Finite Group Databasebeta

← #25086857

Subgroups — #25086857

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#19147505C211yesmaximal, characteristic
2#19147474C211yesmaximal, characteristic
3#19147268C211yesmaximal, characteristic, complemented
4#19146983C211yesmaximal, characteristic
5#19134274C211yesmaximal, characteristic, complemented
6#19134099C211yesmaximal, characteristic, complemented
7#19134044C211yesmaximal, characteristic
8#19133998C211yesmaximal, characteristic, complemented
9#19133998C211yesmaximal, characteristic, complemented
10#19133750C211yesmaximal, characteristic, complemented
11#19133737C211yesmaximal, characteristic, complemented
12#19133731C211yesmaximal, characteristic
13#19133448C211yesmaximal, characteristic, complemented
14#19133404C211yesmaximal, characteristic
15C43×#1644C211yesmaximal, characteristic
16Q8×Dic86C2211yescharacteristic
17#14583624C2211yescharacteristic
18#14583606C2211yescharacteristic
19#14583309—21no—
20#14583302C2211yescharacteristic
21#14583302C2211yescharacteristic
22#14583300—21no—
23#14583295C2211yescharacteristic
24#14583279C2211yescharacteristic
25#14583249C2211yescharacteristic
26#14583248—21no—
27#14583234—21no—
28#14583232—21no—
29#14583205—21no—
30#14583203—21no—
31#14583197—21no—
32#14583195C2211yescharacteristic
33#14583195C2211yescharacteristic
34#14583194C2211yescharacteristic
35#14583192—21no—
36#14583191C2211yescharacteristic
37#14583191C2211yescharacteristic
38#14583189C2211yescharacteristic
39#14583179—21no—
40#14583138—21no—
41#14583107—21no—
42#14583030C2211yescharacteristic
43#14583023C2211yescharacteristic
44#14583023C2211yescharacteristic
45#14582999—21no—
46Q16×Dic43—21no—
47C4×#10621885C2211yescharacteristic
48#14582990—21no—
49C4×#10621883C2211yescharacteristic
50D4×C43⋊C8C2211yescharacteristic
51C2×#13063258—21no—
52#14582651C2211yescharacteristic
53#14582651C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582645C2211yescharacteristic
57#14582631C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582621C2211yescharacteristic
60C43×#554C2211yescharacteristic
61C43×#487C2211yescharacteristic
62C43×#474C2211yescharacteristic
63C43×#462C2211yescharacteristic
64C43×#333C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×D4⋊C8C2211yescharacteristic
67C2×Dic172—41no—
68C2×#10621885D411yescharacteristic
69C2×#10621883D411yescharacteristic
70C22×C43⋊C8—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063324—21no—
75#13063324—41no—
76#13063323—21no—
77#13063316—21no—
78#13063316—21no—
79#13063315—41no—
80#13063304—21no—
81#13063302—41no—
82Q8×Dic43—21no—
83Q8×Dic43—21no—
84C4×Dic86—21no—
85C4×Dic86C2311yescharacteristic
86C4×Dic86C2311yescharacteristic
87#13063290—21no—
88D4×Dic43—21no—
89C2×C4⋊Dic43—21no—
90#13063259—21no—
91#13063259—21no—
92#13063258—21no—
93#13063258—21no—
94#13063258—21no—
95#13063258—21no—
96#13063258—21no—
97#13063258—21no—
98#13063258—21no—
99#13063258D411yescharacteristic
100#13063256—21no—
101#13063256—21no—
102#13063256—21no—
103#13063256D411yescharacteristic
104C4⋊(C43⋊C8)—21no—
105C4⋊(C43⋊C8)C2311yescharacteristic
106C4⋊(C43⋊C8)C2311yescharacteristic
107Dic43⋊C8—21no—
108Dic43⋊C8—21no—
109#13063250—21no—
110#13063250—21no—
111#13063249—21no—
112#13063249—21no—
113#13063249—21no—
114#13063249D411yescharacteristic
115#13063248—21no—
116#13063248—21no—
117#13063248D411yescharacteristic
118#13063248D411yescharacteristic
119#13063246—21no—
120#13063246D411yescharacteristic
121C22⋊(C43⋊C8)—21no—
122#13063236—21no—
123C4×C43⋊C8C2311yescharacteristic
124C4×C43⋊C8C2311yescharacteristic
125C8×Dic43—21no—
126C8×Dic43—21no—
127C2×Q16×C43—21no—
128C4⋊Q8×C43C2311yescharacteristic
129C4⋊Q8×C43C2311yescharacteristic
130#125×C43—21no—
131C22⋊Q8×C43—21no—
