Finite Group Databasebeta

← #25082122

Subgroups — #25082122

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#19145727C211yesmaximal, characteristic, complemented
2#19144758C211yesmaximal, characteristic, complemented
3#19144649C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic, complemented
5#19134038C211yesmaximal, characteristic, complemented
6#19134031C211yesmaximal, characteristic, complemented
7#19134010C211yesmaximal, characteristic, complemented
8#19134003C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133993C211yesmaximal, characteristic, complemented
11#19133980C211yesmaximal, characteristic, complemented
12#19133973C211yesmaximal, characteristic, complemented
13#19133376C211yesmaximal, characteristic, complemented
14#19133253C211yesmaximal, characteristic, complemented
15C43×#1551C211yesmaximal, characteristic, complemented
16#14583456C2211yescharacteristic
17C4×#10621898C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583295C2211yescharacteristic
20#14583245C2211yescharacteristic
21#14583245C2211yescharacteristic
22#14583241—21no—
23#14583220—21no—
24#14583220—21no—
25#14583220—21no—
26#14583199—21no—
27#14583199—21no—
28#14583195C2211yescharacteristic
29#14583191C2211yescharacteristic
30#14583190C2211yescharacteristic
31#14583186C2211yescharacteristic
32#14583110C2211yescharacteristic
33#14583105C2211yescharacteristic
34#14583096C2211yescharacteristic
35#14583091C2211yescharacteristic
36#14583063—21no—
37#14583042—21no—
38#14583023C2211yescharacteristic
39#14583023C2211yescharacteristic
40#14583007—21no—
41#14583001—21no—
42C4×#10621883—21no—
43C4×#10621882—21no—
44#14582964C2211yescharacteristic
45#14582964C2211yescharacteristic
46C8×C22⋊D43—21no—
47C8×C22⋊D43—21no—
48#14582952C2211yescharacteristic
49#14582952C2211yescharacteristic
50#14582951—21no—
51C4⋊C8×D43—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621898D411yescharacteristic
68C2×Dic172—21no—
69C2×#10621873—21no—
70C2×#10621883—21no—
71C2×#10621882—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063317—21no—
77#13063304—21no—
78#13063304—21no—
79C4×Dic86—21no—
80C4×Dic86—21no—
81C4×Dic86D411yescharacteristic
82C4×Dic86C2311yescharacteristic
83C4×D172D411yescharacteristic
84C4×D172C2311yescharacteristic
85C4×C22⋊D43—21no—
86C4×C22⋊D43—21no—
87#13063284—21no—
88#13063284D411yescharacteristic
89#13063282—21no—
90C42×D43—21no—
91#13063259—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063257—21no—
96#13063256—21no—
97#13063256—21no—
98#13063256—21no—
99C4⋊(C43⋊C8)D411yescharacteristic
100C4⋊(C43⋊C8)D411yescharacteristic
101C4⋊(C43⋊C8)C2311yescharacteristic
102C4⋊(C43⋊C8)C2311yescharacteristic
103Dic43⋊C8—21no—
104Dic43⋊C8—21no—
105#13063250—21no—
106#13063250—21no—
107#13063250—21no—
108#13063248—21no—
109#13063247—21no—
110#13063246—21no—
111#13063246—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063245—21no—
117C22⋊(C43⋊C8)—21no—
118C22⋊(C43⋊C8)D411yescharacteristic
119C22⋊(C43⋊C8)D411yescharacteristic
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×#41×C43—21no—
128C22×C8×C43—21no—
129C4⋊Q8×C43C2311yescharacteristic
130#127×C43C2311yescharacteristic
131#124×C43—21no—
132#121×C43—21no—
133#121×C43—21no—
134C4×D4×C43—21no—
135C4×D4×C43—21no—
136C2×C42×C43C2311yescharacteristic
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C4⋊C8×C43C2311yescharacteristic
141C4⋊C8×C43C2311yescharacteristic
142C22⋊C8×C43—21no—
143#97×C43—21no—
144#41×C43—82no—
145C2×Q8×C43—21no—
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×D4×C43—41no—
150C22×C4×C43—41no—
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43C2×D411yescharacteristic
153C22×C4×C43#4111yescharacteristic
154C2×C22⋊D43—21no—
155#10621898—22no—
156#10621898—22no—
157C2×D172C2×D411yescharacteristic
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86C2×D411yescharacteristic
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—81no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C22⋊C4×C43—41no—
172C22⋊C4×C43—41no—
173C42×C43C2×D411yescharacteristic
174C42×C43C2×D411yescharacteristic
175C42×C43#4111yescharacteristic
176C42×C43C2411yescharacteristic
177C22⋊Dic43—21no—
178C22⋊Dic43—41no—
179#10621883—42no—
180#10621882—42no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43C2×D411yescharacteristic
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203Dic172—42no—
204#10621873—42no—
205C8×D43—81no—
206C8×D43—81no—
207C23×C43—41no—
208C23×C43#12111yescharacteristic
209C22×D43—21no—
210Q8×C43—81no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—81no—
216D4×C43—82no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—82no—
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43#12111yescharacteristic
226C2×C4×C43#12111yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C22⋊D43—24no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236D172—21no—
237D172#13512yes—
238C4×D43—24no—
239C4×D43—41no—
240C4×D43—41no—
241C4×D43—81no—
242Dic86—21no—
243Dic86—41no—
244Dic86—41no—
245Dic86—81no—
246Dic86#13512yes—
247C8×C43—41no—
248C8×C43—41no—
249C8×C43—41no—
250C8×C43—41no—
251C43⋊C8—21no—
252C43⋊C8—21no—
253C43⋊C8—21no—
