Finite Group Databasebeta

← #25079385

Subgroups — #25079385

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145137C211yesmaximal, characteristic, complemented
2#19144604C211yesmaximal, characteristic
3C2×#14583101C211yesmaximal, characteristic
4#19143330C211yesmaximal, characteristic
5#19134107C212yesmaximal, complemented
6#19134093C212yesmaximal, complemented
7#19133983C212yesmaximal, complemented
8#19133969C212yesmaximal, complemented
9#19133348C211yesmaximal, characteristic, complemented
10#19133286C211yesmaximal, characteristic, complemented
11C43×#1549C211yesmaximal, characteristic, complemented
12C22×#10621884—21no—
13C2×M16×D43—21no—
14#14583456C2211yescharacteristic
15C2×C4×D172C2211yescharacteristic
16#14583305—22no—
17#14583302C2212yescomplemented
18#14583295C2212yescomplemented
19#14583230—21no—
20#14583190C2211yescharacteristic
21#14583190C2211yescharacteristic
22#14583105C2211yescharacteristic
23#14583105C2211yescharacteristic
24#14583101—21no—
25#14583101—21no—
26#14583101C2212yes—
27#14583101C2212yes—
28#14583052—21no—
29C4×#10621873—21no—
30C4×#10621873—21no—
31#14582976C2212yes—
32#14582969—22no—
33#14582964C2212yes—
34#14582939—21no—
35#14582939—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C2×#13063249—21no—
38#14582862—21no—
39C4×#10621877C2211yescharacteristic
40#14582651C2212yescomplemented
41#14582649C2212yescomplemented
42#14582647C2212yescomplemented
43#14582644C2212yescomplemented
44C2×C4⋊Q8×C43C2211yescharacteristic
45C43×#431C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C43×#332C2212yescomplemented
48C43×#332C2212yescomplemented
49C22×D172D411yescharacteristic
50C22×C4×D43—21no—
51C2×#10621873—21no—
52C2×#10621873—21no—
53C2×#10621884—22no—
54C2×#10621884—22no—
55C2×#10621884—44no—
56C2×#10621877D411yescharacteristic
57C2×#10621877D411yescharacteristic
58C2×#10621872—22no—
59M16×D43—44no—
60C22×C43⋊C8—21no—
61C2×C8×D43—22no—
62#13063325C2311yescharacteristic
63#13063325C2311yescharacteristic
64#13063317—21no—
65#13063304—21no—
66#13063304—21no—
67C4×Dic86—21no—
68C4×Dic86—21no—
69C4×D172—21no—
70C4×D172—21no—
71C4×D172D411yescharacteristic
72C4×D172D411yescharacteristic
73C4×D172C2311yescharacteristic
74C4×D172C2311yescharacteristic
75#13063284—21no—
76C2×C4⋊Dic43D411yescharacteristic
77C2×(C2×D43)⋊C4—21no—
78#13063258—22no—
79#13063258—22no—
80#13063257—21no—
81#13063257—21no—
82#13063256—22no—
83#13063256—22no—
84C4⋊(C43⋊C8)—21no—
85C4⋊(C43⋊C8)C2312yes—
86#13063250—21no—
87#13063250—21no—
88#13063249—22no—
89#13063249—22no—
90#13063247—21no—
91#13063247—21no—
92(C2×D43)⋊C8—22no—
93(C2×D43)⋊C8—22no—
94#13063236D412yes—
95C4×C43⋊C8C2312yes—
96C22×Q8×C43—21no—
97C2×M16×C43—21no—
98C4⋊Q8×C43—21no—
99C4⋊Q8×C43—21no—
100C4⋊Q8×C43—21no—
101C4⋊Q8×C43C2312yes—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—21no—
106C4⋊C8×C43C2311yescharacteristic
107C4⋊C8×C43C2311yescharacteristic
108C4⋊C8×C43C2312yes—
109C22⋊C8×C43—21no—
110C4×C8×C43—21no—
111C23×D43—21no—
112C2×Q8×C43—22no—
113C2×Q8×C43—42no—
114C2×Q8×C43—42no—
115C2×Q8×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43C2×D411yescharacteristic
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43#4111yescharacteristic
120C22×Dic43—21no—
121C2×D172—21no—
122C2×D172—22no—
123C2×D172—41no—
124C2×D172C2×D411yescharacteristic
125C2×D172C2×D411yescharacteristic
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×C4×D43—42no—
131C2×C4×D43—42no—
132C2×Dic86—21no—
133C2×Dic86—21no—
134M16×C43—42no—
135C2×C8×C43—21no—
136C2×C8×C43—21no—
137C2×C8×C43—22no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43#4111yescharacteristic
145C42×C43C2411yescharacteristic
146C22⋊Dic43—41no—
147#10621884—44no—
148#10621884—44no—
149(C2×D43)⋊C4—21no—
150(C2×D43)⋊C4—21no—
151(C2×D43)⋊C4—21no—
152(C2×D43)⋊C4—21no—
