Finite Group Databasebeta

← #25087069

Subgroups — #25087069

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#10621884C211yesmaximal, characteristic
2#19147280C211yesmaximal, characteristic
3#19146880C211yesmaximal, characteristic
4#19134242C211yesmaximal, characteristic, complemented
5#19134167C211yesmaximal, characteristic
6#19134027C211yesmaximal, characteristic, complemented
7#19134025C211yesmaximal, characteristic, complemented
8#19133979C211yesmaximal, characteristic, complemented
9#19133842C211yesmaximal, characteristic
10#19133837C211yesmaximal, characteristic, complemented
11#19133816C211yesmaximal, characteristic, complemented
12#19133766C211yesmaximal, characteristic
13#19133438C211yesmaximal, characteristic
14#19133414C211yesmaximal, characteristic, complemented
15C43×#3363C211yesmaximal, characteristic, complemented
16#14583622C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295—21no—
20#14583295C2211yescharacteristic
21#14583256—21no—
22#14583251C2211yescharacteristic
23#14583250C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583242—21no—
26#14583203—21no—
27#14583186—21no—
28#14583186C2211yescharacteristic
29#14583184—21no—
30#14583184C2211yescharacteristic
31#14583184C2211yescharacteristic
32#14583176C2211yescharacteristic
33#14583156—21no—
34#14583121—21no—
35#14583109C2211yescharacteristic
36#14583109C2211yescharacteristic
37#14583053—21no—
38Q8×C43⋊C8C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621884—21no—
42C4×#10621884C2211yescharacteristic
43#14582978C2211yescharacteristic
44#14582906—21no—
45#14582650C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582620C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#487—21no—
59C43×#487C2211yescharacteristic
60C43×#477—21no—
61C43×#477C2211yescharacteristic
62C43×#462—21no—
63C43×#462C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×Q16×C43—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621885—21no—
70C2×#10621884D411yescharacteristic
71C2×#10621872—21no—
72#13063325—21no—
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063320—41no—
76#13063313—21no—
77#13063305—21no—
78#13063305—41no—
79#13063301—21no—
80C4×Dic86—21no—
81C4×D172—21no—
82C4×D172C2311yescharacteristic
83#13063283—21no—
84#13063258—21no—
85#13063258—41no—
86#13063256—21no—
87#13063256—21no—
88#13063256—21no—
89#13063256—21no—
90#13063256—21no—
91#13063256D411yescharacteristic
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)C2311yescharacteristic
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97#13063250—21no—
98#13063250—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43—21no—
116C2×Q16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—21no—
124#125×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43D411yescharacteristic
134C4⋊C8×C43—21no—
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
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×Q8×C43C2×D411yescharacteristic
150Q8×D43—42no—
151Q8×D43—81no—
152C2×D172C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—41no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—41no—
158Q16×C43—22no—
159Q16×C43—42no—
160C2×C8×C43—21no—
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
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×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C4⋊C4×C43C2×D411yescharacteristic
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43—41no—
183C42×C43C2411yescharacteristic
184#10621885—42no—
185#10621885—81no—
186#10621884—22no—
187(C2×D43)⋊C4—21no—
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⋊Dic43—41no—
196C4⋊Dic43C2×D411yescharacteristic
197Dic43⋊C4—41no—
198C4×Dic43—41no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205#10621872—81no—
206C22×D43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—81no—
214Q8×C43—161no—
215Q8×C43#13512yes—
216Q8×C43#13712yes—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235C4×D43—82no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—82no—
241C8×C43—21no—
242C8×C43—21no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—41no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19830—431nomaximal, Sylow
251C22×C43D4211yescharacteristic
252C2×D43—41no—
253C2×D43—41no—
254C2×D43—41no—
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—21no—
258C4×C43—41no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—81no—
263C4×C43—81no—
264C4×C43C2×#13511yescharacteristic
265C4×C43C2×#13711yescharacteristic
266C4×C43#57711yescharacteristic
267C4×C43#57811yescharacteristic
268Dic43—41no—
269Dic43—81no—
270Dic43—81no—
271Q8×SD16—431no—
272#3364—431no—
273#3363D4311yescharacteristic, complemented
274#3328—431no—
275#1718—431no—
276#1703—431no—
277#1680—431no—
278#1680—431no—
279#1672—431no—
280#1649—431no—
281#1648—431no—
282#1645—431no—
283#1638—431no—
284#1583—431no—
285#1579—431no—
286C2×C43#327011yescharacteristic
