Finite Group Databasebeta

← #25085915

Subgroups — #25085915

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145340C211yesmaximal, characteristic, complemented
2#19145313C211yesmaximal, characteristic
3#19145313C211yesmaximal, characteristic
4#19145141C211yesmaximal, characteristic, complemented
5#19144989C211yesmaximal, characteristic
6#19144976C211yesmaximal, characteristic, complemented
7#19134272C211yesmaximal, characteristic, complemented
8#19134255C211yesmaximal, characteristic, complemented
9#19134248C211yesmaximal, characteristic, complemented
10#19134241C211yesmaximal, characteristic, complemented
11#19134241C211yesmaximal, characteristic, complemented
12#19134217C211yesmaximal, characteristic, complemented
13#19134205C211yesmaximal, characteristic, complemented
14#19134196C211yesmaximal, characteristic, complemented
15C43×#1455C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583449C2211yescharacteristic
19C2×#13063325C2211yescharacteristic
20#14583308—22no—
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583304C2211yescharacteristic
24#14583304C2211yescharacteristic
25#14583297C2211yescharacteristic
26#14583297C2211yescharacteristic
27#14583297C2211yescharacteristic
28#14583279C2211yescharacteristic
29#14583272C2211yescharacteristic
30#14583272C2211yescharacteristic
31#14583268—22no—
32#14583259—22no—
33#14583250C2211yescharacteristic
34#14583250C2211yescharacteristic
35#14583250C2211yescharacteristic
36#14583250C2211yescharacteristic
37#14583250C2211yescharacteristic
38#14583250C2211yescharacteristic
39#14583250C2211yescharacteristic
40#14583250C2211yescharacteristic
41#14583250C2211yescharacteristic
42#14583250C2211yescharacteristic
43#14583246C2211yescharacteristic
44#14583246C2211yescharacteristic
45#14583246C2211yescharacteristic
46#14583246C2211yescharacteristic
47#14583157—22no—
48#14583145—22no—
49#14583145—22no—
50#14583007—22no—
51#14583001—22no—
52#14583001—22no—
53#14582941—22no—
54#14582909—22no—
55#14582901—22no—
56C4×M16×C43C2211yescharacteristic
57C4×M16×C43C2211yescharacteristic
58C4×M16×C43C2211yescharacteristic
59C43×#322C2211yescharacteristic
60C43×#322C2211yescharacteristic
61C43×#322C2211yescharacteristic
62C82×C43C2211yescharacteristic
63C2×#10621898—21no—
64C22×Dic86—21no—
65C2×Dic172—22no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68#13063325—21no—
69#13063325—21no—
70#13063325—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063317—21no—
80#13063317—21no—
81#13063313—21no—
82#13063304—21no—
83#13063304—21no—
84#13063304—21no—
85#13063304—21no—
86#13063299—21no—
87#13063299—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86—21no—
91C4×Dic86—21no—
92C4×D172—21no—
93C4×D172—21no—
94#13063284—21no—
95#13063284—21no—
96C2×C4⋊Dic43—21no—
97C2×C4⋊Dic43—21no—
98#13063259—22no—
99#13063259—22no—
100#13063259—22no—
101#13063259—22no—
102#13063257—22no—
103#13063257—22no—
104#13063257—22no—
105#13063250—22no—
106#13063250—22no—
107#13063250—22no—
108#13063250—22no—
109#13063250—22no—
110#13063250—22no—
111#13063250—22no—
112#13063250—22no—
113#13063250—22no—
114#13063250—22no—
115#13063247—22no—
116#13063247—22no—
117#13063247—22no—
118#13063247—22no—
119C2×M16×C43D412yes—
120C2×M16×C43D412yes—
121C2×M16×C43D412yes—
122C2×C42×C43C2311yescharacteristic
123#97×C43D412yes—
124#97×C43D412yes—
125#97×C43D412yes—
126C4×C8×C43C2311yescharacteristic
127C4×C8×C43C2311yescharacteristic
128C4×C8×C43C2311yescharacteristic
129C4×C8×C43C2311yescharacteristic
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C2×C22⋊D43—41no—
136C22×Dic43—41no—
137#10621898—44no—
138C2×D172—21no—
139C2×D172—21no—
140C2×D172—21no—
