Finite Group Databasebeta

← #14762847

Subgroups — #14762847

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622820C211yesmaximal, characteristic, complemented
2#13070999C211yesmaximal, characteristic, complemented
3#13069055C214yesmaximal, complemented
4#13068939C214yesmaximal, complemented
5#13068702C212yesmaximal, complemented
6#13068547C212yesmaximal, complemented
7C22×C11×#121C211yesmaximal, characteristic
8C23×D4×C11—21no—
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11C2211yescharacteristic
11C2×C11×#121—24no—
12C2×C11×#121—21no—
13C2×C11×#121—21no—
14C2×C11×#121C418yescomplemented
15C2×C11×#121C2212yes—
16C2×C11×#121C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4—21no—
19C2×#66979C2212yescomplemented
20C22×#4318C2212yescomplemented
21#10622860—21no—
22C2×#66896C2218yescomplemented
23#10622825C2212yes—
24#10622825C2212yescomplemented
25#10622824—21no—
26C4×C22⋊Dic11—21no—
27C4×C22⋊Dic11—21no—
28#10622820—24no—
29C2×C22⋊(C11⋊C8)C2212yes—
30C2×C22⋊(C11⋊C8)C2212yescomplemented
31#10622167C2218yescomplemented
32C25×C11—21no—
33C25×C11D411yescharacteristic
34C22×D4×C11—28no—
35C22×D4×C11—22no—
36C22×D4×C11—22no—
37C22×D4×C11—21no—
38C22×D4×C11—22no—
39C22×D4×C11—44no—
40C22×D4×C11—48no—
41C22×D4×C11C2×C414yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11—44no—
45C23×C4×C11C2×C414yes—
46C23×C4×C11D411yescharacteristic
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D414yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C11×#121—28no—
54C11×#121—28no—
55C11×#121—24no—
56C11×#121—24no—
57C11×#121C2×C418yes—
58C11×#121C2×C418yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2×C414yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C22⋊C4—28no—
64C2×C11×C22⋊C4—22no—
65C2×C11×C22⋊C4—22no—
66C2×C22⋊Dic11—22no—
67C2×C22⋊Dic11—22no—
68C2×C22⋊Dic11—22no—
69#66979—44no—
70C2×C4⋊Dic11C2314yes—
71C2×C4×Dic11—22no—
72C2×#4318—24no—
73C2×#4318—44no—
74C22×C11⋊C8C2314yes—
75#66896—48no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78C22⋊(C11⋊C8)—24no—
79C22⋊(C11⋊C8)—24no—
80#21767—111nomaximal, Sylow
81C24×C11—24no—
82C24×C11—24no—
83C24×C11—22no—
84C24×C11—42no—
85C24×C11—42no—
86C24×C11—44no—
87C24×C11—44no—
88C24×C11—44no—
89C24×C11C22⋊C414yes—
90C24×C11C2×D411yescharacteristic
91C24×C11C2×D411yescharacteristic
92C24×C11C2×D411yescharacteristic
93C2×D4×C11—28no—
94C2×D4×C11—28no—
95C2×D4×C11—24no—
96C2×D4×C11—22no—
97C2×D4×C11—28no—
98C2×D4×C11—48no—
99C2×D4×C11—44no—
100C2×D4×C11—48no—
101C2×D4×C11—48no—
102C2×D4×C11—48no—
103C2×D4×C11—432no—
104C2×D4×C11C22×C414yes—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—48no—
111C22×C4×C11—48no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—44no—
116C22×C4×C11C22⋊C414yes—
117C22×C4×C11C22⋊C414yes—
118C22×C4×C11C22⋊C414yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4C22×C414yes—
133C11×C22⋊C4—28no—
134C11×C22⋊C4—28no—
135C22⋊Dic11—44no—
136C22⋊Dic11—44no—
137C22⋊Dic11—44no—
138C4⋊Dic11—28no—
139C4×Dic11—44no—
140#4318—48no—
141C2×C11⋊C8—24no—
142C2×C11⋊C8—28no—
143C22×#121D1111yescharacteristic
144C2×#407—111no—
145#2280—111no—
146#1895—114no—
147#1875—114no—
148#1823—112no—
149#1786—112no—
150C23×C11—22no—
151C23×C11—22no—
