Finite Group Databasebeta

← #25081718

Subgroups — #25081718

Order 11008.

572 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145822C211yesmaximal, characteristic
2#19144977C211yesmaximal, characteristic, complemented
3#19143600C211yesmaximal, characteristic
4#19134179C211yesmaximal, characteristic, complemented
5#19134172C211yesmaximal, characteristic, complemented
6#19134151C211yesmaximal, characteristic, complemented
7#19134144C211yesmaximal, characteristic, complemented
8#19134055C211yesmaximal, characteristic, complemented
9#19134048C211yesmaximal, characteristic, complemented
10#19134027C211yesmaximal, characteristic, complemented
11#19134020C211yesmaximal, characteristic, complemented
12#19133360C211yesmaximal, characteristic, complemented
13#19133305C211yesmaximal, characteristic, complemented
14#19133281C211yesmaximal, characteristic, complemented
15C43×#3252C211yesmaximal, characteristic
16C2×#13063325C2211yescharacteristic
17#14583309—21no—
18#14583269—21no—
19#14583269—21no—
20#14583258—21no—
21#14583251C2211yescharacteristic
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583232—21no—
26#14583215—21no—
27#14583184C2211yescharacteristic
28#14583184C2211yescharacteristic
29#14583179C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583030C2211yescharacteristic
32Q8×C43⋊C8C2211yescharacteristic
33#14582977—21no—
34#14582977C2211yescharacteristic
35#14582971—21no—
36D4×C43⋊C8C2211yescharacteristic
37#14582960—21no—
38#14582956C2211yescharacteristic
39#14582952C2211yescharacteristic
40#14582907—21no—
41#14582907—21no—
42#14582855—21no—
43C4×#10621877C2211yescharacteristic
44#14582651C2211yescharacteristic
45#14582651C2211yescharacteristic
46#14582649C2211yescharacteristic
47#14582649C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582648C2211yescharacteristic
50#14582645C2211yescharacteristic
51#14582645C2211yescharacteristic
52#14582644C2211yescharacteristic
53#14582644C2211yescharacteristic
54#14582644C2211yescharacteristic
55#14582644C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#529C2211yescharacteristic
58C43×#479—21no—
59C43×#477C2211yescharacteristic
60C43×#476C2211yescharacteristic
61C43×#470—21no—
62C43×#468—21no—
63C43×#464—21no—
64C43×#462C2211yescharacteristic
65C43×#461C2211yescharacteristic
66C43×#423C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621877—21no—
69C2×#10621877D411yescharacteristic
70C2×#10621877D411yescharacteristic
71C22×C43⋊C8—21no—
72#13063325—21no—
73#13063325—21no—
74#13063325—21no—
75#13063325C2311yescharacteristic
76#13063325C2311yescharacteristic
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79#13063258—21no—
80#13063258—21no—
81#13063256—21no—
82#13063256—21no—
83C4⋊(C43⋊C8)—21no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)C2311yescharacteristic
86C4⋊(C43⋊C8)C2311yescharacteristic
87C4⋊(C43⋊C8)C2311yescharacteristic
88C4⋊(C43⋊C8)C2311yescharacteristic
89#13063249—21no—
90#13063249—21no—
91#13063248—21no—
92#13063248—21no—
93#13063248—21no—
94#13063248—21no—
95#13063248—21no—
96#13063248—21no—
97#13063248—21no—
98#13063248—21no—
99#13063246—21no—
100#13063246—21no—
101C22⋊(C43⋊C8)—21no—
102C22⋊(C43⋊C8)—21no—
103C22⋊(C43⋊C8)—21no—
104C22⋊(C43⋊C8)—21no—
105#13063236—21no—
106#13063236—21no—
107#13063236D411yescharacteristic
108#13063236D411yescharacteristic
109C4×C43⋊C8—21no—
110C4×C43⋊C8—21no—
111C4×C43⋊C8C2311yescharacteristic
112C4×C43⋊C8C2311yescharacteristic
113C2×Q16×C43—21no—
114C2×SD16×C43—21no—
115C2×M16×C43—21no—
116C4⋊Q8×C43C2311yescharacteristic
117C4⋊Q8×C43C2311yescharacteristic
118#126×C43—21no—
119#125×C43—21no—
120#125×C43D411yescharacteristic
121#124×C43D411yescharacteristic
122#123×C43—21no—
