Finite Group Databasebeta

← #24991459

Subgroups — #24991459

Order 11008.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144591C211yesmaximal, characteristic
2M16×D172C211yesmaximal, characteristic, complemented
3C4×#13063245C211yesmaximal, characteristic, complemented
4#19133046C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1980C211yesmaximal, characteristic, complemented
8C2×M16×D43—21no—
9C2×C4×D172C2211yescharacteristic
10#14583210—21no—
11#14583176C411yescharacteristic, complemented
12#14583176C411yescharacteristic, complemented
13#14583091C411yescharacteristic, complemented
14#14583091C411yescharacteristic, complemented
15#14583032—21no—
16C4×#10621882—21no—
17C4×#10621882—21no—
18#14582978—21no—
19#14582972—22no—
20C8×D172—21no—
21#14582952C2211yescharacteristic
22#14582923C2211yescharacteristic
23C2×#13063245—21no—
24#14582862—21no—
25C2×C4×C43⋊C8C2211yescharacteristic
26#14582661—21no—
27D4⋊(C43⋊C8)—22no—
28C43×#532C2211yescharacteristic
29C2×#104×C43—21no—
30C2×#104×C43—21no—
31C4×M16×C43C2211yescharacteristic
32C4×C4⋊C4×C43C2211yescharacteristic
33C22×D172D411yescharacteristic
34C22×C4×D43—21no—
35C2×#10621882—21no—
36C2×#10621882—21no—
37C2×#10621877—21no—
38C2×#10621872—22no—
39M16×D43—42no—
40M16×D43—42no—
41C22×C43⋊C8—21no—
42C2×C8×D43—22no—
43C4×D172—21no—
44C4×D172—21no—
45C4×D172C2×C411yescharacteristic
46C4×D172C2×C411yescharacteristic
47C4×D172D411yescharacteristic
48C4×D172D411yescharacteristic
49C2×C4⋊Dic43D411yescharacteristic
50C2×(C2×D43)⋊C4—21no—
51#13063258—21no—
52#13063258—21no—
53C4⋊(C43⋊C8)—21no—
54C4⋊(C43⋊C8)C2×C411yescharacteristic
55C4⋊(C43⋊C8)C2×C411yescharacteristic
56C4⋊(C43⋊C8)D412yes—
57#13063246—21no—
58#13063246—21no—
59#13063245—24no—
60#13063245—21no—
61#13063245—21no—
62C22⋊(C43⋊C8)—21no—
63(C2×D43)⋊C8—22no—
64(C2×D43)⋊C8—22no—
65C4×C43⋊C8—21no—
66C4×C43⋊C8—21no—
67C4×C43⋊C8—21no—
68C2×#41×C43—21no—
69C2×M16×C43D411yescharacteristic
70C2×M16×C43D411yescharacteristic
71C4⋊Q8×C43C2×C411yescharacteristic
72#127×C43C2×C411yescharacteristic
73#124×C43—21no—
74#121×C43—21no—
75#121×C43—21no—
76C4×D4×C43—21no—
77C4×D4×C43—21no—
78C2×C4⋊C4×C43—21no—
79C2×C42×C43—21no—
80C2×C42×C43C2311yescharacteristic
81#104×C43—42no—
82#104×C43—42no—
83#97×C43—21no—
84C4×C8×C43—21no—
85#95×C43—21no—
86C23×D43—21no—
87#41×C43—41no—
88#41×C43—41no—
89#41×C43—41no—
90#41×C43—41no—
91C2×Q8×C43—21no—
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×Dic43—21no—
102C2×D172—21no—
103C2×D172—22no—
104C2×D172—41no—
105C2×D172C22⋊C411yescharacteristic
106C2×D172C22⋊C411yescharacteristic
107C2×C4×D43—21no—
108C2×C4×D43—21no—
109C2×C4×D43—21no—
110C2×C4×D43—21no—
111C2×C4×D43—41no—
112C2×C4×D43—41no—
113C2×C4×D43—41no—
114C2×C4×D43—41no—
115M16×C43—21no—
116M16×C43—21no—
117M16×C43—21no—
118M16×C43D812yescomplemented
119C2×C8×C43—21no—
120C2×C8×C43—21no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—41no—
125C22⋊C4×C43—41no—
126C22⋊C4×C43—41no—
127C42×C43—41no—
128C42×C43—41no—
129C42×C43C22×C411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43C2×D411yescharacteristic
132C42×C43#4111yescharacteristic
133#10621882—42no—
134#10621882—42no—
135(C2×D43)⋊C4—21no—
136(C2×D43)⋊C4—21no—
137(C2×D43)⋊C4—21no—
138(C2×D43)⋊C4—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43C22⋊C411yescharacteristic
141C4⋊Dic43C22⋊C411yescharacteristic
142#10621877—41no—
143#10621877—41no—
144C2×C43⋊C8—22no—
145C2×C43⋊C8—21no—
146C2×C43⋊C8—21no—
147C2×C43⋊C8—22no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150#10621872—44no—
151C8×D43—44no—
152C23×C43—41no—
153C23×C43#12111yescharacteristic
