Finite Group Databasebeta

← #14758352

Subgroups — #14758352

Order 2816.

1270 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×C4×#4313C211yesmaximal, characteristic
3D11×#384C211yesmaximal, characteristic
4#13069583C214yesmaximal, complemented
5#13069578C211yesmaximal, characteristic, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069576C211yesmaximal, characteristic, complemented
8#13068334C214yesmaximal
9C11×#1990C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13C22×#4313C2212yes—
14#10623259—24no—
15#10623259C418yescomplemented
16C2×#66950—21no—
17C2×#66945C2212yes—
18C2×C4⋊C4×D11—21no—
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11C2212yes—
21C2×#66943C2212yes—
22C2×#66940—21no—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C2×#66879C2212yes—
28#10622589—21no—
29#10622589—21no—
30#10622589C2212yes—
31#10622548C2211yescharacteristic
32C2×C4×C11⋊C8C2211yescharacteristic
33C4×#4313—24no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11—22no—
40C22×C4×D11D411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11C2311yescharacteristic
43C22×Dic22—21no—
44C22×C8×C11C2312yes—
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8C2×C414yescomplemented
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2312yes—
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11C2311yescharacteristic
53#66999—28no—
54Q8×Dic11—28no—
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C22×C11⋊C8C2312yes—
71C2×#4313—24no—
72C2×#4313—24no—
73C2×#4313Q818yescomplemented
74#66950—28no—
75#66945—24no—
76#66945C2×C418yes—
77C4⋊C4×D11—28no—
78C4⋊C4×D11—44no—
79C4⋊C4×D11—44no—
80#66943—24no—
81#66943C2×C418yescomplemented
82#66940—28no—
83C42×D11C2×C414yes—
84C42×D11D414yes—
85#66922—22no—
86#66922C2×C414yescomplemented
87C4×C8×C11—22no—
88#66879—24no—
89C4×C11⋊C8—22no—
90#21322—111nomaximal, Sylow
91C23×D11C2×D411yescharacteristic
92C2×Q8×C11—24no—
93C2×Q8×C11—42no—
94C2×Q8×C11—42no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—44no—
110C2×C4×D11—44no—
111C2×C4×D11—44no—
112C2×C4×D11C22⋊C414yes—
113C2×C4×D11C22⋊C414yes—
114C2×C4×D11C22×C412yes—
115C2×C4×D11C2×D412yes—
116C2×C4×D11C2×Q814yes—
117C2×C4×D11#4114yes—
118C2×Dic22—24no—
119C2×Dic22—42no—
120C2×Dic22—42no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11C2×Q814yes—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4C22×C414yes—
130C42×C11C22×C412yes—
131C42×C11C2×D412yes—
132(C2×D11)⋊C4—28no—
133C4⋊Dic11—28no—
134C4⋊Dic11—24no—
135C4⋊Dic11—22no—
136C4⋊Dic11—24no—
137C4⋊Dic11—42no—
138C4⋊Dic11—42no—
139C4⋊Dic11C22×C414yes—
140Dic11⋊C4—28no—
141Dic11⋊C4—44no—
142Dic11⋊C4—44no—
143Dic11⋊C4—44no—
144C4×Dic11—28no—
145C4×Dic11C22⋊C414yes—
146C4×Dic11C22⋊C414yes—
147C4×Dic11C22×C412yes—
148C4×Dic11C2×D412yes—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8C2×Q814yes—
152#4313—216no—
153C2×#533—111no—
154C2×C4×M16—111no—
155C2×#384—111no—
156#1992—114no—
157#1990—111no—
158#1990—111no—
159#1990—111no—
160#1990D1111yescharacteristic, complemented
161#1736—114no—
162C23×C11C22×D411yescharacteristic
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11C2×C22⋊C412yes—
168C22×D11#12412yes—
169C22×D11C4⋊Q812yes—
170Q8×C11—48no—
171C2×C4×C11—24no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11C2×C22⋊C412yes—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11AGL(1,ℤ/8)12yes—
180C2×C4×C11AGL(1,ℤ/8)12yes—
181C2×C4×C11#13712yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C22×Q812yes—
186C2×C4×C11C2×#4112yes—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—24no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11C2×C22⋊C412yes—
198C2×Dic11C2×C22⋊C412yes—
199C2×Dic11C2×C22⋊C412yes—
200C2×Dic11#12412yes—
201C2×Dic11C4⋊Q812yes—
202C4×D11—28no—
203C4×D11—28no—
204C4×D11—88no—
205C4×D11C4×Q818yes—
206C4×D11C22⋊Q818yes—
207Dic22—48no—
208C8×C11—24no—
209C11⋊C8—24no—
210C22×M16—112no—
211#533—118no—
212#533—224no—
213C2×C4⋊Q8—111no—
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#125—112no—
216C2×C22⋊Q8—221no—
217C2×C22⋊Q8—221no—
