Finite Group Databasebeta

← #25082118

Subgroups — #25082118

Order 11008.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144751C211yesmaximal, characteristic, complemented
2#19144649C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic, complemented
4#19134036C211yesmaximal, characteristic, complemented
5#19134029C211yesmaximal, characteristic, complemented
6#19134008C211yesmaximal, characteristic, complemented
7#19134001C211yesmaximal, characteristic, complemented
8#19133996C211yesmaximal, characteristic, complemented
9#19133991C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133967C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3228C211yesmaximal, characteristic, complemented
16C4×#10621898C2211yescharacteristic
17#14583237—21no—
18#14583220—21no—
19#14583191C2211yescharacteristic
20#14583191C2211yescharacteristic
21#14583186C2211yescharacteristic
22#14583186C2211yescharacteristic
23#14583106C2211yescharacteristic
24#14583101C2211yescharacteristic
25#14583096C2211yescharacteristic
26#14583091C2211yescharacteristic
27#14583059—21no—
28#14583042—21no—
29C8×Dic86C2211yescharacteristic
30C8×Dic86C2211yescharacteristic
31#14583004—21no—
32#14582997—21no—
33C4×#10621883—21no—
34C4×#10621882—21no—
35C8×D172C2211yescharacteristic
36C8×D172C2211yescharacteristic
37(C22⋊D43)⋊C8—21no—
38(C22⋊D43)⋊C8—21no—
39#14582956C2211yescharacteristic
40#14582952C2211yescharacteristic
41#14582951—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C4⋊C8×D43—21no—
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582648C2211yescharacteristic
51#14582648C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#532C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#498C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#482—21no—
63C43×#482—21no—
64C43×#478—21no—
65C43×#478—21no—
66C43×#431C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74C2×C8×D43—21no—
75C4×Dic86D411yescharacteristic
76C4×Dic86C2311yescharacteristic
77C4×D172D411yescharacteristic
78C4×D172C2311yescharacteristic
79C4×C22⋊D43—21no—
80C4×C22⋊D43—21no—
81#13063284D411yescharacteristic
82#13063282—21no—
83C42×D43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—21no—
89C4⋊(C43⋊C8)C2311yescharacteristic
90C4⋊(C43⋊C8)C2311yescharacteristic
91C4⋊(C43⋊C8)C2311yescharacteristic
92C4⋊(C43⋊C8)C2311yescharacteristic
93C4⋊(C43⋊C8)C2311yescharacteristic
94C4⋊(C43⋊C8)C2311yescharacteristic
95Dic43⋊C8—21no—
96Dic43⋊C8—21no—
97#13063249—21no—
98#13063249—21no—
99#13063248—21no—
100#13063248—21no—
101#13063246—21no—
102#13063246—21no—
103#13063245—21no—
104#13063245—21no—
105C22⋊(C43⋊C8)—21no—
106C22⋊(C43⋊C8)—21no—
107(C2×D43)⋊C8—21no—
108(C2×D43)⋊C8—21no—
109#13063236—21no—
110C4×C43⋊C8—21no—
111C8×Dic43—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C4⋊Q8×C43C2311yescharacteristic
115C4⋊Q8×C43C2311yescharacteristic
116C4⋊Q8×C43C2311yescharacteristic
117#127×C43C2311yescharacteristic
118#125×C43—21no—
119#124×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122#121×C43—21no—
123#121×C43—21no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×D4×C43—21no—
127C4×D4×C43—21no—
128#117×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#107×C43—21no—
131#107×C43—21no—
132#106×C43—21no—
133#106×C43—21no—
134C4⋊C8×C43D411yescharacteristic
135C4⋊C8×C43D411yescharacteristic
136#102×C43—21no—
137#102×C43—21no—
138#102×C43—21no—
139#102×C43—21no—
140C22⋊C8×C43D411yescharacteristic
141C22⋊C8×C43D411yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×Q8×C43—21no—
147C2×Q8×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—21no—
150C2×D4×C43—21no—
151C2×D4×C43—41no—
152C22×C4×C43—41no—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43C2×D411yescharacteristic
155C22×C4×C43#4111yescharacteristic
156C2×C22⋊D43—21no—
157#10621898—22no—
158#10621898—22no—
159C2×D172C2×D411yescharacteristic
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C4×D43—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C2×C8×C43C2×D411yescharacteristic
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—41no—
175C4⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C22⋊C4×C43—41no—
178C22⋊C4×C43—41no—
179C42×C43—41no—
180C42×C43C2×D411yescharacteristic
181C42×C43C2×D411yescharacteristic
182C42×C43#4111yescharacteristic
183C42×C43C2411yescharacteristic
184C22⋊Dic43—21no—
185#10621885—42no—
186#10621884—42no—
187#10621883—42no—
188#10621882—42no—
189(C2×D43)⋊C4—21no—
190(C2×D43)⋊C4—21no—
191C4⋊Dic43C2×D411yescharacteristic
192C4⋊Dic43C2×D411yescharacteristic
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—81no—
205C8×D43—81no—
206C8×D43—81no—
207C23×C43—41no—
208C23×C43#12111yescharacteristic
209C22×D43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213Q8×C43—81no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—41no—
218D4×C43—81no—
219D4×C43—82no—
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#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C22⋊D43—24no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239D172—21no—
240D172#13512yes—
241C4×D43—24no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—81no—
245Dic86—21no—
246Dic86#13512yes—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—22no—
266C2×D43—41no—
267C2×D43—41no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—81no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43C2×#13511yescharacteristic