152C23×C11—22no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11—28no—
159C23×C11—24no—
160C23×C11—44no—
161C23×C11—44no—
162C23×C11—416no—
163C23×C11—48no—
164C23×C11—48no—
165C23×C11—44no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11—48no—
169C23×C11—816no—
170C23×C11C2×C22⋊C412yes—
171C23×C11C2×C22⋊C412yes—
172C23×C11C2×C22⋊C412yes—
173C23×C11AGL(1,ℤ/8)14yes—
174C23×C11C22×D411yescharacteristic
175D4×C11—28no—
176D4×C11—48no—
177D4×C11—416no—
178D4×C11—416no—
179D4×C11—44no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—24no—
189C2×C4×C11—24no—
190C2×C4×C11—44no—
191C2×C4×C11—44no—
192C2×C4×C11—44no—
193C2×C4×C11—44no—
194C2×C4×C11—48no—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11C2×C22⋊C412yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11H(5,𝔽2)14yes—
201C2×Dic11—44no—
202C2×Dic11—44no—
203C2×Dic11—44no—
204C11⋊C8—44no—
205C23×D4—21no—
206C23×D4C2×D1111yescharacteristic
207C24×C4C2×D1111yescharacteristic
208C22×M16—112no—
209C2×#121—24no—
210C2×#121—21no—
211C2×#121—21no—
212C2×#121Dic1118yescomplemented
213C2×#121C2×D1112yes—
214C2×#121C2×D1112yes—
215C2×#117—112no—
216C22×C4⋊C4C2×D1111yescharacteristic
217C22×C22⋊C4—21no—
218C2×#102—118no—
219#407—224no—
220C2×C22⋊C8—112no—
221C2×C22⋊C8—112no—
222#381—221no—
223#380—112no—
224#380—112no—
225#379—221no—
226C4×C22⋊C4—221no—
227C4×C22⋊C4—221no—
228#340—118no—
229C22×C11—22no—
230C22×C11—22no—
231C22×C11—28no—
232C22×C11—22no—
233C22×C11—22no—
234C22×C11—22no—
235C22×C11—22no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—416no—
239C22×C11—44no—
240C22×C11—44no—
241C22×C11—44no—
242C22×C11—44no—
243C22×C11—44no—
244C22×C11—816no—
245C22×C11—88no—
246C22×C11#41814yes—
247C22×C11C22×C22⋊C411yescharacteristic
248C22×C11#53412yes—
249C22×C11C2×AGL(1,ℤ/8)12yes—
250C22×C11#57512yes—
251C4×C11—22no—
252C4×C11—22no—
253C4×C11—22no—
254C4×C11—44no—
255C4×C11#51812yes—
256C4×C11#53412yes—
257Dic11—84no—
258C25—21no—
259C25C22⋊D1111yescharacteristic
260C22×D4—28no—
261C22×D4—22no—
262C22×D4—22no—
263C22×D4—21no—
264C22×D4—22no—
265C22×D4—44no—
266C22×D4—48no—
267C22×D4C2×Dic1114yes—
268C22×D4C22×D1112yes—
269C23×C4—21no—
270C23×C4—44no—
271C23×C4C2×Dic1114yes—
272C23×C4C22⋊D1111yescharacteristic
273C23×C4C22⋊D1111yescharacteristic
274C23×C4C22⋊D1111yescharacteristic
275C23×C4C22⋊D1114yes—
276C23×C4C22×D1111yescharacteristic
277C23×C4C22×D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C2×M16—224no—
280C2×M16—444no—
281C22×C8—114no—
282#121—28no—
283#121—28no—
284#121—24no—
285#121—24no—
286#121C2×Dic1118yes—
287#121C2×Dic1118yes—
288#117—444no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4C2×Dic1114yes—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—28no—
295C2×C22⋊C4—22no—
296C2×C22⋊C4—22no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C42—222no—
301#102—448no—
302C22⋊C8—224no—
303C22⋊C8—224no—
304#95—222no—
305#95—222no—
306C2×C11—24no—
307C2×C11—42no—
308C2×C11—42no—
309C2×C11—84no—
310C2×C11#230811yescharacteristic
311C2×C11C2×#41811yescharacteristic
312C2×C11#289611yescharacteristic
313C2×C11#319414yes—
314C24—24no—
315C24—24no—
316C24—22no—
317C24—42no—
318C24—42no—
319C24—44no—
320C24—44no—
321C24—44no—
322C24C22⋊Dic1114yes—
323C24C2×C22⋊D1111yescharacteristic
