Finite Group Databasebeta

← #25081850

Subgroups — #25081850

Order 11008.

650 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145731C211yesmaximal, characteristic, complemented
2#19144687C211yesmaximal, characteristic
3#19144599C211yesmaximal, characteristic, complemented
4#19143618C211yesmaximal, characteristic, complemented
5#19134035C212yesmaximal, complemented
6#19134007C212yesmaximal, complemented
7#19133993C212yesmaximal, complemented
8#19133969C212yesmaximal, complemented
9#19133376C211yesmaximal, characteristic, complemented
10#19133255C211yesmaximal, characteristic, complemented
11C43×#1554C211yesmaximal, characteristic, complemented
12#14583449C2211yescharacteristic
13C2×C4×D172C2211yescharacteristic
14#14583302C2211yescharacteristic, complemented
15#14583295C2211yescharacteristic, complemented
16#14583247C2211yescharacteristic, complemented
17#14583247C2211yescharacteristic, complemented
18#14583227—21no—
19#14583223—22no—
20#14583218—21no—
21#14583196—22no—
22#14583190C2212yes—
23#14583186C2212yes—
24#14583101C2212yes—
25#14583095C2212yes—
26#14583049—21no—
27#14583035—21no—
28#14583012—22no—
29C4×#10621884—22no—
30C8×D172—22no—
31#14582964C2212yes—
32#14582964C2212yes—
33#14582952C2211yescharacteristic
34#14582952C2211yescharacteristic
35C22⋊C8×D43—22no—
36#14582651C2212yescomplemented
37#14582649C2212yescomplemented
38#14582647C2212yescomplemented
39#14582642C2212yescomplemented
40C43×#533C2211yescharacteristic
41C43×#432C2211yescharacteristic
42C43×#431C2211yescharacteristic
43C43×#333C2212yescomplemented
44C43×#332C2212yescomplemented
45C2×#10621898—21no—
46C22×D172D411yescharacteristic
47C22×C4×D43—21no—
48C2×#10621884—22no—
49C2×D344—22no—
50C2×C8×D43—22no—
51C2×C8×D43—22no—
52#13063325C2311yescharacteristic
53#13063322C2311yescharacteristic
54#13063313—21no—
55#13063299—21no—
56#13063299—21no—
57C4×D172—21no—
58C4×D172—21no—
59C4×D172—21no—
60C4×D172—21no—
61C4×D172D412yes—
62C4×D172C2312yes—
63C2×C4⋊Dic43D411yescharacteristic
64C2×(C2×D43)⋊C4—21no—
65#13063258—22no—
66#13063257—22no—
67#13063256—22no—
68#13063256—22no—
69C4⋊(C43⋊C8)D412yes—
70C4⋊(C43⋊C8)C2312yes—
71#13063249—22no—
72#13063247—22no—
73#13063247—22no—
74#13063245—22no—
75#13063245—22no—
76#13063245—22no—
77C22⋊(C43⋊C8)—21no—
78C22⋊(C43⋊C8)D412yes—
79(C2×D43)⋊C8—22no—
80(C2×D43)⋊C8—22no—
81C4×C43⋊C8—21no—
82C4×C43⋊C8C2311yescharacteristic
83C4×C43⋊C8C2311yescharacteristic
84C4⋊Q8×C43C2311yescharacteristic
85C4⋊Q8×C43C2311yescharacteristic
86#125×C43—21no—
87C22⋊Q8×C43—21no—
88C22⋊Q8×C43—21no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91#117×C43—21no—
92C2×C42×C43C2311yescharacteristic
93C4⋊C8×C43C2312yes—
94C4⋊C8×C43C2312yes—
95C22⋊C8×C43—21no—
96C22⋊C8×C43—21no—
97#97×C43—21no—
98C4×C8×C43—21no—
99C23×D43—21no—
100C2×Q8×C43—21no—
101C2×Q8×C43—21no—
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43#4111yescharacteristic
105C2×C22⋊D43—41no—
106C22×Dic43—21no—
107#10621898—82no—
108C2×D172—21no—
109C2×D172—24no—
110C2×D172—21no—
111C2×D172—21no—
112C2×D172—21no—
113C2×D172C2×D412yes—
114C2×C4×D43—22no—
115C2×C4×D43—22no—
116C2×C4×D43—41no—
117C2×C4×D43—82no—
118C2×Dic86—21no—
119C2×C8×C43—22no—
120C2×C8×C43—22no—
121C4⋊C4×C43—21no—
122C4⋊C4×C43—21no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—41no—
126C4⋊C4×C43—41no—
127C22⋊C4×C43—41no—
128C42×C43—41no—
