Finite Group Databasebeta

← #25084222

Subgroups — #25084222

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145915C211yesmaximal, characteristic
2#19145818C211yesmaximal, characteristic, complemented
3#19145713C211yesmaximal, characteristic, complemented
4#19143751C211yesmaximal, characteristic, complemented
5#19134134C211yesmaximal, characteristic, complemented
6#19134127C211yesmaximal, characteristic, complemented
7#19134122C211yesmaximal, characteristic, complemented
8#19134117C211yesmaximal, characteristic, complemented
9#19134010C211yesmaximal, characteristic, complemented
10#19134003C211yesmaximal, characteristic, complemented
11#19133998C211yesmaximal, characteristic, complemented
12#19133993C211yesmaximal, characteristic, complemented
13#19133381C211yesmaximal, characteristic, complemented
14C2×#14582647C211yesmaximal, characteristic, complemented
15C43×#1551C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583308—21no—
19#14583302C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583259—21no—
22#14583245C2211yescharacteristic
23#14583245C2211yescharacteristic
24#14583230—21no—
25#14583213—21no—
26#14583210—21no—
27#14583210—21no—
28#14583199—21no—
29#14583195C2211yescharacteristic
30#14583195C2211yescharacteristic
31#14583191C2211yescharacteristic
32#14583190C2211yescharacteristic
33#14583190C2211yescharacteristic
34#14583186C2211yescharacteristic
35#14583179—21no—
36#14583179—21no—
37#14583133—21no—
38#14583126—21no—
39#14583114—21no—
40#14583096C2211yescharacteristic
41#14583091C2211yescharacteristic
42#14583026C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14582976C2211yescharacteristic
45#14582970—21no—
46#14582964C2211yescharacteristic
47C8×C22⋊D43—21no—
48#14582959—21no—
49#14582952C2211yescharacteristic
50#14582924—21no—
51C2×C4⋊(C43⋊C8)C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582647C2211yescharacteristic
59#14582647C2211yescharacteristic
60C43×#532C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C2×C4⋊C8×C43C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#331C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621883—21no—
69C2×#10621882—21no—
70C2×#10621872—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325—21no—
76#13063325C2311yescharacteristic
77#13063325C2311yescharacteristic
78#13063319—21no—
79#13063317D411yescharacteristic
80#13063313D411yescharacteristic
81#13063308—21no—
82#13063304D411yescharacteristic
83#13063299D411yescharacteristic
84C4×Dic86C2311yescharacteristic
85C4×D172C2311yescharacteristic
86C4×C22⋊D43—21no—
87#13063282—21no—
88C2×C4⋊Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063259—21no—
91#13063259—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063257—21no—
98#13063257—21no—
99#13063256—21no—
100C4⋊(C43⋊C8)—21no—
101C4⋊(C43⋊C8)D411yescharacteristic
102C4⋊(C43⋊C8)D411yescharacteristic
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105Dic43⋊C8—21no—
106Dic43⋊C8—21no—
107#13063250—21no—
108#13063250—21no—
109#13063248—21no—
110#13063247—21no—
111#13063247—21no—
112#13063246—21no—
113#13063246—21no—
114#13063246—21no—
115#13063246—21no—
116#13063246—21no—
117#13063246—21no—
118#13063245—21no—
119C22⋊(C43⋊C8)D411yescharacteristic
120C22⋊(C43⋊C8)D411yescharacteristic
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
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—
155C22×Dic43—41no—
156C2×D172C2×D411yescharacteristic
157C2×C4×D43—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—41no—
161C2×Dic86—82no—
162C2×Dic86C2×D411yescharacteristic
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—81no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C22⋊C4×C43—41no—
171C22⋊C4×C43—41no—
172C42×C43C2×D411yescharacteristic
173C42×C43C2×D411yescharacteristic
174C42×C43#4111yescharacteristic
175C42×C43C2411yescharacteristic
176C22⋊Dic43—21no—
177#10621883—81no—
178#10621882—81no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182(C2×D43)⋊C4—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43C2×D411yescharacteristic
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194Dic43⋊C4—21no—
195C4×Dic43—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—81no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203#10621872—81no—
204C8×D43—81no—
205C23×C43—41no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208Q8×C43—81no—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—81no—
214D4×C43—82no—
215C2×C4×C43—22no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—82no—
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43#12111yescharacteristic
224C2×C4×C43#12111yescharacteristic
225C2×C4×C43C22×D411yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C2×C4×C43C2×#4111yescharacteristic
228C22⋊D43—42no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—82no—
235D172—21no—
236D172—21no—
237C4×D43—41no—
238C4×D43—41no—
239Dic86—21no—
240Dic86—21no—
241Dic86—82no—
242Dic86—81no—
243Dic86—81no—
244C8×C43—41no—
245C8×C43—41no—
246C8×C43—41no—
247C8×C43—41no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—21no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19591—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—81no—
258C22×C43—81no—
259C22×C43—81no—
260C22×C43#47212yes—
261C22×C43C2×#12111yescharacteristic
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—81no—
270C4×C43#57711yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273C4×C43#57811yescharacteristic
274Dic43—41no—
