Finite Group Databasebeta

← #25081953

Subgroups — #25081953

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145747C211yesmaximal, characteristic
2#19144401C211yesmaximal, characteristic
3#477×D43C211yesmaximal, characteristic
4#19143674C211yesmaximal, characteristic
5#19134056C211yesmaximal, characteristic, complemented
6#19134055C211yesmaximal, characteristic, complemented
7#19134054C211yesmaximal, characteristic, complemented
8#19134053C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133996C211yesmaximal, characteristic, complemented
12#19133368C211yesmaximal, characteristic
13#19133274C211yesmaximal, characteristic
14#19133249C211yesmaximal, characteristic
15C43×#1676C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18C4×Q8×D43C2211yescharacteristic
19#14583302C2211yescharacteristic
20#14583251C2211yescharacteristic
21#14583250C2211yescharacteristic
22#14583236—21no—
23#14583236—21no—
24#14583205—21no—
25#14583204—21no—
26#14583195C2211yescharacteristic
27#14583194C2211yescharacteristic
28#14583193—21no—
29#14583193—21no—
30#14583193—21no—
31#14583192—21no—
32#14583191C2211yescharacteristic
33#14583191C2211yescharacteristic
34#14583185C2211yescharacteristic
35#14583184C2211yescharacteristic
36Q8×C43⋊C8C2211yescharacteristic
37C8×Dic86—21no—
38C8×Dic86C2211yescharacteristic
39#14583023—21no—
40#14583023C2211yescharacteristic
41#14582951—21no—
42#14582951C2211yescharacteristic
43#14582950—21no—
44#14582950C2211yescharacteristic
45#14582940—21no—
46#107×D43—21no—
47#14582921C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582906—21no—
50#103×D43—21no—
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582648C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#500C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#477C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#333C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×Q8×D43D411yescharacteristic
69C2×#10621872—21no—
70C2×C8×D43—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063324—21no—
74#13063324—21no—
75#13063323—21no—
76#13063316—21no—
77#13063305—21no—
78#13063301—21no—
79Q8×Dic43—21no—
80Q8×Dic43D411yescharacteristic
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83#13063290—21no—
84#13063290—21no—
85#13063290D411yescharacteristic
86#13063283—21no—
87C4⋊C4×D43—21no—
88C4⋊C4×D43—21no—
89C4⋊C4×D43—21no—
90C4⋊C4×D43D411yescharacteristic
91C42×D43—21no—
92C42×D43C2311yescharacteristic
93#13063259—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063257—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)C2311yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109Dic43⋊C8D411yescharacteristic
110Dic43⋊C8D411yescharacteristic
111#13063250—21no—
112#13063250—21no—
113#13063250—21no—
114#13063250—21no—
115#13063249—21no—
116#13063249—21no—
117#13063248—21no—
118#13063248—21no—
119#13063248—21no—
120#13063248—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8D411yescharacteristic
123(C2×D43)⋊C8D411yescharacteristic
124C4×C43⋊C8—21no—
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130C4⋊Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#107×C43—21no—
135#107×C43—21no—
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147Q8×D43—22no—
148Q8×D43—82no—
149Q8×D43Q1614yes—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—41no—
153C2×C4×D43C2×D411yescharacteristic
154C2×C4×D43C2×D411yescharacteristic
155C2×C4×D43#4111yescharacteristic
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—41no—
160C2×Dic86C2×D411yescharacteristic
