Finite Group Databasebeta

← #25080337

Subgroups — #25080337

Order 11008.

568 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145928C211yesmaximal, characteristic
2#19145773C211yesmaximal, characteristic
3#19145341C211yesmaximal, characteristic, complemented
4#19143602C211yesmaximal, characteristic
5#19134180C211yesmaximal, characteristic, complemented
6#19134152C211yesmaximal, characteristic, complemented
7#19134084C211yesmaximal, characteristic, complemented
8#19134048C211yesmaximal, characteristic, complemented
9#19134020C211yesmaximal, characteristic, complemented
10#19133974C211yesmaximal, characteristic, complemented
11#19133966C211yesmaximal, characteristic, complemented
12#19133346C211yesmaximal, characteristic, complemented
13#19133258C211yesmaximal, characteristic, complemented
14#19133249C211yesmaximal, characteristic, complemented
15C43×#1691C211yesmaximal, characteristic, complemented
16#14583454C2211yescharacteristic
17#14583454C2211yescharacteristic
18#14583431C2211yescharacteristic
19#14583299—21no—
20#14583279C2211yescharacteristic
21#14583252—21no—
22#14583251C2211yescharacteristic
23#14583251C2211yescharacteristic
24#14583243—21no—
25#14583222—21no—
26#14583204—21no—
27#14583191C2211yescharacteristic
28#14583185C2211yescharacteristic
29#14583185C2211yescharacteristic
30#14583179C2211yescharacteristic
31#14583179C2211yescharacteristic
32#14583158—21no—
33#14583158—21no—
34#14583139—21no—
35#14583125—21no—
36#14583119—21no—
37#14583106C2211yescharacteristic
38#14583026C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40#14583005—21no—
41#14583005—21no—
42#14582975—21no—
43#14582967—21no—
44D4×C43⋊C8C2211yescharacteristic
45#14582957—21no—
46#14582951C2211yescharacteristic
47#14582951C2211yescharacteristic
48C4⋊C8×D43C2211yescharacteristic
49#14582857—21no—
50C4×#10621872C2211yescharacteristic
51#14582651C2211yescharacteristic
52#14582650C2211yescharacteristic
53#14582649C2211yescharacteristic
54#14582648C2211yescharacteristic
55#14582646C2211yescharacteristic
56#14582646C2211yescharacteristic
57#14582645C2211yescharacteristic
58#14582644C2211yescharacteristic
59#14582644C2211yescharacteristic
60C43×#498C2211yescharacteristic
61C43×#476C2211yescharacteristic
62C43×#461C2211yescharacteristic
63C43×#436C2211yescharacteristic
64C43×#335C2211yescharacteristic
65C43×#333C2211yescharacteristic
66C43×#332C2211yescharacteristic
67C2×Dic172—21no—
68C2×Dic172—21no—
69C2×#10621885—21no—
70C2×#10621872D411yescharacteristic
71C2×#10621872D411yescharacteristic
72C22×C43⋊C8—21no—
73C2×C8×D43—21no—
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063318—21no—
77#13063316—21no—
78#13063316—21no—
79#13063316D411yescharacteristic
80#13063312D411yescharacteristic
81#13063307—21no—
82#13063305—21no—
83#13063305—21no—
84#13063305D411yescharacteristic
85#13063301—21no—
86#13063301—21no—
87#13063296D411yescharacteristic
88Q8×Dic43—21no—
89Q8×Dic43—21no—
90C4×Dic86C2311yescharacteristic
91#13063290—21no—
92#13063290—21no—
93C4×C22⋊D43—21no—
94#13063284—21no—
95#13063283—21no—
96#13063283—21no—
97C42×D43C2311yescharacteristic
98#13063258—21no—
99#13063258—21no—
100#13063258—21no—
101#13063257—21no—
102#13063257—21no—
103C4⋊(C43⋊C8)C2311yescharacteristic
104C4⋊(C43⋊C8)C2311yescharacteristic
105C4⋊(C43⋊C8)C2311yescharacteristic
106Dic43⋊C8—21no—
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063248—21no—
113#13063248—21no—
114#13063248—21no—
115#13063248—21no—
116#13063248—21no—
117#13063246—21no—
118#13063246—21no—
119C22⋊(C43⋊C8)—21no—
120(C2×D43)⋊C8—21no—
121(C2×D43)⋊C8—21no—
122#13063235—21no—
123#13063235D411yescharacteristic
124#13063235D411yescharacteristic
125C4×C43⋊C8C2311yescharacteristic
126C8×Dic43—21no—
127C8×Dic43—21no—
128C8×Dic43—21no—
129C2×SD16×C43—21no—
130C2×M16×C43—21no—
131C4⋊Q8×C43C2311yescharacteristic
132C4⋊Q8×C43C2311yescharacteristic
133C4×D4×C43C2311yescharacteristic
134#106×C43—21no—
135#106×C43—21no—
136#106×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#102×C43—21no—
142C22⋊C8×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×D4×C43C2×D411yescharacteristic
