Finite Group Databasebeta

← #25086560

Subgroups — #25086560

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1SD16×Dic86C211yesmaximal, characteristic, complemented
2#19147331C211yesmaximal, characteristic, complemented
3#19146454C211yesmaximal, characteristic
4#19134243C211yesmaximal, characteristic, complemented
5#19134151C211yesmaximal, characteristic, complemented
6#19134044C211yesmaximal, characteristic, complemented
7#19134022C211yesmaximal, characteristic, complemented
8#19133970C211yesmaximal, characteristic, complemented
9#19133851C211yesmaximal, characteristic, complemented
10#19133843C211yesmaximal, characteristic, complemented
11#19133814C211yesmaximal, characteristic, complemented
12#19133746C211yesmaximal, characteristic
13#19133432C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3302C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17D4×Dic86C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583296—21no—
21#14583258—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583229—21no—
26#14583189C2211yescharacteristic
27#14583189C2211yescharacteristic
28#14583187—21no—
29#14583184—21no—
30#14583184C2211yescharacteristic
31#14583182—21no—
32#14583181C2211yescharacteristic
33#14583126—21no—
34#14583118—21no—
35#14583106C2211yescharacteristic
36#14583104C2211yescharacteristic
37#14583037—21no—
38#14583030C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14583004—21no—
41SD16×Dic43—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063248—21no—
45#14582651C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52#14582629C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#547C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#485—21no—
60C43×#474C2211yescharacteristic
61C43×#467—21no—
62C43×#462C2211yescharacteristic
63C43×#452—21no—
64C4×SD16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#416—21no—
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621883D411yescharacteristic
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063324—21no—
76#13063324—21no—
77#13063324—41no—
78#13063304—21no—
79#13063302—41no—
80Q8×Dic43—21no—
81C4×Dic86—21no—
82C4×Dic86C2311yescharacteristic
83D4×Dic43—21no—
84#13063258—41no—
85#13063257—21no—
86#13063257—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—41no—
106#13063248D411yescharacteristic
107#13063246—21no—
108#13063246—21no—
109#13063246D411yescharacteristic
110C22⋊(C43⋊C8)—21no—
111#13063236—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×#41×C43—21no—
116C2×Q16×C43—21no—
117C2×SD16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#126×C43—41no—
122#124×C43—21no—
123#123×C43—41no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—21no—
126#121×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130C4×D4×C43C2311yescharacteristic
131#117×C43—21no—
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#106×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144#41×C43—42no—
145#41×C43—81no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—41no—
150C2×D4×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43—41no—
155C22×Dic43—41no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—42no—
159C2×Dic86—41no—
160C2×Dic86—41no—
161C2×Dic86—81no—
162C2×Dic86C2×D411yescharacteristic
163Q16×C43—81no—
164SD16×C43—22no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C4⋊C4×C43C2×D411yescharacteristic
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C22⋊C4×C43—41no—
183C22⋊C4×C43—41no—
184C42×C43—21no—
185C42×C43—41no—
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—42no—
189#10621883—22no—
190#10621883—81no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—21no—
198Dic43⋊C4—41no—
199Dic43⋊C4—41no—
200C4×Dic43—21no—
201C4×Dic43—41no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—81no—
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43—21no—
219D4×C43—21no—
220D4×C43—82no—
221D4×C43#13712yes—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—82no—
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241Dic86—21no—
242Dic86—41no—
243Dic86—41no—
244Dic86—82no—
245Dic86—81no—
246Dic86—161no—
247Dic86#13512yes—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19796—431nomaximal, Sylow
258C22×C43—22no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43D4211yescharacteristic
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—41no—
270C4×C43—81no—
271C4×C43—81no—
272C4×C43C2×#13511yescharacteristic
273C4×C43C2×#13711yescharacteristic
274C4×C43#57711yescharacteristic
275C4×C43#57711yescharacteristic
276Dic43—22no—
277Dic43—41no—
278Dic43—81no—
279Dic43—81no—
280Q8×SD16—431no—
281#3369—431no—
282#3302D4311yescharacteristic
283#3298—431no—
284#1718—431no—
285#1700—431no—
286#1683—431no—
287#1680—431no—
288#1671—431no—
289#1650—431no—
290#1649—431no—
291#1645—431no—
292#1635—431no—
293#1582—431no—
294SD16⋊C8—431no—
295C2×C43—42no—
296C2×C43—81no—
297C2×C43#326611yescharacteristic
298C2×C43#328211yescharacteristic
299C2×C43#328911yescharacteristic
300Q82—431no—