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C2×D411yescharacteristic
172C42×C43—21no—
173C42×C43C2411yescharacteristic
174(C2×D43)⋊C4—41no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—41no—
181C4⋊Dic43C2×D411yescharacteristic
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—41no—
186Dic43⋊C4—41no—
187Dic43⋊C4—41no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—21no—
191C4×Dic43—41no—
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200#10621872—42no—
201C8×D43—42no—
202C22×D43#12111yescharacteristic
203Q8×C43—21no—
204Q8×C43—81no—
205Q8×C43—81no—
206Q8×C43C2×Q1612yes—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C2×C4×C43C2×#4111yescharacteristic
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43#12111yescharacteristic
219C2×Dic43#12111yescharacteristic
220C2×Dic43#12111yescharacteristic
221C4×D43—24no—
222C4×D43—21no—
223C4×D43—21no—
224C4×D43—41no—
225C4×D43—81no—
226C4×D43—82no—
227C4×D43C2×Q1612yes—
228C4×D43#13512yes—
229Dic86—21no—
230Dic86—24no—
231Dic86—41no—
232Dic86—41no—
233Dic86—82no—
234Dic86—81no—
235Dic86C2×Q1612yes—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—41no—
239C8×C43—41no—
240C8×C43—41no—
241C43⋊C8—21no—
242C43⋊C8—21no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245C43⋊C8—41no—
246#19405—431nomaximal, Sylow
247C22×C43C2×#12111yescharacteristic
248C2×D43—21no—
249C2×D43—21no—
250C2×D43#46712yes—
251C4×C43—22no—
252C4×C43—21no—
253C4×C43—41no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43C22×Q1611yescharacteristic
257C4×C43C2×#13511yescharacteristic
258C4×C43#57811yescharacteristic
259C4×C43#57811yescharacteristic
260Dic43—21no—
261Dic43—22no—
262Dic43—21no—
263Dic43—41no—
264Dic43—81no—
265Dic43—81no—
266Dic43#46712yes—
267#3230—431no—
268#3078—431no—
269C2×#477—431no—
270#2982—431no—
271#1684—431no—
272#1684—431no—
273#1684—431no—
274#1684—431no—
275#1676—431no—
276#1676—431no—
277#1676—431no—
278#1676D4311yescharacteristic, complemented
279#1571—431no—
280#1548—431no—
281#1542—431no—
282C2×C43#304411yescharacteristic
283C2×C43C2×#46711yescharacteristic
284C2×C43#306811yescharacteristic
285D43—22no—
286#533—431no—
287C2×C4⋊Q8—431no—
288C2×C4×Q8—431no—
289#500—431no—
290#500C2×D4311yescharacteristic
291#487—431no—
292#487—431no—
293#484—861no—
294#484—861no—
295#479—861no—
296#479—861no—
297#477—431no—
298#477—431no—
299#477—431no—
300#477—431no—
301#477—861no—
302#477—861no—
303#477—861no—
304#477—861no—
305#477C2×D4311yescharacteristic
306#477C2×D4311yescharacteristic
307#475—431no—
308#475—431no—
309C8×Q8—431no—
310C8×Q8—431no—
311C8×Q8—431no—
312C8×Q8—861no—
313C8×Q8—861no—
314C8×Q8C2×D4311yescharacteristic
315#431—431no—
316#431—431no—
317#431—861no—
318#431—861no—
319#428—861no—
320C2×#107—861no—
321#423—431no—
322C2×C4⋊C8—431no—
323#419—861no—
324C2×#103—861no—
325#335—431no—
326#335—431no—
327#335—431no—
328#335C2×D4311yescharacteristic
329#333—431no—
330#333—431no—
331#333—431no—
332#333—431no—
333#333C2×D4311yescharacteristic
334#333C2×D4311yescharacteristic
335#332—431no—
336#332—431no—
337C43#1940511yescharacteristic, complemented, Sylow
338C22×Q8—431no—
339C22×Q8—861no—
340C2×M16—861no—
341C22×C8—861no—
342C4⋊Q8—431no—
343C4⋊Q8—431no—
344C4⋊Q8—861no—
345C4⋊Q8—861no—
346C4⋊Q8—861no—
347C4⋊Q8C22×D4311yescharacteristic
348C4⋊Q8C22×D4311yescharacteristic
349#125—861no—
350C22⋊Q8—861no—
351C22⋊Q8—861no—
352C4×Q8—431no—
353C4×Q8—431no—
354C4×Q8—431no—
355C4×Q8—861no—
356C4×Q8—861no—
357C4×Q8—861no—
358C4×Q8—861no—
359C4×Q8C22×D4311yescharacteristic
360#117—861no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—861no—