141C2×C4×D43—41no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—44no—
150C2×Dic86—41no—
151M16×C43—24no—
152M16×C43—42no—
153M16×C43—42no—
154C2×C8×C43C2×D412yes—
155C2×C8×C43C2×D412yes—
156C2×C8×C43C2×D412yes—
157C2×C8×C43C2×D412yes—
158C2×C8×C43C2×D412yes—
159C2×C8×C43C2×D412yes—
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162C42×C43C2×D411yescharacteristic
163C42×C43C2411yescharacteristic
164C22⋊Dic43—41no—
165C22⋊Dic43—41no—
166(C2×D43)⋊C4—41no—
167(C2×D43)⋊C4—41no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184Dic43⋊C4—41no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188C4×Dic43—41no—
189C4×Dic43—41no—
190Dic172—44no—
191#10621873—44no—
192#10621873—44no—
193C23×C43#12711yescharacteristic
194C22×D43—41no—
195C2×C4×C43—22no—
196C2×C4×C43—22no—
197C2×C4×C43—22no—
198C2×C4×C43#12711yescharacteristic
199C2×C4×C43#12711yescharacteristic
200C2×C4×C43#12711yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C22⋊D43—82no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—82no—
213D172—42no—
214D172—42no—
215D172—42no—
216C4×D43—82no—
217Dic86—42no—
218Dic86—42no—
219Dic86—42no—
220Dic86—42no—
221Dic86—42no—
222Dic86—42no—
223Dic86—42no—
224Dic86—82no—
225C8×C43—22no—
226C8×C43—22no—
227C8×C43—22no—
228C8×C43—22no—
229C8×C43—22no—
230C8×C43#13714yes—
231#19752—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43C2×#12711yescharacteristic
236C2×D43—81no—
237C2×D43—81no—
238C2×D43—81no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43C2×#13712yes—
243C4×C43#57512yes—
244C4×C43#57512yes—
245Dic43—81no—
246Dic43—81no—
247Dic43—81no—
248Dic43—81no—
249Dic43—81no—
250Dic43—81no—
251Dic43—81no—
252#3185—431no—
253#3182—431no—
254#3182—431no—
255#3165—431no—
256#3141—431no—
257#3139—431no—
258#1723—431no—
259#1720—431no—
260#1719—431no—
261#1718—431no—
262#1718—431no—
263#1714—431no—
264#1710—431no—
265#1708—431no—
266#1455D4311yescharacteristic, complemented
267C2×C43—41no—
268C2×C43#315211yescharacteristic
269C2×C43#315311yescharacteristic
270C2×C43#315311yescharacteristic
271D43—161no—
272#533—431no—
273#533—431no—
274#532—431no—
275C2×C4⋊Q8—431no—
276#501—862no—
277#500—431no—
278#500—431no—
279#500—431no—
280#500—431no—
281#498—431no—
282#498—431no—
283#498—431no—
284#494—431no—
285#492—431no—
286#492—431no—
287#491—862no—
288#489—862no—
289#487—431no—
290#487—431no—
291#487—431no—
292#487—431no—
293#487—431no—
294#487—431no—
295#487—431no—
296#487—431no—
297#487—431no—
298#487—431no—
299#486—431no—
300#486—431no—
301#486—431no—
302#486—431no—
303#470—862no—
304#468—862no—
305#468—862no—
306#441—862no—
307#440—862no—
308#440—862no—
309#428—862no—
310#419—862no—
311#417—862no—
312C4×M16C2×D4311yescharacteristic
313C4×M16C2×D4311yescharacteristic
314C4×M16C2×D4311yescharacteristic
315#322C2×D4311yescharacteristic
316#322C2×D4311yescharacteristic
317#322C2×D4311yescharacteristic
318C82C2×D4311yescharacteristic
319C43#1975211yescharacteristic, complemented, Sylow
320C2×#41—861no—
321C22×Q8—861no—
322C2×Q16—862no—
323C2×SD16—862no—
324C2×SD16—862no—
325C2×M16D17212yes—
326C2×M16D17212yes—
327C2×M16D17212yes—
328C4⋊Q8—431no—
329C4⋊Q8—431no—
330C4⋊Q8—431no—
331C4⋊Q8—431no—
332C4⋊Q8—431no—
333C4⋊Q8—431no—
334C4⋊Q8—431no—
335C4⋊Q8—861no—
336C4⋊Q8—861no—
337C4⋊Q8—861no—
338#127—431no—
339#125—861no—
340#125—861no—
341#124—861no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344C22⋊Q8—861no—
345C22⋊Q8—861no—
346#121—861no—
347#121—861no—
348C4×Q8—861no—
349C4×Q8—861no—
350C4×Q8—861no—
351C4×Q8—861no—
352C4×D4—861no—
353C4×D4—861no—
354#117—861no—
355#117—861no—
356C2×C4⋊C4—861no—
357C2×C4⋊C4—861no—
358C2×C42C22×D4311yescharacteristic
