Finite Group Databasebeta

← #25079620

Subgroups — #25079620

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145309C211yesmaximal, characteristic, complemented
2#19144383C211yesmaximal, characteristic, complemented
3#19143615C211yesmaximal, characteristic, complemented
4#19134172C211yesmaximal, characteristic, complemented
5#19134126C211yesmaximal, characteristic, complemented
6#19134116C211yesmaximal, characteristic, complemented
7#19134058C211yesmaximal, characteristic, complemented
8#19134055C211yesmaximal, characteristic, complemented
9#19134009C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133941C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133303C211yesmaximal, characteristic, complemented
14#19133290C211yesmaximal, characteristic, complemented
15C43×#3106C211yesmaximal, characteristic
16#14583456C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583271C2211yescharacteristic
19#14583251C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583206—21no—
22#14583199—21no—
23#14583194C2211yescharacteristic
24#14583189C2211yescharacteristic
25#14583184C2211yescharacteristic
26#14583179C2211yescharacteristic
27#14583143—21no—
28#14583143—21no—
29Q8×C43⋊C8C2211yescharacteristic
30Q8×C43⋊C8C2211yescharacteristic
31#14582999—21no—
32#14582999—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#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C4×#41×C43C2211yescharacteristic
58C43×#482—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#460C2211yescharacteristic
62C43×#459C2211yescharacteristic
63C43×#449—21no—
64C4×SD16×C43—21no—
65C4×D8×C43—21no—
66C43×#431C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621883—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#13063258—21no—
85#13063258—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#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—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×C43—21no—
114C2×#41×C43D411yescharacteristic
115C2×SD16×C43—21no—
116C2×D8×C43—21no—
117C4⋊Q8×C43C2311yescharacteristic
118#127×C43C2311yescharacteristic
119#124×C43—21no—
120#121×C43—21no—
121#121×C43—21no—
122C4×Q8×C43D411yescharacteristic
123C4×Q8×C43C2311yescharacteristic
124C4×D4×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128C4×D4×C43D411yescharacteristic
129C4×D4×C43C2311yescharacteristic
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#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144#41×C43—22no—
145#41×C43—41no—
146#41×C43—82no—
147C2×Q8×C43—21no—
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C2×D4×C43C2×D411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—41no—
159C22×C4×C43C2×D411yescharacteristic
160C22×C4×C43C2×D411yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C2×Dic86—21no—
163C2×Dic86—21no—
164SD16×C43—42no—
165D8×C43—42no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43#4111yescharacteristic
185C42×C43C2411yescharacteristic
186C22⋊Dic43—41no—
187#10621883—42no—
188#10621883—42no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—41no—
196#10621877—22no—
197#10621877—41no—
198#10621877—42no—
199#10621877—42no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—42no—
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C2×C43⋊C8C2×D411yescharacteristic
208C2×C43⋊C8C2×D411yescharacteristic
209C23×C43—21no—
210C23×C43—41no—
211C23×C43#12111yescharacteristic
212Q8×C43—21no—
213Q8×C43—81no—
214Q8×C43#13712yes—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—42no—
218D4×C43—41no—
219D4×C43—41no—
220D4×C43—41no—
221D4×C43—41no—
222D4×C43—81no—
223D4×C43—82no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43—82no—
238C2×C4×C43#12111yescharacteristic
239C2×C4×C43#12111yescharacteristic
240C2×C4×C43#12111yescharacteristic
241C2×C4×C43C22×D411yescharacteristic
242C2×C4×C43C22×D411yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×Dic43—41no—
245C2×Dic43—41no—
246Dic86—41no—
247Dic86—41no—
248Dic86—81no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257C43⋊C8—41no—
258C43⋊C8#13512yes—
259#19183—431nomaximal, Sylow
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43—81no—
267C22×C43—81no—
268C22×C43—81no—
269C22×C43C2×#12111yescharacteristic
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—22no—
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—41no—
276C4×C43—41no—
277C4×C43—81no—
278C4×C43C2×#13511yescharacteristic
279C4×C43C2×#13711yescharacteristic
280C4×C43#57511yescharacteristic
281C4×C43#57511yescharacteristic
282Dic43—81no—
283Dic43—81no—
284#3182—431no—
285#3106D4311yescharacteristic
286#3076—431no—
287#2971—431no—
288#1703—431no—
289#1697—431no—
290#1695—431no—
291#1685—431no—
292#1684—431no—
293#1678—431no—
294#1676—431no—
295#1666—431no—
296#1565—431no—
297#1554—431no—
298#1551—431no—
299C2×C43—41no—
300C2×C43—81no—
301C2×C43—161no—
302C2×C43#303511yescharacteristic
303C2×C43#305611yescharacteristic
304C2×C43#306811yescharacteristic
305#533—431no—
306#532C2×D4311yescharacteristic
307C4×#41C2×D4311yescharacteristic
308#500—431no—
309#492—431no—
310#487—431no—
311#486—431no—
312#482—21no—
313#479—861no—
314#478—861no—
315#477—431no—
316#477C2×D4311yescharacteristic
317#476—431no—