132C22⋊Q8×C43—41no—
133C4×Q8×C43C2311yescharacteristic
134C4×D4×C43—21no—
135C4×D4×C43C2311yescharacteristic
136C2×C4⋊C4×C43—21no—
137#107×C43—21no—
138C4⋊C8×C43C2311yescharacteristic
139C4⋊C8×C43C2311yescharacteristic
140#103×C43—21no—
141#103×C43—41no—
142#102×C43—21no—
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43—21no—
145C2×Q8×C43—21no—
146C2×Q8×C43C2×D411yescharacteristic
147C2×D4×C43C2×D411yescharacteristic
148C22×C4×C43—21no—
149C22×C4×C43—41no—
150C22×Dic43—41no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—41no—
154C2×Dic86C2×D411yescharacteristic
155C2×Dic86C2×D411yescharacteristic
156Q16×C43—42no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—41no—
166C4⋊C4×C43—41no—
167C4⋊C4×C43C2×D411yescharacteristic
168C4⋊C4×C43C2×D411yescharacteristic
169C22⋊C4×C43—21no—
170C22⋊C4×C43—41no—
171C42×C43—21no—
172C42×C43C2411yescharacteristic
173C22⋊Dic43—41no—
174#10621885—41no—
175#10621883Q1614yescomplemented
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—41no—
181C4⋊Dic43—41no—
182C4⋊Dic43—41no—
183C4⋊Dic43C2×D411yescharacteristic
184C4⋊Dic43C2×D411yescharacteristic
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—41no—
194C4×Dic43—41no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—42no—
198C2×C43⋊C8C2×D411yescharacteristic
199C2×C43⋊C8C2×D411yescharacteristic
200C2×C43⋊C8C2×D411yescharacteristic
201C2×C43⋊C8C2×D411yescharacteristic
202Dic172—82no—
203C23×C43—21no—
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43—81no—
209D4×C43—21no—
210D4×C43C2×Q1612yes—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—161no—
219C2×C4×C43C22×D411yescharacteristic
220C2×C4×C43C22×D411yescharacteristic
221C2×C4×C43H(5,𝔽2)11yescharacteristic
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—21no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—161no—
229Dic86—21no—
230Dic86—21no—
231Dic86—21no—
232Dic86—81no—
233Dic86—81no—
234Dic86—161no—
235Dic86C2×Q1612yes—
236C8×C43—41no—
237C8×C43—41no—
238C8×C43—41no—
239C43⋊C8—21no—
240C43⋊C8—21no—
241C43⋊C8—21no—
242C43⋊C8—41no—
243C43⋊C8—41no—
244C43⋊C8C2×Q1612yes—
245#19816—431nomaximal, Sylow
246C22×C43—22no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43D4211yescharacteristic
250C4×C43—21no—
251C4×C43—41no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—81no—
255C4×C43—81no—
256C4×C43C22×Q1611yescharacteristic
257C4×C43#57511yescharacteristic
258C4×C43#57811yescharacteristic
259C4×C43#57811yescharacteristic
260Dic43—22no—
261Dic43—41no—
262Dic43—41no—
263Dic43—41no—
264Dic43—81no—
265Dic43—81no—
266#3385—431no—
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#1644D4311yescharacteristic
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
285Q82—431no—
286#557—431no—
287#554—431no—
288#554C2×D4311yescharacteristic
289#501—861no—
290#500—431no—
291#500—431no—
292#499—861no—
293#498—431no—
294#494—431no—
295#487—431no—
296#487—861no—
297#487C2×D4311yescharacteristic
298#484—861no—
299#484—861no—
300#479—861no—
301#479—861no—
302#478—861no—
303#477—431no—
304#477—431no—
305#477—431no—
306#477—431no—
307#477—431no—
308#477—861no—
309#476—431no—
310#474—861no—
311#474C2×D4311yescharacteristic
312#467—861no—
313#462—861no—
314#462C2×D4311yescharacteristic
315#446—431no—
316C8×Q8—431no—
317C8×Q8—431no—
318#440—861no—
319C4×Q16—431no—
320C4×Q16—861no—
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#333C2×D4311yescharacteristic
330#332—431no—
331Q8⋊C8—431no—
332Q8⋊C8—431no—
333Q8⋊C8C2×D4311yescharacteristic
334D4⋊C8C2×D4311yescharacteristic
335#322—431no—
336C43#1981611yescharacteristic, complemented, Sylow
337C2×Q16—21no—
338C2×Q16—431no—
339C2×Q16—1721no—
340C2×SD16—431no—
341C22×C8—861no—
342C4⋊Q8—431no—
343C4⋊Q8—431no—
344C4⋊Q8—861no—
345C4⋊Q8—861no—