147C22×C4×C43—21no—
148C2×C22⋊D43—21no—
149C2×C4×D43C2×D411yescharacteristic
150C2×C4×D43C2×D411yescharacteristic
151C2×C4×D43#4111yescharacteristic
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86C2×D411yescharacteristic
155SD16×C43—81no—
156M16×C43—42no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C2×D411yescharacteristic
167C22⋊C4×C43—21no—
168C42×C43C2411yescharacteristic
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171C22⋊Dic43—21no—
172#10621885—81no—
173(C2×D43)⋊C4—21no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—41no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—41no—
183C4⋊Dic43—41no—
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189C4×Dic43—21no—
190C4×Dic43—41no—
191C4×Dic43—41no—
192C4×Dic43C2×D411yescharacteristic
193C4×Dic43C2×D411yescharacteristic
194C4×Dic43#4111yescharacteristic
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—42no—
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201Dic172—42no—
202Dic172—42no—
203#10621872—22no—
204#10621872—41no—
205C8×D43—81no—
206C23×C43—21no—
207C22×D43#12111yescharacteristic
208Q8×C43—41no—
209Q8×C43—41no—
210Q8×C43—81no—
211D4×C43—21no—
212D4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43C22×D411yescharacteristic
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C2×#4111yescharacteristic
221C22⋊D43—81no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43#12111yescharacteristic
227C2×Dic43#12111yescharacteristic
228C2×Dic43#12111yescharacteristic
229C4×D43—21no—
230C4×D43—21no—
231C4×D43—21no—
232C4×D43—21no—
233C4×D43—41no—
234Dic86—21no—
235Dic86—21no—
236Dic86—41no—
237Dic86—41no—
238Dic86—41no—
239Dic86—41no—
240C8×C43—21no—
241C8×C43—41no—
242C8×C43—41no—
243C8×C43—41no—
244C8×C43#13512yes—
245C43⋊C8—21no—
246C43⋊C8—21no—
247C43⋊C8—41no—
248C43⋊C8—41no—
249C43⋊C8—41no—
250#19251—431nomaximal, Sylow
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43C2×#12111yescharacteristic
255C2×D43—21no—
256C2×D43—21no—
257C2×D43—21no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—81no—
261C4×C43—81no—
262C4×C43C2×#13511yescharacteristic
263C4×C43#57511yescharacteristic
264C4×C43#57711yescharacteristic
265C4×C43#57811yescharacteristic
266Dic43—21no—
267Dic43—21no—
268Dic43—21no—
269Dic43—41no—
270Dic43—41no—
271Dic43—81no—
272Dic43—81no—
273#3248—431no—
274#3233—431no—
275#3185—431no—
276#2969—431no—
277#1704—431no—
278#1700—431no—
279#1691D4311yescharacteristic, complemented
280#1689—431no—
281#1683—431no—
282#1679—431no—
283#1672—431no—
284#1670—431no—
285#1565—431no—
286#1544—431no—
287#1542—431no—
288C2×C43—81no—
289C2×C43#303511yescharacteristic
290C2×C43#306311yescharacteristic
291C2×C43#306911yescharacteristic
292D43—41no—
293#533—431no—
294#533—431no—
295#529—431no—
296#499—861no—
297#498C2×D4311yescharacteristic
298#494—431no—
299#488—861no—
300#487—431no—
301#487—431no—
302#485—861no—
303#482—861no—
304#479—861no—
305#477—431no—
306#476C2×D4311yescharacteristic
307#475—431no—
308#475—431no—
309#474—431no—
310#474—431no—
311#470—861no—
312#470—861no—
313#467—861no—
314#465—861no—
315#464—861no—
316#462—431no—
317#461C2×D4311yescharacteristic
318#446—431no—
319C8×Q8—431no—
320#441—861no—
321#441—861no—
322#436—861no—
323#436C2×D4311yescharacteristic
324#435—861no—
325C8×D4—431no—
326#433—861no—
327#431—431no—
328#431—431no—
329C2×C4⋊C8—431no—
330#405—861no—
331C4×M16—431no—
332#335—431no—
333#335C2×D4311yescharacteristic
334#334—431no—
335#334—431no—
336#333—431no—
337#333C2×D4311yescharacteristic
338#332—431no—
339#332—431no—
340#332—431no—
341#332—431no—
342#332—431no—
343#332C2×D4311yescharacteristic
344C43#1925111yescharacteristic, complemented, Sylow
345C2×Q16—861no—
346C2×Q16—861no—
347C2×Q16—861no—
348C2×SD16—21no—
349C2×M16—21no—
350C2×M16—431no—
351C2×M16—431no—
352C22×C8—861no—
353C22×C8—861no—
354C4⋊Q8—431no—
355C4⋊Q8—431no—
356C4⋊Q8C22×D4311yescharacteristic
357C4⋊Q8C22×D4311yescharacteristic
358#126—861no—
359#125—431no—
360#125—861no—
361#125—861no—
362#124—431no—
363#123—861no—
