Finite Group Databasebeta

← #14724730

Subgroups — #14724730

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078620C211yesmaximal, characteristic
2M16×D44C211yesmaximal, characteristic
3#13067516C212yesmaximal, complemented
4#13067494C212yesmaximal, complemented
5#13067471C212yesmaximal, complemented
6#13067426C212yesmaximal, complemented
7#13067390C211yesmaximal, characteristic, complemented
8#13067071C211yesmaximal, characteristic, complemented
9C2×#10622121C211yesmaximal, characteristic
10#13066903C211yesmaximal, characteristic, complemented
11C11×#2962C211yesmaximal, characteristic, complemented
12C11×#533C2211yescharacteristic
13C2×M16×D11—21no—
14C2×C4×D44C2211yescharacteristic
15C11×#446—22no—
16C11×#446C2212yescomplemented
17C8×Q8×C11C2212yescomplemented
18C11×#424—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C11×#405—21no—
21C4×C11×M16C2211yescharacteristic
22#10622739—21no—
23#10622697C411yescharacteristic
24#10622697C411yescharacteristic
25#10622696C411yescharacteristic
26#10622696C411yescharacteristic
27#10622659C412yes—
28#10622656C412yes—
29C4×#4325C2212yes—
30C4×#4325C2212yes—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622319—22no—
35#10622301C2212yes—
36C8×D44C2212yes—
37Q8⋊(C11⋊C8)C2212yescomplemented
38Q8⋊(C11⋊C8)C2212yescomplemented
39#10622121C2211yescharacteristic
40#10622121C2211yescharacteristic
41#10622121C2211yescharacteristic
42#10622121C2211yescharacteristic
43#10622117C2212yescomplemented
44#10622117C2212yescomplemented
45#10622092C2212yescomplemented
46#10622092C2212yescomplemented
47C22×D44C2×C411yescharacteristic
48C22×C4×D11—21no—
49C2×C11×M16D411yescharacteristic
50C2×C11×M16D411yescharacteristic
51C22×C8×C11—21no—
52C11×C4⋊Q8C2×C411yescharacteristic
53C11×C4⋊Q8C2×C411yescharacteristic
54C11×#125—21no—
55C11×C22⋊Q8—21no—
56C11×C22⋊Q8C2×C412yes—
57C4×Q8×C11—21no—
58C4×Q8×C11C2312yes—
59C11×#117—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4325C2×C412yes—
62C2×#4325C2×C412yes—
63C2×(C2×D11)⋊C4—21no—
64C2×C4⋊Dic11C2×C411yescharacteristic
65C2×#4318—21no—
66C22×C11⋊C8—21no—
67M16×D11—44no—
68C2×#4313—22no—
69C2×C8×D11—22no—
70C4×D44—21no—
71C4×D44—21no—
72C4×D44C2×C411yescharacteristic
73C4×D44C2×C411yescharacteristic
74C4×D44C2311yescharacteristic
75C4×D44C2311yescharacteristic
76C11×C4⋊C8—22no—
77C11×C4⋊C8—22no—
78C11×C4⋊C8—21no—
79C11×C4⋊C8C2311yescharacteristic
80C11×C4⋊C8C2311yescharacteristic
81C11×#97—22no—
82C11×#97D412yes—
83C4×C8×C11—22no—
84C4×C8×C11C2312yes—
85#66899C2×C412yes—
86#66899C2×C412yes—
87C22⋊(C11⋊C8)C2×C412yes—
88(C2×D11)⋊C8—22no—
89(C2×D11)⋊C8—22no—
90#66873C2×C412yes—
91#66873C2×C412yes—
92#66872C2×C412yes—
93#66872C2×C412yes—
94C4⋊(C11⋊C8)—21no—
95C4⋊(C11⋊C8)C2×C411yescharacteristic
96C4⋊(C11⋊C8)C2×C411yescharacteristic
97C4⋊(C11⋊C8)C2312yes—
98C4×C11⋊C8—21no—
99C4×C11⋊C8C2311yescharacteristic
100C4×C11⋊C8C2311yescharacteristic
101C4×C11⋊C8C2312yes—
102#18000—111nomaximal, Sylow
103C23×D11—21no—
104C2×Q8×C11—21no—
105C2×Q8×C11C22×C412yes—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×Dic11—21no—
110C2×D44—22no—
111C2×D44—21no—
112C2×D44—41no—
113C2×D44C22×C411yescharacteristic
114C2×D44C22×C411yescharacteristic
115C2×C4×D11—21no—
116C2×C4×D11—21no—
117C2×C4×D11—21no—
118C2×C4×D11—21no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C11×M16—22no—
122C11×M16—22no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—42no—
126C2×C8×C11C2×D412yes—
127C2×C8×C11C2×D412yes—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4C22×C412yes—
134C11×C22⋊C4—22no—
135C42×C11—22no—
136C42×C11C22×C411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139C42×C11C2411yescharacteristic
