Finite Group Databasebeta

← #25087200

Subgroups — #25087200

Order 11008.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147313C211yesmaximal, characteristic
2#19147244C211yesmaximal, characteristic
3#19147027C211yesmaximal, characteristic, complemented
4#19134244C211yesmaximal, characteristic, complemented
5#19134179C211yesmaximal, characteristic, complemented
6#19134043C211yesmaximal, characteristic, complemented
7#19134027C211yesmaximal, characteristic, complemented
8#19133984C211yesmaximal, characteristic, complemented
9#19133863C211yesmaximal, characteristic, complemented
10#19133858C211yesmaximal, characteristic, complemented
11#19133802C211yesmaximal, characteristic, complemented
12#19133766C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic
15C43×#3299C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17#14583622C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583261—21no—
21#14583256—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583239—21no—
26#14583239—21no—
27#14583203—21no—
28#14583191—21no—
29#14583186C2211yescharacteristic
30#14583184C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583137—21no—
34#14583114—21no—
35#14583114—21no—
36#14583104C2211yescharacteristic
37#14583104C2211yescharacteristic
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582999—21no—
41C4×#10621883—21no—
42C4×#10621882C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#14582936—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582645C2211yescharacteristic
49#14582644C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#554C2211yescharacteristic
57D4×Q8×C43C2211yescharacteristic
58C43×#487C2211yescharacteristic
59C43×#484—21no—
60C43×#477C2211yescharacteristic
61C43×#467—21no—
62C43×#462C2211yescharacteristic
63C43×#451—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C2×#103×C43—21no—
67C2×#10621883—21no—
68C2×#10621883—21no—
69C2×#10621882D411yescharacteristic
70C2×C8×D43—21no—
71#13063325C2311yescharacteristic
72#13063325C2311yescharacteristic
73#13063320—41no—
74#13063320—41no—
75#13063313—21no—
76#13063313—21no—
77#13063301—21no—
78#13063301—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×D172C2311yescharacteristic
82#13063283—21no—
83#13063283—21no—
84#13063259—21no—
85#13063259—21no—
86#13063258—21no—
87#13063258D411yescharacteristic
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256—41no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063249—21no—
98#13063249—21no—
99#13063249—41no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063246D411yescharacteristic
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C22×Q8×C43—21no—
116C2×Q16×C43—21no—
117C2×Q16×C43D411yescharacteristic
118C22×C8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43C2311yescharacteristic
121C4⋊Q8×C43C2311yescharacteristic
122#125×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43—41no—
126C22⋊Q8×C43—41no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43—21no—
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132C2×C4⋊C4×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43—42no—
148C2×Q8×C43—81no—
149C2×Q8×C43C2×D411yescharacteristic
150C2×Q8×C43C2×D411yescharacteristic
151C2×D4×C43C2×D411yescharacteristic
152C22×C4×C43—21no—
153C22×C4×C43—41no—
154C22×C4×C43—41no—
155C2×D172C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159Q16×C43—41no—
160Q16×C43—81no—
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—21no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43C2411yescharacteristic
183#10621883—42no—
184#10621883—42no—
185#10621882—22no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—41no—
188(C2×D43)⋊C4—41no—
189(C2×D43)⋊C4—41no—
190(C2×D43)⋊C4—41no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43C2×D411yescharacteristic
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C4×Dic43—41no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C8×D43—42no—
207C23×C43—21no—
208C22×D43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—21no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—81no—
216Q8×C43—82no—
217D4×C43—21no—
218D4×C43#13512yes—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—82no—
229C2×C4×C43—161no—
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172—21no—
238C4×D43—41no—
239C4×D43—41no—
240Dic86—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—41no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253#19839—431nomaximal, Sylow
254C22×C43—22no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43D4211yescharacteristic
258C2×D43—41no—
259C2×D43—41no—
260C2×D43—41no—
261C4×C43—21no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43C2×#13511yescharacteristic
270C4×C43#57511yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—41no—
274Dic43—81no—
275Dic43—81no—
276#3367—431no—
277#3360—431no—
278#3342—431no—
279#3299D4311yescharacteristic, complemented
280#1718—431no—
281#1704—431no—
282#1683—431no—
283#1680—431no—
284#1673—431no—
285#1652—431no—
286#1651—431no—
287#1643—431no—
288#1638—431no—
289#1584—431no—
290#1580—431no—
291C2×C43—42no—
292C2×C43#326711yescharacteristic
293C2×C43#328511yescharacteristic
294C2×C43#328911yescharacteristic