276C4×C43C2×#13511yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—22no—
280Dic43—41no—
281Dic43—41no—
282#3228D4311yescharacteristic, complemented
283#3116—431no—
284#3106—431no—
285#2988—431no—
286#1682—431no—
287#1681—431no—
288#1678—431no—
289#1677—431no—
290#1676—431no—
291#1675—431no—
292#1672—431no—
293#1671—431no—
294#1572—431no—
295#1551—431no—
296#1542—431no—
297C2×C43—41no—
298C2×C43—161no—
299C2×C43#304611yescharacteristic
300C2×C43#305011yescharacteristic
301C2×C43#306811yescharacteristic
302D43—42no—
303#533C2×D4311yescharacteristic
304#532C2×D4311yescharacteristic
305C4×#41—431no—
306#500C2×D4311yescharacteristic
307#498C2×D4311yescharacteristic
308#486C2×D4311yescharacteristic
309#486C2×D4311yescharacteristic
310#485—861no—
311#482—21no—
312#482—21no—
313#482—861no—
314#478—21no—
315#478—21no—
316#477—431no—
317#477—431no—
318#476—431no—
319#476—431no—
320#462—431no—
321#461—431no—
322#460—431no—
323#459—431no—
324#452—861no—
325#449—861no—
326C8×Q8—431no—
327C8×Q8—431no—
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—431no—
333C8×D4—431no—
334C8×D4—861no—
335C8×D4—861no—
336#432—431no—
337#431—431no—
338#431—861no—
339#431C2×D4311yescharacteristic
340C2×C4⋊C8—431no—
341C2×C4⋊C8—861no—
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333—431no—
349#333—431no—
350#332—431no—
351#332—431no—
352#331—431no—
353#331—431no—
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C2×#41—431no—
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—861no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8C22×D4311yescharacteristic
365C4⋊Q8C22×D4311yescharacteristic
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372#121—21no—
373#121—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—431no—
377C4×Q8—431no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—431no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384#117—21no—
385#117—431no—
386#117—861no—
387C2×C42—861no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—21no—
391#107—861no—
392#107—861no—
393#106—21no—
394#106—21no—
395#106—861no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8—861no—
406C4⋊C8C22⋊D4311yescharacteristic
407C4⋊C8C22⋊D4311yescharacteristic
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8C22⋊D4311yescharacteristic
425C22⋊C8C22⋊D4311yescharacteristic
426#97—861no—
427C4×C8—861no—
428C4×C8—861no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432#41—82no—
433#41—862no—
434#41—862no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—431no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—41no—
443C2×D4—431no—
444C2×D4—861no—
445C22×C4—41no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4D4×D4311yescharacteristic
450C22×C4#1062190011yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452Q16—1722no—
453SD16—1722no—
454SD16—1722no—
455D8—1722no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C2×C8—3441no—
464C2×C8—3441no—
465C2×C8C2×C22⋊D4311yescharacteristic
466C2×C8C2×C22⋊D4311yescharacteristic
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—431no—
478C4⋊C4—431no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C42—41no—
488C42—861no—
489C42—861no—
490C42—861no—
491C42D4×D4311yescharacteristic
492C42#1062190011yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—41no—
496C23—861no—
497C23#1306329611yescharacteristic
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502Q8—432no—
503Q8—861no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—82no—
510D4—432no—
511D4—864no—
512D4—861no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—82no—
522C2×C4—864no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—3441no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329611yescharacteristic
530C2×C4#1306329611yescharacteristic
531C2×C4#1306329611yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C22×C22⋊D4311yescharacteristic
534C2×C4C2×#1062190011yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—1721no—
540C8—1721no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—862no—
552C22—1721no—
553C22—1721no—
554C22C2×#1306329611yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—862no—
563C4—1721no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4#135×D4311yescharacteristic
567C4#1458370711yescharacteristic
568C4#1458371411yescharacteristic
569C2—41no—
570C2—161no—
571C2—1722no—
572C2#1914414111yescharacteristic
573C2#1914417211yescharacteristic
574C2#1914431911yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3228C2
socleC22×C43C2×#121
prime radical#19144649C2
hypercenter#3228D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3228

Complements

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

NH ≅ G/Ntype
1. #19144751C2semidirect
3. #19143703C2semidirect
4. #19134036C2semidirect
5. #19134029C2semidirect
6. #19134008C2semidirect
7. #19134001C2semidirect
8. #19133996C2semidirect
9. #19133991C2semidirect
10. #19133974C2semidirect
11. #19133967C2semidirect
12. #19133375C2semidirect
13. #19133290C2semidirect
14. #19133252C2semidirect
15. C43×#3228C2semidirect
282. #3228D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191447512
#191446492
#191437032
#191340362
#191340292
#191340082
#191340012
#191339962
#191339912
#191339742
#191339672
#191333752
#191332902
#191332522
C43×#32282
#1941943