Finite Group Databasebeta

← #14763277

Subgroups — #14763277

Order 2816.

1030 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×#10623219C211yesmaximal, characteristic
2C2×#10622298C211yesmaximal, characteristic
3#13071009C211yesmaximal, characteristic
4#13069582C211yesmaximal, characteristic, complemented
5#13069581C211yesmaximal, characteristic, complemented
6#13069580C211yesmaximal, characteristic, complemented
7#13069566C212yesmaximal, complemented
8#13069562C212yesmaximal, complemented
9#13068710C212yesmaximal
10#13068709C212yesmaximal
11C11×#1991C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13#10623219—24no—
14#10623219C418yescomplemented
15C2×#66949—21no—
16C2×#66949—21no—
17C2×#66945C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66941C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66940—21no—
22C2×#66940—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66923C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#382C2211yescharacteristic
27C2×(C2×D11)⋊C8C2212yes—
28C2×Dic11⋊C8C2212yes—
29#10622600C2212yes—
30C4⋊C4×Dic11C2212yes—
31#10622549C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33#10622298—24no—
34#10622279—21no—
35#10622277—21no—
36#10622264—21no—
37#10622261—21no—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×Dic22—21no—
50C22×Dic22—21no—
51C22×C8×C11C2312yes—
52C11×#125—22no—
53C11×#125C2×C414yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C42×C11C2311yescharacteristic
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—22no—
63C2×C4⋊Dic11C2312yes—
64C2×C4⋊Dic11C2311yescharacteristic
65C2×C4⋊Dic11C2311yescharacteristic
66C2×Dic11⋊C4—21no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11—21no—
71C2×C4×Dic11—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11D411yescharacteristic
74C2×C4×Dic11D411yescharacteristic
75C2×C4×Dic11C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77#66949—28no—
78#66949—28no—
79#66945—22no—
80#66945—22no—
81#66945C2×C414yes—
82#66945C2×C414yes—
83#66941—22no—
84#66941—22no—
85#66941C2×C414yes—
86#66941C2×C414yes—
87#66940—28no—
88#66940—28no—
89C42×D11C2×C414yes—
90C42×D11D414yes—
91#66923—22no—
92#66923C2×C414yes—
93C4×C8×C11—22no—
94C11×#95—21no—
95C11×#95—21no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100(C2×D11)⋊C8—24no—
101Dic11⋊C8—24no—
102C4×C11⋊C8—22no—
103#21837—111nomaximal, Sylow
104C23×D11C2×D411yescharacteristic
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11C2×D411yescharacteristic
115C22×Dic11C2×D411yescharacteristic
116C22×Dic11C2×D411yescharacteristic
117C2×C4×D11—24no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—42no—
121C2×C4×D11C22⋊C414yes—
122C2×C4×D11C22⋊C414yes—
123C2×C4×D11C22×C412yes—
124C2×C4×D11C2×D412yes—
125C2×Dic22—24no—
126C2×Dic22—24no—
127C2×Dic22—44no—
128C2×Dic22—44no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—24no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4C22×C412yes—
138C11×C4⋊C4C22×C412yes—
139C42×C11C22×C412yes—
140C42×C11C2×D412yes—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—44no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—24no—
147C4⋊Dic11C22×C412yes—
148C4⋊Dic11C22×C412yes—
149Dic11⋊C4—24no—
150Dic11⋊C4—24no—
151Dic11⋊C4—24no—
152Dic11⋊C4—24no—
153C4×Dic11—24no—
154C4×Dic11—24no—
155C4×Dic11—44no—
156C4×Dic11C22⋊C414yes—
157C4×Dic11C22⋊C414yes—
158C4×Dic11C22×C412yes—
159C4×Dic11C2×D412yes—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×#533—111no—
164C2×#431—111no—
165#2283—111no—
166#1991—111no—
167#1991—111no—
168#1991—111no—
169#1991D1111yescharacteristic, complemented
170#1988—112no—
171#1987—112no—
172#1825—112no—
173#1825—112no—
174C23×C11C22×D411yescharacteristic
175C22×D11—21no—
176C22×D11—21no—
177C22×D11—22no—
178C22×D11—22no—
179C22×D11C2×C22⋊C412yes—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11C2×C22⋊C412yes—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C112−1+412yes—
194C2×C4×C112−1+412yes—
195C2×Dic11—21no—
196C2×Dic11—21no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11C2×C22⋊C412yes—
206C2×Dic11C2×C22⋊C412yes—
207C2×Dic11C2×C22⋊C412yes—
208C2×Dic11#13514yes—
209C4×D11—24no—
210C4×D11—24no—
211C4×D11—28no—
212C4×D11—44no—
213Dic22—48no—
214Dic22—48no—
215C8×C11—42no—
216C11⋊C8—42no—
217#533—118no—
218#533—224no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8—111no—
221C2×#125—111no—
222C2×#125C2×D1111yescharacteristic
223C2×C22⋊Q8—221no—
224C2×C22⋊Q8—221no—
225C2×C4×Q8—221no—
226C2×C4×Q8—221no—
227C2×#117—111no—
228C2×#117—111no—
229C22×C42—111no—
230#431—224no—
231C2×C4⋊C8—112no—
232C2×C22⋊C8—112no—
233C2×C4×C8—111no—
234C2×C4×C8C2×D1111yescharacteristic
235#383—221no—
236#382—111no—