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—42no—
157C22×D43—41no—
158C22×D43—41no—
159C22×D43—81no—
160Q8×C43—41no—
161Q8×C43—41no—
162D4×C43—42no—
163D4×C43—41no—
164D4×C43—41no—
165D4×C43—41no—
166D4×C43—41no—
167D4×C43—81no—
168D4×C43—81no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—41no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43—81no—
178C2×C4×C43C2×C22⋊C411yescharacteristic
179C2×C4×C43C4×D411yescharacteristic
180C2×C4×C43C4×D411yescharacteristic
181C2×C4×C43#12011yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#12311yescharacteristic
184C2×C4×C43C2×D811yescharacteristic
185C2×C4×C43#13511yescharacteristic
186C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—41no—
191C2×Dic43—41no—
192D172—21no—
193D172—21no—
194D172—21no—
195D172—42no—
196D172#10412yescomplemented
197C4×D43—41no—
198C4×D43—41no—
199C4×D43—41no—
200C4×D43—41no—
201C4×D43—41no—
202C4×D43—41no—
203C4×D43—41no—
204C4×D43—41no—
205C8×C43—22no—
206C8×C43—41no—
207C43⋊C8—42no—
208C43⋊C8—41no—
209C43⋊C8—41no—
210C43⋊C8—42no—
211#8991—431nomaximal, Sylow
212C22×C43—21no—
213C22×C43—21no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43—81no—
217C22×C43#38611yescharacteristic
218C22×C43#45911yescharacteristic
219C22×C43#46311yescharacteristic
220C2×D43—22no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—82no—
227C2×D43—82no—
228C4×C43—21no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—82no—
232C4×C43—81no—
233C4×C43C2×#10411yescharacteristic
234C4×C43#42111yescharacteristic
235C4×C43C4×D811yescharacteristic
236C4×C43#44211yescharacteristic
237C4×C43#44711yescharacteristic
238C4×C43#44911yescharacteristic
239Dic43—41no—
240Dic43—41no—
241#3100—431no—
242D4×M16—431no—
243#1980D4311yescharacteristic, complemented
244C4×#102—431no—
245#1492—431no—
246#1303—431no—
247#1278—431no—
248C2×C43—21no—
249C2×C43—21no—
250C2×C43—161no—
251C2×C43#187111yescharacteristic
252C2×C43#187911yescharacteristic
253C2×C43#188111yescharacteristic
254D43—42no—
255D43—81no—
256C22×M16—861no—
257#532C2×D4311yescharacteristic
258C2×C4×D4—431no—
259#480—861no—
260#474—431no—
261#474—431no—
262#459—431no—
263#459—431no—
264#447—861no—
265C4×D8—861no—
266C4×D8—861no—
267#436—861no—
268#435—862no—
269C8×D4—861no—
270#431—431no—
271#423—431no—
272C2×#104—21no—
273C2×#104—21no—
274C2×#102—861no—
275#407—861no—
276C4×M16C2×D4311yescharacteristic
277C2×C4×C8—431no—
278C4×C4⋊C4C2×D4311yescharacteristic
279#340—861no—
280D4⋊C8—862no—
281C43#899111yescharacteristic, complemented, Sylow
282C2×#41—21no—
283C22×D4—431no—
284C23×C4—861no—
285C2×D8—861no—
286C2×D8—861no—
287C2×M16—862no—
288C2×M16—861no—
289C2×M16—1722no—
290C2×M16—1722no—
291C2×M16C22⋊D4311yescharacteristic
292C2×M16C22⋊D4311yescharacteristic
293C22×C8—862no—
294C22×C8—861no—
295C4⋊Q8C4×D4311yescharacteristic
296#127C4×D4311yescharacteristic
297#124—21no—
298#121—21no—
299#121—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—431no—
303C4×D4—431no—
304C4×D4—431no—
305C4×D4—431no—
306C4×D4—861no—
307C4×D4—861no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—431no—
310C2×C22⋊C4—861no—
311C2×C42—21no—
312C2×C42C22×D4311yescharacteristic
313#107—861no—
314#107—861no—
315C4⋊C8—431no—
316C4⋊C8—431no—
317C4⋊C8—432no—
318C4⋊C8—861no—
319#104—42no—
320#104—42no—
321#102—861no—
322#102—861no—
323#102—864no—
324#102—861no—
325#102—861no—
326C22⋊C8—862no—
327C22⋊C8—862no—
328C22⋊C8—861no—
329#97—21no—
330C4×C8—21no—
331C4×C8—861no—
332C4×C8—861no—
333C4×C8—861no—
334#95—21no—
335C24—861no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—21no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—41no—
