Finite Group Databasebeta

← #14781435

Subgroups — #14781435

Order 2816.

1422 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081949C211yesmaximal, characteristic
2C2×#10622618C212yesmaximal, complemented
3C2×#10622579C212yesmaximal, complemented
4#13069845C214yesmaximal, complemented
5#13069840C214yesmaximal, complemented
6#13068355C211yesmaximal, characteristic, complemented
7C11×#2317C211yesmaximal, characteristic, complemented
8C22×#4339C2212yes—
9C2×C11×#117C2211yescharacteristic
10C2×C11×#117C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×#4318C2212yes—
13#10623057—22no—
14#10623056—22no—
15#10623055—24no—
16#10623041C2212yes—
17#10623041C2212yes—
18#10623024—22no—
19#10623008—22no—
20C11×#389—22no—
21C11×#385—22no—
22C11×#384C2212yescomplemented
23C11×#382C2212yescomplemented
24#10622618—28no—
25C2×#66874—22no—
26#10622579—24no—
27#10622579C2218yescomplemented
28C2×#66873—22no—
29C2×#66869C2218yescomplemented
30#10622168C2212yescomplemented
31#10622168C2212yescomplemented
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—22no—
35C2×#4339—22no—
36C2×#4339—22no—
37C2×#4339—24no—
38C2×#4339—24no—
39C2×#4339—24no—
40C2×#4339—24no—
41C2×#4339D414yes—
42C2×#4339C2314yes—
43C22×D44D412yes—
44C22×C4×D11—22no—
45C22×Dic22D412yes—
46C11×#117—22no—
47C11×#117—22no—
48C11×#117—22no—
49C11×#117D414yescomplemented
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—24no—
55C2×C11×C4⋊C4C2312yes—
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4D412yes—
60C2×C42×C11D412yes—
61C2×C42×C11C2312yes—
62#66983—24no—
63#66983—24no—
64C2×#4318—22no—
65C2×#4318—24no—
66C2×#4318—24no—
67C2×#4318C2314yes—
68C22×C11⋊C8—22no—
69#66950—24no—
70#66950—24no—
71#66948—24no—
72#66948—24no—
73#66939—28no—
74#66935—28no—
75#66928—24no—
76#66927—22no—
77C4×D44—24no—
78C4×D44—24no—
79#66922—22no—
80C11×#95—24no—
81#66874—28no—
82#66873—28no—
83#66869—216no—
84#23500—111nomaximal, Sylow
85C24×C11C2×D411yescharacteristic
86C23×D11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—42no—
90C22×C4×C11—82no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D412yes—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11#4114yes—
98C22×C4×C11#4112yes—
99C22×C4×C11C2411yescharacteristic
100C2×C22⋊D11—24no—
101C2×C22⋊D11—24no—
102C2×C22⋊D11—44no—
103C2×C22⋊D11—44no—
104C22×Dic11—22no—
105#4339—28no—
106#4339—28no—
107#4339—24no—
108#4339—24no—
109#4339—24no—
110#4339—24no—
111#4339—44no—
112#4339—44no—
113#4339—44no—
114#4339—44no—
115C2×D44—24no—
116C2×D44—24no—
117C2×D44—22no—
118C2×D44—24no—
119C2×D44—24no—
120C2×D44C2×D414yes—
121C2×C4×D11—24no—
122C2×C4×D11—24no—
123C2×C4×D11—44no—
124C2×C4×D11—44no—
125C2×Dic22—22no—
126C2×Dic22—24no—
127C2×Dic22—24no—
128C2×Dic22C2×D414yes—
129C11×C4⋊C4—24no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C4⋊C4—84no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138C42×C11—22no—
139C42×C11—22no—
140C42×C11—22no—
141C42×C11C2×D414yes—
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—28no—
144C4⋊Dic11—24no—
145C4⋊Dic11—24no—
146#4318—24no—
147#4318—24no—
148#4318—44no—
149C2×C11⋊C8—24no—
150C2×C11⋊C8—44no—
151#3449—111no—
152C2×#421—112no—
153C2×#417—112no—
154#2317D1111yescharacteristic, complemented