123C22⋊Q8×C43—21no—
124C22⋊Q8×C43—21no—
125C22⋊Q8×C43D411yescharacteristic
126#121×C43D411yescharacteristic
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×D4×C43—21no—
131C4×D4×C43C2311yescharacteristic
132#117×C43—21no—
133#117×C43—21no—
134C2×C42×C43C2311yescharacteristic
135#107×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—21no—
142#103×C43—21no—
143#102×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
153C22×Dic43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—42no—
157C2×Dic86—42no—
158C2×Dic86—41no—
159Q16×C43—81no—
160SD16×C43—81no—
161M16×C43—81no—
162C2×C8×C43—21no—
163C2×C8×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—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43—41no—
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C22⋊C4×C43—41no—
182C42×C43—21no—
183C42×C43—41no—
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43#4111yescharacteristic
187C42×C43C2411yescharacteristic
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—41no—
193C4⋊Dic43—41no—
194#10621877—41no—
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⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204C2×C43⋊C8C2×D411yescharacteristic
205C2×C43⋊C8C2×D411yescharacteristic
206C23×C43—21no—
207C23×C43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—41no—
211Q8×C43—41no—
212Q8×C43—81no—
213D4×C43—21no—
214D4×C43—21no—
215D4×C43—81no—
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—41no—
227C2×C4×C43—41no—
228C2×C4×C43#12111yescharacteristic
229C2×C4×C43#12111yescharacteristic
230C2×C4×C43#12111yescharacteristic
231C2×C4×C43C22×D411yescharacteristic
232C2×C4×C43C22×D411yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—82no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—82no—
242C8×C43—41no—
243C8×C43—41no—
244C43⋊C8—21no—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43C2×#12111yescharacteristic
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—41no—
265C4×C43—41no—
266C4×C43—41no—
267C4×C43—81no—
268C4×C43—81no—
269C4×C43#57511yescharacteristic
270C4×C43#57511yescharacteristic
271C4×C43#57711yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—81no—
274Dic43—81no—
275#3252D4311yescharacteristic
276#3239—431no—
277#3139—431no—
278#2969—431no—
279#1704—431no—
280#1703—431no—
281#1700—431no—
282#1699—431no—
283#1684—431no—
284#1683—431no—
285#1680—431no—
286#1679—431no—
287#1569—431no—
288#1554—431no—
289#1549—431no—
290C2×C43—41no—
291C2×C43—81no—
292C2×C43#304011yescharacteristic
293C2×C43#306311yescharacteristic
294C2×C43#306911yescharacteristic
295#533C2×D4311yescharacteristic
296C2×C4⋊Q8—431no—
297#529C2×D4311yescharacteristic
298#501—861no—
299#491—861no—
300#491—861no—
301#489—861no—
302#487—431no—
303#487—431no—
304#487—431no—
305#487—431no—
306#484—861no—
307#481—861no—
308#479—21no—
309#477C2×D4311yescharacteristic
310#476C2×D4311yescharacteristic
311#475—431no—
312#475—431no—
313#474—431no—
314#474—431no—
315#470—21no—
316#468—21no—
317#464—21no—
318#462C2×D4311yescharacteristic
319#461C2×D4311yescharacteristic
320#446—431no—
321C8×Q8—431no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#432—431no—
328#431—431no—
329#423C2×D4311yescharacteristic
330#419—861no—
331#419—861no—
332#405—861no—
333C4×M16—431no—
334#335—431no—
335#335—431no—
336#334—431no—
337#334—431no—
338#333—431no—
339#333—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332—431no—
345#332—431no—
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C2×Q16—21no—
349C2×SD16—21no—
350C2×M16—21no—
351C2×M16—431no—
352C2×M16—431no—
353C2×M16—861no—
354C22×C8—861no—
355C4⋊Q8—431no—
356C4⋊Q8—431no—
357C4⋊Q8—861no—
358C4⋊Q8—861no—
359C4⋊Q8—861no—
360C4⋊Q8C22×D4311yescharacteristic
