Finite Group Databasebeta

← #25086864

Subgroups — #25086864

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#19147507C211yesmaximal, characteristic
2#19147472C211yesmaximal, characteristic
3#19147271C211yesmaximal, characteristic, complemented
4#19146989C211yesmaximal, characteristic
5#19134272C211yesmaximal, characteristic, complemented
6#19134101C211yesmaximal, characteristic, complemented
7#19134047C211yesmaximal, characteristic
8#19134000C211yesmaximal, characteristic, complemented
9#19133999C211yesmaximal, characteristic, complemented
10#19133811C211yesmaximal, characteristic
11#19133755C211yesmaximal, characteristic, complemented
12#19133737C211yesmaximal, characteristic, complemented
13#19133732C211yesmaximal, characteristic
14#19133409C211yesmaximal, characteristic
15C43×#1584C211yesmaximal, characteristic, complemented
16Q8×Dic86C2211yescharacteristic
17#14583627C2211yescharacteristic
18#14583609C2211yescharacteristic
19#14583609C2211yescharacteristic
20#14583308—21no—
21#14583304C2211yescharacteristic
22#14583304C2211yescharacteristic
23#14583301—21no—
24#14583297C2211yescharacteristic
25#14583279C2211yescharacteristic
26#14583250C2211yescharacteristic
27#14583250C2211yescharacteristic
28#14583248—21no—
29#14583233—21no—
30#14583233—21no—
31#14583207—21no—
32#14583207—21no—
33#14583200—21no—
34#14583195C2211yescharacteristic
35#14583195C2211yescharacteristic
36#14583194C2211yescharacteristic
37#14583194C2211yescharacteristic
38#14583194C2211yescharacteristic
39#14583193—21no—
40#14583190C2211yescharacteristic
41#14583180—21no—
42#14583180C2211yescharacteristic
43#14583137—21no—
44#14583109C2211yescharacteristic
45#14583107—21no—
46C8×Dic86C2211yescharacteristic
47#14583001—21no—
48#14582991—21no—
49C4×#10621873—21no—
50C4×#10621873C2211yescharacteristic
51C8×D172C2211yescharacteristic
52#107×D43—21no—
53#14582652C2211yescharacteristic
54#14582647C2211yescharacteristic
55#14582647C2211yescharacteristic
56#14582647C2211yescharacteristic
57#14582644C2211yescharacteristic
58#14582631C2211yescharacteristic
59#14582628C2211yescharacteristic
60C43×#446C2211yescharacteristic
61C8×Q8×C43C2211yescharacteristic
62C4×Q16×C43C2211yescharacteristic
63C43×#335C2211yescharacteristic
64C43×Q8⋊C8C2211yescharacteristic
65C43×Q8⋊C8C2211yescharacteristic
66C43×#322C2211yescharacteristic
67C2×Dic172—41no—
68C2×#10621885—21no—
69C2×#10621873D411yescharacteristic
70C2×C8×D43—21no—
71#13063325—21no—
72#13063325C2311yescharacteristic
73#13063325C2311yescharacteristic
74#13063325C2311yescharacteristic
75#13063325C2311yescharacteristic
76#13063324—21no—
77#13063324—41no—
78#13063323—21no—
79#13063317—21no—
80#13063317—21no—
81#13063317—21no—
82#13063315—41no—
83#13063303—41no—
84#13063303—41no—
85#13063301—21no—
86#13063301—21no—
87Q8×Dic43—21no—
88C4×Dic86—21no—
89C4×Dic86—21no—
90C4×Dic86C2311yescharacteristic
91#13063290—21no—
92C4×D172—21no—
93C4×D172—21no—
94C4×D172C2311yescharacteristic
95C4⋊C4×D43—21no—
96C4⋊C4×D43—21no—
97#13063259—21no—
98#13063259—21no—
99#13063259—21no—
100#13063259—21no—
101#13063259—21no—
102#13063259—21no—
103#13063259—21no—
104#13063258—21no—
105#13063258—21no—
106#13063258—21no—
107#13063257—21no—
108#13063257—21no—
109#13063257—21no—
110#13063257D411yescharacteristic
111C4⋊(C43⋊C8)C2311yescharacteristic
112C4⋊(C43⋊C8)C2311yescharacteristic
113Dic43⋊C8—21no—
114#13063250—21no—
115#13063250—21no—
116#13063250—21no—
117#13063250—21no—
118#13063250—41no—
119#13063250D411yescharacteristic
120#13063249—21no—
121#13063249—21no—
122#13063249—21no—
123#13063248—21no—
124#13063247—21no—
125#13063247—21no—
126#13063247D411yescharacteristic
127(C2×D43)⋊C8—21no—
128C8×Dic43—21no—
129C2×Q16×C43D411yescharacteristic
130C4×Q8×C43C2311yescharacteristic
131C4×Q8×C43C2311yescharacteristic
132#107×C43D411yescharacteristic
133C4⋊C8×C43—21no—
134C4⋊C8×C43—21no—
135C4⋊C8×C43C2311yescharacteristic
