Finite Group Databasebeta

← #25081720

Subgroups — #25081720

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#19145962C211yesmaximal, characteristic
2#19145827C211yesmaximal, characteristic
3#19144977C211yesmaximal, characteristic, complemented
4#19143593C211yesmaximal, characteristic
5#19134180C211yesmaximal, characteristic, complemented
6#19134173C211yesmaximal, characteristic, complemented
7#19134152C211yesmaximal, characteristic, complemented
8#19134145C211yesmaximal, characteristic, complemented
9#19134056C211yesmaximal, characteristic, complemented
10#19134049C211yesmaximal, characteristic, complemented
11#19134028C211yesmaximal, characteristic, complemented
12#19134021C211yesmaximal, characteristic, complemented
13#19133363C211yesmaximal, characteristic, complemented
14#19133279C211yesmaximal, characteristic, complemented
15C43×#1554C211yesmaximal, characteristic, complemented
16C2×#13063325C2211yescharacteristic
17#14583433C2211yescharacteristic
18#14583308—21no—
19#14583269—21no—
20#14583269—21no—
21#14583259—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583251C2211yescharacteristic
26#14583235—21no—
27#14583218—21no—
28#14583206—21no—
29#14583191C2211yescharacteristic
30#14583186C2211yescharacteristic
31#14583185C2211yescharacteristic
32#14583185C2211yescharacteristic
33#14583180C2211yescharacteristic
34#14583180C2211yescharacteristic
35#14583155—21no—
36#14583147—21no—
37#14583121—21no—
38#14583106C2211yescharacteristic
39#14583101C2211yescharacteristic
40#14583026C2211yescharacteristic
41#14583023C2211yescharacteristic
42#14582976C2211yescharacteristic
43#14582974—21no—
44#14582973—21no—
45#14582964C2211yescharacteristic
46#14582958—21no—
47#14582923C2211yescharacteristic
48#14582907—21no—
49#14582907—21no—
50#14582853—21no—
51C4×#10621877C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582649C2211yescharacteristic
55#14582649C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582646C2211yescharacteristic
58#14582646C2211yescharacteristic
59#14582646C2211yescharacteristic
60C43×#533C2211yescharacteristic
61C43×#432C2211yescharacteristic
62C43×#431C2211yescharacteristic
63C43×#333C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×#332C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C22×Dic86—21no—
68C2×#10621885—21no—
69C2×#10621884—21no—
70C2×#10621877—21no—
71C2×#10621877D411yescharacteristic
72C2×#10621877D411yescharacteristic
73C2×#10621872—21no—
74C2×C8×D43—21no—
75#13063325—21no—
76#13063325—21no—
77#13063325—21no—
78#13063325C2311yescharacteristic
79#13063325C2311yescharacteristic
80#13063319—21no—
81#13063317D411yescharacteristic
82#13063313D411yescharacteristic
83#13063308—21no—
84#13063304D411yescharacteristic
85#13063299D411yescharacteristic
86C4×Dic86C2311yescharacteristic
87C4×D172C2311yescharacteristic
88C4×C22⋊D43—21no—
89#13063282—21no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43—21no—
92#13063259—21no—
93#13063259—21no—
94#13063258—21no—
95#13063257—21no—
96#13063257—21no—
97#13063256—21no—
98C4⋊(C43⋊C8)—21no—
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101Dic43⋊C8—21no—
102Dic43⋊C8—21no—
103#13063250—21no—
104#13063250—21no—
105#13063249—21no—
106#13063249—21no—
107#13063248—21no—
108#13063248—21no—
109#13063248—21no—
110#13063248—21no—
111#13063248—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063247—21no—
117#13063247—21no—
118#13063245—21no—
119(C2×D43)⋊C8—21no—
120(C2×D43)⋊C8—21no—
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063235—21no—
124C4×C43⋊C8C2311yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C4⋊Q8×C43C2311yescharacteristic
128C4⋊Q8×C43C2311yescharacteristic
129#125×C43—21no—
130C22⋊Q8×C43—21no—
131C22⋊Q8×C43—21no—
132C4×Q8×C43—21no—
133C4×Q8×C43—21no—