155#2040—114no—
156#2039—114no—
157#1742—111no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11#12012yes—
161C23×C11#12112yes—
162C23×C11#12412yes—
163C23×C11C22×D411yescharacteristic
164C22×D11—24no—
165C22×D11—44no—
166C22×D11—82no—
167C22×D11—82no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—44no—
176C2×C4×C11—42no—
177C2×C4×C11—84no—
178C2×C4×C11#12011yescharacteristic
179C2×C4×C11#12011yescharacteristic
180C2×C4×C11#12114yes—
181C2×C4×C11#12114yes—
182C2×C4×C11#12112yes—
183C2×C4×C11#12314yes—
184C2×C4×C11#12314yes—
185C2×C4×C11#12412yes—
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C22×D412yes—
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4112yes—
190C22⋊D11—44no—
191C22⋊D11—44no—
192C22⋊D11—48no—
193C2×Dic11—24no—
194C2×Dic11—44no—
195D44—24no—
196D44—24no—
197D44—44no—
198D44—84no—
199D44—84no—
200C4×D11—44no—
201C4×D11—44no—
202C4×D11—48no—
203Dic22—24no—
204Dic22—24no—
205Dic22—44no—
206C11⋊C8—44no—
207C22×#41—112no—
208C22×M16—112no—
209#537—112no—
210#537—112no—
211#536—222no—
212#535—222no—
213#534—222no—
214#532—222no—
215#525—224no—
216C2×#117C2×D1111yescharacteristic
217C2×#117C2×D1111yescharacteristic
218C22×C4⋊C4C2×D1111yescharacteristic
219#421—228no—
220C2×#104—118no—
221#417—118no—
222#417—224no—
223C2×#103—222no—
224C2×#102—222no—
225#389—22no—
226#385—22no—
227#384C2×D1112yescomplemented
228#382C2×D1112yescomplemented
229#343—112no—
230#343—112no—
231C22×C11—21no—
232C22×C11—22no—
233C22×C11—21no—
234C22×C11—22no—
235C22×C11—42no—
236C22×C11—42no—
237C22×C11#39414yes—
238C22×C11C2×#12011yescharacteristic
239C22×C11C2×#12111yescharacteristic
240C22×C11C2×#12411yescharacteristic
241C2×D11—44no—
242C2×D11—44no—
243C2×D11—44no—
244C2×D11—88no—
245C4×C11—44no—
246C4×C11—42no—
247C4×C11—42no—
248C4×C11—82no—
249C4×C11#39412yes—
250C4×C11#39412yes—
251C4×C11C2×#12112yes—
252C4×C11C2×#12312yes—
253Dic11—44no—
254C2×#41—114no—
255C2×#41—114no—
256C2×#41—222no—
257C2×#41—222no—
258C2×#41—224no—
259C2×#41—224no—
260C2×#41—224no—
261C2×#41—224no—
262C22×Q8—112no—
263C22×D4—112no—
264C22×D4—222no—
265C23×C4—21no—
266C23×C4—222no—
267C23×C4C22×D1111yescharacteristic
268C2×M16—114no—
269C2×M16—222no—
270C2×M16—224no—
271C2×M16—224no—
272C22×C8—222no—
273C4⋊Q8—222no—
274#127—222no—
275#124—224no—
276#123—228no—
277C22⋊Q8—224no—
278C22⋊Q8—224no—
279#121—224no—
280#121—224no—
281#121—224no—
282#121—224no—
283#120—228no—
284C4×D4—224no—
285C4×D4—224no—
286#117—22no—
287#117—22no—
288#117—22no—
289#117D4414yescomplemented
290C2×C4⋊C4—21no—
291C2×C4⋊C4—22no—
292C2×C4⋊C4—22no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—24no—
295C2×C4⋊C4C22×D1112yes—
296C2×C4⋊C4C22×D1111yescharacteristic
297C2×C4⋊C4C22×D1111yescharacteristic
298C2×C22⋊C4—21no—
299C2×C22⋊C4C22⋊D1112yes—
300C2×C42C22⋊D1112yes—
301C2×C42C22×D1112yes—
302#104—2216no—
303#103—228no—
304#102—228no—
305#95—24no—
306C2×C11—21no—
307C2×C11—24no—
308C2×C11—21no—
309C2×C11C2×#39411yescharacteristic
310C2×C11#302111yescharacteristic
311C2×C11#302211yescharacteristic
312D11—84no—
313C24—222no—
314C24C2×C22⋊D1111yescharacteristic
315#41—228no—
316#41—228no—
317#41—224no—
318#41—224no—
319#41—224no—
320#41—224no—
321#41—444no—