136C4⋊C8×C43C2311yescharacteristic
137#103×C43D411yescharacteristic
138#103×C43D411yescharacteristic
139#97×C43—21no—
140C4×C8×C43—21no—
141C4×C8×C43C2311yescharacteristic
142C4×C8×C43C2311yescharacteristic
143C4×C8×C43C2311yescharacteristic
144C2×Q8×C43C2×D411yescharacteristic
145C2×Q8×C43C2×D411yescharacteristic
146C2×D172C2×D411yescharacteristic
147C2×C4×D43—21no—
148C2×C4×D43—41no—
149C2×C4×D43—41no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—41no—
155C2×Dic86C2×D411yescharacteristic
156Q16×C43—41no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C2×C8×C43—21no—
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43C2×D411yescharacteristic
162C2×C8×C43C2×D411yescharacteristic
163C2×C8×C43C2×D411yescharacteristic
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43C2×D411yescharacteristic
167C4⋊C4×C43C2×D411yescharacteristic
168C42×C43—21no—
169C42×C43—21no—
170C42×C43C2411yescharacteristic
171#10621885—42no—
172(C2×D43)⋊C4—21no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—41no—
184C4⋊Dic43C2×D411yescharacteristic
185C4⋊Dic43C2×D411yescharacteristic
186Dic43⋊C4—21no—
187Dic43⋊C4—41no—
188Dic43⋊C4—41no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—41no—
192Dic43⋊C4—41no—
193Dic43⋊C4—41no—
194Dic43⋊C4—41no—
195C4×Dic43—21no—
196C4×Dic43—41no—
197C4×Dic43—41no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200Dic172—82no—
201#10621873Q1614yescomplemented
202C8×D43—42no—
203C22×D43—21no—
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—21no—
207Q8×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43C22×D411yescharacteristic
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43H(5,𝔽2)11yescharacteristic
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222D172—21no—
223D172C2×Q1612yes—
224C4×D43—41no—
225C4×D43—41no—
226C4×D43—161no—
227C4×D43—161no—
228Dic86—21no—
229Dic86—41no—
230Dic86—41no—
231Dic86—81no—
232Dic86—81no—
233Dic86—81no—
234Dic86—161no—
235Dic86C2×Q1612yes—
236C8×C43—21no—
237C8×C43—21no—
238C8×C43—21no—
239C8×C43—41no—
240C8×C43—41no—
241C8×C43—41no—
242C8×C43C2×Q1612yes—
243C43⋊C8—41no—
244C43⋊C8—41no—
245#19816—431nomaximal, Sylow
246C22×C43D4211yescharacteristic
247C2×D43—22no—
248C2×D43—41no—
249C2×D43—41no—
250C4×C43—21no—
251C4×C43—41no—
252C4×C43—41no—
253C4×C43—41no—
254C4×C43—41no—
255C4×C43C22×Q1611yescharacteristic
256C4×C43#57511yescharacteristic
257C4×C43#57811yescharacteristic
258C4×C43#57811yescharacteristic
259Dic43—22no—
260Dic43—41no—
261Dic43—41no—
262Dic43—81no—
263Dic43—81no—
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#1644—431no—
276#1636—431no—
277#1633—431no—
278#1632—431no—
279#1584D4311yescharacteristic, complemented
280SD16⋊C8—431no—
281C2×C43#326911yescharacteristic
282C2×C43D4×Q1611yescharacteristic
283C2×C43#328811yescharacteristic
284D43—42no—
285Q82—431no—
286#557—431no—
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—431no—
296#487—431no—
297#487—861no—
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—431no—
311#474—861no—
312#467—861no—
313#462—431no—
314#462—861no—
315#446C2×D4311yescharacteristic
316C8×Q8—431no—
317C8×Q8C2×D4311yescharacteristic
318#440—861no—
319C4×Q16—861no—
320C4×Q16C2×D4311yescharacteristic
321C4×SD16—431no—
322C4×SD16—861no—
323C8×D4—431no—
324C2×#107—861no—
325#335—431no—
326#335C2×D4311yescharacteristic
327#333—431no—
328#333—431no—
329#333—431no—
330#332—431no—
331Q8⋊C8—431no—
332Q8⋊C8C2×D4311yescharacteristic
333Q8⋊C8C2×D4311yescharacteristic
334D4⋊C8—431no—
335#322C2×D4311yescharacteristic
336C43#1981611yescharacteristic, complemented, Sylow
337C2×Q16—861no—
338C2×Q16—1721no—
339C2×Q16D17211yescharacteristic
340C2×SD16—431no—
341C22×C8—861no—
342C4⋊Q8—431no—
343C4⋊Q8—431no—
344C4⋊Q8—431no—
345C4⋊Q8—431no—
346C4⋊Q8—861no—
347C4⋊Q8—861no—
348C4⋊Q8—861no—
349C4⋊Q8—1721no—
350#125—861no—
351#125—861no—
352#125—861no—
353#125—1721no—
354C22⋊Q8—861no—
355C22⋊Q8—861no—
356C22⋊Q8—1721no—