345C2×D4—431no—
346C2×D4—431no—
347C2×D4—862no—
348C2×D4—861no—
349C2×D4—1721no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—861no—
353C22×C4—861no—
354C22×C4—861no—
355C22×C4—861no—
356C22×C4—861no—
357C22×C4—1721no—
358C22×C4—1721no—
359C22×C4—1721no—
360C22×C4—1721no—
361C22×C4D4×D4311yescharacteristic
362C22×C4#1062190011yescharacteristic
363C22×C4C2×C22⋊D4311yescharacteristic
364D8—1722no—
365D8—1722no—
366M16—21no—
367M16—21no—
368M16—21no—
369M16—1724no—
370M16—1721no—
371M16—1721no—
372M16#1062188212yescomplemented
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—862no—
376C2×C8—861no—
377C2×C8—861no—
378C2×C8—862no—
379C2×C8—1724no—
380C2×C8—1721no—
381C2×C8—1721no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—41no—
386C4⋊C4—431no—
387C4⋊C4—431no—
388C4⋊C4—861no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—861no—
392C22⋊C4—861no—
393C22⋊C4—861no—
394C22⋊C4—861no—
395C42—41no—
396C42—41no—
397C42C2×C4×D4311yescharacteristic
398C42#1062189811yescharacteristic
399C42D4×D4311yescharacteristic
400C42D4×D4311yescharacteristic
401C23—41no—
402C23—861no—
403C23—861no—
404C23—3441no—
405C23—1722no—
406C23—1721no—
407C23—1721no—
408C23#1306329611yescharacteristic
409Q8—41no—
410Q8—41no—
411D4—42no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—81no—
418D4—432no—
419D4—861no—
420D4—861no—
421D4—861no—
422D4—1722no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—81no—
429C2×C4—81no—
430C2×C4—81no—
431C2×C4—81no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—1721no—
435C2×C4—1721no—
436C2×C4—1721no—
437C2×C4—1721no—
438C2×C4—1721no—
439C2×C4—1721no—
440C2×C4—1721no—
441C2×C4—1721no—
442C2×C4—1721no—
443C2×C4—1721no—
444C2×C4C22⋊C4×D4311yescharacteristic
445C2×C4(C22⋊D43)⋊C411yescharacteristic
446C2×C4C4×C22⋊D4311yescharacteristic
447C2×C4#1306329311yescharacteristic
448C2×C4#1306329811yescharacteristic
449C2×C4#1306330711yescharacteristic
450C2×C4C2×#1062188211yescharacteristic
451C2×C4#1306334511yescharacteristic
452C2×C4#1306335011yescharacteristic
453C2×C4#1306335111yescharacteristic
454C8—22no—
455C8—41no—
456C8—1722no—
457C8—1721no—
458C8—1721no—
459C8—1722no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—862no—
466C22—3442no—
467C22—3442no—
468C22—1721no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22#1458277511yescharacteristic
474C22#1458309111yescharacteristic
475C22#1458311111yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—82no—
480C4—81no—
481C4—1721no—
482C4—1721no—
483C4#104×D4311yescharacteristic
484C4#1458291411yescharacteristic
485C4C4×#1062188211yescharacteristic
486C4#1458300911yescharacteristic
487C4#1458303211yescharacteristic
488C4#1458304211yescharacteristic
489C2—21no—
490C2—21no—
491C2—161no—
492C2—3441no—
493C2—1722no—
494C2#1913489411yescharacteristic
495C2#1913494611yescharacteristic
496C2#1913495411yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1980C2
socleC22×C43#386
prime radical#19144591C2
cosocleC2×C42×C43C23
hypercenter#1980D43
hypocenterC43#8991
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. M16×D172C2semidirect
3. C4×#13063245C2semidirect
4. #19133046C2semidirect
5. #19132498C2semidirect
6. #19132433C2semidirect
7. C43×#1980C2semidirect
11. #14583176C4semidirect
12. #14583176C4semidirect
13. #14583091C4semidirect
14. #14583091C4semidirect
118. M16×C43D8semidirect
196. D172#104semidirect
243. #1980D43semidirect
281. C43#8991semidirect
372. M16#10621882semidirect

Maximal subgroups

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

subgroupindex
#191445912
M16×D1722
C4×#130632452
#191330462
#191324982
#191324332
C43×#19802
#899143