275Dic43—41no—
276Dic43—41no—
277Dic43—81no—
278Dic43—81no—
279#3247—431no—
280#3238—431no—
281#3226—431no—
282#2994—431no—
283#1698—431no—
284#1697—431no—
285#1696—431no—
286#1695—431no—
287#1678—431no—
288#1677—431no—
289#1676—431no—
290#1675—431no—
291#1573—431no—
292#1551D4311yescharacteristic, complemented
293C2×#333—431no—
294C2×C43—22no—
295C2×C43—161no—
296C2×C43#304611yescharacteristic
297C2×C43#306311yescharacteristic
298C2×C43C2×#47211yescharacteristic
299D43—81no—
300#532C2×D4311yescharacteristic
301C2×C4⋊Q8—431no—
302#529—431no—
303#501—861no—
304#500—431no—
305#500—431no—
306#489—861no—
307#486—431no—
308#486—431no—
309#483—861no—
310#480—861no—
311#480—861no—
312#480—861no—
313#478—861no—
314#477—431no—
315#477—431no—
316#477—431no—
317#476—431no—
318#476—431no—
319#476—431no—
320#474—861no—
321#474—861no—
322#466—861no—
323#465—861no—
324#463—861no—
325#460—431no—
326#459—431no—
327#446—431no—
328C8×Q8—431no—
329#436—431no—
330#435—861no—
331C8×D4—431no—
332C8×D4—861no—
333#433—861no—
334#432C2×D4311yescharacteristic
335#431—431no—
336#424—861no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8C2×D4311yescharacteristic
339#335—431no—
340#335—431no—
341#334—431no—
342#334—431no—
343#333—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333C2×D4311yescharacteristic
348#333C2×D4311yescharacteristic
349#331C2×D4311yescharacteristic
350#331C2×D4311yescharacteristic
351C43#1959111yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—861no—
354C2×SD16—861no—
355C2×D8—861no—
356C2×M16—861no—
357C22×C8—21no—
358C22×C8—861no—
359C22×C8—861no—
360C4⋊Q8—431no—
361C4⋊Q8—431no—
362C4⋊Q8—861no—
363C4⋊Q8—861no—
364C4⋊Q8—861no—
365C4⋊Q8C22×D4311yescharacteristic
366#127C22×D4311yescharacteristic
367#126—861no—
368#125—431no—
369#124—21no—
370#124—431no—
371#123—861no—
372C22⋊Q8—431no—
373#121—21no—
374#121—21no—
375#121—431no—
376C4×Q8—431no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—431no—
380C4×D4—861no—
381#117—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C42C22×D4311yescharacteristic
385#107—861no—
386#107—861no—
387#107—861no—
388#107—861no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—21no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—861no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8C22×D4311yescharacteristic
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#102—861no—
411#102—861no—
412#102—861no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—21no—
420C22⋊C8—431no—
421C22⋊C8—431no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—21no—
425#97—861no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429#41—82no—
430C2×Q8—21no—
431C2×Q8—431no—
432C2×Q8—861no—
433C2×Q8—861no—
434C2×Q8—3442no—
435C2×Q8—1721no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—431no—
441C2×D4—861no—
442C22×C4—41no—
443C22×C4—861no—
444C22×C4—1721no—
445C22×C4#1062189811yescharacteristic
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448SD16—3441no—
449D8—3441no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—81no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—431no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—3441no—
463C2×C8—3441no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—431no—
467C4⋊C4—431no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—1721no—
477C4⋊C4—1721no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C42—861no—
486C42#1062189811yescharacteristic
487C42D4×D4311yescharacteristic
488C42D4×D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—41no—
491C23—861no—
492C23#1306329811yescharacteristic
493Q8—81no—
494Q8—861no—
495Q8—861no—
496Q8—3441no—
497Q8—3441no—
498Q8—3442no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—81no—
504D4—82no—
505D4—861no—
506D4—861no—
507D4—1722no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—82no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—3442no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4#1306329811yescharacteristic
524C2×C4#1306329811yescharacteristic
525C2×C4#1306329811yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4C2×#1062189811yescharacteristic
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—861no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22#1458316812yes—
548C22C2×#1306329811yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—3441no—
555C4—3441no—
556C4—1721no—
557C4—1721no—
558C4—1721no—
559C4#1458370611yescharacteristic
560C4#1458370911yescharacteristic
561C4#1458371311yescharacteristic
562C4#1458371511yescharacteristic
563C2—22no—
564C2—161no—
565C2—3441no—
566C2#1914414411yescharacteristic
567C2#1914428911yescharacteristic
568C2C2×#1458316811yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1551C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#1551D43
hypocenterC43#19591
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
2. #19145818C2semidirect
3. #19145713C2semidirect
4. #19143751C2semidirect
5. #19134134C2semidirect
6. #19134127C2semidirect
7. #19134122C2semidirect
8. #19134117C2semidirect
9. #19134010C2semidirect
10. #19134003C2semidirect
11. #19133998C2semidirect
12. #19133993C2semidirect
13. #19133381C2semidirect
14. C2×#14582647C2semidirect
15. C43×#1551C2semidirect
292. #1551D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191458182
#191457132
#191437512
#191341342
#191341272
#191341222
#191341172
#191340102
#191340032
#191339982
#191339932
#191333812
C2×#145826472
C43×#15512
#1959143