153C4⋊Dic43—21no—
154C4⋊Dic43—21no—
155C4⋊Dic43—21no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158C4⋊Dic43C2×D411yescharacteristic
159C4⋊Dic43C2×D411yescharacteristic
160Dic43⋊C4—41no—
161Dic43⋊C4—41no—
162C4×Dic43—41no—
163#10621877—22no—
164#10621877SD1614yescomplemented
165C2×C43⋊C8—22no—
166C2×C43⋊C8—42no—
167C2×C43⋊C8C2×D412yes—
168C2×C43⋊C8C2×D412yes—
169#10621873—42no—
170#10621873—42no—
171#10621872—44no—
172C8×D43—44no—
173C23×C43#12111yescharacteristic
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—42no—
177C22×D43—42no—
178C22×D43—81no—
179Q8×C43—42no—
180Q8×C43—42no—
181Q8×C43—82no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—41no—
185C2×C4×C43—42no—
186C2×C4×C43—82no—
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43C2×SD1612yes—
191C2×C4×C43#13712yes—
192C2×C4×C43C22×D411yescharacteristic
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C2×#4111yescharacteristic
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43—42no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200D172—21no—
201D172—21no—
202D172—21no—
203D172—42no—
204D172AGL(1,ℤ/8)12yes—
205C4×D43—41no—
206C4×D43—41no—
207C4×D43—41no—
208C4×D43—41no—
209C4×D43—42no—
210C4×D43—42no—
211Dic86—41no—
212Dic86—41no—
213Dic86—81no—
214C8×C43—42no—
215C8×C43—41no—
216C8×C43—41no—
217C43⋊C8—22no—
218C43⋊C8—42no—
219C43⋊C8C2×SD1614yescomplemented
220#19164—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43#46112yes—
224C22×C43C2×#12111yescharacteristic
225C2×D43—22no—
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—41no—
229C2×D43—41no—
230C2×D43—41no—
231C2×D43—84no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—82no—
236C4×C43#46112yes—
237C4×C43C22×SD1611yescharacteristic
238C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
239C4×C43C2×#13711yescharacteristic
240C4×C43#57511yescharacteristic
241Dic43—41no—
242Dic43—41no—
243Dic43—81no—
244Dic43—81no—
245#3165—431no—
246#3101—431no—
247C2×#461—431no—
248D4×M16—431no—
249#1693—432no—
250#1691—432no—
251#1673—432no—
252#1671—432no—
253#1565—431no—
254#1550—431no—
255#1549D4311yescharacteristic, complemented
256C2×C43—22no—
257C2×C43C2×#46111yescharacteristic
258C2×C43#305511yescharacteristic
259C2×C43#306911yescharacteristic
260D43—42no—
261D43—81no—
262C22×SD16—861no—
263C22×M16—861no—
264#533—431no—
265C2×C4⋊Q8C2×D4311yescharacteristic
266C2×C4×D4—431no—
267#501—862no—
268#500—432no—
269#498—432no—
270#483—861no—
271#476—431no—
272#476—431no—
273#461—432no—
274#461—432no—
275#461—431no—
276#461—431no—
277#461—861no—
278#461—861no—
279#450—861no—
280C4×SD16—861no—
281C4×SD16—861no—
282#436—432no—
283#435—862no—
284C8×D4—432no—
285#431C2×D4311yescharacteristic
286#428—861no—
287#428—861no—
288#423C2×D4311yescharacteristic
289C2×C4⋊C8—431no—
290C2×#103—861no—
291#407—861no—
292C4×M16—431no—
293#335—432no—
294#334—432no—
295#333—432no—
296#332—432no—
297#332C2×D4312yescomplemented
298#332C2×D4312yescomplemented
299C43#1916411yescharacteristic, complemented, Sylow
300C22×Q8—21no—
301C22×D4—431no—
302C23×C4—861no—
303C2×SD16—861no—
304C2×SD16—861no—
305C2×SD16—862no—
306C2×SD16—862no—
307C2×SD16—1724no—
308C2×M16—21no—
309C2×M16—431no—
310C2×M16—431no—
311C2×M16—862no—
312C2×M16—1724no—
313C22×C8—862no—
314C22×C8—861no—
315C4⋊Q8—21no—
316C4⋊Q8—21no—
317C4⋊Q8—21no—
318C4⋊Q8—431no—
319C4⋊Q8—431no—
320C4⋊Q8C22×D4312yes—
321#125—861no—
322C22⋊Q8—861no—
323C22⋊Q8—861no—
324C4×Q8—861no—
325C4×Q8—861no—
326C4×D4—431no—
327C4×D4—431no—
328C4×D4—431no—
329C4×D4—431no—
330C4×D4—861no—
331C4×D4—861no—
332#117—861no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—431no—
336C2×C22⋊C4—861no—
337C2×C42C22×D4311yescharacteristic
338#107—862no—
339#107—862no—
340#106—862no—
341#106—862no—
342#106—861no—
343#106—861no—
344C4⋊C8—21no—
