Finite Group Databasebeta

← #25084218

Subgroups — #25084218

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#19145816C211yesmaximal, characteristic, complemented
3#19143757C211yesmaximal, characteristic, complemented
4#19134132C211yesmaximal, characteristic, complemented
5#19134125C211yesmaximal, characteristic, complemented
6#19134120C211yesmaximal, characteristic, complemented
7#19134115C211yesmaximal, characteristic, complemented
8#19134008C211yesmaximal, characteristic, complemented
9#19134001C211yesmaximal, characteristic, complemented
10#19133996C211yesmaximal, characteristic, complemented
11#19133991C211yesmaximal, characteristic, complemented
12#19133380C211yesmaximal, characteristic, complemented
13#19133290C211yesmaximal, characteristic, complemented
14C2×#14582648C211yesmaximal, characteristic, complemented
15C43×#3226C211yesmaximal, characteristic, complemented
16#14583433C2211yescharacteristic
17#14583305—21no—
18#14583261—21no—
19#14583229—21no—
20#14583212—21no—
21#14583199—21no—
22#14583191C2211yescharacteristic
23#14583191C2211yescharacteristic
24#14583191C2211yescharacteristic
25#14583186C2211yescharacteristic
26#14583186C2211yescharacteristic
27#14583186C2211yescharacteristic
28#14583133—21no—
29#14583126—21no—
30#14583114—21no—
31#14583096C2211yescharacteristic
32#14583091C2211yescharacteristic
33#14583029C2211yescharacteristic
34C8×Dic86C2211yescharacteristic
35#14582978C2211yescharacteristic
36#14582967—21no—
37C8×D172C2211yescharacteristic
38(C22⋊D43)⋊C8—21no—
39#14582959—21no—
40#14582956C2211yescharacteristic
41#14582924—21no—
42C2×C4⋊(C43⋊C8)C2211yescharacteristic
43C2×C4⋊(C43⋊C8)C2211yescharacteristic
44#14582652C2211yescharacteristic
45#14582652C2211yescharacteristic
46#14582650C2211yescharacteristic
47#14582650C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582648C2211yescharacteristic
51#14582648C2211yescharacteristic
52#14582648C2211yescharacteristic
53#14582648C2211yescharacteristic
54#14582643C2211yescharacteristic
55#14582643C2211yescharacteristic
56C43×#532C2211yescharacteristic
57C2×C4⋊Q8×C43C2211yescharacteristic
58C43×#500C2211yescharacteristic
59C43×#500C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#486C2211yescharacteristic
62C43×#480—21no—
63C43×#480—21no—
64C43×#474—21no—
65C43×#474—21no—
66C43×#431C2211yescharacteristic
67C2×#10621883—21no—
68C2×#10621882—21no—
69C2×#10621872—21no—
70C22×C43⋊C8—21no—
71C22×C43⋊C8—21no—
72C2×C8×D43—21no—
73#13063319—21no—
74#13063317D411yescharacteristic
75#13063313D411yescharacteristic
76#13063308—21no—
77#13063304D411yescharacteristic
78#13063299D411yescharacteristic
79C4×Dic86C2311yescharacteristic
80C4×D172C2311yescharacteristic
81C4×C22⋊D43—21no—
82#13063282—21no—
83#13063258—21no—
84#13063258—21no—
85#13063258—21no—
86#13063256—21no—
87#13063256—21no—
88#13063256—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
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97Dic43⋊C8—21no—
98Dic43⋊C8—21no—
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063246—21no—
103#13063246—21no—
104#13063245—21no—
105#13063245—21no—
106#13063245—21no—
107C22⋊(C43⋊C8)—21no—
108(C2×D43)⋊C8—21no—
109(C2×D43)⋊C8—21no—
110#13063236—21no—
111#13063235—21no—
112C8×Dic43—21no—
113C2×#41×C43—21no—
114C22×Q8×C43—21no—
115C4⋊Q8×C43—21no—
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43C2311yescharacteristic
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#127×C43C2311yescharacteristic
122#124×C43—21no—
123#121×C43—21no—
124#121×C43—21no—
125C4×D4×C43—21no—
126C4×D4×C43—21no—
127C2×C4⋊C4×C43—21no—
128C2×C4⋊C4×C43—21no—
129C2×C42×C43C2311yescharacteristic
130#107×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#107×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×Q8×C43—41no—
149C2×Q8×C43—82no—
150C2×D4×C43—21no—
151C2×D4×C43—21no—
152C2×D4×C43—21no—
153C2×D4×C43—41no—
154C22×C4×C43—41no—
155C22×C4×C43—41no—
156C22×C4×C43C2×D411yescharacteristic
157C22×C4×C43C2×D411yescharacteristic
158C22×C4×C43#4111yescharacteristic
159C2×C22⋊D43—21no—
160C2×D172C2×D411yescharacteristic
161C2×C4×D43—21no—
162C2×Dic86C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C2×C8×C43C2×D411yescharacteristic
165C2×C8×C43C2×D411yescharacteristic
166C2×C8×C43C2×D411yescharacteristic
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—41no—
177C42×C43C2×D411yescharacteristic
178C42×C43C2×D411yescharacteristic
179C42×C43#4111yescharacteristic
180C42×C43C2411yescharacteristic
181C22⋊Dic43—21no—
182#10621883—81no—
183#10621882—81no—
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—21no—
186(C2×D43)⋊C4—21no—
187(C2×D43)⋊C4—21no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—81no—
202C2×C43⋊C8—81no—
203#10621872—81no—
204C8×D43—81no—
205C23×C43—41no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208Q8×C43—81no—
209Q8×C43—81no—
210Q8×C43—81no—
211Q8×C43—82no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—41no—
216D4×C43—81no—
217D4×C43—82no—
218C2×C4×C43—22no—
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—82no—
227C2×C4×C43—82no—
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C22⋊D43—42no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238D172—21no—
