Finite Group Databasebeta

← #25085913

Subgroups — #25085913

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#19145309C211yesmaximal, characteristic
3#19145309C211yesmaximal, characteristic
4#19145137C211yesmaximal, characteristic, complemented
5#19144975C211yesmaximal, characteristic, complemented
6#19134274C211yesmaximal, characteristic, complemented
7#19134254C211yesmaximal, characteristic, complemented
8#19134245C211yesmaximal, characteristic, complemented
9#19134243C211yesmaximal, characteristic, complemented
10#19134242C211yesmaximal, characteristic, complemented
11#19134216C211yesmaximal, characteristic, complemented
12#19134203C211yesmaximal, characteristic, complemented
13#19134195C211yesmaximal, characteristic, complemented
14#19132898C211yesmaximal, characteristic, complemented
15C43×#3141C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583456C2211yescharacteristic
18#14583305—22no—
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583302C2211yescharacteristic
23#14583297C2211yescharacteristic
24#14583295C2211yescharacteristic
25#14583295C2211yescharacteristic
26#14583279C2211yescharacteristic
27#14583271C2211yescharacteristic
28#14583271C2211yescharacteristic
29#14583267—22no—
30#14583251C2211yescharacteristic
31#14583251C2211yescharacteristic
32#14583250C2211yescharacteristic
33#14583250C2211yescharacteristic
34#14583249C2211yescharacteristic
35#14583249C2211yescharacteristic
36#14583249C2211yescharacteristic
37#14583249C2211yescharacteristic
38#14583245C2211yescharacteristic
39#14583245C2211yescharacteristic
40#14583157—22no—
41#14583143—22no—
42#14583143—22no—
43#14583007—22no—
44#14582999—22no—
45#14582999—22no—
46#14582939—22no—
47#14582908—22no—
48C4×#10621877C2211yescharacteristic
49C4×#10621877C2211yescharacteristic
50#14582621C2211yescharacteristic
51#14582621C2211yescharacteristic
52#14582620C2211yescharacteristic
53C8×C43⋊C8C2211yescharacteristic
54C43×#532C2211yescharacteristic
55C2×C4⋊Q8×C43C2211yescharacteristic
56C43×#489—22no—
57C43×#487C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#486C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#417—22no—
62C4×M16×C43C2211yescharacteristic
63C2×Dic172—22no—
64C2×#10621883—22no—
65C2×#10621883—22no—
66C2×#10621877D412yes—
67C2×#10621877D412yes—
68#13063325C2311yescharacteristic
69#13063325C2311yescharacteristic
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063317—21no—
73#13063317—21no—
74#13063304—21no—
75#13063304—21no—
76#13063304—21no—
77#13063304—21no—
78C4×Dic86—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86—21no—
82#13063284—21no—
83#13063284—21no—
84#13063258—22no—
85#13063258—22no—
86#13063258—22no—
87#13063258—22no—
88#13063257—22no—
89#13063256—22no—
90#13063256—22no—
91#13063250—22no—
92#13063250—22no—
93#13063249—22no—
94#13063249—22no—
95#13063249—22no—
96#13063249—22no—
97#13063248—22no—
98#13063248—22no—
99#13063246—22no—
100#13063246—22no—
101#13063236D412yes—
102#13063236D412yes—
103C4×C43⋊C8C2311yescharacteristic
104C4×C43⋊C8C2311yescharacteristic
105C4×C43⋊C8C2311yescharacteristic
106C4×C43⋊C8C2311yescharacteristic
107C2×#41×C43—21no—
108C22×Q8×C43—21no—
109C2×M16×C43D412yes—
110C4⋊Q8×C43—21no—
111C4⋊Q8×C43—21no—
112C4⋊Q8×C43—21no—
113C4⋊Q8×C43C2311yescharacteristic
114C4⋊Q8×C43C2311yescharacteristic
115C4⋊Q8×C43C2311yescharacteristic
116#127×C43C2311yescharacteristic
117#124×C43—21no—
118#121×C43—21no—
119#121×C43—21no—
120C4×D4×C43—21no—
121C4×D4×C43—21no—
122C2×C4⋊C4×C43—21no—
123C2×C4⋊C4×C43—21no—
124C2×C42×C43C2311yescharacteristic