140#4325—24no—
141#4325—42no—
142(C2×D11)⋊C4—21no—
143(C2×D11)⋊C4—21no—
144(C2×D11)⋊C4—21no—
145(C2×D11)⋊C4—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11C22×C411yescharacteristic
148C4⋊Dic11C22×C411yescharacteristic
149#4318—42no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—42no—
154C2×C11⋊C8C22×C412yes—
155C2×C11⋊C8C22×C412yes—
156#4313—44no—
157C8×D11—44no—
158#3101—111no—
159#2962D1111yescharacteristic, complemented
160D4×M16—111no—
161#1592—112no—
162#1588—112no—
163#1585—112no—
164SD16⋊C8—112no—
165#1571—111no—
166#1493—111no—
167C2×D4⋊C8—111no—
168#1451—111no—
169C23×C11C4×D411yescharacteristic
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—81no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—81no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
183C2×C4×C11C4×D411yescharacteristic
184C2×C4×C11C4×D411yescharacteristic
185C2×C4×C11C4×D411yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11#13712yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—42no—
194D44—21no—
195D44—21no—
196D44—21no—
197D44—42no—
198D44#13112yes—
199C4×D11—41no—
200C4×D11—41no—
201C4×D11—41no—
202C4×D11—41no—
203C4×D11—42no—
204C4×D11—42no—
205C8×C11—22no—
206C8×C11—22no—
207C8×C11—41no—
208C8×C11—41no—
209C11⋊C8—22no—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C11⋊C8—41no—
213C11⋊C8—42no—
214C22×M16—221no—
215#533C2×D1111yescharacteristic
216C2×C4×D4—111no—
217#483—112no—
218#476—111no—
219#476—111no—
220#461—111no—
221#461—111no—
222#450—112no—
223#446—22no—
224#446C2×D1112yescomplemented
225C8×Q8C2×D1112yescomplemented
226C4×SD16—112no—
227C4×SD16—112no—
228#436—112no—
229#435—222no—
230C8×D4—112no—
231#431—111no—
232#424—21no—
233#423—111no—
234C2×C4⋊C8C2×D1111yescharacteristic
235#407—221no—
236#405—21no—
237C4×M16C2×D1111yescharacteristic
238C2×C4×C8—111no—
239#335—112no—
240#335—112no—
241Q8⋊C8—112no—
242Q8⋊C8—112no—
243D4⋊C8—111no—
244D4⋊C8—111no—
245D4⋊C8—111no—
246D4⋊C8—111no—
247#322—112no—
248#322—112no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11#44012yes—
252C22×C11C2×C4×D411yescharacteristic
253C2×D11—22no—
254C2×D11—41no—
255C2×D11—41no—
256C2×D11—41no—
257C2×D11—41no—
258C2×D11—41no—
259C2×D11—84no—
260C4×C11—21no—
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—42no—
264C4×C11—42no—
265C4×C11#44012yes—
266C4×C11C2×#13111yescharacteristic
267C4×C11#56811yescharacteristic
268C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C4×C11C2×#13711yescharacteristic
270Dic11—41no—
271Dic11—41no—
272C22×D4—111no—
273C23×C4—221no—
274C2×SD16—112no—
275C2×SD16—112no—
276C2×M16—221no—
277C2×M16—222no—
278C2×M16—444no—
279C2×M16C22⋊D1111yescharacteristic
280C2×M16C22⋊D1111yescharacteristic
281C22×C8—21no—
282C22×C8—221no—
283C22×C8—222no—
284C4⋊Q8C4×D1111yescharacteristic
285C4⋊Q8C4×D1111yescharacteristic
286#125—21no—
287C22⋊Q8—21no—
288C22⋊Q8C4×D1112yes—
289C4×Q8—21no—
290C4×Q8C22×D1112yes—
291C4×D4—111no—
292C4×D4—111no—
293C4×D4—111no—
294C4×D4—111no—
295C4×D4—221no—
296C4×D4—221no—
297#117—21no—
298C2×C4⋊C4—111no—
299C2×C22⋊C4—221no—
300C2×C42C22×D1111yescharacteristic
301#106—112no—
302#106—112no—
303C4⋊C8—22no—
304C4⋊C8—22no—
305C4⋊C8—21no—
306C4⋊C8—111no—
307C4⋊C8—111no—
308C4⋊C8—112no—
309C4⋊C8—221no—
310C4⋊C8C22×D1111yescharacteristic
311C4⋊C8C22×D1111yescharacteristic
312#103—112no—
313#103—112no—
314#102—112no—
315#102—112no—
316C22⋊C8—112no—
317C22⋊C8—222no—
318C22⋊C8—222no—
319#97—22no—
320#97C22⋊D1112yes—
321C4×C8—22no—
322C4×C8—112no—
323C4×C8—111no—
324C4×C8—111no—
325C4×C8—221no—
326C4×C8C22×D1112yes—
327C2×C11—22no—
