Finite Group Databasebeta

← #25082124

Subgroups — #25082124

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#19145733C211yesmaximal, characteristic, complemented
2#19144757C211yesmaximal, characteristic, complemented
3#19144655C211yesmaximal, characteristic
4#19134039C211yesmaximal, characteristic, complemented
5#19134032C211yesmaximal, characteristic, complemented
6#19134011C211yesmaximal, characteristic, complemented
7#19134004C211yesmaximal, characteristic, complemented
8#19133999C211yesmaximal, characteristic, complemented
9#19133994C211yesmaximal, characteristic, complemented
10#19133977C211yesmaximal, characteristic, complemented
11#19133970C211yesmaximal, characteristic, complemented
12#19133375C211yesmaximal, characteristic, complemented
13#19133288C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#2988C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17#14583449C2211yescharacteristic
18#14583304C2211yescharacteristic
19#14583297C2211yescharacteristic
20#14583246C2211yescharacteristic
21#14583246C2211yescharacteristic
22#14583240—21no—
23#14583224—21no—
24#14583224—21no—
25#14583223—21no—
26#14583200—21no—
27#14583200—21no—
28#14583194C2211yescharacteristic
29#14583194C2211yescharacteristic
30#14583189C2211yescharacteristic
31#14583189C2211yescharacteristic
32#14583109C2211yescharacteristic
33#14583104C2211yescharacteristic
34#14583099C2211yescharacteristic
35#14583094C2211yescharacteristic
36#14583061—21no—
37#14583044—21no—
38#14583004—21no—
39#14582999—21no—
40C4×#10621884—21no—
41C4×#10621882—21no—
42#14582956C2211yescharacteristic
43#14582952C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C4×#41×C43C2211yescharacteristic
57C8×Q8×C43C2211yescharacteristic
58C8×Q8×C43C2211yescharacteristic
59C8×D4×C43—21no—
60C8×D4×C43—21no—
61C8×D4×C43C2211yescharacteristic
62C8×D4×C43C2211yescharacteristic
63C43×#431—21no—
64C43×#431C2211yescharacteristic
65C2×C4⋊C8×C43—21no—
66C2×C4⋊C8×C43C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621885—21no—
69C2×#10621883—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063322C2311yescharacteristic
76#13063317—21no—
77#13063313—21no—
78#13063304—21no—
79#13063304—21no—
80#13063299—21no—
81#13063299—21no—
82C4×Dic86—21no—
83C4×Dic86—21no—
84C4×D172—21no—
85C4×D172—21no—
86#13063284—21no—
87#13063259—21no—
88#13063259—21no—
89#13063258—21no—
90#13063258—21no—
91#13063257—21no—
92#13063257—21no—
93#13063256—21no—
94#13063256—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98C4⋊(C43⋊C8)C2311yescharacteristic
99#13063249—21no—
100#13063249—21no—
101#13063248—21no—
102#13063248—21no—
103#13063247—21no—
104#13063247—21no—
105#13063247—21no—
106#13063247—21no—
107#13063246—21no—
108#13063246—21no—
109#13063245—21no—
110#13063245—21no—
111C22⋊(C43⋊C8)—21no—
112C22⋊(C43⋊C8)—21no—
113#13063236—21no—
114C4×C43⋊C8—21no—
115C2×#41×C43D411yescharacteristic
116C22×C8×C43—21no—
117C22×C8×C43—21no—
118C22×C8×C43—21no—
119C4×Q8×C43D411yescharacteristic
120C4×Q8×C43C2311yescharacteristic
121C4×D4×C43—21no—
122C4×D4×C43—21no—
123C4×D4×C43D411yescharacteristic
124C4×D4×C43C2311yescharacteristic
125#117×C43—21no—
126#117×C43D411yescharacteristic
127C2×C42×C43—21no—
128C2×C42×C43C2311yescharacteristic
129C4⋊C8×C43—21no—
130C4⋊C8×C43—21no—
131C4⋊C8×C43—21no—
132C4⋊C8×C43D411yescharacteristic
133C4⋊C8×C43D411yescharacteristic
134C4⋊C8×C43C2311yescharacteristic
135C4⋊C8×C43C2311yescharacteristic
136C22⋊C8×C43—21no—
137C22⋊C8×C43—21no—
138C22⋊C8×C43D411yescharacteristic
139C22⋊C8×C43D411yescharacteristic
140C4×C8×C43—21no—
141C4×C8×C43—21no—
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144#41×C43—22no—
145#41×C43—22no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4111yescharacteristic
