Finite Group Databasebeta

← #25084231

Subgroups — #25084231

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#19145919C211yesmaximal, characteristic
2#19145820C211yesmaximal, characteristic, complemented
3#19145712C211yesmaximal, characteristic, complemented
4#19143754C211yesmaximal, characteristic, complemented
5#19134133C211yesmaximal, characteristic, complemented
6#19134125C211yesmaximal, characteristic, complemented
7#19134121C211yesmaximal, characteristic, complemented
8#19134119C211yesmaximal, characteristic, complemented
9#19134003C211yesmaximal, characteristic, complemented
10#19133999C211yesmaximal, characteristic, complemented
11#19133993C211yesmaximal, characteristic, complemented
12#19133377C211yesmaximal, characteristic, complemented
13#19133287C211yesmaximal, characteristic, complemented
14#333×D43C211yesmaximal, characteristic, complemented
15C43×#1678C211yesmaximal, characteristic, complemented
16#14583447C2211yescharacteristic
17C4⋊Q8×D43C2211yescharacteristic
18#14583436C2211yescharacteristic
19#14583307—21no—
20#14583304C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583260—21no—
23#14583245C2211yescharacteristic
24#14583228—21no—
25#14583214—21no—
26#14583211—21no—
27#14583211—21no—
28#14583201—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583190C2211yescharacteristic
32#14583190C2211yescharacteristic
33#14583186C2211yescharacteristic
34#14583177—21no—
35#14583177—21no—
36#14583134—21no—
37#14583125—21no—
38#14583116—21no—
39#14583091C2211yescharacteristic
40#14583030C2211yescharacteristic
41#14582978C2211yescharacteristic
42#14582969—21no—
43C8×D172—21no—
44#14582964C2211yescharacteristic
45#14582958—21no—
46#14582955C2211yescharacteristic
47#14582950C2211yescharacteristic
48#14582924—21no—
49C4⋊C8×D43C2211yescharacteristic
50C4⋊C8×D43C2211yescharacteristic
51#14582652C2211yescharacteristic
52#14582651C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582647C2211yescharacteristic
58#14582647C2211yescharacteristic
59#14582643C2211yescharacteristic
60C43×#486C2211yescharacteristic
61C43×#477C2211yescharacteristic
62C43×#460C2211yescharacteristic
63C8×Q8×C43C2211yescharacteristic
64C43×#334C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#331C2211yescharacteristic
67C2×#10621900—21no—
68C2×Q8×D43—21no—
69C2×#10621882—21no—
70C2×#10621872—21no—
71C2×C8×D43—21no—
72C2×C8×D43—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—21no—
78#13063323—21no—
79#13063320—21no—
80#13063316D411yescharacteristic
81#13063314D411yescharacteristic
82#13063312—21no—
83#13063310—21no—
84#13063301D411yescharacteristic
85#13063300D411yescharacteristic
86#13063296—21no—
87#13063296—21no—
88C4×D172—21no—
89C4×D172C2311yescharacteristic
90D4×Dic43—21no—
91D4×Dic43—21no—
92#13063282—21no—
93C4⋊C4×D43—21no—
94C4⋊C4×D43—21no—
95C42×D43C2311yescharacteristic
96#13063259—21no—
97#13063259—21no—
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063258—21no—
102#13063257—21no—
103#13063257—21no—
104#13063256—21no—
105C4⋊(C43⋊C8)—21no—
106C4⋊(C43⋊C8)C2311yescharacteristic
107C4⋊(C43⋊C8)C2311yescharacteristic
108C4⋊(C43⋊C8)C2311yescharacteristic
109Dic43⋊C8—21no—
110Dic43⋊C8—21no—
111Dic43⋊C8D411yescharacteristic
112Dic43⋊C8D411yescharacteristic
113#13063249—21no—
114#13063249—21no—
115#13063247—21no—
116#13063247—21no—
117#13063246—21no—
118#13063246—21no—
119#13063246—21no—
120#13063245—21no—
121(C2×D43)⋊C8—21no—
122(C2×D43)⋊C8—21no—
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8D411yescharacteristic
125(C2×D43)⋊C8D411yescharacteristic
126#13063236—21no—
127#13063235—21no—
128C4×C43⋊C8C2311yescharacteristic
129C2×SD16×C43—21no—
130C4⋊Q8×C43C2311yescharacteristic
131#127×C43C2311yescharacteristic
132C4×Q8×C43C2311yescharacteristic
133#107×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#102×C43—21no—
140#102×C43—21no—
141#102×C43—21no—
