Finite Group Databasebeta

← #25086853

Subgroups — #25086853

Order 11008.

564 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147468C211yesmaximal, characteristic
2#19147273C211yesmaximal, characteristic, complemented
3#19146983C211yesmaximal, characteristic
4#19134273C211yesmaximal, characteristic, complemented
5#19134101C211yesmaximal, characteristic, complemented
6#19134048C211yesmaximal, characteristic
7#19133997C211yesmaximal, characteristic, complemented
8#19133996C211yesmaximal, characteristic, complemented
9#19133809C211yesmaximal, characteristic
10#19133752C211yesmaximal, characteristic, complemented
11#19133735C211yesmaximal, characteristic, complemented
12#19133727C211yesmaximal, characteristic
13#19133443C211yesmaximal, characteristic, complemented
14SD16⋊(C43⋊C8)C211yesmaximal, characteristic
15C43×#3385C211yesmaximal, characteristic
16#14583628C2211yescharacteristic
17#14583606C2211yescharacteristic
18#14583302C2211yescharacteristic
19#14583299—21no—
20#14583297C2211yescharacteristic
21#14583278C2211yescharacteristic
22#14583251—21no—
23#14583251C2211yescharacteristic
24#14583249C2211yescharacteristic
25#14583234—21no—
26#14583232—21no—
27#14583204—21no—
28#14583201—21no—
29#14583194C2211yescharacteristic
30#14583194C2211yescharacteristic
31#14583191—21no—
32#14583191C2211yescharacteristic
33#14583191C2211yescharacteristic
34#14583179C2211yescharacteristic
35#14583138—21no—
36#14583109—21no—
37#14583109C2211yescharacteristic
38Q8×C43⋊C8C2211yescharacteristic
39C8×Dic86C2211yescharacteristic
40C4×#10621885—21no—
41C4×#10621885C2211yescharacteristic
42SD16×Dic43—21no—
43D4×C43⋊C8C2211yescharacteristic
44C2×#13063258—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582648C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582644C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53#14582629C2211yescharacteristic
54D4⋊(C43⋊C8)C2211yescharacteristic
55#14582620C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#554C2211yescharacteristic
58C43×#501—21no—
59C43×#500C2211yescharacteristic
60C43×#479—21no—
61C43×#477C2211yescharacteristic
62C43×#476C2211yescharacteristic
63C43×#474—21no—
64C43×#446C2211yescharacteristic
65C43×#440—21no—
66C4×SD16×C43C2211yescharacteristic
67C2×#10621885—21no—
68C2×#10621885—41no—
69C2×#10621885D411yescharacteristic
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063316—21no—
75#13063316—21no—
76#13063316—41no—
77#13063304—21no—
78#13063302—41no—
79Q8×Dic43—21no—
80C4×Dic86—21no—
81C4×Dic86C2311yescharacteristic
82D4×Dic43—21no—
83C2×C4⋊Dic43—21no—
84#13063258—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258D411yescharacteristic
92#13063257—21no—
93#13063257—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)C2311yescharacteristic
96C4⋊(C43⋊C8)C2311yescharacteristic
97C4⋊(C43⋊C8)C2311yescharacteristic
98Dic43⋊C8—21no—
99#13063249—21no—
100#13063249—21no—
101#13063249—41no—
102#13063249D411yescharacteristic
103#13063248—21no—
104#13063248—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248D411yescharacteristic
109#13063246—21no—
110C22⋊(C43⋊C8)—21no—
111C4×C43⋊C8—21no—
112C4×C43⋊C8C2311yescharacteristic
113C4×C43⋊C8C2311yescharacteristic
114C8×Dic43—21no—
115C2×SD16×C43D411yescharacteristic
116C4⋊Q8×C43—21no—
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—41no—
119C4⋊Q8×C43C2311yescharacteristic
120C4⋊Q8×C43C2311yescharacteristic
121#125×C43—21no—
122C22⋊Q8×C43—21no—
123C22⋊Q8×C43—41no—
124C4×Q8×C43—21no—
125C4×Q8×C43—21no—
126C4×Q8×C43C2311yescharacteristic
127C4×Q8×C43C2311yescharacteristic
128C4×D4×C43—21no—
129C4×D4×C43C2311yescharacteristic
130C2×C4⋊C4×C43—21no—
131#107×C43—21no—
132#107×C43—21no—
133#107×C43—21no—
134#106×C43—21no—
135#106×C43D411yescharacteristic
136C4⋊C8×C43—21no—
137C4⋊C8×C43C2311yescharacteristic
138#103×C43—21no—
