C4×Dic43—41no—
193C2×C43⋊C8—24no—
194C2×C43⋊C8—24no—
195C2×C43⋊C8C2×D412yes—
196C2×C43⋊C8C2×D412yes—
197C2×C43⋊C8C2×D412yes—
198C2×C43⋊C8C2×D412yes—
199#10621873—44no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43#12711yescharacteristic
203C22×D43—41no—
204Q8×C43—42no—
205Q8×C43—42no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—42no—
211D4×C43—42no—
212D4×C43—82no—
213D4×C43—82no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—82no—
219C2×C4×C43—82no—
220C2×C4×C43#12711yescharacteristic
221C2×C4×C43#12711yescharacteristic
222C2×C4×C43#12711yescharacteristic
223C2×C4×C43AGL(1,ℤ/8)14yes—
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C22⋊D43—82no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—42no—
232D172—42no—
233D172—42no—
234C4×D43—82no—
235Dic86—42no—
236Dic86—42no—
237Dic86—42no—
238C8×C43—22no—
239C8×C43—22no—
240C43⋊C8—22no—
241C43⋊C8—22no—
242C43⋊C8—22no—
243C43⋊C8#13514yescomplemented
244#19619—431nomaximal, Sylow
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43#49612yes—
254C22×C43C2×#12711yescharacteristic
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43#49612yes—
263C4×C43C2×#13512yes—
264C4×C43C2×AGL(1,ℤ/8)12yes—
265C4×C43#57512yes—
266Dic43—81no—
267Dic43—81no—
268Dic43—81no—
269#3169—431no—
270#3169D4311yescharacteristic, complemented
271#3167—431no—
272#3167—431no—
273#3147—431no—
274#3131—431no—
275#1723—431no—
276#1721—431no—
277#1720—431no—
278#1719—431no—
279#1717—431no—
280#1717—431no—
281#1715—431no—
282#1714—431no—
283C2×#322—431no—
284C2×C43—22no—
285C2×C43—161no—
286C2×C43—161no—
287C2×C43#314711yescharacteristic
288C2×C43C2×#49611yescharacteristic
289C2×C43#315011yescharacteristic
290D43—161no—
291C2×#135—862no—
292#533—431no—
293#532—431no—
294#532C2×D4311yescharacteristic
295#532C2×D4311yescharacteristic
296#500—431no—
297#500C2×D4311yescharacteristic
298#498—431no—
299#498—431no—
300#495—862no—
301#494—431no—
302#493—431no—
303#493—431no—
304#493C2×D4311yescharacteristic
305#492—431no—
306#492—431no—
307#492—431no—
308#492—431no—
309#488—862no—
310#487—431no—
311#487—431no—
312#487—431no—
313#487—431no—
314#486—431no—
315#486—431no—
316#486—431no—
317#486—431no—
318#486—431no—
319#486—431no—
320#486C2×D4311yescharacteristic
321#486C2×D4311yescharacteristic
322#466—22no—
323#466—862no—
324#465—862no—
325#465—862no—
326C4×SD16—862no—
327C4×SD16—862no—
328C4×D8—22no—
329C4×D8—862no—
330#416—862no—
331C2×C4×C8—431no—
332C2×C4×C8—431no—
333C2×C4×C8C2×D4311yescharacteristic
334#322—431no—
335#322—431no—
336#322—431no—
337#322—431no—
338C43#1961911yescharacteristic, complemented, Sylow
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—861no—
342#135—1728no—
343C2×Q16—862no—
344C2×SD16—862no—
345C2×SD16—862no—
346C2×SD16—862no—
347C2×SD16—862no—
348C2×D8—22no—
349C2×D8—862no—
350C2×D8—862no—
351C22×C8—432no—
352C22×C8—432no—
353C22×C8C22⋊D4312yes—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8C22×D4311yescharacteristic
358C4⋊Q8C22×D4311yescharacteristic
359#127—431no—
360#127C22×D4311yescharacteristic
361#127C22×D4311yescharacteristic
362#125—861no—
363#124—21no—
364#124—21no—
365#124—861no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368#121—21no—
369#121—21no—
370#121—21no—
371#121—21no—
372#121—861no—
373#121—861no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—861no—
381C4×D4—861no—
382#117—861no—
383C2×C42C22×D4311yescharacteristic
384#107—22no—
385#107—862no—
