Finite Group Databasebeta

← #25087410

Subgroups — #25087410

Order 11008.

588 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147626C211yesmaximal, characteristic, complemented
2#19147468C211yesmaximal, characteristic, complemented
3#19146952C211yesmaximal, characteristic
4#19134230C211yesmaximal, characteristic, complemented
5#19134099C211yesmaximal, characteristic, complemented
6#19134022C211yesmaximal, characteristic, complemented
7#19133970C211yesmaximal, characteristic, complemented
8#19133958C211yesmaximal, characteristic, complemented
9#19133879C211yesmaximal, characteristic
10#19133870C211yesmaximal, characteristic, complemented
11#19133808C211yesmaximal, characteristic, complemented
12#19133767C211yesmaximal, characteristic, complemented
13#19133432C211yesmaximal, characteristic, complemented
14#19133407C211yesmaximal, characteristic, complemented
15C43×#3302C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583299—21no—
19#14583297C2211yescharacteristic
20#14583295C2211yescharacteristic
21#14583295C2211yescharacteristic
22#14583294—21no—
23#14583278C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583229—21no—
26#14583215—21no—
27#14583204—21no—
28#14583201—21no—
29#14583194C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583181C2211yescharacteristic
32#14583179C2211yescharacteristic
33#14583126—21no—
34#14583118—21no—
35#14583109—21no—
36#14583106C2211yescharacteristic
37#14583104C2211yescharacteristic
38#14583030C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14583004—21no—
41SD16×Dic43—21no—
42C4×#10621883C2211yescharacteristic
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063256—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—
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621883—21no—
71C2×#10621883D411yescharacteristic
72C22×C43⋊C8—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063316—21no—
77#13063316—21no—
78#13063316—41no—
79#13063304—21no—
80#13063302—41no—
81Q8×Dic43—21no—
82C4×Dic86—21no—
83C4×Dic86C2311yescharacteristic
84D4×Dic43—21no—
85C2×C4⋊Dic43—21no—
86#13063258—21no—
87#13063258—21no—
88#13063257—21no—
89#13063257—21no—
90#13063256—21no—
91#13063256—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—41no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100Dic43⋊C8—21no—
101#13063249—21no—
102#13063249—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×Dic86C2×D411yescharacteristic
159Q16×C43—81no—
160SD16×C43—22no—
161C2×C8×C43—21no—
162C2×C8×C43—81no—
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2411yescharacteristic
183C22⋊Dic43—41no—
184#10621885—42no—
185#10621885—81no—
186#10621885—81no—
187#10621883—22no—
188#10621883—81no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—41no—
194C4⋊Dic43—41no—
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—42no—
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—161no—
241Dic86—21no—
242Dic86—21no—
243Dic86—41no—
244Dic86—41no—
245Dic86—81no—
246C8×C43—21no—
247C8×C43—21no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19853—431nomaximal, Sylow
256C22×C43—22no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43D4211yescharacteristic
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43—81no—
270C4×C43C2×#13511yescharacteristic
271C4×C43C2×#13711yescharacteristic
272C4×C43#57711yescharacteristic
273C4×C43#57711yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—81no—
277Dic43—81no—
278#3398—431no—
279#3381—431no—
280#3335—431no—
281#3302D4311yescharacteristic
282#1716—431no—
283#1692—431no—
284#1680—431no—
285#1671—431no—
286#1669—431no—
287#1654—431no—
288#1653—431no—
289#1644—431no—
290#1638—431no—
291#1582—431no—
292SD16⋊C8—431no—
293C2×C43—42no—
294C2×C43—81no—
295C2×C43#326611yescharacteristic
296C2×C43#328411yescharacteristic
297C2×C43#328911yescharacteristic
298#557—431no—
299#556C2×D4311yescharacteristic
300#554—431no—
301#547C2×D4311yescharacteristic
302#499—861no—
303#498—431no—
304#498—431no—
305#498—431no—
306#497—861no—
307#494—431no—
308#487—431no—
309#487C2×D4311yescharacteristic
310#485—21no—
311#483—861no—
312#481—861no—
313#479—861no—
314#478—861no—
315#477—431no—
316#476—431no—
317#475—431no—
318#474—431no—
319#474C2×D4311yescharacteristic
320#467—21no—
321#465—861no—
322#464—861no—
323#462—431no—
324#462—861no—
325#462C2×D4311yescharacteristic
326#461—431no—
327#452—21no—
328#446—431no—
