Finite Group Databasebeta

← #25080358

Subgroups — #25080358

Order 11008.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145921C211yesmaximal, characteristic
2#19145314C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic, complemented
4#19134175C211yesmaximal, characteristic, complemented
5#19134137C211yesmaximal, characteristic, complemented
6#19134116C211yesmaximal, characteristic, complemented
7#19134062C211yesmaximal, characteristic, complemented
8#19134044C211yesmaximal, characteristic, complemented
9#19134006C211yesmaximal, characteristic, complemented
10#19133997C211yesmaximal, characteristic, complemented
11#19133945C211yesmaximal, characteristic, complemented
12#19133348C211yesmaximal, characteristic, complemented
13#19133255C211yesmaximal, characteristic, complemented
14#19133252C211yesmaximal, characteristic, complemented
15C43×#3233C211yesmaximal, characteristic, complemented
16#14583449C2211yescharacteristic
17#14583302C2211yescharacteristic
18#14583273C2211yescharacteristic
19#14583249C2211yescharacteristic
20#14583247C2211yescharacteristic
21#14583196—21no—
22#14583194C2211yescharacteristic
23#14583189C2211yescharacteristic
24#14583147—21no—
25#14583147—21no—
26#14583133—21no—
27#14583130—21no—
28#14583111—21no—
29#14583099C2211yescharacteristic
30#14583094C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582997—21no—
34#14582997—21no—
35#14582977—21no—
36#14582977C2211yescharacteristic
37#14582971—21no—
38D4×C43⋊C8C2211yescharacteristic
39#14582960—21no—
40#14582952C2211yescharacteristic
41C2×C4⋊(C43⋊C8)C2211yescharacteristic
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582647C2211yescharacteristic
51#14582647C2211yescharacteristic
52#14582645C2211yescharacteristic
53#14582645C2211yescharacteristic
54#14582642C2211yescharacteristic
55#14582642C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#499—21no—
59C43×#488—21no—
60C43×#485—21no—
61C43×#482—21no—
62C43×#477C2211yescharacteristic
63C43×#476C2211yescharacteristic
64C43×#475C2211yescharacteristic
65C43×#474C2211yescharacteristic
66C43×#431C2211yescharacteristic
67C2×#10621898—21no—
68C2×#10621884—21no—
69C2×#10621884—21no—
70C2×#10621884—21no—
71C2×#10621882—21no—
72C2×#10621877—21no—
73C2×#10621877D411yescharacteristic
74C2×#10621877D411yescharacteristic
75C22×C43⋊C8—21no—
76C22×C43⋊C8—21no—
77#13063325C2311yescharacteristic
78#13063322C2311yescharacteristic
79#13063313—21no—
80#13063299—21no—
81#13063299—21no—
82C4×D172—21no—
83C4×D172—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063256—21no—
88C4⋊(C43⋊C8)—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
95#13063249—21no—
96#13063249—21no—
97#13063249—21no—
98#13063246—21no—
99#13063245—21no—
100#13063245—21no—
101#13063245—21no—
102#13063245—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105C22⋊(C43⋊C8)—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C4⋊Q8×C43C2311yescharacteristic
114C4⋊Q8×C43C2311yescharacteristic
115#126×C43—21no—
116#125×C43—21no—
117#125×C43D411yescharacteristic
118#124×C43D411yescharacteristic
119#123×C43—21no—
120C22⋊Q8×C43—21no—
121C22⋊Q8×C43—21no—
122C22⋊Q8×C43D411yescharacteristic
123#121×C43D411yescharacteristic
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×D4×C43—21no—
128C4×D4×C43C2311yescharacteristic
129#117×C43—21no—
130#117×C43—21no—
131C2×C42×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43—21no—
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43—21no—
148C2×D4×C43C2×D411yescharacteristic
149C22×C4×C43—21no—
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×C4×C43#4111yescharacteristic
153C2×C22⋊D43—41no—
154#10621898—82no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×C4×D43—41no—