134#117×C43—21no—
135C2×C42×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140C22⋊C8×C43—21no—
141C22⋊C8×C43—21no—
142#97×C43—21no—
143C4×C8×C43—21no—
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4111yescharacteristic
149C2×C22⋊D43—21no—
150C22×Dic43—41no—
151C2×D172C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—42no—
156C2×Dic86—42no—
157C2×Dic86—41no—
158C2×Dic86C2×D411yescharacteristic
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C22⋊C4×C43—41no—
170C42×C43—41no—
171C42×C43C2×D411yescharacteristic
172C42×C43C2×D411yescharacteristic
173C42×C43#4111yescharacteristic
174C42×C43C2411yescharacteristic
175C22⋊Dic43—21no—
176#10621885—81no—
177#10621884—81no—
178(C2×D43)⋊C4—21no—
179(C2×D43)⋊C4—21no—
180(C2×D43)⋊C4—21no—
181(C2×D43)⋊C4—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—41no—
187C4⋊Dic43—41no—
188C4⋊Dic43C2×D411yescharacteristic
189C4⋊Dic43C2×D411yescharacteristic
190Dic43⋊C4—21no—
191Dic43⋊C4—21no—
192Dic43⋊C4—21no—
193Dic43⋊C4—21no—
194C4×Dic43—21no—
195#10621877—41no—
196#10621877—41no—
197#10621877—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C2×C43⋊C8C2×D411yescharacteristic
204#10621872—42no—
205C8×D43—42no—
206C23×C43#12111yescharacteristic
207C22×D43—21no—
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43#12111yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C2×C4×C43#12111yescharacteristic
221C2×C4×C43C22×D411yescharacteristic
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C2×#4111yescharacteristic
224C22⋊D43—81no—
225C2×Dic43—21no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—82no—
231D172—21no—
232D172—21no—
233C4×D43—41no—
234C4×D43—41no—
235Dic86—21no—
236Dic86—21no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240Dic86—41no—
241Dic86—82no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43—41no—
245C8×C43—41no—
246C43⋊C8—21no—
247C43⋊C8—21no—
248C43⋊C8—21no—
249C43⋊C8—21no—
250C43⋊C8—41no—
251C43⋊C8—41no—
252#19381—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43C2×#12111yescharacteristic
257C2×D43—41no—
258C2×D43—41no—
259C2×D43—41no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—21no—
264C4×C43—81no—
265C4×C43—81no—
266C4×C43#57511yescharacteristic
267C4×C43#57511yescharacteristic
268C4×C43#57711yescharacteristic
269C4×C43#57811yescharacteristic
270Dic43—41no—
271Dic43—41no—
272Dic43—41no—
273Dic43—81no—
274Dic43—81no—
275#3252—431no—
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#1554D4311yescharacteristic, complemented
289#1549—431no—
290C2×C43—41no—
291C2×C43#304011yescharacteristic
292C2×C43#306311yescharacteristic
293C2×C43#306911yescharacteristic
294D43—81no—
295#533C2×D4311yescharacteristic
296C2×C4⋊Q8—431no—
297#529—431no—
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—861no—
309#477—431no—
310#476—431no—
311#475—431no—
312#475—431no—
313#474—431no—
314#474—431no—
315#470—861no—
316#468—861no—
317#464—861no—
318#462—431no—
319#461—431no—
320#446—431no—
321C8×Q8—431no—
322#436—431no—
323#436—861no—
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#432C2×D4311yescharacteristic
328#431C2×D4311yescharacteristic
329#423—431no—
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#333C2×D4311yescharacteristic
339#333C2×D4311yescharacteristic
340#332—431no—
341#332—431no—
342#332—431no—
343#332—431no—
344#332C2×D4311yescharacteristic
345#332C2×D4311yescharacteristic
346C43#1938111yescharacteristic, complemented, Sylow
347C22×Q8—861no—
348C2×Q16—861no—
349C2×SD16—861no—
350C2×M16—431no—
351C2×M16—431no—
352C2×M16—861no—
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—861no—
363#125—21no—
364#125—431no—
365#124—431no—
366#123—861no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C22⋊Q8—431no—
370#121—431no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—431no—
