Finite Group Databasebeta

← #14763263

Subgroups — #14763263

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic
3#13071021C211yesmaximal, characteristic
4#13069578C211yesmaximal, characteristic, complemented
5#13069577C211yesmaximal, characteristic, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069572C214yesmaximal, complemented
8#13068709C214yesmaximal
9C11×#1990C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13#10623259—24no—
14#10623259C418yescomplemented
15C2×#66950—21no—
16C2×#66945—21no—
17C2×#66945C2212yes—
18C2×#66943C2212yes—
19C2×#66940—21no—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C11×#384C2211yescharacteristic
24C2×(C2×D11)⋊C8C2212yes—
25C2×Dic11⋊C8C2212yes—
26#10622600—21no—
27#10622600C2212yes—
28#10622590—21no—
29C4⋊C4×Dic11—21no—
30C4⋊C4×Dic11C2212yes—
31#10622548C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622298—24no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11D411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×Dic22—21no—
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C4⋊C4C2312yes—
51C2×C42×C11C2311yescharacteristic
52#66999—28no—
53Q8×Dic11—28no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—22no—
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11D411yescharacteristic
67C2×C4×Dic11C2311yescharacteristic
68C22×C11⋊C8C2312yes—
69#66950—28no—
70#66945—24no—
71#66945—44no—
72#66945C2×C418yes—
73#66943—24no—
74#66943C2×C418yes—
75#66940—28no—
76C42×D11C2×C414yes—
77C42×D11D414yes—
78#66922—22no—
79#66922C2×C414yes—
80C4×C8×C11—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83(C2×D11)⋊C8—24no—
84Dic11⋊C8—24no—
85C4×C11⋊C8—22no—
86#21835—111nomaximal, Sylow
87C23×D11C2×D411yescharacteristic
88C2×Q8×C11—24no—
89C2×Q8×C11—42no—
90C2×Q8×C11—42no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2411yescharacteristic
96C22×Dic11—22no—
97C22×Dic11—22no—
98C22×Dic11C2×D411yescharacteristic
99C22×Dic11C2×D411yescharacteristic
100C22×Dic11C2×D411yescharacteristic
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11C22⋊C414yes—
108C2×C4×D11C22⋊C414yes—
109C2×C4×D11C22×C412yes—
110C2×C4×D11C2×D412yes—
111C2×Dic22—24no—
112C2×Dic22—42no—
113C2×Dic22—42no—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4—42no—
121C11×C4⋊C4—42no—
122C11×C4⋊C4C22×C414yes—
123C42×C11C22×C412yes—
124C42×C11C2×D412yes—
125(C2×D11)⋊C4—28no—
126(C2×D11)⋊C4—44no—
127C4⋊Dic11—28no—
128C4⋊Dic11—24no—
129C4⋊Dic11—22no—
130C4⋊Dic11—24no—
131C4⋊Dic11—42no—
132C4⋊Dic11—42no—
133C4⋊Dic11C22×C414yes—
134Dic11⋊C4—28no—
135C4×Dic11—28no—
136C4×Dic11—44no—
137C4×Dic11C22⋊C414yes—
138C4×Dic11C22⋊C414yes—
139C4×Dic11C22×C412yes—
140C4×Dic11C2×D412yes—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×#533—111no—
145C2×#431—111no—
146#2285—111no—
147#1990—111no—
148#1990—111no—
149#1990—111no—
150#1990D1111yescharacteristic, complemented
151#1989—114no—
152#1825—114no—
153C23×C11C22×D411yescharacteristic
154C22×D11—21no—
155C22×D11—21no—
156C22×D11—21no—
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—21no—
