Finite Group Databasebeta

← #14762827

Subgroups — #14762827

Order 2816.

1538 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66977C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13069047C214yesmaximal, complemented
4#13068923C214yesmaximal, complemented
5#13068700C212yesmaximal, complemented
6#13068550C212yesmaximal, complemented
7C2×C11×#380C211yesmaximal, characteristic
8C24×C4×C11C2211yescharacteristic
9C23×Dic22C2211yescharacteristic
10C22×C11×C4⋊C4C2212yes—
11C22×C11×C22⋊C4—21no—
12C22×C22⋊Dic11—21no—
13C22×C4⋊Dic11C2211yescharacteristic
14C2×#66977—24no—
15C2×#66977—21no—
16C2×#66977—21no—
17C2×#66977C418yescomplemented
18C2×#66977C2212yes—
19C2×#66977C2212yes—
20C22×Dic11⋊C4—21no—
21C22×#4318C2212yes—
22C11×#380—21no—
23C11×#380—21no—
24C11×#380C2212yes—
25C11×#380C2212yes—
26C2×C11×#95—21no—
27#10622820—24no—
28C2×C22⋊(C11⋊C8)C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×#66874C2218yescomplemented
31#10622167C2218yescomplemented
32C25×C11D411yescharacteristic
33C23×C4×C11—22no—
34C23×C4×C11—44no—
35C23×C4×C11C2×C414yes—
36C23×C4×C11D414yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11—21no—
44C23×Dic11—21no—
45C22×Dic22—22no—
46C22×Dic22—21no—
47C22×Dic22—44no—
48C22×Dic22C2×C414yescomplemented
49C22×Dic22C2312yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—44no—
52C2×C11×C4⋊C4C2314yes—
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—44no—
56C2×C22⋊Dic11—28no—
57C2×C22⋊Dic11—22no—
58C2×C22⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2×C414yescomplemented
62C2×C4⋊Dic11C2312yes—
63#66977—28no—
64#66977—28no—
65#66977—24no—
66#66977—24no—
67#66977C2×C418yes—
68#66977C2×C418yescomplemented
69C2×Dic11⋊C4—28no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—22no—
72C2×#4318—24no—
73C2×#4318—44no—
74C22×C11⋊C8C2314yes—
75C11×#95—22no—
76C11×#95—22no—
77C22⋊(C11⋊C8)—24no—
78C22⋊(C11⋊C8)—24no—
79#66874—48no—
80#21765—111nomaximal, Sylow
81C24×C11—22no—
82C24×C11—22no—
83C24×C11—24no—
84C24×C11—42no—
85C24×C11C22⋊C414yes—
86C24×C11C2×D411yescharacteristic
87C24×C11C2×D411yescharacteristic
88C24×C11C2×D411yescharacteristic
89C22×C4×C11—24no—
90C22×C4×C11—24no—
91C22×C4×C11—24no—
92C22×C4×C11—24no—
93C22×C4×C11—48no—
94C22×C4×C11—48no—
95C22×C4×C11—42no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—44no—
99C22×C4×C11—44no—
100C22×C4×C11—44no—
101C22×C4×C11C22⋊C414yes—
102C22×C4×C11C22⋊C414yes—
103C22×C4×C11C22⋊C414yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D412yes—
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—24no—
115C22×Dic11—24no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—44no—
119C22×Dic11—42no—
120C22×Dic11—42no—
121C2×Dic22—24no—
122C2×Dic22—22no—
123C2×Dic22—28no—
124C2×Dic22—48no—
125C2×Dic22—44no—
126C2×Dic22—48no—
127C2×Dic22C22×C414yes—
128C11×C4⋊C4—28no—
129C11×C4⋊C4—44no—
130C11×C22⋊C4—44no—
131C11×C22⋊C4—44no—
132C22⋊Dic11—28no—
133C22⋊Dic11—28no—
134C4⋊Dic11—24no—
135C4⋊Dic11—22no—
136C4⋊Dic11C22×C414yes—
137Dic11⋊C4—28no—
138Dic11⋊C4—28no—
139#4318—48no—
140C2×C11⋊C8—24no—
141C2×C11⋊C8—28no—
142C22×C22⋊Q8—111no—
143C2×#407—111no—
144C2×#380D1111yescharacteristic
145#1894—114no—
146#1872—114no—
147#1823—112no—
148#1787—112no—
149C23×C11—22no—
150C23×C11—22no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—28no—