254C43⋊C8—21no—
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×C43C2×#13511yescharacteristic
274C4×C43C2×#13511yescharacteristic
275C4×C43#57711yescharacteristic
276C4×C43#57811yescharacteristic
277Dic43—22no—
278Dic43—41no—
279Dic43—41no—
280Dic43—81no—
281Dic43—81no—
282#3228—431no—
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#1551D4311yescharacteristic, complemented
296#1542—431no—
297C2×C43—41no—
298C2×C43—161no—
299C2×C43#304611yescharacteristic
300C2×C43#305011yescharacteristic
301C2×C43#306811yescharacteristic
302D43—42no—
303#533—431no—
304#532C2×D4311yescharacteristic
305C4×#41—431no—
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×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#432C2×D4311yescharacteristic
337#431—431no—
338#431—431no—
339#431—861no—
340C2×C4⋊C8—861no—
341C2×C4⋊C8C2×D4311yescharacteristic
342#335—431no—
343#335—431no—
344#334—431no—
345#334—431no—
346#333—431no—
347#333—431no—
348#333C2×D4311yescharacteristic
349#333C2×D4311yescharacteristic
350#332—431no—
351#332—431no—
352#331C2×D4311yescharacteristic
353#331C2×D4311yescharacteristic
354C43#1941911yescharacteristic, complemented, Sylow
355C2×#41—21no—
356C2×#41—431no—
357C2×Q16—861no—
358C2×SD16—861no—
359C2×SD16—861no—
360C2×D8—861no—
361C22×C8—21no—
362C22×C8—861no—
363C22×C8—861no—
364C4⋊Q8—431no—
365C4⋊Q8—431no—
366C4⋊Q8C22×D4311yescharacteristic
367#127C22×D4311yescharacteristic
368#125—861no—
369#124—21no—
370C22⋊Q8—861no—
371C22⋊Q8—861no—
372#121—21no—
373#121—21no—
374C4×Q8—431no—
375C4×Q8—431no—
376C4×Q8—861no—
377C4×Q8—861no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—431no—
381C4×D4—431no—
382C4×D4—861no—
383C4×D4—861no—
384#117—431no—
385#117—861no—
386#117—861no—
387C2×C42—861no—
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—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—431no—
402C4⋊C8—861no—
403C4⋊C8—861no—
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—431no—
422C22⋊C8—431no—
423C22⋊C8—861no—
424C22⋊C8—861no—
425C22⋊C8—861no—
426#97—21no—
427C4×C8—431no—
428C4×C8—431no—
429C4×C8—861no—
430C4×C8—861no—
431C4×C8—861no—
432#41—82no—
433#41—862no—
434#41—862no—
435C2×Q8—21no—
436C2×Q8—431no—
437C2×Q8—861no—
438C2×Q8—861no—
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×C4#1062189811yescharacteristic
450C22×C4D4×D4311yescharacteristic
451C22×C4D4×D4311yescharacteristic
452Q16—1722no—
453SD16—1722no—
454SD16—1722no—
455D8—1722no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8—431no—
462C2×C8—431no—
463C2×C8—431no—
464C2×C8—431no—
465C2×C8—861no—
466C2×C8—861no—
467C2×C8—3441no—
468C2×C8—3441no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—431no—
472C4⋊C4—431no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—1721no—
480C4⋊C4—1721no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C22⋊C4—861no—
486C22⋊C4—1721no—
487C42—861no—
488C42—861no—
489C42—861no—
490C42—1721no—
491C42#1062189811yescharacteristic
492C42D4×D4311yescharacteristic
493C42D4×D4311yescharacteristic
494C42C23×D4311yescharacteristic
495C23—41no—
496C23—861no—
497C23#1306329811yescharacteristic
498Q8—81no—
499Q8—432no—
500Q8—861no—
501Q8—3441no—
502Q8—1721no—
503Q8—1721no—
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—82no—
520C2×C4—864no—
521C2×C4—861no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—3441no—
525C2×C4—1721no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4#1306329811yescharacteristic
530C2×C4#1306329811yescharacteristic
531C2×C4#1306329811yescharacteristic
532C2×C4C2×D4×D4311yescharacteristic
533C2×C4C2×D4×D4311yescharacteristic
534C2×C4C2×#1062189811yescharacteristic
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—861no—
540C8—861no—
541C8—861no—
542C8—861no—
543C8—1721no—
544C8—1721no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—81no—
549C22—81no—
550C22—81no—
551C22—862no—
552C22—1721no—
553C22—1721no—
554C22C2×#1306329811yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—81no—
560C4—862no—
561C4—3441no—
562C4—3441no—
563C4—1721no—
564C4—1721no—
565C4#135×D4311yescharacteristic
566C4#135×D4311yescharacteristic
567C4#1458370911yescharacteristic
568C4#1458371511yescharacteristic
569C2—41no—
570C2—161no—
571C2—1722no—
572C2#1914414411yescharacteristic
573C2#1914417511yescharacteristic
574C2#1914432211yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
prime radical#19144649C2
hypercenter#1551D43
hypocenterC43#19419
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
1. #19145727C2semidirect
2. #19144758C2semidirect
4. #19143704C2semidirect
5. #19134038C2semidirect
6. #19134031C2semidirect
7. #19134010C2semidirect
8. #19134003C2semidirect
9. #19133998C2semidirect
10. #19133993C2semidirect
11. #19133980C2semidirect
12. #19133973C2semidirect
13. #19133376C2semidirect
14. #19133253C2semidirect
15. C43×#1551C2semidirect
295. #1551D43semidirect
354. C43#19419semidirect

Maximal subgroups

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

subgroupindex
#191457272
#191447582
#191446492
#191437042
#191340382
#191340312
#191340102
#191340032
#191339982
#191339932
#191339802
#191339732
#191333762
#191332532
C43×#15512
#1941943