239D172—21no—
240C4×D43—41no—
241C4×D43—41no—
242Dic86—21no—
243Dic86—21no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—21no—
247C8×C43—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
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—81no—
271C4×C43—81no—
272C4×C43#57711yescharacteristic
273C4×C43#57711yescharacteristic
274C4×C43#57811yescharacteristic
275C4×C43#57811yescharacteristic
276Dic43—41no—
277Dic43—41no—
278Dic43—41no—
279#3247—431no—
280#3238—431no—
281#3226D4311yescharacteristic, complemented
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#1551—431no—
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⋊Q8C2×D4311yescharacteristic
302#529—431no—
303#501—861no—
304#500C2×D4311yescharacteristic
305#500C2×D4311yescharacteristic
306#489—861no—
307#486C2×D4311yescharacteristic
308#486C2×D4311yescharacteristic
309#483—861no—
310#480—21no—
311#480—21no—
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—21no—
321#474—21no—
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#432—431no—
335#431C2×D4311yescharacteristic
336#424—861no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8—431no—
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#333—431no—
348#333—431no—
349#331—431no—
350#331—431no—
351C43#1959111yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—21no—
354C2×SD16—861no—
355C2×D8—861no—
356C2×M16—861no—
357C22×C8—861no—
358C22×C8—861no—
359C22×C8—861no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C22×D4311yescharacteristic
364C4⋊Q8C22×D4311yescharacteristic
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—21no—
383C2×C4⋊C4—21no—
384C2×C42C22×D4311yescharacteristic
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—861no—
390#107—861no—
391#107—861no—
392#106—861no—
393#106—861no—
394#106—861no—
395C4⋊C8—431no—
396C4⋊C8—431no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8—861no—
405C4⋊C8C22⋊D4311yescharacteristic
406C4⋊C8C22⋊D4311yescharacteristic
407#103—861no—
408#103—861no—
409#103—861no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422C22⋊C8C22⋊D4311yescharacteristic
423C22⋊C8C22⋊D4311yescharacteristic
424#97—861no—
425#97—861no—
426C4×C8—861no—
427C4×C8C22×D4311yescharacteristic
428C4×C8C22×D4311yescharacteristic
429#41—82no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—82no—
435C2×Q8—431no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—431no—
441C2×D4—861no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—861no—
445C22×C4D4×D4311yescharacteristic
446C22×C4#1062190011yescharacteristic
447C22×C4C2×C22⋊D4311yescharacteristic
448SD16—3441no—
449D8—3441no—
450M16—3441no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—3441no—
458C2×C8—3441no—
459C2×C8—3441no—
460C2×C8C2×C22⋊D4311yescharacteristic
461C2×C8C2×C22⋊D4311yescharacteristic
462C2×C8C2×C22⋊D4311yescharacteristic
463C2×C8C2×C22⋊D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—431no—
473C4⋊C4—431no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—861no—
484C22⋊C4—861no—
485C42—861no—
486C42D4×D4311yescharacteristic
487C42#1062190011yescharacteristic
488C42C2×C22⋊D4311yescharacteristic
489C42C23×D4311yescharacteristic
490C23—41no—
491C23—861no—
492C23#1306329611yescharacteristic
493Q8—81no—
494Q8—81no—
495Q8—81no—
496Q8—82no—
497Q8—861no—
498Q8—861no—
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—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—861no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4#1306329611yescharacteristic
524C2×C4#1306329611yescharacteristic
525C2×C4#1306329611yescharacteristic
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C22×C22⋊D4311yescharacteristic
528C2×C4C2×#1062190011yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—1721no—
534C8—1721no—
535C8—1721no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C22—21no—
540C22—21no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—1721no—
545C22—1721no—
546C22—1721no—
547C22#1458316612yes—
548C22C2×#1306329611yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—1721no—
557C4—1721no—
558C4—1721no—
559C4#1458370711yescharacteristic
560C4#1458370811yescharacteristic
561C4#1458371411yescharacteristic
562C4#1458371511yescharacteristic
563C2—22no—
564C2—161no—
565C2—3441no—
566C2#1914414111yescharacteristic
567C2#1914428011yescharacteristic
568C2C2×#1458316611yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3226C2
socleC22×C43C2×#121
prime radical#19145915C2
hypercenter#3226D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. #19145816C2semidirect
3. #19143757C2semidirect
4. #19134132C2semidirect
5. #19134125C2semidirect
6. #19134120C2semidirect
7. #19134115C2semidirect
8. #19134008C2semidirect
9. #19134001C2semidirect
10. #19133996C2semidirect
11. #19133991C2semidirect
12. #19133380C2semidirect
13. #19133290C2semidirect
14. C2×#14582648C2semidirect
15. C43×#3226C2semidirect
281. #3226D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459152
#191458162
#191437572
#191341322
#191341252
#191341202
#191341152
#191340082
#191340012
#191339962
#191339912
#191333802
#191332902
C2×#145826482
C43×#32262
#1959143