159C23×C11—28no—
160C23×C11—44no—
161C23×C11—48no—
162C23×C11—48no—
163C23×C11C2×C22⋊C412yes—
164C23×C11C2×C22⋊C412yes—
165C23×C11C2×C22⋊C412yes—
166C23×C11AGL(1,ℤ/8)12yes—
167C23×C11#13712yes—
168C23×C11#13714yes—
169C23×C11C22×D411yescharacteristic
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
176C2×C4×C11—24no—
177C2×C4×C11—24no—
178C2×C4×C11—24no—
179C2×C4×C11—44no—
180C2×C4×C11—44no—
181C2×C4×C11—44no—
182C2×C4×C11—44no—
183C2×C4×C11—44no—
184C2×C4×C11—44no—
185C2×C4×C11—88no—
186C2×C4×C11C2×C22⋊C412yes—
187C2×C4×C11C2×C22⋊C412yes—
188C2×C4×C11C2×C22⋊C412yes—
189C2×C4×C11C23×C411yescharacteristic
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11H(5,𝔽2)14yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—48no—
195C2×Dic11—44no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—48no—
199Dic22—28no—
200Dic22—48no—
201Dic22—44no—
202C11⋊C8—44no—
203C23×Q8—111no—
204C24×C4C2×D1111yescharacteristic
205C22×M16—112no—
206C2×C22⋊Q8—112no—
207C2×C22⋊Q8—112no—
208C2×C22⋊Q8—118no—
209C2×C22⋊Q8—224no—
210C2×C22⋊Q8—221no—
211C2×C22⋊Q8—221no—
212C22×C4⋊C4—111no—
213C22×C4⋊C4—221no—
214C22×C4⋊C4C2×D1112yes—
215C22×C22⋊C4—21no—
216C22×C22⋊C4—221no—
217C2×#103—118no—
218#407—224no—
219C2×C22⋊C8—112no—
220C2×C22⋊C8—112no—
221#380—21no—
222#380—21no—
223#380C2×D1112yes—
224#380C2×D1112yes—
225C2×#95—21no—
226#340—118no—
227C22×C11—22no—
228C22×C11—22no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—24no—
232C22×C11—24no—
233C22×C11—24no—
234C22×C11—24no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—416no—
239C22×C11—42no—
240C22×C11—42no—
241C22×C11#41714yes—
242C22×C11#41914yes—
243C22×C11C22×C22⋊C411yescharacteristic
244C22×C11#53412yes—
245C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
246C22×C11C2×#13711yescharacteristic
247C22×C11C2×#13712yes—
248C4×C11—22no—
249C4×C11—22no—
250C4×C11—22no—
251C4×C11—84no—
252C4×C11#51812yes—
253C4×C11#53412yes—
254Dic11—44no—
255Dic11—44no—
256C25C22⋊D1111yescharacteristic
257C22×Q8—114no—
258C22×Q8—112no—
259C22×Q8—222no—
260C22×Q8—221no—
261C22×Q8—444no—
262C23×C4—22no—
263C23×C4—44no—
264C23×C4—221no—
265C23×C4—221no—
266C23×C4C4×D1114yes—
267C23×C4D4414yes—
268C23×C4C22⋊D1111yescharacteristic
269C23×C4C22⋊D1111yescharacteristic
270C23×C4C22⋊D1111yescharacteristic
271C23×C4C22×D1111yescharacteristic
272C23×C4C22×D1111yescharacteristic
273C23×C4C22×D1111yescharacteristic
274C2×M16—224no—
275C2×M16—444no—
276C22×C8—114no—
277C22⋊Q8—118no—
278C22⋊Q8—118no—
279C22⋊Q8—228no—
280C22⋊Q8—228no—
281C22⋊Q8—224no—
282C22⋊Q8—224no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—44no—
285C2×C4⋊C4—114no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—228no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1114yes—
293C2×C22⋊C4—22no—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—44no—
296C2×C22⋊C4—228no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299#103—448no—
300C22⋊C8—224no—
301C22⋊C8—224no—
302#95—22no—
303#95—22no—
304C2×C11—24no—
305C2×C11—24no—
306C2×C11—42no—
307C2×C11#230811yescharacteristic
308C2×C11C2×#41911yescharacteristic
309C2×C11C2×#41711yescharacteristic
310C2×C11#319312yes—
311C2×C11#319512yes—
312C24—22no—
313C24—22no—
314C24—24no—
315C24—42no—