159C2×Dic86—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43C2×D411yescharacteristic
173C4⋊C4×C43C2×D411yescharacteristic
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—41no—
180C42×C43—21no—
181C42×C43—41no—
182C42×C43C2×D411yescharacteristic
183C42×C43C2×D411yescharacteristic
184C42×C43#4111yescharacteristic
185C42×C43C2411yescharacteristic
186#10621884—42no—
187#10621884—42no—
188#10621884—81no—
189#10621882—81no—
190(C2×D43)⋊C4—41no—
191(C2×D43)⋊C4—41no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194#10621877—22no—
195#10621877—41no—
196#10621877—42no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—42no—
202C2×C43⋊C8—81no—
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C2×C43⋊C8C2×D411yescharacteristic
207C23×C43—21no—
208C23×C43#12111yescharacteristic
209C22×D43—41no—
210Q8×C43—21no—
211Q8×C43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—81no—
215D4×C43—21no—
216D4×C43—21no—
217D4×C43—81no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43#12111yescharacteristic
232C2×C4×C43#12111yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C22⋊D43—82no—
237C2×Dic43—41no—
238D172—41no—
239D172—41no—
240D172—41no—
241D172—41no—
242D172—81no—
243C4×D43—82no—
244Dic86—81no—
245C8×C43—41no—
246C8×C43—41no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254C43⋊C8#13512yes—
255#19253—431nomaximal, Sylow
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—41no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43C2×#12111yescharacteristic
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—81no—
274C4×C43—81no—
275C4×C43C2×#13511yescharacteristic
276C4×C43#57511yescharacteristic
277C4×C43#57711yescharacteristic
278C4×C43#57811yescharacteristic
279Dic43—81no—
280#3247—431no—
281#3233D4311yescharacteristic, complemented
282#3182—431no—
283#2969—431no—
284#1704—431no—
285#1698—431no—
286#1695—431no—
287#1685—431no—
288#1683—431no—
289#1677—431no—
290#1676—431no—
291#1666—431no—
292#1565—431no—
293#1543—431no—
294#1542—431no—
295C2×C43—41no—
296C2×C43—81no—
297C2×C43#303511yescharacteristic
298C2×C43#306311yescharacteristic
299C2×C43#306811yescharacteristic
300D43—161no—
301#533C2×D4311yescharacteristic
302#532—431no—
303#529C2×D4311yescharacteristic
304#500—431no—
305#499—21no—
306#492—431no—
307#488—21no—
308#487—431no—
309#486—431no—
310#485—21no—
311#482—21no—
312#478—861no—
313#477—431no—
314#477C2×D4311yescharacteristic
315#476—431no—
316#476C2×D4311yescharacteristic
317#475C2×D4311yescharacteristic
318#474C2×D4311yescharacteristic
319#468—861no—
320#468—861no—
321#466—861no—
322#465—861no—
323#463—861no—
324#460—431no—
325#459—431no—
326#446—431no—
327C8×Q8—431no—
328#440—861no—
329#440—861no—
330#436—431no—
331#436—861no—
332#435—861no—
333C8×D4—431no—
334#433—861no—
335#431—431no—
336#431C2×D4311yescharacteristic
337C2×C4⋊C8—431no—
338#405—861no—
339C4×M16—431no—
340#335—431no—
341#335—431no—
342#334—431no—
343#334—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#332—431no—
349#332—431no—
350#331—431no—
351#331—431no—
352C43#1925311yescharacteristic, complemented, Sylow
353C2×#41—861no—
354C2×SD16—861no—
355C2×SD16—861no—
356C2×SD16—861no—
357C2×D8—861no—
358C2×M16—431no—
359C2×M16—431no—
360C2×M16—861no—
361C22×C8—861no—
362C22×C8—861no—
363C4⋊Q8—431no—
364C4⋊Q8C22×D4311yescharacteristic
365C4⋊Q8C22×D4311yescharacteristic
366#127—431no—
367#126—21no—
368#125—21no—
369#125C22⋊D4311yescharacteristic
370#124—861no—
371#124C22⋊D4311yescharacteristic
372#123—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8C22⋊D4311yescharacteristic
376#121—861no—
377#121—861no—
378#121C22⋊D4311yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C22×D4311yescharacteristic
382C4×D4—21no—
383C4×D4—861no—
384C4×D4—861no—