155C2×C22⋊D43—41no—
156#10621898—82no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×C4×D43—41no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—81no—
167C2×C8×C43—81no—
168C2×C8×C43—81no—
169C2×C8×C43C2×D411yescharacteristic
170C2×C8×C43C2×D411yescharacteristic
171C2×C8×C43C2×D411yescharacteristic
172C2×C8×C43C2×D411yescharacteristic
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43C2×D411yescharacteristic
176C4⋊C4×C43C2×D411yescharacteristic
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—21no—
183C42×C43C2×D411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43#4111yescharacteristic
186C42×C43C2411yescharacteristic
187C22⋊Dic43—41no—
188#10621885—42no—
189#10621884—42no—
190#10621883—42no—
191#10621882—42no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200Dic43⋊C4—41no—
201Dic43⋊C4—41no—
202C4×Dic43—41no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209C22×D43—41no—
210Q8×C43—21no—
211Q8×C43#13512yes—
212D4×C43—24no—
213D4×C43—21no—
214D4×C43#13512yes—
215C2×C4×C43—24no—
216C2×C4×C43—21no—
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×C43—41no—
226C2×C4×C43—81no—
227C2×C4×C43#12111yescharacteristic
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43C22×D411yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C22⋊D43—82no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237D172—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—81no—
242C4×D43—82no—
243Dic86—41no—
244Dic86—41no—
245Dic86—81no—
246Dic86—81no—
247C8×C43—21no—
248C8×C43—21no—
249C8×C43—21no—
250C8×C43—21no—
251C8×C43—41no—
252C8×C43—41no—
253C43⋊C8—41no—
254C43⋊C8—41no—
255C43⋊C8—41no—
256C43⋊C8—41no—
257#19419—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—22no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43C2×#12111yescharacteristic
265C2×D43—81no—
266C2×D43—81no—
267C2×D43—81no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—22no—
271C4×C43—21no—
272C4×C43—21no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43C2×#13511yescharacteristic
276C4×C43C2×#13511yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—81no—
280Dic43—81no—
281Dic43—81no—
282#3228—431no—
283#3116—431no—
284#3106—431no—
285#2988D4311yescharacteristic, complemented
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—42no—
299C2×C43#304611yescharacteristic
300C2×C43#305011yescharacteristic
301C2×C43#306811yescharacteristic
302D43—161no—
303#533—431no—
304#532—431no—
305C4×#41C2×D4311yescharacteristic
306#500—431no—
307#498—431no—
308#486—431no—
309#486—431no—
310#485—861no—
311#482—861no—
312#482—861no—
313#482—861no—
314#478—861no—
315#478—861no—
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×Q8C2×D4311yescharacteristic
327C8×Q8C2×D4311yescharacteristic
328#441—861no—
329#440—861no—
330C4×SD16—861no—
331C4×D8—861no—
332C8×D4—21no—
333C8×D4—21no—
334C8×D4C2×D4311yescharacteristic
335C8×D4C2×D4311yescharacteristic
336#432—431no—
337#431—21no—
338#431—431no—
339#431C2×D4311yescharacteristic
340C2×C4⋊C8—21no—
341C2×C4⋊C8C2×D4311yescharacteristic
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—861no—
356C2×#41D17211yescharacteristic
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8—431no—
367#127—431no—
368#125—861no—
369#124—861no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—861no—
373#121—861no—
374C4×Q8—861no—
375C4×Q8—861no—
376C4×Q8D17211yescharacteristic
377C4×Q8C22×D4311yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—861no—
381C4×D4—861no—
382C4×D4D17211yescharacteristic
383C4×D4C22×D4311yescharacteristic
384#117—21no—
385#117—861no—
386#117D17211yescharacteristic
387C2×C42—21no—
388C2×C42C22×D4311yescharacteristic
389#107—861no—
390#107—861no—
391#107—861no—
392#107—861no—
393#106—861no—
394#106—861no—
