Finite Group Databasebeta

← #14763266

Subgroups — #14763266

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622331C211yesmaximal, characteristic
3#13071018C211yesmaximal, characteristic
4#13069575C212yesmaximal, complemented
5#13069575C212yesmaximal, complemented
6#13069572C212yesmaximal, complemented
7#13069570C212yesmaximal, complemented
8#13068712C211yesmaximal, characteristic
9#13068711C211yesmaximal, characteristic
10#13068708C211yesmaximal, characteristic
11C11×#1825C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15#10623048—24no—
16#10623048C418yescomplemented
17C2×#66943C2211yescharacteristic
18C2×#66943C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66931—21no—
22C2×#66931—21no—
23C2×#66930—21no—
24C2×C4×Dic22—21no—
25C2×C4×Dic22—21no—
26C2×C11×C22⋊C8C2211yescharacteristic
27C11×#380C2211yescharacteristic
28#10622825C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×Dic11⋊C8C2212yes—
31C2×C8×Dic11C2212yes—
32#10622589C2212yes—
33C4⋊C4×Dic11C2212yes—
34#10622555—21no—
35#10622331—24no—
36#10622263—21no—
37#10622262—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11D411yescharacteristic
48C23×Dic11D411yescharacteristic
49C22×Dic22—21no—
50C22×Dic22—21no—
51C22×C8×C11C2312yes—
52C11×#117—22no—
53C11×#117C2×C414yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C42×C11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11—21no—
62#66979—22no—
63#66979C2×C414yes—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×C4×Dic11—21no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11C2×C414yes—
78C2×C4×Dic11D411yescharacteristic
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D414yes—
81C2×C4×Dic11C2311yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84#66943—22no—
85#66943—22no—
86#66943C2×C414yes—
87#66943C2×C414yes—
88#66941—22no—
89#66941—22no—
90#66941C2×C414yes—
91#66941C2×C414yes—
92#66931—28no—
93#66931—28no—
94#66930—44no—
95C4×Dic22—28no—
96C4×Dic22—28no—
97C11×C22⋊C8—22no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—22no—
101C22⋊(C11⋊C8)—22no—
102Dic11⋊C8—24no—
103C8×Dic11—24no—
104#21835—111nomaximal, Sylow
105C24×C11C2×D411yescharacteristic
106C22×C4×C11—24no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C22×Dic11—24no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—21no—
118C22×Dic11—21no—
119C22×Dic11—22no—
120C22×Dic11C22⋊C414yes—
121C22×Dic11C22⋊C414yes—
122C22×Dic11C2×D411yescharacteristic
123C22×Dic11C2×D411yescharacteristic
124C22×Dic11C2×D411yescharacteristic
125C22×Dic11C2×D411yescharacteristic
126C2×Dic22—24no—
127C2×Dic22—24no—
128C2×Dic22—44no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×C8×C11—22no—
132C2×C8×C11—24no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—24no—
136C11×C4⋊C4C22×C412yes—
137C11×C4⋊C4C22×C412yes—
138C11×C22⋊C4—24no—
139C11×C22⋊C4—42no—
140C42×C11—24no—
141C22⋊Dic11—24no—
142C22⋊Dic11—42no—
143C4⋊Dic11—24no—
144C4⋊Dic11—24no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—24no—
148C4⋊Dic11C22×C412yes—
149C4⋊Dic11C22×C412yes—
150Dic11⋊C4—24no—
151Dic11⋊C4—24no—
152Dic11⋊C4—24no—
153Dic11⋊C4—24no—
154Dic11⋊C4—44no—
155Dic11⋊C4—44no—
156C4×Dic11—24no—
157C4×Dic11—44no—
158C4×Dic11C22⋊C414yes—
159C4×Dic11C22⋊C414yes—
160C4×Dic11C22×C412yes—
161C4×Dic11C22×C412yes—
162C4×Dic11C2×D412yes—
163C4×Dic11C2×D412yes—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—24no—
166C2×#533—111no—
167C2×#431—111no—
168#2285—111no—
169#1990—112no—
170#1990—112no—
171#1989—112no—
172#1989—112no—
173#1825—111no—
174#1825—111no—
175#1825—111no—
176#1825D1111yescharacteristic
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—21no—
180C23×C11—21no—
181C23×C11C2×C22⋊C412yes—
182C23×C11C22×D411yescharacteristic
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C23×C411yescharacteristic
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C112−1+414yes—
198C2×Dic11—22no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—28no—
202C2×Dic11—28no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11C2×C22⋊C412yes—
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C412yes—
215C2×Dic11#13514yes—
216C2×Dic11AGL(1,ℤ/8)12yes—
217C2×Dic11#13712yes—
218Dic22—48no—
219Dic22—48no—
220C8×C11—42no—
221C11⋊C8—42no—
222#533—118no—
223#533—224no—
224C2×C4⋊Q8—111no—
225C2×C4⋊Q8—111no—
226C2×#125—111no—
227C2×#125—111no—
228C2×C22⋊Q8—221no—
229C2×C22⋊Q8—221no—
230C2×C4×Q8—221no—
231C2×C4×Q8—221no—
232C2×#117—111no—
233C2×#117—221no—
234C2×#117C2×D1111yescharacteristic
235C22×C42—111no—
236#431—224no—
237C2×C4⋊C8—112no—
238C2×C22⋊C8—111no—
239C2×C22⋊C8C2×D1111yescharacteristic