324C24C2×C22⋊D1111yescharacteristic
325C24C2×C22⋊D1111yescharacteristic
326C2×D4—28no—
327C2×D4—28no—
328C2×D4—24no—
329C2×D4—28no—
330C2×D4—22no—
331C2×D4—48no—
332C2×D4—44no—
333C2×D4—48no—
334C2×D4—48no—
335C2×D4—48no—
336C2×D4—432no—
337C2×D4C22×Dic1114yes—
338C22×C4—24no—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—24no—
342C22×C4—22no—
343C22×C4—48no—
344C22×C4—48no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—44no—
349C22×C4—224no—
350C22×C4C22⋊Dic1114yes—
351C22×C4C22⋊Dic1114yes—
352C22×C4C22⋊Dic1114yes—
353C22×C4C22×Dic1112yes—
354C22×C4C22×Dic1112yes—
355C22×C4C22×Dic1112yes—
356C22×C4C2×C22⋊D1111yescharacteristic
357C22×C4C2×C22⋊D1111yescharacteristic
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1112yes—
360C22×C4C2×C22⋊D1112yes—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C23×D1111yescharacteristic
363M16—448no—
364C2×C8—228no—
365C2×C8—224no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—228no—
369C4⋊C4C22×Dic1114yes—
370C22⋊C4—28no—
371C22⋊C4—28no—
372C22⋊C4—444no—
373C22⋊C4—444no—
374C22⋊C4—444no—
375C42—444no—
376C11#2176711yescharacteristic, complemented, Sylow
377C23—22no—
378C23—22no—
379C23—22no—
380C23—22no—
381C23—22no—
382C23—22no—
383C23—28no—
384C23—22no—
385C23—22no—
386C23—24no—
387C23—44no—
388C23—44no—
389C23—416no—
390C23—48no—
391C23—48no—
392C23—44no—
393C23—44no—
394C23—48no—
395C23—44no—
396C23—816no—
397C23#6698514yes—
398C23C2×C22⋊Dic1112yes—
399C23C2×C22⋊Dic1112yes—
400C23C2×C22⋊Dic1112yes—
401C23C22×C22⋊D1111yescharacteristic
402D4—28no—
403D4—48no—
404D4—416no—
405D4—416no—
406D4—44no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—48no—
422C2×C4—444no—
423C2×C4—444no—
424C2×C4—444no—
425C2×C4C2×C22⋊Dic1112yes—
426C2×C4C2×C22⋊Dic1112yes—
427C2×C4C2×C22⋊Dic1112yes—
428C2×C4#6703714yes—
429C2×C4C23×Dic1111yescharacteristic
430C2×C4C22×C22⋊D1111yescharacteristic
431C8—444no—
432C22—22no—
433C22—28no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—416no—
442C22—44no—
443C22—44no—
444C22—44no—
445C22—44no—
446C22—44no—
447C22—816no—
448C22—88no—
449C22#1062282814yes—
450C22C2×#6698512yes—
451C22#1062333512yes—
452C22#1062335312yes—
453C22C22×C22⋊Dic1111yescharacteristic
454C4—22no—
455C4—22no—
456C4—22no—
457C4—44no—
458C4—884no—
459C4#1062332912yes—
460C4#1062333512yes—
461C2—24no—
462C2—42no—
463C2—42no—
464C2—84no—
465C2#1307119411yescharacteristic
466C2C2×#1062282811yescharacteristic
467C2#1307713511yescharacteristic
468C2#1307943014yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×#121C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC22×#121D11
hypocenterC11#21767
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622820C2semidirect
2. #13070999C2semidirect
3. #13069055C2semidirect
4. #13068939C2semidirect
5. #13068702C2semidirect
6. #13068547C2semidirect
14. C2×C11×#121C4semidirect
19. C2×#66979C22semidirect
20. C22×#4318C22semidirect
22. C2×#66896C22semidirect
24. #10622825C22semidirect
30. C2×C22⋊(C11⋊C8)C22semidirect
31. #10622167C22semidirect
212. C2×#121Dic11semidirect
376. C11#21767semidirect

Maximal subgroups

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

subgroupindex
C2×#106228202
#130709992
#130690552
#130689392
#130687022
#130685472
C22×C11×#1212
#2176711