395#106—861no—
396#106—861no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—431no—
403C4⋊C8—431no—
404C4⋊C8C22⋊D4311yescharacteristic
405C4⋊C8C22⋊D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407C4⋊C8C22×D4311yescharacteristic
408#103—861no—
409#103—861no—
410#103—861no—
411#103—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419#102—861no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424C22⋊C8C22⋊D4311yescharacteristic
425C22⋊C8C22⋊D4311yescharacteristic
426#97—861no—
427C4×C8—21no—
428C4×C8—21no—
429C4×C8—861no—
430C4×C8C22×D4311yescharacteristic
431C4×C8C22×D4311yescharacteristic
432#41—22no—
433#41—22no—
434#41—3442no—
435C2×Q8—861no—
436C2×Q8—861no—
437C2×Q8—861no—
438C2×Q8C2×D17211yescharacteristic
439C2×D4—21no—
440C2×D4—861no—
441C2×D4—861no—
442C2×D4—861no—
443C2×D4—1721no—
444C2×D4C2×D17211yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—1721no—
449C22×C4C2×D17211yescharacteristic
450C22×C4#1062189811yescharacteristic
451C22×C4C2×C22⋊D4311yescharacteristic
452Q16—1722no—
453SD16—1722no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—81no—
459C2×C8—81no—
460C2×C8—81no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8C2×C22⋊D4311yescharacteristic
466C2×C8C2×C22⋊D4311yescharacteristic
467C2×C8C2×C22⋊D4311yescharacteristic
468C2×C8C2×C22⋊D4311yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1721no—
478C4⋊C4—1721no—
479C4⋊C4C2×D17211yescharacteristic
480C4⋊C4C2×D17211yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—1721no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—1721no—
491C42C2×D17211yescharacteristic
492C42#1062189811yescharacteristic
493C42C2×C22⋊D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—21no—
496C23—1721no—
497C23#1306329911yescharacteristic
498Q8—21no—
499Q8—3441no—
500Q8—3441no—
501Q8—1721no—
502Q8—1721no—
503Q8#1306334712yes—
504D4—24no—
505D4—21no—
506D4—3441no—
507D4—3442no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511D4—1721no—
512D4#1306334712yes—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—81no—
525C2×C4—3442no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329911yescharacteristic
530C2×C4#1306329911yescharacteristic
531C2×C4#1306329911yescharacteristic
532C2×C4C22×C22⋊D4311yescharacteristic
533C2×C4C22×D17211yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—1721no—
542C8—1721no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—22no—
549C22—41no—
550C22—41no—
551C22—3441no—
552C22—3441no—
553C22—3441no—
554C22C2×#1306329911yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—22no—
560C4—41no—
561C4—41no—
562C4—3441no—
563C4—3441no—
564C4—3441no—
565C4C2×#1306334711yescharacteristic
566C4C2×#1306334711yescharacteristic
567C4#1458371011yescharacteristic
568C4#1458371411yescharacteristic
569C2—41no—
570C2—42no—
571C2—6881no—
572C2#1914414511yescharacteristic
573C2#1914417611yescharacteristic
574C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#2988C2
socleC22×C43C2×#121
prime radical#19144655C2
hypercenter#2988D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2988

Complements

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

NH ≅ G/Ntype
1. #19145733C2semidirect
2. #19144757C2semidirect
4. #19134039C2semidirect
5. #19134032C2semidirect
6. #19134011C2semidirect
7. #19134004C2semidirect
8. #19133999C2semidirect
9. #19133994C2semidirect
10. #19133977C2semidirect
11. #19133970C2semidirect
12. #19133375C2semidirect
13. #19133288C2semidirect
14. #19133253C2semidirect
15. C43×#2988C2semidirect
285. #2988D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457332
#191447572
#191446552
#191340392
#191340322
#191340112
#191340042
#191339992
#191339942
#191339772
#191339702
#191333752
#191332882
#191332532
C43×#29882
#1941943