Finite Group Databasebeta

← #25086860

Subgroups — #25086860

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#19147501C211yesmaximal, characteristic
2#19147466C211yesmaximal, characteristic
3#19146989C211yesmaximal, characteristic
4#19134275C211yesmaximal, characteristic, complemented
5#19134099C211yesmaximal, characteristic, complemented
6#19134043C211yesmaximal, characteristic
7#19133999C211yesmaximal, characteristic, complemented
8#19133997C211yesmaximal, characteristic, complemented
9#19133807C211yesmaximal, characteristic
10#19133753C211yesmaximal, characteristic, complemented
11#19133735C211yesmaximal, characteristic, complemented
12#19133728C211yesmaximal, characteristic
13#19133446C211yesmaximal, characteristic, complemented
14#19133405C211yesmaximal, characteristic
15C43×#3363C211yesmaximal, characteristic, complemented
16#14583609C2211yescharacteristic
17#14583609C2211yescharacteristic
18#14583305—21no—
19#14583304C2211yescharacteristic
20#14583302C2211yescharacteristic
21#14583298—21no—
22#14583295C2211yescharacteristic
23#14583278C2211yescharacteristic
24#14583251C2211yescharacteristic
25#14583233—21no—
26#14583233—21no—
27#14583206—21no—
28#14583206—21no—
29#14583196—21no—
30#14583194C2211yescharacteristic
31#14583194C2211yescharacteristic
32#14583194C2211yescharacteristic
33#14583194C2211yescharacteristic
34#14583186C2211yescharacteristic
35#14583176—21no—
36#14583176C2211yescharacteristic
37#14583137—21no—
38#14583030C2211yescharacteristic
39Q8×C43⋊C8C2211yescharacteristic
40#14582997—21no—
41C4×#10621884—21no—
42C4×#10621884C2211yescharacteristic
43C8×D172C2211yescharacteristic
44#107×D43—21no—
45#14582652C2211yescharacteristic
46#14582651C2211yescharacteristic
47#14582648C2211yescharacteristic
48#14582647C2211yescharacteristic
49#14582647C2211yescharacteristic
50#14582645C2211yescharacteristic
51Q8⋊(C43⋊C8)C2211yescharacteristic
52Q8⋊(C43⋊C8)C2211yescharacteristic
53Q8⋊(C43⋊C8)C2211yescharacteristic
54#14582626C2211yescharacteristic
55#14582621C2211yescharacteristic
56Q82×C43C2211yescharacteristic
57C43×#557C2211yescharacteristic
58C43×#487—21no—
59C43×#487C2211yescharacteristic
60C43×#477—21no—
61C43×#477C2211yescharacteristic
62C43×#462—21no—
63C43×#462C2211yescharacteristic
64C8×Q8×C43C2211yescharacteristic
65C4×Q16×C43—21no—
66C4×Q16×C43C2211yescharacteristic
67C2×#10621885—41no—
68C2×#10621884D411yescharacteristic
69C2×C8×D43—21no—
70#13063325C2311yescharacteristic
71#13063325C2311yescharacteristic
72#13063317—21no—
73#13063317—21no—
74#13063303—41no—
75#13063303—41no—
76#13063301—21no—
77#13063301—21no—
78C4×D172—21no—
79C4×D172—21no—
80C4×D172C2311yescharacteristic
81C4⋊C4×D43—21no—
82C4⋊C4×D43—21no—
83#13063259—21no—
84#13063259—21no—
85#13063258—21no—
86#13063258—21no—
87#13063258—21no—
88#13063258—21no—
89#13063258—21no—
90#13063258—21no—
91#13063258—21no—
92#13063256—21no—
93#13063256—21no—
94#13063256—21no—
95#13063256D411yescharacteristic
96C4⋊(C43⋊C8)—21no—
97C4⋊(C43⋊C8)—21no—
98C4⋊(C43⋊C8)C2311yescharacteristic
99C4⋊(C43⋊C8)C2311yescharacteristic
100C4⋊(C43⋊C8)C2311yescharacteristic
101#13063249—21no—
102#13063249—21no—
103#13063249—21no—
104#13063249—21no—
105#13063249D411yescharacteristic
106#13063248—41no—
107#13063245—21no—
108#13063245—21no—
109#13063245D411yescharacteristic
110(C2×D43)⋊C8—21no—
111#13063236—21no—
112C4×C43⋊C8—21no—
113C4×C43⋊C8C2311yescharacteristic
114C4×C43⋊C8C2311yescharacteristic
115C2×Q16×C43—21no—
116C2×Q16×C43D411yescharacteristic
117C4⋊Q8×C43—21no—
118C4⋊Q8×C43—21no—
119C4⋊Q8×C43—21no—
120C4⋊Q8×C43—41no—
121C4⋊Q8×C43C2311yescharacteristic
122C4⋊Q8×C43C2311yescharacteristic
123#125×C43—21no—