139#103×C43D411yescharacteristic
140#102×C43—21no—
141#102×C43D411yescharacteristic
142#97×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43—41no—
147C2×Q8×C43C2×D411yescharacteristic
148C2×Q8×C43C2×D411yescharacteristic
149C2×D4×C43C2×D411yescharacteristic
150C22×C4×C43—21no—
151C22×C4×C43—41no—
152C22×Dic43—41no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86C2×D411yescharacteristic
156SD16×C43Q1614yescomplemented
157C2×C8×C43—21no—
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43—41no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43C2×D411yescharacteristic
171C4⋊C4×C43C2×D411yescharacteristic
172C4⋊C4×C43C2×D411yescharacteristic
173C22⋊C4×C43—21no—
174C22⋊C4×C43—41no—
175C42×C43—21no—
176C42×C43—21no—
177C42×C43—41no—
178C42×C43C2411yescharacteristic
179C22⋊Dic43—41no—
180#10621885—41no—
181#10621885—42no—
182#10621885—82no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—41no—
188C4⋊Dic43—41no—
189C4⋊Dic43—41no—
190C4⋊Dic43C2×D411yescharacteristic
191Dic43⋊C4—21no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194C4×Dic43—21no—
195C4×Dic43—41no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—42no—
201C2×C43⋊C8C2×D411yescharacteristic
202C2×C43⋊C8C2×D411yescharacteristic
203C23×C43—21no—
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—81no—
208Q8×C43—81no—
209Q8×C43—161no—
210Q8×C43C2×Q1612yes—
211D4×C43—21no—
212D4×C43C2×Q1612yes—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—161no—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—161no—
231Dic86—21no—
232Dic86—21no—
233Dic86—41no—
234Dic86—41no—
235Dic86—81no—
236C8×C43—21no—
237C8×C43—41no—
238C8×C43C2×Q1612yes—
239C43⋊C8—21no—
240C43⋊C8—21no—
241C43⋊C8—41no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8—41no—
245#19816—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43D4211yescharacteristic
250C4×C43—22no—
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43C22×Q1611yescharacteristic
259C4×C43#57511yescharacteristic
260C4×C43#57811yescharacteristic
261C4×C43#57811yescharacteristic
262Dic43—41no—
263Dic43—41no—
264Dic43—81no—
265Dic43—81no—
266#3385D4311yescharacteristic
267#3381—431no—
268#3363—431no—
269#3338—431no—
270#1723—431no—
271#1692—431no—
272#1683—431no—
273#1676—431no—
274#1676—431no—
275#1644—431no—
276#1636—431no—
277#1633—431no—
278#1632—431no—
279#1584—431no—
280SD16⋊C8—431no—
281C2×C43—42no—
282C2×C43#326911yescharacteristic
283C2×C43D4×Q1611yescharacteristic
284C2×C43#328811yescharacteristic
285Q82C2×D4311yescharacteristic
286#557—431no—
287#554—431no—
288#554C2×D4311yescharacteristic
289#501—21no—
290#500—431no—
291#500C2×D4311yescharacteristic
292#499—861no—
293#498—431no—
294#494—431no—
295#487—431no—
296#487—431no—
297#487—861no—
298#484—861no—
299#484—861no—
300#479—21no—
301#479—861no—
302#478—861no—
303#477—431no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—861no—
308#477C2×D4311yescharacteristic
309#476C2×D4311yescharacteristic
310#474—21no—
311#474—431no—
312#467—861no—
313#462—431no—
314#462—861no—
315#446C2×D4311yescharacteristic
316C8×Q8—431no—
317C8×Q8—431no—
318#440—21no—
319C4×Q16—431no—
320C4×Q16—861no—
321C4×SD16—861no—
322C4×SD16C2×D4311yescharacteristic
323C8×D4—431no—
324C2×#107—861no—
325#335—431no—
326#335—431no—
327#333—431no—
328#333—431no—
329#333—431no—
330#332—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8—431no—
334D4⋊C8—431no—
335#322—431no—
336C43#1981611yescharacteristic, complemented, Sylow
337C2×Q16—431no—
338C2×Q16—861no—
339C2×Q16—1721no—
340C2×SD16C22⋊D4311yescharacteristic
341C22×C8—861no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—41no—
345C4⋊Q8—431no—
346C4⋊Q8—431no—
347C4⋊Q8—861no—
348C4⋊Q8C22×D4311yescharacteristic
349C4⋊Q8C22×D4311yescharacteristic
350#125—21no—
351#125—861no—
352#125—861no—
353#125—1721no—
354C22⋊Q8—21no—