125#103×C43—22no—
126#103×C43—22no—
127#102×C43—22no—
128#102×C43—22no—
129#97×C43D412yes—
130C4×C8×C43C2311yescharacteristic
131C4×C8×C43C2311yescharacteristic
132#41×C43—44no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—44no—
137C2×Q8×C43—41no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C2×D4×C43—21no—
141C2×D4×C43—41no—
142C22×C4×C43—41no—
143C22×C4×C43—41no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151M16×C43—42no—
152C2×C8×C43C2×D412yes—
153C2×C8×C43C2×D412yes—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—41no—
161C4⋊C4×C43—41no—
162C22⋊C4×C43—41no—
163C22⋊C4×C43—41no—
164C42×C43C2×D411yescharacteristic
165C42×C43C2×D411yescharacteristic
166C42×C43C2×D411yescharacteristic
167C42×C43C2411yescharacteristic
168C22⋊Dic43—41no—
169C22⋊Dic43—41no—
170#10621883—44no—
171#10621883—44no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180Dic43⋊C4—41no—
181Dic43⋊C4—41no—
182Dic43⋊C4—41no—
183Dic43⋊C4—41no—
184C4×Dic43—41no—
185C4×Dic43—41no—
186#10621877—24no—
187#10621877—42no—
188C2×C43⋊C8C2×D412yes—
189C2×C43⋊C8C2×D412yes—
190C2×C43⋊C8C2×D412yes—
191C2×C43⋊C8C2×D412yes—
192Dic172—44no—
193C23×C43—41no—
194C23×C43#12711yescharacteristic
195Q8×C43—42no—
196Q8×C43—42no—
197Q8×C43—42no—
198Q8×C43—82no—
199D4×C43—42no—
200D4×C43—42no—
201D4×C43—42no—
202D4×C43—82no—
203C2×C4×C43—22no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—82no—
210C2×C4×C43—82no—
211C2×C4×C43#12711yescharacteristic
212C2×C4×C43#12711yescharacteristic
213C2×C4×C43#12711yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C22×D411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221Dic86—42no—
222Dic86—42no—
223Dic86—42no—
224Dic86—42no—
225C8×C43—22no—
226C8×C43—22no—
227C43⋊C8—22no—
228C43⋊C8—22no—
229C43⋊C8—22no—
230C43⋊C8#13714yes—
231#19752—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43C2×#12711yescharacteristic
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—81no—
243C4×C43—81no—
244C4×C43—81no—
245C4×C43C2×#13712yes—
246C4×C43#57512yes—
247C4×C43#57512yes—
248Dic43—81no—
249Dic43—81no—
250Dic43—81no—
251Dic43—81no—
252#3185—431no—
253#3182—431no—
254#3182—431no—
255#3165—431no—
256#3141D4311yescharacteristic
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#1455—431no—
267C2×C43—41no—
268C2×C43—161no—
269C2×C43#315211yescharacteristic
270C2×C43#315311yescharacteristic
271C2×C43#315311yescharacteristic
272#533—431no—
273#533—431no—
274#532C2×D4311yescharacteristic
275C2×C4⋊Q8C2×D4311yescharacteristic
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—22no—
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#487C2×D4311yescharacteristic
298#487C2×D4311yescharacteristic
299#486—431no—
300#486—431no—
301#486C2×D4311yescharacteristic
302#486C2×D4311yescharacteristic
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—22no—
312C4×M16—431no—
313C4×M16—431no—
314C4×M16C2×D4311yescharacteristic
315#322—431no—
316#322—431no—
317#322—431no—
318C82—431no—
319C43#1975211yescharacteristic, complemented, Sylow
320C2×#41—21no—
321C22×Q8—21no—
322C2×Q16—862no—
323C2×SD16—862no—
324C2×SD16—862no—
325C2×M16—432no—
326C2×M16—432no—
327C2×M16C22⋊D4312yes—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4⋊Q8—431no—
332C4⋊Q8—431no—
333C4⋊Q8—431no—
334C4⋊Q8—431no—
335C4⋊Q8C22×D4311yescharacteristic
336C4⋊Q8C22×D4311yescharacteristic
337C4⋊Q8C22×D4311yescharacteristic
338#127C22×D4311yescharacteristic
339#125—861no—
340#125—861no—
341#124—21no—
342C22⋊Q8—861no—
343C22⋊Q8—861no—
344C22⋊Q8—861no—
345C22⋊Q8—861no—
346#121—21no—
347#121—21no—