124#125×C43—41no—
125C4×Q8×C43—21no—
126C4×Q8×C43—21no—
127C4×Q8×C43—21no—
128C4×Q8×C43—21no—
129C4×Q8×C43C2311yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43—21no—
133#107×C43D411yescharacteristic
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136#103×C43—21no—
137#103×C43—21no—
138#103×C43—21no—
139#103×C43—21no—
140#103×C43D411yescharacteristic
141#103×C43D411yescharacteristic
142C4×C8×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×Q8×C43C2×D411yescharacteristic
150C2×D172C2×D411yescharacteristic
151C2×C4×D43—21no—
152C2×C4×D43—41no—
153C2×C4×D43—41no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156Q16×C43—41no—
157Q16×C43—42no—
158C2×C8×C43—21no—
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—41no—
171C4⋊C4×C43—41no—
172C4⋊C4×C43—41no—
173C4⋊C4×C43C2×D411yescharacteristic
174C4⋊C4×C43C2×D411yescharacteristic
175C4⋊C4×C43C2×D411yescharacteristic
176C42×C43—21no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—41no—
180C42×C43—41no—
181C42×C43C2411yescharacteristic
182#10621885—82no—
183#10621884Q1614yescomplemented
184(C2×D43)⋊C4—21no—
185(C2×D43)⋊C4—41no—
186(C2×D43)⋊C4—41no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43C2×D411yescharacteristic
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195Dic43⋊C4—41no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202C8×D43—42no—
203C22×D43—21no—
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208Q8×C43—21no—
209Q8×C43—41no—
210Q8×C43—41no—
211Q8×C43—81no—
212Q8×C43—161no—
213Q8×C43C2×Q1612yes—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43C22×D411yescharacteristic
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228D172—21no—
229D172C2×Q1612yes—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—161no—
233C4×D43—161no—
234Dic86—81no—
235Dic86—81no—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—41no—
239C43⋊C8—21no—
240C43⋊C8—41no—
241C43⋊C8—41no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8C2×Q1612yes—
245#19816—431nomaximal, Sylow
246C22×C43D4211yescharacteristic
247C2×D43—22no—
248C2×D43—41no—
249C2×D43—41no—
250C4×C43—22no—
251C4×C43—21no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43—41no—
256C4×C43—41no—
257C4×C43—81no—
258C4×C43—81no—
259C4×C43C22×Q1611yescharacteristic
260C4×C43#57511yescharacteristic
261C4×C43#57811yescharacteristic
262C4×C43#57811yescharacteristic
263Dic43—41no—
264Dic43—81no—
265Dic43—81no—
266#3385—431no—
267#3381—431no—
268#3363D4311yescharacteristic, complemented
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#326911yescharacteristic
282C2×C43D4×Q1611yescharacteristic
283C2×C43#328811yescharacteristic
284D43—42no—
285Q82C2×D4311yescharacteristic
286#557C2×D4311yescharacteristic
287#554—431no—
288#554—431no—
289#501—861no—
290#500—431no—
291#500—431no—
292#499—861no—
293#498—431no—
294#494—431no—
295#487—21no—
296#487—431no—
297#487C2×D4311yescharacteristic
298#484—861no—
299#484—861no—
300#479—861no—
301#479—861no—
302#478—861no—
303#477—21no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—431no—
308#477C2×D4311yescharacteristic
309#476—431no—
310#474—431no—
311#474—861no—
312#467—861no—
313#462—21no—
314#462C2×D4311yescharacteristic
315#446—431no—
316C8×Q8—431no—
317C8×Q8C2×D4311yescharacteristic
318#440—861no—
319C4×Q16—21no—
320C4×Q16C2×D4311yescharacteristic
321C4×SD16—431no—
322C4×SD16—861no—
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—21no—
338C2×Q16—1721no—
339C2×Q16C22⋊D4311yescharacteristic
340C2×SD16—431no—
341C22×C8—861no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—41no—
346C4⋊Q8—431no—
347C4⋊Q8—431no—
348C4⋊Q8C22×D4311yescharacteristic