160C22×D11C2×C22⋊C412yes—
161Q8×C11—48no—
162C2×C4×C11—24no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
168C2×C4×C11C2×C22⋊C412yes—
169C2×C4×C11C2×C22⋊C412yes—
170C2×C4×C11#13512yes—
171C2×C4×C11#13512yes—
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11#13712yes—
174C2×C4×C11C23×C411yescharacteristic
175C2×C4×C11C22×D411yescharacteristic
176C2×C4×C112−1+412yes—
177C2×C4×C112−1+412yes—
178C2×Dic11—21no—
179C2×Dic11—21no—
180C2×Dic11—21no—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—21no—
184C2×Dic11—24no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11C2×C22⋊C412yes—
191C2×Dic11C2×C22⋊C412yes—
192C2×Dic11C2×C22⋊C412yes—
193C4×D11—24no—
194C4×D11—24no—
195C4×D11—28no—
196C4×D11—28no—
197Dic22—48no—
198C8×C11—42no—
199C11⋊C8—42no—
200#533—118no—
201#533—224no—
202C2×C4⋊Q8—111no—
203C2×C4⋊Q8C2×D1111yescharacteristic
204C2×#125—112no—
205C2×C22⋊Q8—221no—
206C2×C22⋊Q8—221no—
207C2×C4×Q8—221no—
208C2×C4×Q8—221no—
209C2×#117—112no—
210C2×#117—221no—
211C22×C42—111no—
212#431—224no—
213C2×C4⋊C8—112no—
214C2×C22⋊C8—112no—
215C2×C4×C8—111no—
216C2×C4×C8C2×D1111yescharacteristic
217#384—111no—
218#384C2×D1111yescharacteristic
219#382—221no—
220#380—112no—
221#380—221no—
222C4×C4⋊C4—112no—
223C4×C4⋊C4—221no—
224#340—114no—
225#340—114no—
226#340—114no—
227#340C2×D1114yes—
228C22×C11C22×C22⋊C411yescharacteristic
229C22×C11#53611yescharacteristic
230C22×C11#53611yescharacteristic
231C22×C11C2×#13511yescharacteristic
232C22×C11C2×#13511yescharacteristic
233C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
234C22×C11C2×#13711yescharacteristic
235C2×D11—22no—
236C2×D11—22no—
237C2×D11—22no—
238C2×D11—41no—
239C2×D11—41no—
240C2×D11—41no—
241C2×D11—41no—
242C4×C11—44no—
243C4×C11—82no—
244C4×C11#41614yes—
245C4×C11#41714yes—
246C4×C11#51912yes—
247C4×C11#53612yes—
248Dic11—22no—
249Dic11—22no—
250Dic11—22no—
251Dic11—44no—
252Dic11—82no—
253C22×Q8—21no—
254C22×Q8—221no—
255C23×C4—111no—
256C23×C4—111no—
257C23×C4—111no—
258C22×C8—112no—
259C22×C8C22×D1112yes—
260C4⋊Q8—22no—
261C4⋊Q8—114no—
262C4⋊Q8—222no—
263C4⋊Q8C4×D1114yes—
264#125—118no—
265#125—224no—
266C22⋊Q8—228no—
267C22⋊Q8—228no—
268C4×Q8—228no—
269C4×Q8—228no—
270#117—118no—
271#117—224no—
272#117—444no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—112no—
277C2×C4⋊C4—112no—
278C2×C4⋊C4—222no—
279C2×C4⋊C4—222no—
280C2×C4⋊C4—221no—
281C2×C4⋊C4—221no—
282C2×C4⋊C4—221no—
283C2×C4⋊C4C22×D1112yes—
284C2×C4⋊C4C22×D1112yes—
285C2×C22⋊C4—222no—
286C2×C22⋊C4—222no—
287C2×C42—111no—
288C2×C42—111no—
289C2×C42—111no—
290C2×C42—114no—
291C2×C42—114no—
292C2×C42—222no—
293C2×C42—222no—
294C2×C42C22×D1111yescharacteristic
295C4⋊C8—224no—
296C22⋊C8—224no—
297C4×C8—22no—
298C4×C8—222no—
299#95—222no—
300#95—222no—
301C2×C11#231011yescharacteristic
302C2×C11C2×#41611yescharacteristic
303C2×C11C2×#41711yescharacteristic
304C2×C11#322811yescharacteristic
305C2×C11#322811yescharacteristic
306C2×C11#323111yescharacteristic
307C2×C11#323111yescharacteristic
308D11—42no—
309C24—111no—
310C2×Q8—24no—