316C24(C2×D11)⋊C414yes—
317C24C2×C22⋊D1111yescharacteristic
318C24C2×C22⋊D1111yescharacteristic
319C24C2×C22⋊D1111yescharacteristic
320C2×Q8—114no—
321C2×Q8—224no—
322C2×Q8—222no—
323C2×Q8—228no—
324C2×Q8—448no—
325C2×Q8—444no—
326C2×Q8—448no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—48no—
332C22×C4—48no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—44no—
337C22×C4—44no—
338C22×C4—44no—
339C22×C4—224no—
340C22×C4—224no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—444no—
344C22×C4—442no—
345C22×C4—442no—
346C22×C4(C2×D11)⋊C414yes—
347C22×C4(C2×D11)⋊C414yes—
348C22×C4(C2×D11)⋊C414yes—
349C22×C4C2×C4×D1112yes—
350C22×C4C2×C4×D1112yes—
351C22×C4C2×C4×D1112yes—
352C22×C4C2×D4412yes—
353C22×C4C2×D4412yes—
354C22×C4C2×D4412yes—
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C23×D1111yescharacteristic
359M16—448no—
360C2×C8—224no—
361C2×C8—228no—
362C4⋊C4—28no—
363C4⋊C4—44no—
364C4⋊C4—114no—
365C4⋊C4—224no—
366C4⋊C4—228no—
367C4⋊C4—228no—
368C4⋊C4—222no—
369C22⋊C4—44no—
370C22⋊C4—44no—
371C22⋊C4—228no—
372C22⋊C4—228no—
373C11#2176511yescharacteristic, complemented, Sylow
374C23—21no—
375C23—22no—
376C23—22no—
377C23—21no—
378C23—22no—
379C23—21no—
380C23—22no—
381C23—21no—
382C23—28no—
383C23—22no—
384C23—28no—
385C23—44no—
386C23—48no—
387C23—48no—
388C23C2×(C2×D11)⋊C412yes—
389C23C2×(C2×D11)⋊C412yes—
390C23C2×(C2×D11)⋊C412yes—
391C23#6698512yes—
392C23#6699512yes—
393C23#6700414yes—
394C23C22×C22⋊D1111yescharacteristic
395Q8—228no—
396Q8—448no—
397Q8—444no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—88no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—448no—
417C2×C4—442no—
418C2×C4—444no—
419C2×C4—442no—
420C2×C4—448no—
421C2×C4C2×(C2×D11)⋊C412yes—
422C2×C4C2×(C2×D11)⋊C412yes—
423C2×C4C2×(C2×D11)⋊C412yes—
424C2×C4C22×C4×D1111yescharacteristic
425C2×C4C22×D4411yescharacteristic
426C2×C4#6703714yes—
427C8—444no—
428C22—22no—
429C22—22no—
430C22—24no—
431C22—24no—
432C22—22no—
433C22—22no—
434C22—24no—
435C22—24no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—416no—
440C22—42no—
441C22—42no—
442C22#1062257914yes—
443C22#1062261714yes—
444C22C22×(C2×D11)⋊C411yescharacteristic
445C22C2×#6698511yescharacteristic
446C22#1062333512yes—
447C22C2×#6699511yescharacteristic
448C22C2×#6700412yes—
449C4—22no—
450C4—22no—
451C4—22no—
452C4—84no—
453C4—444no—
454C4—444no—
455C4#1062301712yes—
456C4#1062302412yes—
457C2—24no—
458C2—24no—
459C2—42no—
460C2#1307119111yescharacteristic
461C2C2×#1062261711yescharacteristic
462C2C2×#1062257911yescharacteristic
463C2#1307942212yes—
464C2#1307943712yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#380C2
socleC23×C11C22×D4
prime radicalC25×C11D4
cosocleC22×C4×C11C24
hypercenterC2×#380D11
hypocenterC11#21765
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. #13069047C2semidirect
4. #13068923C2semidirect
5. #13068700C2semidirect
6. #13068550C2semidirect
17. C2×#66977C4semidirect
30. C2×#66874C22semidirect
31. #10622167C22semidirect
48. C22×Dic22C2×C4semidirect
61. C2×C4⋊Dic11C2×C4semidirect
68. #66977C2×C4semidirect
373. C11#21765semidirect

Maximal subgroups

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

subgroupindex
C22×#669772
C2×#106228202
#130690472
#130689232
#130687002
#130685502
C2×C11×#3802
#2176511