Finite Group Databasebeta

← #25079650

Subgroups — #25079650

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145336C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic
3#19143615C211yesmaximal, characteristic
4#19134168C211yesmaximal, characteristic, complemented
5#19134144C211yesmaximal, characteristic, complemented
6#19134092C211yesmaximal, characteristic, complemented
7#19134082C211yesmaximal, characteristic, complemented
8#19134051C211yesmaximal, characteristic, complemented
9#19134027C211yesmaximal, characteristic, complemented
10#19133975C211yesmaximal, characteristic, complemented
11#19133963C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133303C211yesmaximal, characteristic, complemented
14#19133295C211yesmaximal, characteristic, complemented
15C43×#3107C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583295C2211yescharacteristic
18#14583278C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583249C2211yescharacteristic
21#14583206—21no—
22#14583199—21no—
23#14583194C2211yescharacteristic
24#14583189C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583155—21no—
28#14583155—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14583004—21no—
32#14583004—21no—
33#14582977—21no—
34#14582977—21no—
35#14582977C2211yescharacteristic
36#14582977C2211yescharacteristic
37#14582956—21no—
38#14582956C2211yescharacteristic
39#14582935—21no—
40C2×C4⋊(C43⋊C8)C2211yescharacteristic
41#14582895—21no—
42C4×#10621877—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#485—21no—
59C43×#475C2211yescharacteristic
60C43×#474C2211yescharacteristic
61C43×#462C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#452—21no—
64C4×Q16×C43—21no—
65C4×SD16×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—21no—
69C2×#10621877—21no—
70C2×#10621877—21no—
71C2×#10621877D411yescharacteristic
72C2×#10621877D411yescharacteristic
73C22×C43⋊C8—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81#13063284—21no—
82#13063258—21no—
83#13063258—21no—
84#13063256—21no—
85#13063256—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)—21no—
90C4⋊(C43⋊C8)—21no—
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×#41×C43D411yescharacteristic
114C2×Q16×C43—21no—
115C2×SD16×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#125×C43—21no—
119C22⋊Q8×C43—21no—
120C22⋊Q8×C43—21no—
121C4×Q8×C43—21no—
122C4×Q8×C43—21no—
123C4×Q8×C43D411yescharacteristic
124C4×Q8×C43C2311yescharacteristic
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43D411yescharacteristic
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131#117×C43D411yescharacteristic
132C2×C42×C43—21no—
133C2×C42×C43C2311yescharacteristic
134#107×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—22no—
145#41×C43—41no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43C2×D411yescharacteristic
151C22×C4×C43—21no—
152C22×C4×C43—21no—
153C22×C4×C43—21no—
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43C2×D411yescharacteristic
156C22×C4×C43#4111yescharacteristic
157C2×Dic86—21no—
158C2×Dic86—21no—
159Q16×C43—42no—
160SD16×C43—42no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
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—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—41no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—41no—
181C42×C43C2×D411yescharacteristic
182C42×C43C2×D411yescharacteristic
183C42×C43#4111yescharacteristic
184C42×C43C2411yescharacteristic
185C22⋊Dic43—41no—
186#10621885—42no—
187#10621885—42no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—41no—
195#10621877—22no—
196#10621877—41no—
197#10621877—42no—
198#10621877—42no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—42no—
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C23×C43—21no—
209C23×C43#12111yescharacteristic
210Q8×C43—21no—
211Q8×C43—41no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43#13712yes—
216D4×C43—21no—
217D4×C43—21no—
218D4×C43—42no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—81no—
233C2×C4×C43#12111yescharacteristic
234C2×C4×C43#12111yescharacteristic
235C2×C4×C43#12111yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C2×#4111yescharacteristic
239C2×Dic43—41no—
240C2×Dic43—41no—
241Dic86—41no—
242Dic86—41no—
243Dic86—81no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8#13512yes—
254#19185—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43C2×#12111yescharacteristic
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—22no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—41no—
268C4×C43—41no—
269C4×C43—81no—
270C4×C43—81no—
271C4×C43C2×#13511yescharacteristic
272C4×C43C2×#13711yescharacteristic
273C4×C43#57511yescharacteristic
274C4×C43#57511yescharacteristic
275Dic43—81no—
276Dic43—81no—
277#3185—431no—
278#3107D4311yescharacteristic
279#3076—431no—
280#2971—431no—
281#1703—431no—
282#1699—431no—
283#1691—431no—
284#1689—431no—
285#1684—431no—
286#1680—431no—
287#1672—431no—
288#1670—431no—
289#1565—431no—
290#1554—431no—
291#1552—431no—
292C2×C43—41no—
293C2×C43—81no—
294C2×C43#303511yescharacteristic
295C2×C43#305611yescharacteristic