329C8×Q8—431no—
330#441—861no—
331C4×SD16—431no—
332C4×SD16—861no—
333C4×SD16C2×D4311yescharacteristic
334C8×D4—431no—
335C8×D4C2×D4311yescharacteristic
336C2×#106—861no—
337#416—21no—
338#335—431no—
339#334—431no—
340#333—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344Q8⋊C8—431no—
345Q8⋊C8—431no—
346D4⋊C8—431no—
347D4⋊C8—431no—
348#322—431no—
349C43#1985311yescharacteristic, complemented, Sylow
350C2×#41—21no—
351C2×Q16—21no—
352C2×Q16—861no—
353C2×Q16—861no—
354C2×Q16—861no—
355C2×SD16—431no—
356C2×SD16—861no—
357C2×SD16C22⋊D4311yescharacteristic
358C22×C8—21no—
359C22×C8—861no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—861no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
365#126—41no—
366#125—861no—
367#125—861no—
368#125—1721no—
369#124—21no—
370#123—41no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—861no—
374C22⋊Q8—1721no—
375#121—21no—
376C4×Q8—21no—
377C4×Q8—431no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8C22×D4311yescharacteristic
381C4×D4—861no—
382C4×D4C22×D4311yescharacteristic
383C4×D4C22×D4311yescharacteristic
384#117—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—861no—
387#107—21no—
388#107—861no—
389#107—861no—
390#106—431no—
391#106—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397#106—1721no—
398#106C22⋊D4311yescharacteristic
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—431no—
409#103—861no—
410#103—861no—
411#103—861no—
412#103—861no—
413#103—1721no—
414#103C22⋊D4311yescharacteristic
415#102—21no—
416#102—431no—
417#102—861no—
418#102—861no—
419#102C22⋊D4311yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—861no—
422#97—861no—
423C4×C8—431no—
424C4×C8—431no—
425C4×C8—861no—
426C4×C8C22×D4311yescharacteristic
427#41—42no—
428#41—81no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—431no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8C2×C22⋊D4311yescharacteristic
435C2×D4—41no—
436C2×D4D4×D4311yescharacteristic
437C2×D4C2×C22⋊D4311yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441C22×C4—1721no—
442Q16—81no—
443Q16—3441no—
444Q16—3441no—
445Q16—1722no—
446SD16—22no—
447SD16—862no—
448SD16—3441no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—1722no—
458C2×C8C2×C22⋊D4311yescharacteristic
459C2×C8C2×C22⋊D4311yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—1721no—
474C4⋊C4—1721no—
475C4⋊C4—1721no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C4⋊C4D4×D4311yescharacteristic
479C4⋊C4C2×C22⋊D4311yescharacteristic
480C4⋊C4C2×C22⋊D4311yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—1721no—
487C42—21no—
488C42—41no—
489C42—861no—
490C42—1721no—
491C42C23×D4311yescharacteristic
492C23—21no—
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—861no—
501Q8—861no—
502Q8—3441no—
503Q8—1721no—
504Q8—1721no—
505D4—21no—
506D4—21no—
507D4—21no—
508D4—82no—
509D4#1306335512yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—82no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—6881no—
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4#1306337011yescharacteristic
529C8—21no—
530C8—21no—
531C8—41no—
532C8—432no—
533C8—861no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C22—22no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22D4×C22⋊D4311yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—3441no—
553C4—3441no—
554C4—1721no—
555C4—1721no—
556C4#135×D4311yescharacteristic
557C4C2×#1306335511yescharacteristic
558C4#1458370611yescharacteristic
559C4#1458371011yescharacteristic
560C2—42no—
561C2—81no—
562C2#1914610111yescharacteristic
563C2#1914631911yescharacteristic
564C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3302C2
socleC22×C43D42
prime radicalC43×#547C22
hypercenter#3302D43
hypocenterC43#19853
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. #19147626C2semidirect
2. #19147468C2semidirect
4. #19134230C2semidirect
5. #19134099C2semidirect
6. #19134022C2semidirect
7. #19133970C2semidirect
8. #19133958C2semidirect
10. #19133870C2semidirect
11. #19133808C2semidirect
12. #19133767C2semidirect
13. #19133432C2semidirect
14. #19133407C2semidirect
349. C43#19853semidirect

Maximal subgroups

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

subgroupindex
#191476262
#191474682
#191469522
#191342302
#191340992
#191340222
#191339702
#191339582
#191338792
#191338702
#191338082
#191337672
#191334322
#191334072
C43×#33022
#1985343