142C4×C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43C2×D411yescharacteristic
146C2×D4×C43—21no—
147C2×D4×C43—21no—
148C2×D4×C43—21no—
149C2×C22⋊D43—41no—
150C22×Dic43—41no—
151Q8×D43—82no—
152#10621900—82no—
153C2×D172—21no—
154C2×D172C2×D411yescharacteristic
155C2×C4×D43—21no—
156C2×C4×D43—41no—
157C2×C4×D43C2×D411yescharacteristic
158C2×C4×D43C2×D411yescharacteristic
159C2×C4×D43#4111yescharacteristic
160C2×Dic86—21no—
161C2×Dic86—21no—
162C2×Dic86—41no—
163SD16×C43—81no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43C2×D411yescharacteristic
168C2×C8×C43C2×D411yescharacteristic
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43C2×D411yescharacteristic
173C42×C43—21no—
174C42×C43C2411yescharacteristic
175C22⋊Dic43—41no—
176C22⋊Dic43—41no—
177#10621882—81no—
178(C2×D43)⋊C4—21no—
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—21no—
188C4⋊Dic43C2×D411yescharacteristic
189Dic43⋊C4—21no—
190Dic43⋊C4—21no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43C2×D411yescharacteristic
195C4×Dic43#4111yescharacteristic
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201#10621872—81no—
202C8×D43—81no—
203C8×D43—81no—
204C8×D43—81no—
205C23×C43—41no—
206C22×D43—21no—
207C22×D43#12111yescharacteristic
208Q8×C43—21no—
209Q8×C43—21no—
210Q8×C43—81no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—41no—
214D4×C43—41no—
215D4×C43—81no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43C2×#4111yescharacteristic
222C22⋊D43—82no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—82no—
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229C2×Dic43#12111yescharacteristic
230D172—21no—
231D172—21no—
232D172—42no—
233C4×D43—22no—
234C4×D43—21no—
235C4×D43—21no—
236C4×D43—21no—
237C4×D43—21no—
238C4×D43—41no—
239C4×D43—41no—
240C4×D43—82no—
241Dic86—82no—
242Dic86—81no—
243Dic86—81no—
244C8×C43—21no—
245C8×C43—21no—
246C8×C43—41no—
247C8×C43—41no—
248C8×C43—41no—
249C43⋊C8—21no—
250C43⋊C8—21no—
251C43⋊C8—41no—
252C43⋊C8—41no—
253C43⋊C8—41no—
254#19591—431nomaximal, Sylow
255C22×C43—81no—
256C22×C43—81no—
257C22×C43—81no—
258C22×C43C2×#12111yescharacteristic
259C2×D43—21no—
260C2×D43—21no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43#47212yes—
265C4×C43—21no—
266C4×C43—41no—
267C4×C43—41no—
268C4×C43—81no—
269C4×C43#57711yescharacteristic
270C4×C43#57711yescharacteristic
271C4×C43#57811yescharacteristic
272C4×C43#57811yescharacteristic
273Dic43—21no—
274Dic43—21no—
275Dic43—21no—
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#1678D4311yescharacteristic, complemented
288#1677—431no—
289#1676—431no—
290#1675—431no—
291#1573—431no—
292#1551—431no—
293C2×#333—431no—
294C2×C43—161no—
295C2×C43#304611yescharacteristic
296C2×C43#306311yescharacteristic
297C2×C43C2×#47211yescharacteristic
298D43—22no—
299D43—81no—
300#532—431no—
301C2×C4⋊Q8—431no—
302#529—431no—
303#501—861no—
304#500—431no—
305#500—431no—
306#489—861no—
307#486—431no—
308#486C2×D4311yescharacteristic
309#483—861no—
310#480—861no—
311#480—861no—
312#480—861no—
313#478—861no—
314#477—431no—
315#477—431no—
316#477C2×D4311yescharacteristic
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#460C2×D4311yescharacteristic
326#459—431no—
327#446—431no—
328C8×Q8C2×D4311yescharacteristic
329#436—431no—
330#435—861no—
331C8×D4—431no—
332C8×D4—861no—
333#433—861no—
334#432—431no—
335#431—431no—
336#424—861no—
337C2×C4⋊C8—431no—
338C2×C4⋊C8—431no—
339#335—431no—
340#335—431no—
341#334—431no—
342#334C2×D4311yescharacteristic
343#333—431no—
344#333—431no—
345#333—431no—
346#333—431no—
347#333—431no—
348#333C2×D4311yescharacteristic
349#331—431no—
350#331C2×D4311yescharacteristic
351C43#1959111yescharacteristic, complemented, Sylow
352C2×#41—861no—
353C22×Q8—861no—
354C2×SD16—21no—
355C2×D8—861no—
356C2×M16—861no—
357C22×C8—861no—
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—431no—
370#124—861no—
371#123—861no—
372C22⋊Q8—431no—
373#121—431no—