357C22⋊Q8—1721no—
358C4×Q8—431no—
359C4×Q8—861no—
360C4×Q8—861no—
361C4×Q8—861no—
362C4×Q8—861no—
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—861no—
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#107D17211yescharacteristic
381#106—431no—
382#106—861no—
383#106—861no—
384#106—861no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—431no—
388C4⋊C8—431no—
389C4⋊C8—861no—
390C4⋊C8C22×D4311yescharacteristic
391C4⋊C8C22×D4311yescharacteristic
392#103—431no—
393#103—861no—
394#103—861no—
395#103—861no—
396#103—861no—
397#103—861no—
398#103—861no—
399#103—861no—
400#103—861no—
401#103—1721no—
402#103D17211yescharacteristic
403#103D17211yescharacteristic
404#102—431no—
405#102—861no—
406#102—861no—
407C22⋊C8—861no—
408#97—21no—
409C4×C8—21no—
410C4×C8—861no—
411C4×C8C22×D4311yescharacteristic
412C4×C8C22×D4311yescharacteristic
413C4×C8C22×D4311yescharacteristic
414C2×Q8—431no—
415C2×Q8—861no—
416C2×Q8—861no—
417C2×Q8—861no—
418C2×Q8—861no—
419C2×Q8—1721no—
420C2×Q8C2×D17211yescharacteristic
421C2×Q8C2×D17211yescharacteristic
422C2×D4—431no—
423C22×C4—861no—
424C22×C4—1721no—
425C22×C4—1721no—
426Q16—41no—
427Q16—3442no—
428Q16—1722no—
429SD16—434no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—861no—
434C2×C8—861no—
435C2×C8—1722no—
436C2×C8C2×D17211yescharacteristic
437C2×C8C2×D17211yescharacteristic
438C2×C8D4×D4311yescharacteristic
439C2×C8D4×D4311yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—431no—
443C4⋊C4—431no—
444C4⋊C4—861no—
445C4⋊C4—861no—
446C4⋊C4—861no—
447C4⋊C4—861no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—861no—
451C4⋊C4—861no—
452C4⋊C4—861no—
453C4⋊C4—1721no—
454C4⋊C4—1721no—
455C4⋊C4—1721no—
456C4⋊C4—1721no—
457C4⋊C4—1721no—
458C4⋊C4—1721no—
459C4⋊C4—1721no—
460C4⋊C4—1721no—
461C4⋊C4—1721no—
462C4⋊C4C2×D17211yescharacteristic
463C4⋊C4C2×D17211yescharacteristic
464C22⋊C4—861no—
465C22⋊C4—1721no—
466C22⋊C4—1721no—
467C42—21no—
468C42—21no—
469C42—861no—
470C42—1721no—
471C42—1721no—
472C42C23×D4311yescharacteristic
473C23—861no—
474Q8—21no—
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—432no—
479Q8—861no—
480Q8—3441no—
481Q8—3441no—
482Q8—3441no—
483Q8—1721no—
484Q8—1721no—
485Q8—6881no—
486D4—432no—
487D4—861no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4—1721no—
501C2×C4—6881no—
502C2×C4—6881no—
503C2×C4C2×D4×D4311yescharacteristic
504C2×C4C22×D17211yescharacteristic
505C2×C4#1306337111yescharacteristic
506C8—21no—
507C8—21no—
508C8—21no—
509C8—41no—
510C8—41no—
511C8—41no—
512C8—1721no—
513C8—1721no—
514C8Q16×D4312yes—
515C22—862no—
516C22—1721no—
517C22—1721no—
518C22D4×D17211yescharacteristic
519C4—21no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—41no—
524C4—862no—
525C4—3441no—
526C4—3441no—
527C4—3441no—
528C4—3441no—
529C4—1721no—
530C4—1721no—
531C4C2×Q16×D4311yescharacteristic
532C4#1458369911yescharacteristic
533C4#1458371311yescharacteristic
534C4#1458371611yescharacteristic
535C2—1722no—
536C2#1914615511yescharacteristic
537C2Q16×D17211yescharacteristic
538C2#1914636211yescharacteristic
subgroupG/H
centerC22D4×D172
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1584C2
socleC22×C43D42
prime radicalC2×D172C2×D4
hypercenter#1584D43
hypocenterC43#19816
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #1584

Complements

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

NH ≅ G/Ntype
3. #19147271C2semidirect
5. #19134272C2semidirect
6. #19134101C2semidirect
8. #19134000C2semidirect
9. #19133999C2semidirect
11. #19133755C2semidirect
12. #19133737C2semidirect
15. C43×#1584C2semidirect
201. #10621873Q16semidirect
279. #1584D43semidirect
336. C43#19816semidirect

Maximal subgroups

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

subgroupindex
#191475072
#191474722
#191472712
#191469892
#191342722
#191341012
#191340472
#191340002
#191339992
#191338112
#191337552
#191337372
#191337322
#191334092
C43×#15842
#1981643