318#476C2×D4311yescharacteristic
319#475—431no—
320#474—431no—
321#468—861no—
322#468—861no—
323#460C2×D4311yescharacteristic
324#459C2×D4311yescharacteristic
325#449—21no—
326C8×Q8—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330C4×SD16—21no—
331C4×D8—21no—
332#436—431no—
333#436—431no—
334#436—861no—
335#436—861no—
336#432—431no—
337#432—861no—
338#431C2×D4311yescharacteristic
339#427—861no—
340C2×C4⋊C8—431no—
341#416—861no—
342C4×M16—431no—
343C4×M16—861no—
344#335—431no—
345#335—431no—
346#334—431no—
347#334—431no—
348#333—431no—
349#333—431no—
350#333—431no—
351#333—431no—
352#332—431no—
353#332—431no—
354#331—431no—
355#331—431no—
356C43#1918311yescharacteristic, complemented, Sylow
357C2×#41—21no—
358C2×#41C22⋊D4311yescharacteristic
359C2×SD16—21no—
360C2×SD16—861no—
361C2×SD16—861no—
362C2×D8—21no—
363C2×M16—431no—
364C2×M16—431no—
365C2×M16—861no—
366C2×M16—861no—
367C22×C8—861no—
368C4⋊Q8—431no—
369C4⋊Q8—431no—
370C4⋊Q8C22×D4311yescharacteristic
371#127C22×D4311yescharacteristic
372#125—861no—
373#124—21no—
374C22⋊Q8—861no—
375C22⋊Q8—861no—
376#121—21no—
377#121—21no—
378C4×Q8—861no—
379C4×Q8—861no—
380C4×Q8C22⋊D4311yescharacteristic
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4C22⋊D4311yescharacteristic
387C4×D4C22×D4311yescharacteristic
388#117—21no—
389#117—861no—
390#117C22⋊D4311yescharacteristic
391C2×C42—21no—
392C2×C42C22×D4311yescharacteristic
393#107—21no—
394#107—861no—
395#107—861no—
396#107—861no—
397#107—861no—
398#106—21no—
399#106—861no—
400#106—861no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8—431no—
405C4⋊C8—861no—
406C4⋊C8—861no—
407C4⋊C8—861no—
408C4⋊C8C22×D4311yescharacteristic
409C4⋊C8C22×D4311yescharacteristic
410#103—21no—
411#103—861no—
412#103—861no—
413#103—861no—
414#103—861no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—861no—
419#102—861no—
420#102—861no—
421#102—861no—
422C22⋊C8—21no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—431no—
427#97—431no—
428#97—861no—
429C4×C8—21no—
430C4×C8—431no—
431C4×C8—431no—
432C4×C8—861no—
433C4×C8—861no—
434#41—22no—
435#41—41no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—861no—
439C2×Q8—861no—
440C2×Q8C2×C22⋊D4311yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—41no—
446C2×D4C2×C22⋊D4311yescharacteristic
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—41no—
451C22×C4D4×D4311yescharacteristic
452C22×C4#1062190011yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454SD16—42no—
455SD16—1722no—
456SD16—1722no—
457D8—42no—
458M16—862no—
459M16—1722no—
460M16—1721no—
461M16—1722no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—431no—
465C2×C8—431no—
466C2×C8—431no—
467C2×C8—431no—
468C2×C8—861no—
469C2×C8—861no—
470C2×C8—861no—
471C2×C8—861no—
472C2×C8—1722no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4—1721no—
482C4⋊C4—1721no—
483C4⋊C4C2×C22⋊D4311yescharacteristic
484C4⋊C4C2×C22⋊D4311yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—1721no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—1721no—
495C42D4×D4311yescharacteristic
496C42#1062190011yescharacteristic
497C42C2×C22⋊D4311yescharacteristic
498C42C23×D4311yescharacteristic
499C23—21no—
500C23—41no—
501C23#1306329711yescharacteristic
502Q8—21no—
503Q8—81no—
504Q8—3441no—
505Q8—1721no—
506Q8—1721no—
507Q8#1306335512yes—
508D4—21no—
509D4—21no—
510D4—42no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—81no—
516D4—82no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—81no—
530C2×C4—82no—
531C2×C4—1721no—
532C2×C4—1721no—
533C2×C4#1306329711yescharacteristic
534C2×C4#1306329711yescharacteristic
535C2×C4#1306329711yescharacteristic
536C2×C4C2×D4×D4311yescharacteristic
537C2×C4C22×C22⋊D4311yescharacteristic
538C2×C4C2×#1062190011yescharacteristic
539C8—41no—
540C8—41no—
541C8—432no—
542C8—861no—
543C8—861no—
544C8—861no—
545C8—1721no—
546C8—1721no—
547C8—1721no—
548C8—1721no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22C2×#1306329711yescharacteristic
559C4—21no—
560C4—22no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—41no—
565C4—41no—
566C4—81no—
567C4—3441no—
568C4—3441no—
569C4#135×D4311yescharacteristic
570C4C2×#1306335511yescharacteristic
571C4#1458369611yescharacteristic
572C4#1458369711yescharacteristic
573C2—41no—
574C2—81no—
575C2—161no—
576C2#1914404611yescharacteristic
577C2#1914422711yescharacteristic
578C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3106C2
socleC22×C43C2×#121
hypercenter#3106D43
hypocenterC43#19183
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #19145309C2semidirect
2. #19144383C2semidirect
3. #19143615C2semidirect
4. #19134172C2semidirect
5. #19134126C2semidirect
6. #19134116C2semidirect
7. #19134058C2semidirect
8. #19134055C2semidirect
9. #19134009C2semidirect
10. #19133997C2semidirect
11. #19133941C2semidirect
12. #19133348C2semidirect
13. #19133303C2semidirect
14. #19133290C2semidirect
356. C43#19183semidirect

Maximal subgroups

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

subgroupindex
#191453092
#191443832
#191436152
#191341722
#191341262
#191341162
#191340582
#191340552
#191340092
#191339972
#191339412
#191333482
#191333032
#191332902
C43×#31062
#1918343