364C22⋊Q8—431no—
365C22⋊Q8—861no—
366C22⋊Q8—861no—
367C22⋊Q8—861no—
368C22⋊Q8—861no—
369#121—431no—
370C4×Q8—431no—
371C4×Q8—861no—
372C4×Q8—861no—
373C4×Q8—861no—
374C4×Q8—861no—
375C4×D4—861no—
376C4×D4C22×D4311yescharacteristic
377#117—861no—
378#117—861no—
379#117—861no—
380C2×C42—431no—
381#107—861no—
382#107—861no—
383#107—861no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—861no—
388#106—861no—
389C4⋊C8—431no—
390C4⋊C8—431no—
391C4⋊C8—431no—
392C4⋊C8—861no—
393C4⋊C8—861no—
394C4⋊C8—861no—
395C4⋊C8C22×D4311yescharacteristic
396C4⋊C8C22×D4311yescharacteristic
397C4⋊C8C22×D4311yescharacteristic
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#102—21no—
408#102—861no—
409#102—861no—
410C22⋊C8—21no—
411C22⋊C8—861no—
412C22⋊C8—861no—
413C22⋊C8—861no—
414#97—431no—
415#97—431no—
416#97—861no—
417C4×C8—431no—
418C4×C8—861no—
419C4×C8—861no—
420C4×C8—861no—
421C4×C8C22×D4311yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—431no—
425C2×Q8—861no—
426C2×Q8—861no—
427C2×D4—861no—
428C2×D4D4×D4311yescharacteristic
429C22×C4—21no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—431no—
433Q16—3441no—
434Q16—1722no—
435Q16—1722no—
436SD16—81no—
437M16—42no—
438M16—862no—
439M16—1721no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—431no—
444C2×C8—431no—
445C2×C8—861no—
446C2×C8—861no—
447C2×C8—861no—
448C2×C8—3441no—
449C2×C8—1722no—
450C2×C8D4×D4311yescharacteristic
451C2×C8D4×D4311yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—431no—
457C4⋊C4—861no—
458C4⋊C4—861no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—861no—
463C4⋊C4—861no—
464C4⋊C4—861no—
465C4⋊C4—1721no—
466C4⋊C4—1721no—
467C4⋊C4—1721no—
468C4⋊C4—1721no—
469C4⋊C4D4×D4311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—861no—
472C22⋊C4—861no—
473C22⋊C4—861no—
474C22⋊C4—861no—
475C22⋊C4—1721no—
476C22⋊C4—1721no—
477C42—431no—
478C42—431no—
479C42—431no—
480C42—861no—
481C42—1721no—
482C42—1721no—
483C42C23×D4311yescharacteristic
484C23—21no—
485C23—431no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—861no—
490Q8—861no—
491Q8—1721no—
492Q8—1721no—
493Q8—1721no—
494Q8—1721no—
495D4—21no—
496D4—21no—
497D4—3441no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—431no—
504C2×C4—431no—
505C2×C4—431no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4—1721no—
515C2×C4C2×D4×D4311yescharacteristic
516C2×C4C2×D4×D4311yescharacteristic
517C2×C4#41×D4311yescharacteristic
518C8—21no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—861no—
523C8—861no—
524C8—1721no—
525C8—1721no—
526C8—1721no—
527C8#1306334612yes—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—861no—
532C22—861no—
533C22—861no—
534C22#121×D4311yescharacteristic
535C4—21no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—861no—
540C4—861no—
541C4—861no—
542C4—3441no—
543C4—3441no—
544C4—1721no—
545C4—1721no—
546C4C2×#1306334611yescharacteristic
547C4#1458369811yescharacteristic
548C4#1458370911yescharacteristic
549C4#1458371511yescharacteristic
550C2—81no—
551C2—1721no—
552C2#1914405111yescharacteristic
553C2#1914428111yescharacteristic
554C2#1914432711yescharacteristic
subgroupG/H
centerC22#121×D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1691C2
socleC22×C43C2×#121
prime radical#13063296D4
hypercenter#1691D43
hypocenterC43#19251
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1691

Complements

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

NH ≅ G/Ntype
3. #19145341C2semidirect
5. #19134180C2semidirect
6. #19134152C2semidirect
7. #19134084C2semidirect
8. #19134048C2semidirect
9. #19134020C2semidirect
10. #19133974C2semidirect
11. #19133966C2semidirect
12. #19133346C2semidirect
13. #19133258C2semidirect
14. #19133249C2semidirect
15. C43×#1691C2semidirect
279. #1691D43semidirect
344. C43#19251semidirect

Maximal subgroups

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

subgroupindex
#191459282
#191457732
#191453412
#191436022
#191341802
#191341522
#191340842
#191340482
#191340202
#191339742
#191339662
#191333462
#191332582
#191332492
C43×#16912
#1925143