295D43—81no—
296#556—431no—
297#556—431no—
298#554C2×D4311yescharacteristic
299D4×Q8C2×D4311yescharacteristic
300#500—431no—
301#498—431no—
302#489—861no—
303#488—861no—
304#487—431no—
305#487—431no—
306#487—431no—
307#487C2×D4311yescharacteristic
308#485—861no—
309#485—861no—
310#484—21no—
311#479—861no—
312#477—861no—
313#477C2×D4311yescharacteristic
314#476—431no—
315#475—431no—
316#475—431no—
317#474—431no—
318#467—21no—
319#467—861no—
320#463—861no—
321#463—861no—
322#462C2×D4311yescharacteristic
323#461—431no—
324#461—431no—
325#451—21no—
326#446—431no—
327C8×Q8—431no—
328#440—861no—
329C4×Q16C2×D4311yescharacteristic
330C4×SD16—861no—
331C4×D8—431no—
332C8×D4—431no—
333C8×D4C2×D4311yescharacteristic
334#427—861no—
335C2×#103—21no—
336#335—431no—
337#334—431no—
338#333—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342Q8⋊C8—431no—
343Q8⋊C8—431no—
344D4⋊C8—431no—
345D4⋊C8—431no—
346#322—431no—
347C43#1983911yescharacteristic, complemented, Sylow
348C22×Q8—21no—
349C2×Q16—21no—
350C2×Q16C22⋊D4311yescharacteristic
351C2×SD16—861no—
352C2×SD16—861no—
353C2×D8—431no—
354C22×C8—21no—
355C22×C8—861no—
356C4⋊Q8—21no—
357C4⋊Q8—431no—
358C4⋊Q8—431no—
359C4⋊Q8C22×D4311yescharacteristic
360C4⋊Q8C22×D4311yescharacteristic
361#126—1721no—
362#126—1721no—
363#125—21no—
364#124—861no—
365#124—861no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—41no—
369C22⋊Q8—41no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8C22×D4311yescharacteristic
375C4×Q8C22×D4311yescharacteristic
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—431no—
379C4×D4C22×D4311yescharacteristic
380#117—861no—
381#117—861no—
382C2×C4⋊C4—21no—
383#107—21no—
384#107—431no—
385#107—861no—
386#107—861no—
387#107—861no—
388#107C22⋊D4311yescharacteristic
389#106—861no—
390#106—861no—
391#106—861no—
392#106—1721no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—861no—
397C4⋊C8—861no—
398C4⋊C8C22×D4311yescharacteristic
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#103—1721no—
412#103C22⋊D4311yescharacteristic
413#103C22⋊D4311yescharacteristic
414#102—431no—
415#102—431no—
416#102—861no—
417#102—861no—
418C22⋊C8—21no—
419C22⋊C8—861no—
420#97—861no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—861no—
424C4×C8C22×D4311yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—41no—
428C2×Q8—42no—
429C2×Q8—81no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8C2×C22⋊D4311yescharacteristic
433C2×Q8C2×C22⋊D4311yescharacteristic
434C2×D4—431no—
435C2×D4D4×D4311yescharacteristic
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—861no—
440Q16—41no—
441Q16—81no—
442SD16—1722no—
443SD16—1722no—
444D8—862no—
445C2×C8—21no—
446C2×C8—81no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—1722no—
454C2×C8C2×C22⋊D4311yescharacteristic
455C2×C8C2×C22⋊D4311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—431no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4D4×D4311yescharacteristic
473C4⋊C4C2×C22⋊D4311yescharacteristic
474C4⋊C4C2×C22⋊D4311yescharacteristic
475C22⋊C4—21no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—861no—
479C22⋊C4—1721no—
480C22⋊C4—1721no—
481C22⋊C4—1721no—
482C22⋊C4—1721no—
483C42—21no—
484C42—21no—
485C42—1721no—
486C42—1721no—
487C42C23×D4311yescharacteristic
488C23—21no—
489C23—861no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—81no—
497Q8—82no—
498Q8—1721no—
499Q8—1721no—
500Q8—1721no—
501Q8—1721no—
502D4—21no—
503D4—861no—
504D4—861no—
505D4#1306334812yes—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—82no—
516C2×C4—161no—
517C2×C4—861no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4C2×D4×D4311yescharacteristic
523C2×C4C22×C22⋊D4311yescharacteristic
524C2×C4#1306337011yescharacteristic
525C8—21no—
526C8—21no—
527C8—41no—
528C8—861no—
529C8—861no—
530C8—1721no—
531C8—1721no—
532C8—1721no—
533C8—1721no—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—1721no—
538C22—1721no—
539C22—1721no—
540C22D4×C22⋊D4311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—3441no—
550C4—3441no—
551C4—1721no—
552C4C2×#1306334811yescharacteristic
553C4#1458369711yescharacteristic
554C4#1458371011yescharacteristic
555C4#1458371211yescharacteristic
556C2—42no—
557C2—3441no—
558C2#1914611611yescharacteristic
559C2#1914633611yescharacteristic
560C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3299C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenter#3299D43
hypocenterC43#19839
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3299

Complements

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

NH ≅ G/Ntype
3. #19147027C2semidirect
4. #19134244C2semidirect
5. #19134179C2semidirect
6. #19134043C2semidirect
7. #19134027C2semidirect
8. #19133984C2semidirect
9. #19133863C2semidirect
10. #19133858C2semidirect
11. #19133802C2semidirect
12. #19133766C2semidirect
13. #19133446C2semidirect
15. C43×#3299C2semidirect
279. #3299D43semidirect
347. C43#19839semidirect

Maximal subgroups

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

subgroupindex
#191473132
#191472442
#191470272
#191342442
#191341792
#191340432
#191340272
#191339842
#191338632
#191338582
#191338022
#191337662
#191334462
#191334172
C43×#32992
#1983943