301#556C2×D4311yescharacteristic
302D4×Q8—431no—
303#547C2×D4311yescharacteristic
304#500—431no—
305#498—431no—
306#498—861no—
307#489—861no—
308#487—431no—
309#487—431no—
310#487—431no—
311#487C2×D4311yescharacteristic
312#485—21no—
313#483—861no—
314#476—431no—
315#476—431no—
316#476—861no—
317#475—431no—
318#475—431no—
319#475—861no—
320#475—861no—
321#474C2×D4311yescharacteristic
322#467—21no—
323#465—861no—
324#464—861no—
325#462—431no—
326#462C2×D4311yescharacteristic
327#461—431no—
328#452—21no—
329#448—861no—
330#446—431no—
331C8×Q8—431no—
332#441—861no—
333C4×SD16—431no—
334C4×SD16—861no—
335C4×SD16C2×D4311yescharacteristic
336C8×D4—431no—
337C8×D4C2×D4311yescharacteristic
338#416—21no—
339C2×#103—861no—
340#335—431no—
341#334—431no—
342#333—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346Q8⋊C8—431no—
347Q8⋊C8—431no—
348D4⋊C8—431no—
349D4⋊C8—431no—
350#322—431no—
351C43#1979611yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—861no—
354C2×Q16—21no—
355C2×Q16—861no—
356C2×SD16—431no—
357C2×SD16—861no—
358C2×SD16C22⋊D4311yescharacteristic
359C22×C8—21no—
360C22×C8—861no—
361C4⋊Q8—431no—
362C4⋊Q8—431no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8—861no—
366C4⋊Q8—1721no—
367C4⋊Q8C22×D4311yescharacteristic
368C4⋊Q8C22×D4311yescharacteristic
369#126—41no—
370#124—21no—
371#123—41no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—861no—
375C22⋊Q8—1721no—
376#121—21no—
377C4×Q8—21no—
378C4×Q8—431no—
379C4×Q8—861no—
380C4×Q8—861no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—861no—
383C4×D4C22×D4311yescharacteristic
384C4×D4C22×D4311yescharacteristic
385#117—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—1721no—
389#106—431no—
390#106—861no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106C22⋊D4311yescharacteristic
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8C22×D4311yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—431no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#103—1721no—
416#103C22⋊D4311yescharacteristic
417#102—21no—
418#102—431no—
419#102—861no—
420#102—861no—
421#102C22⋊D4311yescharacteristic
422C22⋊C8—21no—
423C22⋊C8—861no—
424#97—861no—
425C4×C8—431no—
426C4×C8—431no—
427C4×C8—861no—
428C4×C8C22×D4311yescharacteristic
429#41—42no—
430#41—81no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—431no—
434C2×Q8—861no—
435C2×Q8—861no—
436C2×Q8—3441no—
437C2×Q8—1721no—
438C2×Q8—1721no—
439C2×Q8—1722no—
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4—41no—
442C2×D4D4×D4311yescharacteristic
443C2×D4C2×C22⋊D4311yescharacteristic
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—1721no—
448Q16—81no—
449Q16—1722no—
450SD16—22no—
451SD16—862no—
452SD16—3441no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—3441no—
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—431no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4—1721no—
480C4⋊C4D4×D4311yescharacteristic
481C4⋊C4C2×C22⋊D4311yescharacteristic
482C4⋊C4C2×C22⋊D4311yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—1721no—
489C42—21no—
490C42—41no—
491C42—861no—
492C42—1721no—
493C42C23×D4311yescharacteristic
494C23—21no—
495C23—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—432no—
503Q8—861no—
504Q8—3441no—
505Q8—3442no—
506Q8—1721no—
507Q8—1721no—
508Q8—6881no—
509D4—21no—
510D4—21no—
511D4—21no—
512D4—82no—
513D4#1306335512yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—3442no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C2×D4×D4311yescharacteristic
531C2×C4C22×C22⋊D4311yescharacteristic
532C2×C4#1306337011yescharacteristic
533C8—21no—
534C8—21no—
535C8—41no—
536C8—861no—
537C8—861no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C22—22no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22D4×C22⋊D4311yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—81no—
555C4—81no—
556C4—862no—
557C4—3441no—
558C4—3441no—
559C4—1721no—
560C4#135×D4311yescharacteristic
561C4C2×#1306335511yescharacteristic
562C4#1458370611yescharacteristic
563C4#1458371011yescharacteristic
564C2—42no—
565C2—81no—
566C2#1914610111yescharacteristic
567C2#1914629611yescharacteristic
568C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3302C2
socleC22×C43D42
prime radicalC43×#547C22
hypercenter#3302D43
hypocenterC43#19796
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3302

Complements

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

NH ≅ G/Ntype
1. SD16×Dic86C2semidirect
2. #19147331C2semidirect
4. #19134243C2semidirect
5. #19134151C2semidirect
6. #19134044C2semidirect
7. #19134022C2semidirect
8. #19133970C2semidirect
9. #19133851C2semidirect
10. #19133843C2semidirect
11. #19133814C2semidirect
13. #19133432C2semidirect
14. #19133407C2semidirect
351. C43#19796semidirect

Maximal subgroups

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

subgroupindex
SD16×Dic862
#191473312
#191464542
#191342432
#191341512
#191340442
#191340222
#191339702
#191338512
#191338432
#191338142
#191337462
#191334322
#191334072
C43×#33022
#1979643