Finite Group Databasebeta

← #25087205

Subgroups — #25087205

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#19147309C211yesmaximal, characteristic
2#19147240C211yesmaximal, characteristic
3#19146473C211yesmaximal, characteristic, complemented
4#19134240C211yesmaximal, characteristic, complemented
5#19134175C211yesmaximal, characteristic, complemented
6#19134046C211yesmaximal, characteristic, complemented
7#19134023C211yesmaximal, characteristic, complemented
8#19133981C211yesmaximal, characteristic, complemented
9#19133865C211yesmaximal, characteristic, complemented
10#19133857C211yesmaximal, characteristic, complemented
11#19133801C211yesmaximal, characteristic, complemented
12#19133767C211yesmaximal, characteristic, complemented
13#19133446C211yesmaximal, characteristic, complemented
14#19133417C211yesmaximal, characteristic
15C43×#3342C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17Q8×D172C2211yescharacteristic
18#14583295C2211yescharacteristic
19#14583258—21no—
20#14583253—21no—
21#14583251C2211yescharacteristic
22#14583250C2211yescharacteristic
23#14583249C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583236—21no—
26#14583206—21no—
27#14583194—21no—
28#14583194C2211yescharacteristic
29#14583189C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583139—21no—
32#14583111—21no—
33#14583111—21no—
34#14583109C2211yescharacteristic
35#14583101C2211yescharacteristic
36#14583101C2211yescharacteristic
37#14583053—21no—
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582997—21no—
41C4×#10621884—21no—
42C4×#10621882C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#103×D43—21no—
45#14582652C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582647C2211yescharacteristic
48#14582646C2211yescharacteristic
49#14582645C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53D4⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56C43×#556C2211yescharacteristic
57C43×#556C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#485—21no—
60C43×#485—21no—
61C43×#475C2211yescharacteristic
62C43×#475C2211yescharacteristic
63C43×#467—21no—
64C4×Q16×C43C2211yescharacteristic
65C8×D4×C43C2211yescharacteristic
66C43×#427—21no—
67C2×Q8×D43—21no—
68C2×#10621885—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882D411yescharacteristic
72C2×C8×D43—21no—
73#13063325—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063305—21no—
78#13063305—41no—
79#13063303—41no—
80#13063301—21no—
81C4×D172—21no—
82C4×D172—21no—
83C4×D172C2311yescharacteristic
84C4⋊C4×D43—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258D411yescharacteristic
88#13063256—21no—
89#13063256—41no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063250—21no—
96#13063250—21no—
97#13063249—21no—
98#13063249—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063248—21no—
105#13063248—41no—
106#13063246—21no—
107#13063246—21no—
108#13063246D411yescharacteristic
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43D411yescharacteristic
116C22×C8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118C4⋊Q8×C43C2311yescharacteristic
119#126×C43—41no—
120#126×C43—41no—
121#124×C43—21no—
122#124×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43C2311yescharacteristic
128C4×Q8×C43C2311yescharacteristic
129C4×D4×C43C2311yescharacteristic
130#117×C43—21no—
131#117×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#107×C43D411yescharacteristic
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
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×C43C2×D411yescharacteristic
147C2×Q8×C43C2×D411yescharacteristic
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150Q8×D43—42no—
151Q8×D43—81no—
152C2×D172C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—41no—
155C2×C4×D43—41no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—41no—
159Q16×C43—41no—
160C2×C8×C43—21no—
161C2×C8×C43—42no—
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
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×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C22⋊C4×C43—21no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—41no—
183C42×C43—41no—
184C42×C43C2411yescharacteristic
185#10621885—81no—
186#10621884—42no—
187#10621884—42no—
188#10621882—22no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—41no—
197C4⋊Dic43C2×D411yescharacteristic
198Dic43⋊C4—41no—
199Dic43⋊C4—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—81no—
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—41no—
216Q8×C43—41no—
217D4×C43—21no—
218D4×C43—21no—
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×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43H(5,𝔽2)11yescharacteristic