349C4⋊Q8C22×D4311yescharacteristic
350#125—21no—
351#125—41no—
352#125—861no—
353#125—861no—
354C22⋊Q8—861no—
355C22⋊Q8—861no—
356C22⋊Q8—1721no—
357C22⋊Q8—1721no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8C22×D4311yescharacteristic
363C4×Q8C22×D4311yescharacteristic
364C4×Q8C22×D4311yescharacteristic
365C4×D4—431no—
366C4×D4—861no—
367C4×D4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370#107—21no—
371#107—861no—
372#107—861no—
373#107—861no—
374#107—861no—
375#107—861no—
376#107—861no—
377#107—861no—
378#107—861no—
379#107—861no—
380#107C22⋊D4311yescharacteristic
381#106—431no—
382#106—861no—
383#106—861no—
384#106—861no—
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—21no—
394#103—21no—
395#103—21no—
396#103—431no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—1721no—
402#103C22⋊D4311yescharacteristic
403#103C22⋊D4311yescharacteristic
404#102—431no—
405#102—861no—
406#102—861no—
407C22⋊C8—861no—
408#97—861no—
409C4×C8—21no—
410C4×C8—431no—
411C4×C8—431no—
412C4×C8—861no—
413C4×C8C22×D4311yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—41no—
417C2×Q8—861no—
418C2×Q8—861no—
419C2×Q8D4×D4311yescharacteristic
420C2×Q8C2×C22⋊D4311yescharacteristic
421C2×Q8C2×C22⋊D4311yescharacteristic
422C2×D4—431no—
423C22×C4—861no—
424C22×C4—1721no—
425C22×C4—1721no—
426Q16—41no—
427Q16—42no—
428Q16—3442no—
429SD16—434no—
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—21no—
447C4⋊C4—41no—
448C4⋊C4—41no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—431no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—861no—
456C4⋊C4—861no—
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—861no—
465C22⋊C4—1721no—
466C22⋊C4—1721no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42C23×D4311yescharacteristic
473C23—861no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—161no—
483Q8—3441no—
484Q8—3441no—
485Q8Q16×D4312yes—
486D4—432no—
487D4—861no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—861no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1721no—
501C2×C4—6881no—
502C2×C4—6881no—
503C2×C4C2×D4×D4311yescharacteristic
504C2×C4C22×C22⋊D4311yescharacteristic
505C2×C4#1306337011yescharacteristic
506C8—21no—
507C8—21no—
508C8—41no—
509C8—432no—
510C8—861no—
511C8—1721no—
512C8—1721no—
513C8—1721no—
514C8—1721no—
515C22—862no—
516C22—1721no—
517C22—1721no—
518C22D4×C22⋊D4311yescharacteristic
519C4—22no—
520C4—21no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—81no—
527C4—81no—
528C4—3441no—
529C4—3441no—
530C4—1721no—
531C4C2×Q16×D4311yescharacteristic
532C4#1458369711yescharacteristic
533C4#1458371211yescharacteristic
534C4#1458371411yescharacteristic
535C2—1722no—
536C2#1914615111yescharacteristic
537C2Q16×C22⋊D4311yescharacteristic
538C2#1914635711yescharacteristic
subgroupG/H
centerC22D4×C22⋊D43
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3363C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#3363D43
hypocenterC43#19816
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #3363

Complements

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

NH ≅ G/Ntype
4. #19134275C2semidirect
5. #19134099C2semidirect
7. #19133999C2semidirect
8. #19133997C2semidirect
10. #19133753C2semidirect
11. #19133735C2semidirect
13. #19133446C2semidirect
15. C43×#3363C2semidirect
183. #10621884Q16semidirect
268. #3363D43semidirect
336. C43#19816semidirect

Maximal subgroups

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

subgroupindex
#191475012
#191474662
#191469892
#191342752
#191340992
#191340432
#191339992
#191339972
#191338072
#191337532
#191337352
#191337282
#191334462
#191334052
C43×#33632
#1981643