359#107—862no—
360#107—862no—
361#107—862no—
362#107—862no—
363#106—862no—
364#106—862no—
365#106—862no—
366#103—862no—
367#103—862no—
368#103—862no—
369#103—862no—
370#103—862no—
371#103—862no—
372#103—862no—
373#103—862no—
374#103—862no—
375#103—862no—
376#102—862no—
377#102—862no—
378#102—862no—
379#102—862no—
380#97D17212yes—
381#97D17212yes—
382#97D17212yes—
383C4×C8C22×D4311yescharacteristic
384C4×C8C22×D4311yescharacteristic
385C4×C8C22×D4311yescharacteristic
386C4×C8C22×D4311yescharacteristic
387C4×C8C22×D4311yescharacteristic
388C4×C8C22×D4311yescharacteristic
389#41—1724no—
390C2×Q8—861no—
391C2×Q8—861no—
392C2×Q8—861no—
393C2×Q8—861no—
394C2×Q8—861no—
395C2×Q8—861no—
396C2×Q8—861no—
397C2×Q8—1724no—
398C2×Q8—1721no—
399C2×D4—861no—
400C2×D4—861no—
401C2×D4—861no—
402C2×D4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4C2×D17211yescharacteristic
406C22×C4C2×D17211yescharacteristic
407C22×C4C2×D17211yescharacteristic
408Q16—1724no—
409SD16—1724no—
410SD16—1724no—
411M16—24no—
412M16—42no—
413M16—42no—
414C2×C8C2×D17212yes—
415C2×C8C2×D17212yes—
416C2×C8C2×D17212yes—
417C2×C8C2×D17212yes—
418C2×C8C2×D17212yes—
419C2×C8C2×D17212yes—
420C4⋊C4—861no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—1721no—
435C4⋊C4—1721no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C22⋊C4—1721no—
441C22⋊C4—1721no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C42—1721no—
445C42—1721no—
446C42C2×D17211yescharacteristic
447C42C2×D17211yescharacteristic
448C42C2×D17211yescharacteristic
449C42C23×D4311yescharacteristic
450C23—1721no—
451C23#1306332211yescharacteristic
452Q8—3442no—
453Q8—1722no—
454Q8—1722no—
455Q8—1722no—
456Q8—1722no—
457Q8—1722no—
458Q8—1722no—
459Q8—1722no—
460D4—3442no—
461D4—1722no—
462D4—1722no—
463D4—1722no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—3442no—
468C2×C4—3442no—
469C2×C4—1721no—
470C2×C4—1721no—
471C2×C4—1721no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4#1306332211yescharacteristic
477C2×C4#1306332211yescharacteristic
478C2×C4#1306332211yescharacteristic
479C2×C4C22×D17211yescharacteristic
480C2×C4C22×D17211yescharacteristic
481C2×C4C22×D17211yescharacteristic
482C8—22no—
483C8—22no—
484C8—22no—
485C8—22no—
486C8—22no—
487C8#1306335814yes—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—3441no—
492C22—3441no—
493C22—3441no—
494C22C2×#1306332211yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—3441no—
499C4—3441no—
500C4—3441no—
501C4—3441no—
502C4—3441no—
503C4—3441no—
504C4—3441no—
505C4C2×#1306335812yes—
506C4#1458369912yes—
507C4#1458369912yes—
508C2—41no—
509C2—6881no—
510C2#1914505411yescharacteristic
511C2#1914506111yescharacteristic
512C2#1914506111yescharacteristic
subgroupG/H
centerC22C2×#13063322
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1455C2
socleC22×C43C2×#127
prime radical#14583449C22
hypercenter#1455D43
hypocenterC43#19752
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1455

Complements

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

NH ≅ G/Ntype
1. #19145340C2semidirect
4. #19145141C2semidirect
6. #19144976C2semidirect
7. #19134272C2semidirect
8. #19134255C2semidirect
9. #19134248C2semidirect
10. #19134241C2semidirect
11. #19134241C2semidirect
12. #19134217C2semidirect
13. #19134205C2semidirect
14. #19134196C2semidirect
15. C43×#1455C2semidirect
266. #1455D43semidirect
319. C43#19752semidirect

Maximal subgroups

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

subgroupindex
#191453402
#191453132
#191451412
#191449892
#191449762
#191342722
#191342552
#191342482
#191342412
#191342172
#191342052
#191341962
C43×#14552
#1975243