311C2×Q8—42no—
312C2×Q8—42no—
313C2×Q8—224no—
314C2×Q8—442no—
315C2×Q8—442no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—111no—
319C22×C4—111no—
320C22×C4—111no—
321C22×C4—114no—
322C22×C4—114no—
323C22×C4—112no—
324C22×C4—112no—
325C22×C4—222no—
326C22×C4—222no—
327C22×C4—222no—
328C22×C4—222no—
329C22×C4—222no—
330C22×C4—222no—
331C22×C4—222no—
332C22×C4—222no—
333C22×C4D4×D1111yescharacteristic
334C22×C4D4×D1111yescharacteristic
335C22×C4C23×D1111yescharacteristic
336C2×C8—22no—
337C2×C8—22no—
338C2×C8—22no—
339C2×C8—222no—
340C2×C8—222no—
341C2×C8—222no—
342C4⋊C4—24no—
343C4⋊C4—22no—
344C4⋊C4—24no—
345C4⋊C4—42no—
346C4⋊C4—42no—
347C4⋊C4—114no—
348C4⋊C4—228no—
349C4⋊C4—228no—
350C4⋊C4—224no—
351C4⋊C4—222no—
352C4⋊C4—224no—
353C4⋊C4—442no—
354C4⋊C4—442no—
355C4⋊C4C2×C4×D1114yes—
356C22⋊C4—228no—
357C22⋊C4—444no—
358C42—114no—
359C42—114no—
360C42—112no—
361C42—112no—
362C42—228no—
363C42—444no—
364C42C2×C4×D1112yes—
365C42D4×D1112yes—
366C11#2183511yescharacteristic, complemented, Sylow
367C23—112no—
368C23—221no—
369C23—221no—
370C23—221no—
371C23—221no—
372C23—221no—
373C23—221no—
374C23C2×D4×D1111yescharacteristic
375Q8—48no—
376Q8—448no—
377C2×C4—24no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—112no—
384C2×C4—112no—
385C2×C4—112no—
386C2×C4—221no—
387C2×C4—221no—
388C2×C4—221no—
389C2×C4—221no—
390C2×C4—221no—
391C2×C4—221no—
392C2×C4—224no—
393C2×C4—228no—
394C2×C4—224no—
395C2×C4—228no—
396C2×C4—224no—
397C2×C4—442no—
398C2×C4—442no—
399C2×C4—442no—
400C2×C4—442no—
401C2×C4—442no—
402C2×C4C22⋊C4×D1112yes—
403C2×C4C22⋊C4×D1112yes—
404C2×C4#6696512yes—
405C2×C4#6696712yes—
406C2×C4#6696912yes—
407C2×C4#6697112yes—
408C2×C4C22×C4×D1111yescharacteristic
409C2×C4C2×D4×D1111yescharacteristic
410C2×C4#6704012yes—
411C2×C4#6704312yes—
412C8—42no—
413C8—442no—
414C22—222no—
415C22—222no—
416C22—222no—
417C22—441no—
418C22—441no—
419C22—441no—
420C22—441no—
421C22C2×C22⋊C4×D1111yescharacteristic
422C22#1062320611yescharacteristic
423C22#1062325511yescharacteristic
424C22C2×#6696511yescharacteristic
425C22C2×#6696711yescharacteristic
426C22C2×#6696911yescharacteristic
427C22C2×#6697111yescharacteristic
428C4—44no—
429C4—82no—
430C4—222no—
431C4—222no—
432C4—222no—
433C4—444no—
434C4—882no—
435C4#1062238514yes—
436C4#1062241614yes—
437C4#1062310312yes—
438C4#1062315912yes—
439C2—442no—
440C2#1307119911yescharacteristic
441C2C2×#1062238511yescharacteristic
442C2C2×#1062241611yescharacteristic
443C2#1307974711yescharacteristic
444C2#1307975311yescharacteristic
445C2#1307977011yescharacteristic
446C2#1307977611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#21835
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13069578C2semidirect
5. #13069577C2semidirect
6. #13069576C2semidirect
7. #13069572C2semidirect
9. C11×#1990C2semidirect
14. #10623259C4semidirect
150. #1990D11semidirect
366. C11#21835semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106222982
#130710212
#130695782
#130695772
#130695762
#130695722
#130687092
C11×#19902
#2183511