328C2×C11#293311yescharacteristic
329C2×C11C2×#44011yescharacteristic
330C2×C11#295611yescharacteristic
331D11—42no—
332D11—81no—
333C24—221no—
334C2×Q8—21no—
335C2×Q8C2×C4×D1112yes—
336C2×D4—111no—
337C2×D4—111no—
338C2×D4—222no—
339C2×D4—221no—
340C2×D4—441no—
341C22×C4—221no—
342C22×C4—221no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—442no—
347C22×C4—442no—
348C22×C4C2×C4×D1111yescharacteristic
349C22×C4#433911yescharacteristic
350C22×C4C2×C22⋊D1111yescharacteristic
351SD16—224no—
352SD16—442no—
353M16—22no—
354M16—22no—
355M16—444no—
356M16—442no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—42no—
360C2×C8—112no—
361C2×C8—112no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8—222no—
365C2×C8—444no—
366C2×C8—442no—
367C2×C8C2×C22⋊D1112yes—
368C2×C8C2×C22⋊D1112yes—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—111no—
375C4⋊C4—111no—
376C4⋊C4—221no—
377C4⋊C4C2×C4×D1112yes—
378C22⋊C4—22no—
379C22⋊C4—221no—
380C22⋊C4—221no—
381C22⋊C4—221no—
382C22⋊C4—221no—
383C42—22no—
384C42C2×C4×D1111yescharacteristic
385C42#433911yescharacteristic
386C42C2×C22⋊D1111yescharacteristic
387C42C23×D1111yescharacteristic
388C11#1800011yescharacteristic, complemented, Sylow
389C23—221no—
390C23—221no—
391C23—442no—
392C23—442no—
393C23—881no—
394C23C4×C22⋊D1111yescharacteristic
395Q8—22no—
396Q8—22no—
397Q8—81no—
398D4—112no—
399D4—221no—
400D4—221no—
401D4—221no—
402D4—442no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—41no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—442no—
411C2×C4—441no—
412C2×C4—441no—
413C2×C4—441no—
414C2×C4—441no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4C4×C22⋊D1111yescharacteristic
418C2×C4C4×C22⋊D1111yescharacteristic
419C2×C4C4×C22⋊D1111yescharacteristic
420C2×C4#6699512yes—
421C2×C4#6700212yes—
422C2×C4C22×C4×D1111yescharacteristic
423C2×C4C2×#433911yescharacteristic
424C2×C4C22×C22⋊D1111yescharacteristic
425C8—22no—
426C8—22no—
427C8—41no—
428C8—41no—
429C8—222no—
430C8—222no—
431C8—222no—
432C8—441no—
433C8—442no—
434C22—21no—
435C22—21no—
436C22—222no—
437C22—441no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22—441no—
442C22—884no—
443C22#1062263912yes—
444C22C2×C4×C22⋊D1111yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—42no—
449C4—42no—
450C4—441no—
451C4—441no—
452C4#1062263912yes—
453C4D11×#13111yescharacteristic
454C4#1062328111yescharacteristic
455C4C2×#6699511yescharacteristic
456C4C2×#6700211yescharacteristic
457C2—22no—
458C2—442no—
459C2—881no—
460C2#1307733811yescharacteristic
461C2C2×#1062263911yescharacteristic
462C2#1307752311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#2962C2
socleC22×C11C2×C4×D4
prime radicalC22×D44C2×C4
cosocleC42×C11C24
hypercenter#2962D11
hypocenterC11#18000
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2962

Complements

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

NH ≅ G/Ntype
3. #13067516C2semidirect
4. #13067494C2semidirect
5. #13067471C2semidirect
6. #13067426C2semidirect
7. #13067390C2semidirect
8. #13067071C2semidirect
10. #13066903C2semidirect
11. C11×#2962C2semidirect
16. C11×#446C22semidirect
17. C8×Q8×C11C22semidirect
37. Q8⋊(C11⋊C8)C22semidirect
38. Q8⋊(C11⋊C8)C22semidirect
43. #10622117C22semidirect
44. #10622117C22semidirect
45. #10622092C22semidirect
46. #10622092C22semidirect
159. #2962D11semidirect
224. #446C2×D11semidirect
225. C8×Q8C2×D11semidirect
388. C11#18000semidirect

Maximal subgroups

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

subgroupindex
#130786202
M16×D442
#130675162
#130674942
#130674712
#130674262
#130673902
#130670712
C2×#106221212
#130669032
C11×#29622
#1800011