129C42×C43C2×D411yescharacteristic
130C42×C43C2×D411yescharacteristic
131C42×C43#4111yescharacteristic
132C42×C43C2411yescharacteristic
133#10621884—44no—
134(C2×D43)⋊C4—22no—
135(C2×D43)⋊C4—22no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—41no—
138C4⋊Dic43—21no—
139C4⋊Dic43—21no—
140C4⋊Dic43—21no—
141C4⋊Dic43C2×D412yes—
142C2×C43⋊C8—22no—
143C2×C43⋊C8C2×D412yes—
144C2×C43⋊C8C2×D412yes—
145D344—44no—
146C8×D43—82no—
147C8×D43—82no—
148C23×C43#12111yescharacteristic
149C22×D43—22no—
150C22×D43—24no—
151C22×D43—41no—
152C22×D43—81no—
153C22×D43—81no—
154Q8×C43—42no—
155Q8×C43—81no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43—41no—
160C2×C4×C43—41no—
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43#12111yescharacteristic
164C2×C4×C43C22×D411yescharacteristic
165C2×C4×C43C22×D411yescharacteristic
166C2×C4×C43C2×#4111yescharacteristic
167C22⋊D43—82no—
168C2×Dic43—22no—
169C2×Dic43—41no—
170C2×Dic43—81no—
171D172—24no—
172D172—22no—
173D172—42no—
174D172—42no—
175D172—81no—
176D172#13514yes—
177C4×D43—42no—
178C4×D43—42no—
179C4×D43—82no—
180C4×D43—82no—
181Dic86—81no—
182C8×C43—42no—
183C8×C43—42no—
184C43⋊C8—22no—
185C43⋊C8—22no—
186C43⋊C8—42no—
187#19394—431nomaximal, Sylow
188C22×C43—21no—
189C22×C43—21no—
190C22×C43—21no—
191C22×C43C2×#12111yescharacteristic
192C2×D43—24no—
193C2×D43—42no—
194C2×D43—42no—
195C2×D43—84no—
196C2×D43—81no—
197C2×D43—81no—
198C2×D43—81no—
199C4×C43—21no—
200C4×C43—21no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—81no—
204C4×C43—81no—
205C4×C43C2×#13512yes—
206C4×C43#57712yes—
207Dic43—42no—
208Dic43—81no—
209#3228—431no—
210#3109—431no—
211#3101—431no—
212#2972—431no—
213#1681—432no—
214#1677—432no—
215#1675—432no—
216#1671—432no—
217#1572—431no—
218#1554D4311yescharacteristic, complemented
219#1543—431no—
220C2×C43—41no—
221C2×C43#304211yescharacteristic
222C2×C43#305011yescharacteristic
223C2×C43#306811yescharacteristic
224D43—44no—
225D43—161no—
226#533C2×D4311yescharacteristic
227#532—431no—
228C2×C4×D4—431no—
229#500—431no—
230#498—431no—
231#486—431no—
232#486—431no—
233#483—861no—
234#482—862no—
235#481—861no—
236#478—862no—
237#476—432no—
238#476—432no—
239#461—432no—
240#459—432no—
241#450—861no—
242#447—861no—
243#442—862no—
244C4×SD16—862no—
245C8×D4—432no—
246C8×D4—432no—
247C8×D4—862no—
248#432C2×D4311yescharacteristic
249#431—431no—
250#431—431no—
251#431C2×D4311yescharacteristic
252C2×C22⋊C8—862no—
253#335—432no—
254#334—432no—
255#333—432no—
256#333C2×D4312yescomplemented
257#332C2×D4312yescomplemented
258#331—432no—
259C43#1939411yescharacteristic, complemented, Sylow
260C2×#41—861no—
261C22×D4—431no—
262C23×C4—861no—
263C2×SD16—862no—
264C2×D8—862no—
265C22×C8—862no—
266C22×C8—862no—
267C4⋊Q8—431no—
268C4⋊Q8C22×D4311yescharacteristic
269C4⋊Q8C22×D4311yescharacteristic
270#127—431no—
271#125—21no—
272#124—861no—
273C22⋊Q8—21no—
274C22⋊Q8—21no—
275#121—861no—
276#121—861no—
277C4×Q8—21no—
278C4×Q8—21no—
279C4×D4—432no—
280C4×D4—432no—
281C4×D4—861no—
282C4×D4—861no—
283C4×D4—861no—
284C4×D4—861no—
285#117—21no—
286C2×C4⋊C4—431no—
287C2×C22⋊C4—861no—
288C2×C42C22×D4311yescharacteristic
289#107—862no—
290#106—862no—
291#106—862no—
292#106—862no—
293C4⋊C8—432no—
294C4⋊C8—432no—
295C4⋊C8C22×D4312yes—
296C4⋊C8C22×D4312yes—
297#103—862no—
298#102—862no—
299#102—862no—
300#102—862no—