237#382C2×D1111yescharacteristic
238#381—221no—
239#380—112no—
240C4×C4⋊C4—112no—
241C4×C22⋊C4—221no—
242#376—221no—
243#340—112no—
244#340—112no—
245#340—112no—
246#340—112no—
247#340—112no—
248#340—112no—
249#340C2×D1112yes—
250#340C2×D1112yes—
251C22×C11C22×C22⋊C411yescharacteristic
252C22×C11#53611yescharacteristic
253C22×C11#53611yescharacteristic
254C22×C11C2×#13512yes—
255C22×C11#57512yes—
256C2×D11—22no—
257C2×D11—22no—
258C2×D11—22no—
259C2×D11—42no—
260C2×D11—42no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11—82no—
266C4×C11#51912yes—
267C4×C11#53612yes—
268Dic11—22no—
269Dic11—22no—
270Dic11—42no—
271Dic11—42no—
272Dic11—82no—
273Dic11#41614yes—
274C22×Q8—221no—
275C22×Q8—221no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—111no—
279C22×C8—112no—
280C22×C8C22×D1112yes—
281C4⋊Q8—114no—
282C4⋊Q8—114no—
283C4⋊Q8—222no—
284C4⋊Q8—222no—
285#125—22no—
286#125—114no—
287#125—222no—
288#125C4×D1114yes—
289C22⋊Q8—228no—
290C22⋊Q8—228no—
291C4×Q8—228no—
292C4×Q8—228no—
293#117—114no—
294#117—114no—
295#117—222no—
296#117—222no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4C22×D1112yes—
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C22⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—222no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—114no—
316C2×C42—114no—
317C2×C42—221no—
318C2×C42—221no—
319C2×C42—222no—
320C2×C42C22×D1111yescharacteristic
321C4⋊C8—224no—
322C22⋊C8—224no—
323C4×C8—22no—
324C4×C8—222no—
325#95—21no—
326#95—21no—
327#95—222no—
328#95—222no—
329#95—221no—
330#95—221no—
331C2×C11#231011yescharacteristic
332C2×C11C2×#41611yescharacteristic
333C2×C11#289611yescharacteristic
334C2×C11#323312yes—
335C2×C11#323312yes—
336D11—42no—
337C24—111no—
338C2×Q8—224no—
339C2×Q8—224no—
340C2×Q8—444no—
341C2×Q8—444no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—111no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—114no—
349C22×C4—112no—
350C22×C4—112no—
351C22×C4—114no—
352C22×C4—224no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—442no—
359C22×C4D4×D1111yescharacteristic
360C22×C4D4×D1111yescharacteristic
361C22×C4C23×D1111yescharacteristic
362C2×C8—22no—
363C2×C8—22no—
364C2×C8—22no—
365C2×C8—222no—
366C2×C8—222no—
367C2×C8—222no—
368C4⋊C4—24no—
369C4⋊C4—24no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—24no—
373C4⋊C4—112no—
374C4⋊C4—112no—
375C4⋊C4—224no—
376C4⋊C4—224no—
377C4⋊C4—224no—
378C4⋊C4—224no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—224no—
382C4⋊C4C2×C4×D1112yes—
383C4⋊C4C2×C4×D1112yes—
384C22⋊C4—224no—
385C22⋊C4—224no—
386C22⋊C4—444no—
387C42—114no—
388C42—114no—
389C42—112no—
390C42—112no—
391C42—224no—
392C42—224no—
393C42—444no—
394C42C2×C4×D1112yes—
395C42D4×D1112yes—
396C11#2183711yescharacteristic, complemented, Sylow
397C23—112no—
398C23—221no—
399C23—222no—
400C23—222no—
401C23—221no—
402C23C2×D4×D1111yescharacteristic
403Q8—448no—
404Q8—448no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—112no—
415C2×C4—114no—
416C2×C4—112no—
417C2×C4—112no—
418C2×C4—228no—
419C2×C4—221no—
420C2×C4—222no—
421C2×C4—221no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—222no—
425C2×C4—222no—
426C2×C4—444no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4C22⋊C4×D1112yes—
433C2×C4C22⋊C4×D1112yes—
434C2×C4C22×C4×D1111yescharacteristic
435C2×C4C2×D4×D1111yescharacteristic
436C2×C4#6704012yes—
437C2×C4#6704312yes—
438C8—42no—
439C8—442no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—442no—
444C22—442no—
445C22C2×C22⋊C4×D1111yescharacteristic
446C22#1062320611yescharacteristic
447C22#1062325511yescharacteristic
448C22D11×#13512yes—
449C22#1062329912yes—
450C4—22no—
451C4—22no—
452C4—42no—
453C4—42no—
454C4—82no—
455C4—114no—
456C4—222no—
457C4—222no—
458C4—442no—
459C4—442no—
460C4—882no—
461C4#1062310312yes—
462C4#1062315912yes—
463C2—442no—
464C2#1307119911yescharacteristic
465C2D11×#41611yescharacteristic
466C2#1307713111yescharacteristic
467C2#1307979012yes—
468C2#1307979612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1991C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1991D11
hypocenterC11#21837
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1991

Complements

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

NH ≅ G/Ntype
4. #13069582C2semidirect
5. #13069581C2semidirect
6. #13069580C2semidirect
7. #13069566C2semidirect
8. #13069562C2semidirect
11. C11×#1991C2semidirect
14. #10623219C4semidirect
169. #1991D11semidirect
396. C11#21837semidirect

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×#106222982
#130710092
#130695822
#130695812
#130695802
#130695662
#130695622
#130687102
#130687092
C11×#19912
#2183711