374#121—861no—
375#121—861no—
376C4×Q8C22×D4311yescharacteristic
377C4×D4—431no—
378C4×D4—861no—
379C4×D4—861no—
380C4×D4—861no—
381#117—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C42—431no—
385#107—21no—
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—431no—
401C4⋊C8—861no—
402C4⋊C8—861no—
403C4⋊C8—861no—
404C4⋊C8C22×D4311yescharacteristic
405C4⋊C8C22×D4311yescharacteristic
406C4⋊C8C22×D4311yescharacteristic
407#103—21no—
408#103—861no—
409#103—861no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—861no—
414#102—861no—
415#102—861no—
416#102—861no—
417#102—861no—
418#102—861no—
419C22⋊C8—431no—
420C22⋊C8—431no—
421C22⋊C8—861no—
422C22⋊C8—861no—
423C22⋊C8—861no—
424#97—861no—
425#97—861no—
426C4×C8—21no—
427C4×C8—431no—
428C4×C8C22×D4311yescharacteristic
429#41—3442no—
430C2×Q8—21no—
431C2×Q8—861no—
432C2×Q8—861no—
433C2×Q8—3442no—
434C2×Q8—1721no—
435C2×Q8D4×D4311yescharacteristic
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—431no—
440C2×D4—861no—
441C2×D4—1721no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—861no—
446C22×C4—1721no—
447C22×C4—1721no—
448SD16—81no—
449D8—3441no—
450M16—3441no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8—3441no—
460C2×C8—3441no—
461C2×C8—3441no—
462C2×C8D4×D4311yescharacteristic
463C2×C8D4×D4311yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
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—1721no—
476C4⋊C4—1721no—
477C4⋊C4D4×D4311yescharacteristic
478C22⋊C4—861no—
479C22⋊C4—861no—
480C22⋊C4—861no—
481C22⋊C4—861no—
482C22⋊C4—861no—
483C22⋊C4—1721no—
484C22⋊C4—1721no—
485C42—21no—
486C42—431no—
487C42—431no—
488C42—431no—
489C42C23×D4311yescharacteristic
490C23—41no—
491C23—431no—
492C23—861no—
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8—3441no—
497Q8—3441no—
498Q8—3442no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—81no—
504D4—861no—
505D4—861no—
506D4—3442no—
507D4—1722no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—431no—
512C2×C4—431no—
513C2×C4—431no—
514C2×C4—862no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4—3442no—
521C2×C4—3442no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4C2×D4×D4311yescharacteristic
527C2×C4C2×D4×D4311yescharacteristic
528C2×C4#41×D4311yescharacteristic
529C8—21no—
530C8—21no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—861no—
535C8—861no—
536C8—1721no—
537C8—1721no—
538C8—1721no—
539C22—81no—
540C22—81no—
541C22—81no—
542C22—432no—
543C22—861no—
544C22—861no—
545C22—1721no—
546C22—1721no—
547C22—1721no—
548C22#121×D4311yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—861no—
554C4—861no—
555C4—861no—
556C4—3441no—
557C4—3441no—
558C4—1721no—
559C4#1458370511yescharacteristic
560C4#1458370611yescharacteristic
561C4#1458371311yescharacteristic
562C4#1458371511yescharacteristic
563C2—161no—
564C2—862no—
565C2—3441no—
566C2#1914414811yescharacteristic
567C2#1914427911yescharacteristic
568C2#472×D4311yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1678C2
socleC22×C43C2×#121
prime radical#19145919C2
hypercenter#1678D43
hypocenterC43#19591
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1678

Complements

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

NH ≅ G/Ntype
2. #19145820C2semidirect
3. #19145712C2semidirect
4. #19143754C2semidirect
5. #19134133C2semidirect
6. #19134125C2semidirect
7. #19134121C2semidirect
8. #19134119C2semidirect
9. #19134003C2semidirect
10. #19133999C2semidirect
11. #19133993C2semidirect
12. #19133377C2semidirect
13. #19133287C2semidirect
14. #333×D43C2semidirect
15. C43×#1678C2semidirect
287. #1678D43semidirect
351. C43#19591semidirect

Maximal subgroups

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

subgroupindex
#191459192
#191458202
#191457122
#191437542
#191341332
#191341252
#191341212
#191341192
#191340032
#191339992
#191339932
#191333772
#191332872
#333×D432
C43×#16782
#1959143