296C2×C43#306911yescharacteristic
297#533—431no—
298#533C2×D4311yescharacteristic
299C4×#41C2×D4311yescharacteristic
300#498—431no—
301#494—431no—
302#487—431no—
303#487—431no—
304#485—21no—
305#479—861no—
306#478—861no—
307#477—431no—
308#476—431no—
309#475—431no—
310#475C2×D4311yescharacteristic
311#474—431no—
312#474C2×D4311yescharacteristic
313#470—861no—
314#470—861no—
315#462C2×D4311yescharacteristic
316#461C2×D4311yescharacteristic
317#452—21no—
318C8×Q8—431no—
319C8×Q8—431no—
320#441—861no—
321#441—861no—
322C4×Q16—21no—
323C4×SD16—21no—
324#436—431no—
325#436—431no—
326#436—861no—
327#436—861no—
328#432—431no—
329#432—861no—
330#431C2×D4311yescharacteristic
331#427—861no—
332C2×C4⋊C8—431no—
333#416—861no—
334C4×M16—431no—
335C4×M16—861no—
336#335—431no—
337#335—431no—
338#334—431no—
339#334—431no—
340#333—431no—
341#333—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346#332—431no—
347#332—431no—
348C43#1918511yescharacteristic, complemented, Sylow
349C2×#41C22⋊D4311yescharacteristic
350C2×Q16—21no—
351C2×Q16—861no—
352C2×Q16—861no—
353C2×SD16—21no—
354C2×M16—431no—
355C2×M16—431no—
356C2×M16—861no—
357C2×M16—861no—
358C22×C8—861no—
359C4⋊Q8—431no—
360C4⋊Q8—431no—
361C4⋊Q8C22×D4311yescharacteristic
362C4⋊Q8C22×D4311yescharacteristic
363#125—21no—
364#125—861no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8C22⋊D4311yescharacteristic
374C4×Q8C22×D4311yescharacteristic
375C4×D4—21no—
376C4×D4—21no—
377C4×D4C22⋊D4311yescharacteristic
378C4×D4C22×D4311yescharacteristic
379#117—21no—
380#117—21no—
381#117—861no—
382#117C22⋊D4311yescharacteristic
383C2×C42—21no—
384C2×C42C22×D4311yescharacteristic
385#107—21no—
386#107—861no—
387#107—861no—
388#106—21no—
389#106—861no—
390#106—861no—
391#106—861no—
392#106—861no—
393C4⋊C8—431no—
394C4⋊C8—431no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—861no—
398C4⋊C8—861no—
399C4⋊C8—861no—
400C4⋊C8C22×D4311yescharacteristic
401C4⋊C8C22×D4311yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—861no—
413#102—861no—
414C22⋊C8—21no—
415C22⋊C8—861no—
416C22⋊C8—861no—
417C22⋊C8—861no—
418#97—431no—
419#97—431no—
420#97—861no—
421C4×C8—21no—
422C4×C8—431no—
423C4×C8—431no—
424C4×C8—861no—
425C4×C8—861no—
426#41—22no—
427#41—41no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—861no—
431C2×Q8—861no—
432C2×Q8C2×C22⋊D4311yescharacteristic
433C2×D4—21no—
434C2×D4C2×C22⋊D4311yescharacteristic
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4D4×D4311yescharacteristic
439C22×C4#1062190011yescharacteristic
440C22×C4C2×C22⋊D4311yescharacteristic
441Q16—42no—
442Q16—1722no—
443Q16—1722no—
444SD16—42no—
445M16—862no—
446M16—1722no—
447M16—1721no—
448M16—1722no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—1722no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C4⋊C4C2×C22⋊D4311yescharacteristic
475C4⋊C4C2×C22⋊D4311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C22⋊C4—1721no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—41no—
485C42—1721no—
486C42D4×D4311yescharacteristic
487C42#1062190011yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—21no—
491C23#1306329711yescharacteristic
492Q8—21no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—3441no—
498Q8—1721no—
499Q8—1721no—
500Q8#1306335512yes—
501D4—21no—
502D4—21no—
503D4—42no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—81no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4#1306329711yescharacteristic
521C2×C4#1306329711yescharacteristic
522C2×C4#1306329711yescharacteristic
523C2×C4C2×D4×D4311yescharacteristic
524C2×C4C22×C22⋊D4311yescharacteristic
525C2×C4C2×#1062190011yescharacteristic
526C8—41no—
527C8—41no—
528C8—432no—
529C8—861no—
530C8—861no—
531C8—861no—
532C8—1721no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×#1306329711yescharacteristic
543C4—21no—
544C4—22no—
545C4—21no—
546C4—21no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—81no—
551C4—81no—
552C4—3441no—
553C4—3441no—
554C4#135×D4311yescharacteristic
555C4C2×#1306335511yescharacteristic
556C4#1458369611yescharacteristic
557C4#1458369711yescharacteristic
558C2—41no—
559C2—81no—
560C2#1914404611yescharacteristic
561C2#1914422711yescharacteristic
562C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3107C2
socleC22×C43C2×#121
prime radicalC2×#41×C43D4
hypercenter#3107D43
hypocenterC43#19185
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3107

Complements

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

NH ≅ G/Ntype
1. #19145336C2semidirect
4. #19134168C2semidirect
5. #19134144C2semidirect
6. #19134092C2semidirect
7. #19134082C2semidirect
8. #19134051C2semidirect
9. #19134027C2semidirect
10. #19133975C2semidirect
11. #19133963C2semidirect
12. #19133348C2semidirect
13. #19133303C2semidirect
14. #19133295C2semidirect
348. C43#19185semidirect

Maximal subgroups

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

subgroupindex
#191453362
#191443832
#191436152
#191341682
#191341442
#191340922
#191340822
#191340512
#191340272
#191339752
#191339632
#191333482
#191333032
#191332952
C43×#31072
#1918543