361C4⋊Q8C22×D4311yescharacteristic
362#126—21no—
363#125—21no—
364#125C22⋊D4311yescharacteristic
365#124C22⋊D4311yescharacteristic
366#123—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8C22⋊D4311yescharacteristic
370#121C22⋊D4311yescharacteristic
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C22×D4311yescharacteristic
374C4×D4—21no—
375C4×D4C22×D4311yescharacteristic
376#117—21no—
377#117—21no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42C22×D4311yescharacteristic
381#107—21no—
382#107—861no—
383#107—861no—
384#106—21no—
385#106—861no—
386#106—861no—
387C4⋊C8—21no—
388C4⋊C8—431no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#103—861no—
405#103—861no—
406#103—861no—
407#103—861no—
408#103—861no—
409#102—21no—
410#102—861no—
411#102—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—431no—
417#97—431no—
418#97—861no—
419#97—861no—
420C4×C8—431no—
421C4×C8—431no—
422C4×C8—861no—
423C4×C8—861no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—861no—
427C2×Q8—861no—
428C2×Q8—1722no—
429C2×Q8—1722no—
430C2×Q8—1721no—
431C2×Q8C2×C22⋊D4311yescharacteristic
432C2×D4—21no—
433C2×D4C2×C22⋊D4311yescharacteristic
434C22×C4—21no—
435C22×C4—1721no—
436C22×C4D4×D4311yescharacteristic
437C22×C4#1062190011yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439Q16—81no—
440SD16—81no—
441M16—81no—
442M16—1721no—
443M16—1721no—
444M16—1722no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—431no—
448C2×C8—431no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1722no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—1721no—
471C4⋊C4—1721no—
472C4⋊C4C2×C22⋊D4311yescharacteristic
473C4⋊C4C2×C22⋊D4311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—41no—
480C42—21no—
481C42—41no—
482C42D4×D4311yescharacteristic
483C42#1062190011yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—21no—
487C23#1306329711yescharacteristic
488Q8—21no—
489Q8—21no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493Q8—3442no—
494Q8—1721no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498D4—21no—
499D4—21no—
500D4—81no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—3442no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329711yescharacteristic
517C2×C4#1306329711yescharacteristic
518C2×C4#1306329711yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C22×C22⋊D4311yescharacteristic
521C2×C4C2×#1062190011yescharacteristic
522C8—41no—
523C8—41no—
524C8—861no—
525C8—861no—
526C8—861no—
527C8—861no—
528C8—1721no—
529C8—1721no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22C2×#1306329711yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—81no—
547C4—81no—
548C4—3441no—
549C4—3441no—
550C4#1458369811yescharacteristic
551C4#1458369811yescharacteristic
552C4#1458371011yescharacteristic
553C4#1458371411yescharacteristic
554C2—41no—
555C2—81no—
556C2#1914409111yescharacteristic
557C2#1914428811yescharacteristic
558C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3252C2
socleC22×C43C2×#121
prime radical#121×C43D4
hypercenter#3252D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3252

Complements

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

NH ≅ G/Ntype
2. #19144977C2semidirect
4. #19134179C2semidirect
5. #19134172C2semidirect
6. #19134151C2semidirect
7. #19134144C2semidirect
8. #19134055C2semidirect
9. #19134048C2semidirect
10. #19134027C2semidirect
11. #19134020C2semidirect
12. #19133360C2semidirect
13. #19133305C2semidirect
14. #19133281C2semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191458222
#191449772
#191436002
#191341792
#191341722
#191341512
#191341442
#191340552
#191340482
#191340272
#191340202
#191333602
#191333052
#191332812
C43×#32522
#1938143