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234D172—21no—
235D172#13512yes—
236C4×D43—41no—
237C4×D43—41no—
238C4×D43—82no—
239C4×D43—161no—
240Dic86—41no—
241Dic86—41no—
242Dic86—82no—
243Dic86—81no—
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—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43D4211yescharacteristic
258C2×D43—22no—
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#3342D4311yescharacteristic, complemented
279#3299—431no—
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—81no—
292C2×C43#326711yescharacteristic
293C2×C43#328511yescharacteristic
294C2×C43#328911yescharacteristic
295D43—42no—
296#556C2×D4311yescharacteristic
297#556C2×D4311yescharacteristic
298#554—431no—
299D4×Q8—431no—
300#500C2×D4311yescharacteristic
301#498—431no—
302#489—861no—
303#488—861no—
304#487—431no—
305#487—431no—
306#487—431no—
307#487—431no—
308#485—21no—
309#485—21no—
310#484—861no—
311#479—861no—
312#477—431no—
313#477—861no—
314#476—431no—
315#475C2×D4311yescharacteristic
316#475C2×D4311yescharacteristic
317#474—431no—
318#467—21no—
319#467—861no—
320#463—861no—
321#463—861no—
322#462—431no—
323#461—431no—
324#461—431no—
325#451—861no—
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—21no—
335C2×#103—861no—
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—861no—
349C2×Q16—861no—
350C2×Q16C22⋊D4311yescharacteristic
351C2×SD16—861no—
352C2×SD16—861no—
353C2×D8—431no—
354C22×C8—21no—
355C22×C8—861no—
356C4⋊Q8—431no—
357C4⋊Q8—431no—
358C4⋊Q8—861no—
359C4⋊Q8C22×D4311yescharacteristic
360C4⋊Q8C22×D4311yescharacteristic
361#126—41no—
362#126—41no—
363#125—861no—
364#124—21no—
365#124—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—861no—
369C22⋊Q8—861no—
370C22⋊Q8—1721no—
371C22⋊Q8—1721no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8C22×D4311yescharacteristic
375C4×Q8C22×D4311yescharacteristic
376C4×D4—431no—
377C4×D4—861no—
378C4×D4—861no—
379C4×D4C22×D4311yescharacteristic
380#117—21no—
381#117—21no—
382C2×C4⋊C4—861no—
383#107—21no—
384#107—21no—
385#107—431no—
386#107—861no—
387#107—861no—
388#107C22⋊D4311yescharacteristic
389#106—21no—
390#106—21no—
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—861no—
402#103—861no—
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—861no—
428C2×Q8—861no—
429C2×Q8—3441no—
430C2×Q8—1721no—
431C2×Q8—1722no—
432C2×Q8C2×C22⋊D4311yescharacteristic
433C2×Q8C2×C22⋊D4311yescharacteristic
434C2×D4—431no—
435C2×D4D4×D4311yescharacteristic
436C22×C4—21no—
437C22×C4—861no—
438C22×C4—1721no—
439C22×C4—1721no—
440Q16—41no—
441Q16—3441no—
442SD16—1722no—
443SD16—1722no—
444D8—862no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—861no—
450C2×C8—861no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—3441no—
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—431no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—1721no—
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—41no—
479C22⋊C4—41no—
480C22⋊C4—861no—
481C22⋊C4—1721no—
482C22⋊C4—1721no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42—41no—
487C42C23×D4311yescharacteristic
488C23—21no—
489C23—861no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—3441no—
499Q8—3442no—
500Q8—1721no—
501Q8—1721no—
502D4—21no—
503D4—21no—
504D4—432no—
505D4—861no—
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—861no—
516C2×C4—3442no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—6881no—
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—41no—
535C22—41no—
536C22—41no—
537C22—862no—
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—
552C4#135×D4311yescharacteristic
553C4#1458369711yescharacteristic
554C4#1458370711yescharacteristic
555C4#1458371311yescharacteristic
556C2—81no—
557C2—1722no—
558C2#1914612111yescharacteristic
559C2#1914633011yescharacteristic
560C2#1914636611yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3342C2
socleC22×C43D42
prime radicalC2×#10621882D4
hypercenter#3342D43
hypocenterC43#19839
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3342

Complements

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

NH ≅ G/Ntype
3. #19146473C2semidirect
4. #19134240C2semidirect
5. #19134175C2semidirect
6. #19134046C2semidirect
7. #19134023C2semidirect
8. #19133981C2semidirect
9. #19133865C2semidirect
10. #19133857C2semidirect
11. #19133801C2semidirect
12. #19133767C2semidirect
13. #19133446C2semidirect
15. C43×#3342C2semidirect
278. #3342D43semidirect
347. C43#19839semidirect

Maximal subgroups

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

subgroupindex
#191473092
#191472402
#191464732
#191342402
#191341752
#191340462
#191340232
#191339812
#191338652
#191338572
#191338012
#191337672
#191334462
#191334172
C43×#33422
#1983943