301#102—862no—
302#102—862no—
303C22⋊C8—21no—
304C22⋊C8—21no—
305C22⋊C8—432no—
306C22⋊C8—862no—
307C22⋊C8—862no—
308C22⋊C8—861no—
309#97—21no—
310C4×C8—21no—
311C4×C8—431no—
312C4×C8—431no—
313C4×C8—861no—
314C24—861no—
315#41—3442no—
316C2×Q8—21no—
317C2×Q8—21no—
318C2×Q8—861no—
319C2×D4—432no—
320C2×D4—864no—
321C2×D4—861no—
322C2×D4—861no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—1721no—
326C22×C4—861no—
327C22×C4—862no—
328C22×C4—862no—
329C22×C4—3442no—
330C22×C4—1721no—
331C22×C4#1062189811yescharacteristic
332C22×C4D4×D4311yescharacteristic
333C22×C4D4×D4311yescharacteristic
334SD16—1724no—
335D8—1724no—
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—432no—
339C2×C8—432no—
340C2×C8—862no—
341C2×C8—3442no—
342C2×C8—3442no—
343C4⋊C4—21no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—41no—
348C4⋊C4—41no—
349C4⋊C4—432no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C22⋊C4—41no—
354C22⋊C4—862no—
355C22⋊C4—862no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C42—41no—
359C42#1062189811yescharacteristic
360C42D4×D4311yescharacteristic
361C42D4×D4311yescharacteristic
362C42C23×D4311yescharacteristic
363C23—864no—
364C23—862no—
365C23—3441no—
366C23—3441no—
367C23—1721no—
368C23#1306329811yescharacteristic
369Q8—42no—
370Q8—81no—
371Q8—3441no—
372D4—434no—
373D4—864no—
374D4—862no—
375D4—3441no—
376D4—3442no—
377D4—1722no—
378D4—1722no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—862no—
385C2×C4—3442no—
386C2×C4—3442no—
387C2×C4—3441no—
388C2×C4—1721no—
389C2×C4—1722no—
390C2×C4—1722no—
391C2×C4#1306329811yescharacteristic
392C2×C4#1306329811yescharacteristic
393C2×C4#1306329811yescharacteristic
394C2×C4C2×D4×D4311yescharacteristic
395C2×C4C2×D4×D4311yescharacteristic
396C2×C4C2×#1062189811yescharacteristic
397C8—42no—
398C8—42no—
399C8—862no—
400C8—862no—
401C8—1722no—
402C22—21no—
403C22—21no—
404C22—21no—
405C22—864no—
406C22—3444no—
407C22—3441no—
408C22—3441no—
409C22—3441no—
410C22—1722no—
411C22—1722no—
412C22C2×#1306329811yescharacteristic
413C4—21no—
414C4—21no—
415C4—21no—
416C4—21no—
417C4—81no—
418C4—81no—
419C4—3441no—
420C4—1722no—
421C4#135×D4312yes—
422C4#1458370812yes—
423C2—41no—
424C2—1724no—
425C2—6881no—
426C2#1914410611yescharacteristic
427C2#1914417511yescharacteristic
428C2#1914432611yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1554C2
socleC22×C43C2×#121
prime radical#19144687C2
hypercenter#1554D43
hypocenterC43#19394
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
1. #19145731C2semidirect
3. #19144599C2semidirect
4. #19143618C2semidirect
5. #19134035C2semidirect
6. #19134007C2semidirect
7. #19133993C2semidirect
8. #19133969C2semidirect
9. #19133376C2semidirect
10. #19133255C2semidirect
11. C43×#1554C2semidirect
14. #14583302C22semidirect
15. #14583295C22semidirect
16. #14583247C22semidirect
17. #14583247C22semidirect
36. #14582651C22semidirect
37. #14582649C22semidirect
38. #14582647C22semidirect
39. #14582642C22semidirect
43. C43×#333C22semidirect
44. C43×#332C22semidirect
218. #1554D43semidirect
256. #333C2×D43semidirect
257. #332C2×D43semidirect
259. C43#19394semidirect

Maximal subgroups

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

subgroupindex
#191457312
#191446872
#191445992
#191436182
#191340352
#191340072
#191339932
#191339692
#191333762
#191332552
C43×#15542
#1939443