345C4⋊C8—432no—
346C4⋊C8—861no—
347C4⋊C8C22×D4312yes—
348C4⋊C8C22×D4311yescharacteristic
349C4⋊C8C22×D4311yescharacteristic
350#103—861no—
351#103—861no—
352#103—862no—
353#103—862no—
354#102—861no—
355#102—861no—
356C22⋊C8—21no—
357C22⋊C8—862no—
358C22⋊C8—862no—
359#97—432no—
360C4×C8—21no—
361C4×C8—432no—
362C24—861no—
363C2×Q8—22no—
364C2×Q8—42no—
365C2×Q8—42no—
366C2×Q8—41no—
367C2×Q8—861no—
368C2×Q8—861no—
369C2×D4—431no—
370C2×D4—431no—
371C2×D4—862no—
372C2×D4—861no—
373C2×D4—1721no—
374C22×C4—41no—
375C22×C4—861no—
376C22×C4—861no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4—1722no—
381C22×C4—1722no—
382C22×C4#1062189811yescharacteristic
383C22×C4D4×D4311yescharacteristic
384C22×C4D4×D4311yescharacteristic
385SD16—1722no—
386SD16—1722no—
387SD16—1724no—
388SD16—1724no—
389M16—42no—
390M16—434no—
391M16—862no—
392M16—1724no—
393C2×C8—21no—
394C2×C8—21no—
395C2×C8—22no—
396C2×C8—432no—
397C2×C8—432no—
398C2×C8—862no—
399C2×C8—1724no—
400C2×C8—1722no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—431no—
406C4⋊C4—431no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4—1721no—
413C4⋊C4—1721no—
414C22⋊C4—861no—
415C22⋊C4—861no—
416C22⋊C4—861no—
417C22⋊C4—861no—
418C22⋊C4—1721no—
419C42—1721no—
420C42#1062189811yescharacteristic
421C42D4×D4311yescharacteristic
422C42D4×D4311yescharacteristic
423C42C23×D4311yescharacteristic
424C23—861no—
425C23—861no—
426C23—3441no—
427C23—1722no—
428C23—1722no—
429C23#1306329811yescharacteristic
430Q8—42no—
431Q8—42no—
432Q8—82no—
433Q8—3441no—
434Q8—1721no—
435Q8—1721no—
436D4—432no—
437D4—861no—
438D4—861no—
439D4—861no—
440D4—1722no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—82no—
446C2×C4—861no—
447C2×C4—861no—
448C2×C4—1721no—
449C2×C4—1721no—
450C2×C4—1722no—
451C2×C4—1722no—
452C2×C4—1722no—
453C2×C4—1721no—
454C2×C4—1721no—
455C2×C4—1721no—
456C2×C4—1721no—
457C2×C4#1306329811yescharacteristic
458C2×C4#1306329811yescharacteristic
459C2×C4#1306329811yescharacteristic
460C2×C4SD16×D4312yes—
461C2×C4#1306335712yes—
462C2×C4C2×D4×D4311yescharacteristic
463C2×C4C2×D4×D4311yescharacteristic
464C2×C4C2×#1062189811yescharacteristic
465C8—42no—
466C8—41no—
467C8—41no—
468C8—434no—
469C8—862no—
470C8—1722no—
471C22—21no—
472C22—21no—
473C22—862no—
474C22—3444no—
475C22—1721no—
476C22—1721no—
477C22—1721no—
478C22—1721no—
479C22—1721no—
480C22#1458310312yes—
481C22C2×#1306329811yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—82no—
486C4—3441no—
487C4—3441no—
488C4—1721no—
489C4—1721no—
490C4#1458310312yes—
491C4C2×SD16×D4311yescharacteristic
492C4AGL(1,ℤ/8)×D4311yescharacteristic
493C4C2×#1306335711yescharacteristic
494C4#1458369511yescharacteristic
495C2—22no—
496C2—3441no—
497C2—1722no—
498C2C2×#1458310311yescharacteristic
499C2#1914421211yescharacteristic
500C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1549C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#1549D43
hypocenterC43#19164
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. #19145137C2semidirect
5. #19134107C2semidirect
6. #19134093C2semidirect
7. #19133983C2semidirect
8. #19133969C2semidirect
9. #19133348C2semidirect
10. #19133286C2semidirect
11. C43×#1549C2semidirect
17. #14583302C22semidirect
18. #14583295C22semidirect
40. #14582651C22semidirect
41. #14582649C22semidirect
42. #14582647C22semidirect
43. #14582644C22semidirect
47. C43×#332C22semidirect
48. C43×#332C22semidirect
164. #10621877SD16semidirect
219. C43⋊C8C2×SD16semidirect
255. #1549D43semidirect
297. #332C2×D43semidirect
298. #332C2×D43semidirect
299. C43#19164semidirect

Maximal subgroups

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

subgroupindex
#191451372
#191446042
C2×#145831012
#191433302
#191341072
#191340932
#191339832
#191339692
#191333482
#191332862
C43×#15492
#1916443