355C22⋊Q8—41no—
356C22⋊Q8—861no—
357C22⋊Q8—1721no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—431no—
361C4×Q8—861no—
362C4×Q8—861no—
363C4×Q8C22×D4311yescharacteristic
364C4×Q8C22×D4311yescharacteristic
365C4×D4—21no—
366C4×D4—861no—
367C4×D4C22×D4311yescharacteristic
368C2×C4⋊C4—21no—
369C2×C4⋊C4—861no—
370#107—21no—
371#107—21no—
372#107—21no—
373#107—431no—
374#107—861no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107—861no—
381#106—21no—
382#106—861no—
383#106—861no—
384#106C22⋊D4311yescharacteristic
385C4⋊C8—21no—
386C4⋊C8—431no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8C22×D4311yescharacteristic
392#103—21no—
393#103—431no—
394#103—431no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—1721no—
403#103C22⋊D4311yescharacteristic
404#102—21no—
405#102—861no—
406#102C22⋊D4311yescharacteristic
407C22⋊C8—861no—
408#97—21no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8C22×D4311yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—41no—
417C2×Q8—431no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8D4×D4311yescharacteristic
421C2×Q8C2×C22⋊D4311yescharacteristic
422C2×D4C2×C22⋊D4311yescharacteristic
423C22×C4—21no—
424C22×C4—41no—
425C22×C4—1721no—
426Q16—3442no—
427Q16—1721no—
428Q16—1722no—
429SD16#1062188514yescomplemented
430C2×C8—21no—
431C2×C8—431no—
432C2×C8—431no—
433C2×C8—861no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8—861no—
437C2×C8—1722no—
438C2×C8C2×C22⋊D4311yescharacteristic
439C2×C8C2×C22⋊D4311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—41no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—431no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—1721no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4D4×D4311yescharacteristic
462C4⋊C4C2×C22⋊D4311yescharacteristic
463C4⋊C4C2×C22⋊D4311yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—41no—
466C22⋊C4—1721no—
467C42—21no—
468C42—21no—
469C42—41no—
470C42—861no—
471C42—1721no—
472C42C23×D4311yescharacteristic
473C23—21no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—81no—
478Q8—81no—
479Q8—161no—
480Q8—861no—
481Q8—861no—
482Q8—3441no—
483Q8—1721no—
484Q8—1721no—
485Q8C2×#1062188512yes—
486D4—21no—
487D4C2×#1062188512yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—161no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4—6881no—
503C2×C4C2×D4×D4311yescharacteristic
504C2×C4C22×C22⋊D4311yescharacteristic
505C2×C4#1306337011yescharacteristic
506C8—21no—
507C8—41no—
508C8—861no—
509C8—861no—
510C8—1721no—
511C8—1721no—
512C8—1721no—
513C8—1721no—
514C8C2×#1062188512yes—
515C22—22no—
516C22—41no—
517C22—41no—
518C22D4×C22⋊D4311yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—3441no—
528C4—3441no—
529C4—1721no—
530C4—1721no—
531C4C22×#1062188511yescharacteristic
532C4#1458369811yescharacteristic
533C4#1458371411yescharacteristic
534C4#1458371511yescharacteristic
535C2—42no—
536C2#1914614411yescharacteristic
537C2D4×#1062188511yescharacteristic
538C2#1914635911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3385C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#3385D43
hypocenterC43#19816
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3385

Complements

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

NH ≅ G/Ntype
2. #19147273C2semidirect
4. #19134273C2semidirect
5. #19134101C2semidirect
7. #19133997C2semidirect
8. #19133996C2semidirect
10. #19133752C2semidirect
11. #19133735C2semidirect
13. #19133443C2semidirect
156. SD16×C43Q16semidirect
336. C43#19816semidirect
429. SD16#10621885semidirect

Maximal subgroups

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

subgroupindex
#191474682
#191472732
#191469832
#191342732
#191341012
#191340482
#191339972
#191339962
#191338092
#191337522
#191337352
#191337272
#191334432
SD16⋊(C43⋊C8)2
C43×#33852
#1981643