346C4⋊Q8—861no—
347C4⋊Q8—1721no—
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—431no—
359C4×Q8—431no—
360C4×Q8—861no—
361C4×Q8—861no—
362C4×Q8—861no—
363C4×Q8—861no—
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—431no—
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#107—861no—
381#106—431no—
382#106—861no—
383#106—861no—
384#106—861no—
385C4⋊C8—431no—
386C4⋊C8—431no—
387C4⋊C8—861no—
388C4⋊C8—861no—
389C4⋊C8—861no—
390C4⋊C8C22×D4311yescharacteristic
391C4⋊C8C22×D4311yescharacteristic
392#103—21no—
393#103—41no—
394#103—431no—
395#103—431no—
396#103—431no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—861no—
402#103—861no—
403#103—861no—
404#102—21no—
405#102—431no—
406#102—861no—
407C22⋊C8—861no—
408#97—861no—
409C4×C8—431no—
410C4×C8—431no—
411C4×C8—861no—
412C4×C8—861no—
413C4×C8C22×D4311yescharacteristic
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—431no—
417C2×Q8—431no—
418C2×Q8—861no—
419C2×Q8—861no—
420C2×Q8—1721no—
421C2×Q8D4×D4311yescharacteristic
422C2×D4D4×D4311yescharacteristic
423C22×C4—21no—
424C22×C4—41no—
425C22×C4—1721no—
426Q16—42no—
427Q16—3442no—
428Q16—1721no—
429SD16—434no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—431no—
434C2×C8—431no—
435C2×C8—431no—
436C2×C8—431no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—1722no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—41no—
446C4⋊C4—41no—
447C4⋊C4—431no—
448C4⋊C4—431no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—861no—
454C4⋊C4—861no—
455C4⋊C4—1721no—
456C4⋊C4—1721no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4D4×D4311yescharacteristic
463C4⋊C4D4×D4311yescharacteristic
464C22⋊C4—21no—
465C22⋊C4—41no—
466C22⋊C4—1721no—
467C42—21no—
468C42—861no—
469C42—861no—
470C42—1721no—
471C42—1721no—
472C42C23×D4311yescharacteristic
473C23—21no—
474Q8—21no—
475Q8—21no—
476Q8—41no—
477Q8—41no—
478Q8—81no—
479Q8—432no—
480Q8—861no—
481Q8—861no—
482Q8—861no—
483Q8—3441no—
484Q8—3441no—
485Q8—6881no—
486D4—21no—
487D4Q16×D4312yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—161no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—861no—
499C2×C4—861no—
500C2×C4—1721no—
501C2×C4—1721no—
502C2×C4—6881no—
503C2×C4C2×D4×D4311yescharacteristic
504C2×C4C2×D4×D4311yescharacteristic
505C2×C4#1306337011yescharacteristic
506C8—41no—
507C8—41no—
508C8—41no—
509C8—432no—
510C8—861no—
511C8—861no—
512C8—861no—
513C8—1721no—
514C8—1721no—
515C22—22no—
516C22—41no—
517C22—41no—
518C22#1458353111yescharacteristic
519C4—21no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—81no—
524C4—81no—
525C4—862no—
526C4—3441no—
527C4—3441no—
528C4—1721no—
529C4—1721no—
530C4—1721no—
531C4C2×Q16×D4311yescharacteristic
532C4#1458369511yescharacteristic
533C4#1458371311yescharacteristic
534C4#1458371511yescharacteristic
535C2—42no—
536C2#1914614811yescharacteristic
537C2#1914634011yescharacteristic
538C2#1914636411yescharacteristic
subgroupG/H
centerC22#14583531
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1644C2
socleC22×C43D42
prime radicalC2×D4×C43C2×D4
hypercenter#1644D43
hypocenterC43#19816
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1644

Complements

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

NH ≅ G/Ntype
3. #19147268C2semidirect
5. #19134274C2semidirect
6. #19134099C2semidirect
8. #19133998C2semidirect
9. #19133998C2semidirect
10. #19133750C2semidirect
11. #19133737C2semidirect
13. #19133448C2semidirect
175. #10621883Q16semidirect
336. C43#19816semidirect

Maximal subgroups

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

subgroupindex
#191475052
#191474742
#191472682
#191469832
#191342742
#191340992
#191340442
#191339982
#191337502
#191337372
#191337312
#191334482
#191334042
C43×#16442
#1981643