240C2×C4×C8—112no—
241#384—112no—
242#382—221no—
243#380—111no—
244#380—221no—
245#380C2×D1111yescharacteristic
246C4×C4⋊C4—112no—
247C4×C4⋊C4—221no—
248#340—112no—
249#340—112no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340—112no—
254#340C2×D1112yes—
255#340C2×D1112yes—
256C22×C11—22no—
257C22×C11—22no—
258C22×C11—22no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11C22×C22⋊C411yescharacteristic
262C22×C11#53612yes—
263C22×C11C2×#13512yes—
264C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C22×C11C2×#13711yescharacteristic
266C4×C11—22no—
267C4×C11—42no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11#51912yes—
271C4×C11#53612yes—
272Dic11—22no—
273Dic11—22no—
274Dic11—42no—
275Dic11—42no—
276Dic11—82no—
277Dic11#41614yes—
278Dic11#41714yes—
279C22×Q8—221no—
280C22×Q8—221no—
281C23×C4—111no—
282C23×C4—111no—
283C23×C4C22×D1111yescharacteristic
284C22×C8—112no—
285C22×C8C22×D1112yes—
286C4⋊Q8—114no—
287C4⋊Q8—114no—
288C4⋊Q8—222no—
289C4⋊Q8—222no—
290#125—114no—
291#125—114no—
292#125—222no—
293#125—222no—
294C22⋊Q8—228no—
295C22⋊Q8—228no—
296C4×Q8—228no—
297C4×Q8—228no—
298#117—22no—
299#117—114no—
300#117—222no—
301#117—444no—
302#117C4×D1114yes—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—112no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4C22×D1112yes—
315C2×C4⋊C4C22×D1111yescharacteristic
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C42—21no—
322C2×C42—114no—
323C2×C42—111no—
324C2×C42—111no—
325C2×C42—114no—
326C2×C42—111no—
327C2×C42—111no—
328C2×C42—221no—
329C2×C42—222no—
330C4⋊C8—224no—
331C22⋊C8—22no—
332C22⋊C8—222no—
333C4×C8—224no—
334#95—21no—
335#95—222no—
336#95—221no—
337C2×C11—42no—
338C2×C11#231011yescharacteristic
339C2×C11C2×#41611yescharacteristic
340C2×C11C2×#41711yescharacteristic
341C2×C11#322812yes—
342C2×C11#323112yes—
343C24D4×D1111yescharacteristic
344C2×Q8—224no—
345C2×Q8—224no—
346C2×Q8—444no—
347C2×Q8—442no—
348C2×Q8—442no—
349C22×C4—24no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—114no—
356C22×C4—114no—
357C22×C4—111no—
358C22×C4—111no—
359C22×C4—222no—
360C22×C4—224no—
361C22×C4—222no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4C2×C4×D1112yes—
366C22×C4D4×D1111yescharacteristic
367C22×C4D4×D1112yes—
368C22×C4C23×D1111yescharacteristic
369C2×C8—22no—
370C2×C8—24no—
371C2×C8—222no—
372C2×C8—224no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—24no—
376C4⋊C4—112no—
377C4⋊C4—112no—
378C4⋊C4—224no—
379C4⋊C4—224no—
380C4⋊C4—224no—
381C4⋊C4—224no—
382C4⋊C4—224no—
383C4⋊C4—224no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—224no—
387C4⋊C4—444no—
388C4⋊C4—444no—
389C4⋊C4C2×C4×D1112yes—
390C4⋊C4C2×C4×D1112yes—
391C22⋊C4—24no—
392C22⋊C4—42no—
393C22⋊C4—224no—
394C22⋊C4—442no—
395C42—24no—
396C42—114no—
397C42—114no—
398C42—112no—
399C42—112no—
400C42—112no—
401C42—112no—
402C42—224no—
403C42—444no—
404C11#2183511yescharacteristic, complemented, Sylow
405C23—22no—
406C23—21no—
407C23—21no—
408C23—22no—
409C23C22⋊C4×D1112yes—
410C23C2×D4×D1111yescharacteristic
411Q8—448no—
412Q8—448no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—42no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—112no—
425C2×C4—112no—
426C2×C4—114no—
427C2×C4—112no—
428C2×C4—112no—
429C2×C4—112no—
430C2×C4—112no—
431C2×C4—228no—
432C2×C4—228no—
433C2×C4—222no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—222no—
437C2×C4—222no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4C22⋊C4×D1112yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C2×D4×D1111yescharacteristic
447C2×C4#6704314yes—
448C8—42no—
449C8—442no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—42no—
454C22—42no—
455C22C2×C22⋊C4×D1111yescharacteristic
456C22#1062317912yes—
457C22D11×#13512yes—
458C22D11×AGL(1,ℤ/8)11yescharacteristic
459C22D11×#13711yescharacteristic
460C4—22no—
461C4—42no—
462C4—42no—
463C4—82no—
464C4—114no—
465C4—114no—
466C4—222no—
467C4—222no—
468C4—442no—
469C4—442no—
470C4—882no—
471C4#1062304712yes—
472C4#1062317912yes—
473C2—42no—
474C2#1307120111yescharacteristic
475C2D11×#41611yescharacteristic
476C2D11×#41711yescharacteristic
477C2#1307975012yes—
478C2#1307977312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1825D11
hypocenterC11#21835
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
4. #13069575C2semidirect
5. #13069575C2semidirect
6. #13069572C2semidirect
7. #13069570C2semidirect
16. #10623048C4semidirect
404. C11#21835semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106223312
#130710182
#130695752
#130695722
#130695702
#130687122
#130687112
#130687082
C11×#18252
#2183511