363C2×C4⋊C4—861no—
364C2×C4⋊C4—861no—
365C2×C42—431no—
366C2×C42—861no—
367#107—21no—
368#107—21no—
369#107—21no—
370#107—21no—
371#107—861no—
372#107—861no—
373#107—861no—
374#107—861no—
375#107—861no—
376#107—861no—
377#106—861no—
378#106—861no—
379C4⋊C8—21no—
380C4⋊C8—431no—
381C4⋊C8—431no—
382C4⋊C8—431no—
383C4⋊C8—431no—
384C4⋊C8—431no—
385C4⋊C8—861no—
386C4⋊C8—861no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8C22×D4311yescharacteristic
391C4⋊C8C22×D4311yescharacteristic
392C4⋊C8C22×D4311yescharacteristic
393#103—21no—
394#103—21no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405C22⋊C8—431no—
406C22⋊C8—431no—
407C22⋊C8—861no—
408C4×C8—21no—
409C4×C8—431no—
410C4×C8—861no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8—861no—
414C4×C8C22×D4311yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—434no—
418C2×Q8—431no—
419C2×Q8—861no—
420C2×Q8—862no—
421C2×Q8—861no—
422C2×Q8—861no—
423C2×Q8—3442no—
424C2×Q8—1721no—
425C2×Q8D4×D4311yescharacteristic
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—1721no—
432M16—1722no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—431no—
437C2×C8—431no—
438C2×C8—861no—
439C2×C8—861no—
440C2×C8—861no—
441C2×C8—1722no—
442C2×C8D4×D4311yescharacteristic
443C2×C8D4×D4311yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—431no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
457C4⋊C4—861no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4D4×D4311yescharacteristic
463C22⋊C4—1721no—
464C42—21no—
465C42—431no—
466C42—431no—
467C42—431no—
468C42—861no—
469C42—861no—
470C42—861no—
471C42—1721no—
472C42C23×D4311yescharacteristic
473C23—431no—
474Q8—21no—
475Q8—81no—
476Q8—81no—
477Q8—432no—
478Q8—864no—
479Q8—861no—
480Q8—3441no—
481Q8—3442no—
482Q8—1721no—
483Q8—1721no—
484Q8Q16×D4312yes—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—431no—
490C2×C4—432no—
491C2×C4—432no—
492C2×C4—431no—
493C2×C4—431no—
494C2×C4—864no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—3441no—
500C2×C4—3442no—
501C2×C4—1721no—
502C2×C4—1721no—
503C2×C4—1721no—
504C2×C4C2×D4×D4311yescharacteristic
505C2×C4C2×D4×D4311yescharacteristic
506C2×C4#41×D4311yescharacteristic
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—861no—
513C8—861no—
514C8—1721no—
515C8—1721no—
516C8—1721no—
517C22—432no—
518C22—861no—
519C22—861no—
520C22#121×D4311yescharacteristic
521C4—21no—
522C4—22no—
523C4—41no—
524C4—81no—
525C4—81no—
526C4—432no—
527C4—861no—
528C4—861no—
529C4—862no—
530C4—3441no—
531C4—3441no—
532C4—1721no—
533C4C2×Q16×D4311yescharacteristic
534C4#135×D4311yescharacteristic
535C4#1458371211yescharacteristic
536C4#1458371511yescharacteristic
537C2—862no—
538C2#1914412011yescharacteristic
539C2#467×D4311yescharacteristic
540C2#1914432111yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1676C2
socleC22×C43C2×#121
prime radicalC22×D43#121
hypercenter#1676D43
hypocenterC43#19405
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1676

Complements

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

NH ≅ G/Ntype
5. #19134056C2semidirect
6. #19134055C2semidirect
7. #19134054C2semidirect
8. #19134053C2semidirect
9. #19133998C2semidirect
10. #19133997C2semidirect
11. #19133996C2semidirect
15. C43×#1676C2semidirect
278. #1676D43semidirect
337. C43#19405semidirect

Maximal subgroups

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

subgroupindex
#191457472
#191444012
#477×D432
#191436742
#191340562
#191340552
#191340542
#191340532
#191339982
#191339972
#191339962
#191333682
#191332742
#191332492
C43×#16762
#1940543