322#41—444no—
323#41—444no—
324#41—444no—
325C2×Q8—114no—
326C2×Q8—222no—
327C2×Q8—224no—
328C2×Q8—224no—
329C2×D4—114no—
330C2×D4—224no—
331C2×D4—224no—
332C2×D4—224no—
333C2×D4—224no—
334C2×D4—224no—
335C2×D4—224no—
336C2×D4—222no—
337C2×D4—444no—
338C2×D4—444no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—42no—
342C22×C4—82no—
343C22×C4—222no—
344C22×C4—224no—
345C22×C4—224no—
346C22×C4—444no—
347C22×C4—444no—
348C22×C4C2×D4412yes—
349C22×C4#433912yes—
350C22×C4D4×D1112yes—
351C22×C4D4×D1112yes—
352C22×C4#434314yes—
353C22×C4C2×C22⋊D1112yes—
354C22×C4C2×C22⋊D1112yes—
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C23×D1111yescharacteristic
357M16—224no—
358M16—224no—
359M16—444no—
360C2×C8—224no—
361C2×C8—444no—
362C4⋊C4—24no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—84no—
369C4⋊C4—224no—
370C4⋊C4—224no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—228no—
374C22⋊C4—228no—
375C42—22no—
376C42—22no—
377C42—22no—
378C42C2×D4414yes—
379C11#2350011yescharacteristic, complemented, Sylow
380C23—41no—
381C23—41no—
382C23—224no—
383C23—444no—
384C23—882no—
385C23—882no—
386C23#6698312yes—
387C23#6699012yes—
388C23#6700012yes—
389C23C22×C22⋊D1111yescharacteristic
390Q8—224no—
391Q8—224no—
392Q8—444no—
393D4—224no—
394D4—224no—
395D4—444no—
396D4—444no—
397D4—448no—
398D4—444no—
399D4—884no—
400D4—884no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—84no—
411C2×C4—224no—
412C2×C4—444no—
413C2×C4—444no—
414C2×C4—444no—
415C2×C4—448no—
416C2×C4#6694714yes—
417C2×C4#6694714yes—
418C2×C4#6694814yes—
419C2×C4#6694814yes—
420C2×C4#6698312yes—
421C2×C4#6699011yescharacteristic
422C2×C4#6699011yescharacteristic
423C2×C4#6700012yes—
424C2×C4C22×D4411yescharacteristic
425C2×C4C2×#433911yescharacteristic
426C2×C4C2×D4×D1112yes—
427C2×C4C2×#434312yes—
428C8—444no—
429C22—21no—
430C22—22no—
431C22—21no—
432C22—22no—
433C22—42no—
434C22—42no—
435C22—444no—
436C22—444no—
437C22—444no—
438C22—888no—
439C22#1062260414yes—
440C22C2×#6698311yescharacteristic
441C22C2×#6699011yescharacteristic
442C22C2×#6700011yescharacteristic
443C4—44no—
444C4—42no—
445C4—42no—
446C4—82no—
447C4—444no—
448C4#1062260412yes—
449C4#1062260412yes—
450C4C2×#6694712yes—
451C4C2×#6694812yes—
452C2—21no—
453C2—24no—
454C2—21no—
455C2—884no—
456C2C2×#1062260411yescharacteristic
457C2#1307798711yescharacteristic
458C2#1307799411yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC22×C11C2×#120
prime radical#13081949C2
hypercenter#2317D11
hypocenterC11#23500
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. C2×#10622618C2semidirect
3. C2×#10622579C2semidirect
4. #13069845C2semidirect
5. #13069840C2semidirect
6. #13068355C2semidirect
7. C11×#2317C2semidirect
22. C11×#384C22semidirect
23. C11×#382C22semidirect
27. #10622579C22semidirect
29. C2×#66869C22semidirect
30. #10622168C22semidirect
31. #10622168C22semidirect
49. C11×#117D4semidirect
154. #2317D11semidirect
227. #384C2×D11semidirect
228. #382C2×D11semidirect
289. #117D44semidirect
379. C11#23500semidirect

Maximal subgroups

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

subgroupindex
#130819492
C2×#106226182
C2×#106225792
#130698452
#130698402
#130683552
C11×#23172
#2350011