287C2×C43#328211yescharacteristic
288C2×C43#328911yescharacteristic
289D43—81no—
290Q82C2×D4311yescharacteristic
291#557C2×D4311yescharacteristic
292#556—431no—
293D4×Q8—431no—
294#500—431no—
295#498—431no—
296#498—861no—
297#488—861no—
298#487—21no—
299#487—431no—
300#487—431no—
301#487—431no—
302#487C2×D4311yescharacteristic
303#485—861no—
304#479—861no—
305#477—21no—
306#477C2×D4311yescharacteristic
307#476—431no—
308#476—861no—
309#475—431no—
310#475—431no—
311#475—861no—
312#474—431no—
313#470—861no—
314#464—861no—
315#462—21no—
316#462—431no—
317#462—431no—
318#462C2×D4311yescharacteristic
319#451—861no—
320C8×Q8—431no—
321C8×Q8—431no—
322C8×Q8C2×D4311yescharacteristic
323C4×Q16—21no—
324C4×Q16—861no—
325C4×Q16C2×D4311yescharacteristic
326C4×SD16—431no—
327C4×SD16—861no—
328#436—431no—
329#419—861no—
330#334—431no—
331#334—431no—
332#333—431no—
333#332—431no—
334#332—431no—
335#332—431no—
336Q8⋊C8—431no—
337Q8⋊C8—431no—
338Q8⋊C8—431no—
339D4⋊C8—431no—
340#322—431no—
341C43#1983011yescharacteristic, complemented, Sylow
342C22×Q8—861no—
343C2×Q16—21no—
344C2×Q16—861no—
345C2×Q16—861no—
346C2×Q16C22⋊D4311yescharacteristic
347C2×SD16—431no—
348C2×M16—861no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—41no—
353C4⋊Q8—431no—
354C4⋊Q8—431no—
355C4⋊Q8—861no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—1721no—
359#125—21no—
360#125—41no—
361#124—861no—
362C22⋊Q8—861no—
363C22⋊Q8—861no—
364C22⋊Q8—1721no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8—861no—
370C4×Q8C22×D4311yescharacteristic
371C4×Q8C22×D4311yescharacteristic
372C4×Q8C22×D4311yescharacteristic
373C4×D4—431no—
374C4×D4—861no—
375#117—861no—
376#107—21no—
377#107—861no—
378#107—1721no—
379#107C22⋊D4311yescharacteristic
380#106—431no—
381#106—861no—
382#106—861no—
383#106—861no—
384#106—861no—
385#106—861no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—431no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—1721no—
407#103C22⋊D4311yescharacteristic
408#103C22⋊D4311yescharacteristic
409#102—431no—
410#102—861no—
411#102—861no—
412C22⋊C8—861no—
413C4×C8—21no—
414C4×C8—431no—
415C4×C8—431no—
416C4×C8—861no—
417C4×C8—861no—
418C4×C8C22×D4311yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—41no—
422C2×Q8—861no—
423C2×Q8—861no—
424C2×Q8—3441no—
425C2×Q8—1721no—
426C2×Q8—1722no—
427C2×Q8D4×D4311yescharacteristic
428C2×Q8C2×C22⋊D4311yescharacteristic
429C2×Q8C2×C22⋊D4311yescharacteristic
430C2×D4—431no—
431C22×C4—861no—
432C22×C4—1721no—
433Q16—22no—
434Q16—42no—
435Q16—3441no—
436Q16—1722no—
437SD16—862no—
438M16—3441no—
439C2×C8—21no—
440C2×C8—431no—
441C2×C8—431no—
442C2×C8—861no—
443C2×C8—861no—
444C2×C8—861no—
445C2×C8—861no—
446C2×C8C2×C22⋊D4311yescharacteristic
447C2×C8C2×C22⋊D4311yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—431no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4D4×D4311yescharacteristic
468C4⋊C4C2×C22⋊D4311yescharacteristic
469C4⋊C4C2×C22⋊D4311yescharacteristic
470C22⋊C4—861no—
471C22⋊C4—1721no—
472C22⋊C4—1721no—
473C22⋊C4—1721no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42—1721no—
480C42C23×D4311yescharacteristic
481C23—861no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—161no—
490Q8—3442no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495Q8#1306334512yes—
496Q8#1306335712yes—
497D4—861no—
498D4—861no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—861no—
508C2×C4—3442no—
509C2×C4—1721no—
510C2×C4—1721no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4C2×D4×D4311yescharacteristic
514C2×C4C22×C22⋊D4311yescharacteristic
515C2×C4#1306337011yescharacteristic
516C8—21no—
517C8—21no—
518C8—41no—
519C8—861no—
520C8—861no—
521C8—1721no—
522C8—1721no—
523C8—1721no—
524C8—1721no—
525C22—1721no—
526C22—1721no—
527C22—1721no—
528C22D4×C22⋊D4311yescharacteristic
529C4—22no—
530C4—21no—
531C4—22no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—3441no—
539C4—3441no—
540C4—1721no—
541C4C2×#1306334511yescharacteristic
542C4C2×#1306335711yescharacteristic
543C4#1458370711yescharacteristic
544C4#1458371211yescharacteristic
545C2—3441no—
546C2#1914616511yescharacteristic
547C2#1914630311yescharacteristic
548C2#1914636811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3363C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#3363D43
hypocenterC43#19830
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
4. #19134242C2semidirect
6. #19134027C2semidirect
7. #19134025C2semidirect
8. #19133979C2semidirect
10. #19133837C2semidirect
11. #19133816C2semidirect
14. #19133414C2semidirect
15. C43×#3363C2semidirect
273. #3363D43semidirect
341. C43#19830semidirect

Maximal subgroups

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

subgroupindex
Q8×#106218842
#191472802
#191468802
#191342422
#191341672
#191340272
#191340252
#191339792
#191338422
#191338372
#191338162
#191337662
#191334382
#191334142
C43×#33632
#1983043