385C4×D4C22×D4311yescharacteristic
386#117—21no—
387#117—21no—
388C2×C42C22×D4311yescharacteristic
389#107—21no—
390#107—21no—
391#107—861no—
392#107—861no—
393#107—861no—
394#106—21no—
395#106—21no—
396#106—861no—
397C4⋊C8—431no—
398C4⋊C8—431no—
399C4⋊C8—431no—
400C4⋊C8—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406#103—21no—
407#103—21no—
408#103—861no—
409#103—861no—
410#103—861no—
411#102—21no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418C22⋊C8—21no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8—861no—
422#97—431no—
423#97—431no—
424#97—861no—
425C4×C8—21no—
426C4×C8—431no—
427C4×C8—431no—
428C4×C8—861no—
429C4×C8—861no—
430#41—3442no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—861no—
434C2×Q8C2×C22⋊D4311yescharacteristic
435C2×D4—21no—
436C2×D4—861no—
437C2×D4—861no—
438C2×D4—861no—
439C2×D4—1721no—
440C2×D4C2×C22⋊D4311yescharacteristic
441C22×C4—21no—
442C22×C4—1721no—
443C22×C4D4×D4311yescharacteristic
444C22×C4#1062190011yescharacteristic
445C22×C4C2×C22⋊D4311yescharacteristic
446SD16—3441no—
447SD16—1722no—
448SD16—1722no—
449D8—3441no—
450M16—862no—
451M16—1722no—
452M16—1721no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—431no—
459C2×C8—861no—
460C2×C8—861no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—3441no—
464C2×C8—1722no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4C2×C22⋊D4311yescharacteristic
478C4⋊C4C2×C22⋊D4311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—1721no—
486C22⋊C4—1721no—
487C42—21no—
488C42—41no—
489C42D4×D4311yescharacteristic
490C42#1062190011yescharacteristic
491C42C2×C22⋊D4311yescharacteristic
492C42C23×D4311yescharacteristic
493C23—21no—
494C23—1721no—
495C23#1306329711yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—3441no—
502D4—21no—
503D4—21no—
504D4—81no—
505D4—3441no—
506D4—3442no—
507D4—1721no—
508D4—1721no—
509D4—1721no—
510D4—1721no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—3442no—
524C2×C4—1721no—
525C2×C4#1306329711yescharacteristic
526C2×C4#1306329711yescharacteristic
527C2×C4#1306329711yescharacteristic
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C22×C22⋊D4311yescharacteristic
530C2×C4C2×#1062190011yescharacteristic
531C8—41no—
532C8—41no—
533C8—432no—
534C8—861no—
535C8—861no—
536C8—861no—
537C8—1721no—
538C8—1721no—
539C8—1721no—
540C8—1721no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—3441no—
548C22—3441no—
549C22—3441no—
550C22C2×#1306329711yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—3441no—
561C4#135×D4311yescharacteristic
562C4#1458369611yescharacteristic
563C4#1458370711yescharacteristic
564C4#1458371411yescharacteristic
565C2—41no—
566C2—81no—
567C2—6881no—
568C2#1914404611yescharacteristic
569C2#1914428211yescharacteristic
570C2#1914432511yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3233C2
socleC22×C43C2×#121
prime radical#19145921C2
hypercenter#3233D43
hypocenterC43#19253
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3233

Complements

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

NH ≅ G/Ntype
2. #19145314C2semidirect
3. #19143600C2semidirect
4. #19134175C2semidirect
5. #19134137C2semidirect
6. #19134116C2semidirect
7. #19134062C2semidirect
8. #19134044C2semidirect
9. #19134006C2semidirect
10. #19133997C2semidirect
11. #19133945C2semidirect
12. #19133348C2semidirect
13. #19133255C2semidirect
14. #19133252C2semidirect
15. C43×#3233C2semidirect
281. #3233D43semidirect
352. C43#19253semidirect

Maximal subgroups

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

subgroupindex
#191459212
#191453142
#191436002
#191341752
#191341372
#191341162
#191340622
#191340442
#191340062
#191339972
#191339452
#191333482
#191332552
#191332522
C43×#32332
#1925343