386#106—862no—
387#106—862no—
388#103—862no—
389#103—862no—
390#103—862no—
391#103—862no—
392#102—22no—
393#102—22no—
394#102—862no—
395#102—862no—
396#102—862no—
397#102—862no—
398#102—862no—
399#102—862no—
400C4×C8—432no—
401C4×C8—432no—
402C4×C8—431no—
403C4×C8—431no—
404C4×C8—431no—
405C4×C8—431no—
406C4×C8C22⋊D4312yes—
407C4×C8C22×D4311yescharacteristic
408C4×C8C22×D4311yescharacteristic
409#41—44no—
410#41—44no—
411#41—1724no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—861no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—861no—
426C2×D4—861no—
427C2×D4—861no—
428C2×D4—1721no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—1721no—
432C22×C4D4×D4311yescharacteristic
433C22×C4D4×D4311yescharacteristic
434C22×C4C2×C22⋊D4311yescharacteristic
435Q16—1724no—
436SD16—1724no—
437SD16—1724no—
438SD16—1724no—
439SD16—1724no—
440D8—44no—
441D8—1724no—
442D8—1724no—
443C2×C8—42no—
444C2×C8—432no—
445C2×C8—432no—
446C2×C8—432no—
447C2×C8—432no—
448C2×C8—864no—
449C2×C8—864no—
450C2×C8C2×C22⋊D4312yes—
451C2×C8C2×C22⋊D4312yes—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—1721no—
463C4⋊C4—1721no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C22⋊C4—1721no—
469C22⋊C4—1721no—
470C22⋊C4—1721no—
471C42—1721no—
472C42D4×D4311yescharacteristic
473C42D4×D4311yescharacteristic
474C42C2×C22⋊D4311yescharacteristic
475C42C23×D4311yescharacteristic
476C23—41no—
477C23—41no—
478C23—1721no—
479C23#1306332111yescharacteristic
480Q8—42no—
481Q8—42no—
482Q8—1722no—
483Q8—1722no—
484Q8—1722no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—82no—
492D4—82no—
493D4—3442no—
494D4—1722no—
495D4—1722no—
496D4—1722no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—3442no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4#1306332111yescharacteristic
508C2×C4#1306332111yescharacteristic
509C2×C4#1306332111yescharacteristic
510C2×C4#1306334914yes—
511C2×C4C2×D4×D4311yescharacteristic
512C2×C4C2×D4×D4311yescharacteristic
513C2×C4C22×C22⋊D4311yescharacteristic
514C8—22no—
515C8—22no—
516C8—434no—
517C8—862no—
518C8—862no—
519C8—862no—
520C22—21no—
521C22—21no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—3441no—
529C22—3441no—
530C22—3441no—
531C22#1458328712yes—
532C22C2×#1306332111yescharacteristic
533C4—21no—
534C4—21no—
535C4—81no—
536C4—81no—
537C4—3441no—
538C4—3441no—
539C4—3441no—
540C4#1458328712yes—
541C4#135×D4312yes—
542C4C2×#1306334912yes—
543C4#1458369712yes—
544C2—22no—
545C2—161no—
546C2—161no—
547C2—6881no—
548C2#1914501911yescharacteristic
549C2C2×#1458328711yescharacteristic
550C2#1914504011yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3169C2
socleC22×C43C2×#127
hypercenter#3169D43
hypocenterC43#19619
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #19145170C2semidirect
2. #19145154C2semidirect
3. #19145150C2semidirect
4. #19145021C2semidirect
5. #19144917C2semidirect
6. #19134271C2semidirect
7. #19134260C2semidirect
8. #19134257C2semidirect
9. #19134251C2semidirect
10. #19134236C2semidirect
11. #19134233C2semidirect
12. #19134225C2semidirect
13. #19134216C2semidirect
14. C2×#14582621C2semidirect
15. C43×#3169C2semidirect
243. C43⋊C8#135semidirect
270. #3169D43semidirect
338. C43#19619semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191451542
#191451502
#191450212
#191449172
#191342712
#191342602
#191342572
#191342512
#191342362
#191342332
#191342252
#191342162
C2×#145826212
C43×#31692
#1961943