348C4×Q8—861no—
349C4×Q8—861no—
350C4×Q8—861no—
351C4×Q8—861no—
352C4×D4—21no—
353C4×D4—21no—
354#117—861no—
355#117—861no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
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—22no—
367#103—22no—
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—22no—
377#102—22no—
378#102—862no—
379#102—862no—
380#97—432no—
381#97—432no—
382#97C22⋊D4312yes—
383C4×C8—431no—
384C4×C8—431no—
385C4×C8—431no—
386C4×C8—431no—
387C4×C8C22×D4311yescharacteristic
388C4×C8C22×D4311yescharacteristic
389#41—44no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—21no—
393C2×Q8—44no—
394C2×Q8—41no—
395C2×Q8—861no—
396C2×Q8—861no—
397C2×Q8—861no—
398C2×Q8—861no—
399C2×D4—21no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—41no—
403C22×C4—41no—
404C22×C4—41no—
405C22×C4D4×D4311yescharacteristic
406C22×C4D4×D4311yescharacteristic
407C22×C4C2×C22⋊D4311yescharacteristic
408Q16—1724no—
409SD16—1724no—
410SD16—1724no—
411M16—42no—
412M16—864no—
413M16—1722no—
414C2×C8—432no—
415C2×C8—432no—
416C2×C8—432no—
417C2×C8—432no—
418C2×C8C2×C22⋊D4312yes—
419C2×C8C2×C22⋊D4312yes—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4—861no—
433C4⋊C4—861no—
434C4⋊C4—861no—
435C4⋊C4—861no—
436C4⋊C4—1721no—
437C4⋊C4—1721no—
438C4⋊C4—1721no—
439C4⋊C4—1721no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—1721no—
443C22⋊C4—1721no—
444C42—1721no—
445C42—1721no—
446C42D4×D4311yescharacteristic
447C42D4×D4311yescharacteristic
448C42C2×C22⋊D4311yescharacteristic
449C42C23×D4311yescharacteristic
450C23—41no—
451C23#1306332111yescharacteristic
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—82no—
456Q8—1722no—
457Q8—1722no—
458Q8—1722no—
459Q8—1722no—
460D4—42no—
461D4—42no—
462D4—42no—
463D4—82no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—82no—
471C2×C4—82no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4—1721no—
475C2×C4—1721no—
476C2×C4#1306332111yescharacteristic
477C2×C4#1306332111yescharacteristic
478C2×C4#1306332111yescharacteristic
479C2×C4C2×D4×D4311yescharacteristic
480C2×C4C2×D4×D4311yescharacteristic
481C2×C4C22×C22⋊D4311yescharacteristic
482C8—22no—
483C8—22no—
484C8—434no—
485C8—862no—
486C8—862no—
487C8—862no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—81no—
492C22—81no—
493C22—81no—
494C22C2×#1306332111yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—81no—
499C4—81no—
500C4—81no—
501C4—3441no—
502C4—3441no—
503C4—3441no—
504C4—3441no—
505C4#137×D4312yes—
506C4#1458369512yes—
507C4#1458369712yes—
508C2—41no—
509C2—161no—
510C2#1914505011yescharacteristic
511C2#1914505711yescharacteristic
512C2#1914505911yescharacteristic
subgroupG/H
centerC22C2×#13063321
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3141C2
socleC22×C43C2×#127
prime radicalC43×#532C22
hypercenter#3141D43
hypocenterC43#19752
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3141

Complements

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

NH ≅ G/Ntype
1. #19145340C2semidirect
4. #19145137C2semidirect
5. #19144975C2semidirect
6. #19134274C2semidirect
7. #19134254C2semidirect
8. #19134245C2semidirect
9. #19134243C2semidirect
10. #19134242C2semidirect
11. #19134216C2semidirect
12. #19134203C2semidirect
13. #19134195C2semidirect
14. #19132898C2semidirect
319. C43#19752semidirect

Maximal subgroups

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

subgroupindex
#191453402
#191453092
#191451372
#191449752
#191342742
#191342542
#191342452
#191342432
#191342422
#191342162
#191342032
#191341952
#191328982
C43×#31412
#1975243