374C4×D4—431no—
375C4×D4—861no—
376#117—21no—
377#117—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C42C22×D4311yescharacteristic
381#107—861no—
382#107—861no—
383#107—861no—
384#106—861no—
385#106—861no—
386#106—861no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C4⋊C8C22×D4311yescharacteristic
393C4⋊C8C22×D4311yescharacteristic
394C4⋊C8C22×D4311yescharacteristic
395C4⋊C8C22×D4311yescharacteristic
396#103—861no—
397#103—861no—
398#103—861no—
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—861no—
410#102—861no—
411#102—861no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—861no—
415C22⋊C8—861no—
416#97—21no—
417#97—431no—
418#97—431no—
419#97—861no—
420C4×C8—21no—
421C4×C8—431no—
422C4×C8—431no—
423C4×C8—861no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—431no—
427C2×Q8—861no—
428C2×Q8—861no—
429C2×Q8—1722no—
430C2×Q8—1722no—
431C2×Q8—1721no—
432C2×D4—431no—
433C2×D4—861no—
434C22×C4—861no—
435C22×C4—1721no—
436C22×C4#1062189811yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439Q16—3441no—
440SD16—3441no—
441M16—3441no—
442M16—1722no—
443M16—1721no—
444M16—1721no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—431no—
450C2×C8—431no—
451C2×C8—431no—
452C2×C8—431no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8—1722no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—431no—
463C4⋊C4—431no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—1721no—
473C4⋊C4—1721no—
474C22⋊C4—41no—
475C22⋊C4—861no—
476C22⋊C4—861no—
477C22⋊C4—861no—
478C22⋊C4—861no—
479C22⋊C4—861no—
480C42—41no—
481C42—861no—
482C42#1062189811yescharacteristic
483C42D4×D4311yescharacteristic
484C42D4×D4311yescharacteristic
485C42C23×D4311yescharacteristic
486C23—861no—
487C23#1306329811yescharacteristic
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—861no—
492Q8—861no—
493Q8—3442no—
494Q8—1721no—
495Q8—1721no—
496Q8—1721no—
497Q8—1721no—
498D4—861no—
499D4—861no—
500D4—3441no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—3442no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4—1721no—
516C2×C4#1306329811yescharacteristic
517C2×C4#1306329811yescharacteristic
518C2×C4#1306329811yescharacteristic
519C2×C4C2×D4×D4311yescharacteristic
520C2×C4C2×D4×D4311yescharacteristic
521C2×C4C2×#1062189811yescharacteristic
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—861no—
527C8—861no—
528C8—861no—
529C8—861no—
530C8—1721no—
531C8—1721no—
532C22—21no—
533C22—21no—
534C22—21no—
535C22—1721no—
536C22—1721no—
537C22—1721no—
538C22C2×#1306329811yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—21no—
543C4—81no—
544C4—81no—
545C4—3441no—
546C4—3441no—
547C4—1721no—
548C4—1721no—
549C4—1721no—
550C4#1458369811yescharacteristic
551C4#1458369811yescharacteristic
552C4#1458370611yescharacteristic
553C4#1458371311yescharacteristic
554C2—41no—
555C2—3441no—
556C2#1914409211yescharacteristic
557C2#1914428911yescharacteristic
558C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1554C2
socleC22×C43C2×#121
prime radical#13063299D4
hypercenter#1554D43
hypocenterC43#19381
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
3. #19144977C2semidirect
5. #19134180C2semidirect
6. #19134173C2semidirect
7. #19134152C2semidirect
8. #19134145C2semidirect
9. #19134056C2semidirect
10. #19134049C2semidirect
11. #19134028C2semidirect
12. #19134021C2semidirect
13. #19133363C2semidirect
14. #19133279C2semidirect
15. C43×#1554C2semidirect
288. #1554D43semidirect
346. C43#19381semidirect

Maximal subgroups

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

subgroupindex
#191459622
#191458272
#191449772
#191435932
#191341802
#191341732
#191341522
#191341452
#191340562
#191340492
#191340282
#191340212
#191333632
#191332792
C43×#15542
#1938143