218C2×C4×Q8—221no—
219C2×C4×Q8—221no—
220C2×#117—112no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—221no—
223C22×C4⋊C4—221no—
224C22×C42—111no—
225C4×M16—224no—
226C2×#97—112no—
227C2×C4×C8—111no—
228C2×C4×C8C2×D1111yescharacteristic
229#384—112no—
230#384—111no—
231#384—221no—
232#384—221no—
233#384C2×D1111yescharacteristic
234#340—114no—
235#340—114no—
236#340—114no—
237#340C2×D1114yes—
238C22×C11C22×C22⋊C411yescharacteristic
239C22×C11C2×#12411yescharacteristic
240C22×C11C2×C4⋊Q811yescharacteristic
241C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
242C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C11C2×#13711yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C2×D11—22no—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—22no—
250C2×D11—22no—
251C2×D11#39114yes—
252C4×C11—44no—
253C4×C11—82no—
254C4×C11#41714yes—
255C4×C11#41714yes—
256C4×C11C2×C4×Q812yes—
257C4×C11C2×C22⋊Q812yes—
258Dic11—22no—
259Dic11—22no—
260Dic11—44no—
261Dic11—82no—
262Dic11#39114yes—
263C22×Q8—21no—
264C22×Q8—221no—
265C23×C4—111no—
266C23×C4—111no—
267C23×C4—111no—
268C23×C4—222no—
269C2×M16—118no—
270C2×M16—224no—
271C2×M16—224no—
272C22×C8—112no—
273C22×C8C22×D1112yes—
274C4⋊Q8—22no—
275C4⋊Q8—114no—
276C4⋊Q8—222no—
277C4⋊Q8C4×D1114yescomplemented
278#125—118no—
279#125—224no—
280C22⋊Q8—228no—
281C22⋊Q8—228no—
282C4×Q8—228no—
283C4×Q8—228no—
284#117—118no—
285#117—224no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—228no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4—222no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—222no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—444no—
301C2×C4⋊C4—444no—
302C2×C4⋊C4C22×D1112yes—
303C2×C4⋊C4C22×D1112yes—
304C2×C22⋊C4—222no—
305C2×C42—111no—
306C2×C42—111no—
307C2×C42—111no—
308C2×C42—114no—
309C2×C42—114no—
310C2×C42—222no—
311C2×C42C22×D1111yescharacteristic
312#97—224no—
313C4×C8—22no—
314C4×C8—222no—
315C2×C11C2×#39111yescharacteristic
316C2×C11C2×#41711yescharacteristic
317C2×C11C2×#41711yescharacteristic
318C2×C11#313811yescharacteristic
319C2×C11#313911yescharacteristic
320C2×C11#316511yescharacteristic
321C2×C11#316511yescharacteristic
322D11—24no—
323C24—111no—
324C2×Q8—24no—
325C2×Q8—42no—
326C2×Q8—42no—
327C2×Q8—224no—
328C2×Q8—442no—
329C2×Q8—442no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—111no—
333C22×C4—112no—
334C22×C4—112no—
335C22×C4—114no—
336C22×C4—114no—
337C22×C4—111no—
338C22×C4—111no—
339C22×C4—114no—
340C22×C4—114no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—444no—
348C22×C4—444no—
349C22×C4—444no—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1111yescharacteristic
352C22×C4C23×D1111yescharacteristic
353M16—2216no—
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—114no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8Q8×D1114yes—
360C4⋊C4—24no—
361C4⋊C4—22no—
362C4⋊C4—24no—
363C4⋊C4—42no—
364C4⋊C4—42no—
365C4⋊C4—114no—
366C4⋊C4—228no—
367C4⋊C4—228no—
368C4⋊C4—224no—
369C4⋊C4—222no—
370C4⋊C4—224no—
371C4⋊C4—444no—
372C4⋊C4—444no—
373C4⋊C4—444no—
374C4⋊C4—442no—
375C4⋊C4—442no—
376C4⋊C4C2×C4×D1114yes—
377C22⋊C4—228no—
378C42—114no—
379C42—114no—
380C42—112no—
381C42—112no—
382C42—228no—
383C42C2×C4×D1112yes—
384C42D4×D1112yes—
385C11#2132211yescharacteristic, complemented, Sylow
386C23—112no—
387C23—112no—
388C23—112no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23—221no—
393C23C2×D4×D1111yescharacteristic
394Q8—48no—
395Q8—448no—
396C2×C4—24no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—112no—
403C2×C4—112no—
404C2×C4—112no—
405C2×C4—118no—
406C2×C4—118no—
407C2×C4—112no—
408C2×C4—112no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—228no—
414C2×C4—228no—
415C2×C4—224no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—888no—
422C2×C4C22⋊C4×D1112yes—
423C2×C4C22⋊C4×D1112yes—
424C2×C4#6696412yes—
425C2×C4#6696712yes—
426C2×C4#6696812yes—
427C2×C4#6697112yes—
428C2×C4C22×C4×D1111yescharacteristic
429C2×C4C2×D4×D1111yescharacteristic
430C2×C4C2×Q8×D1112yes—
431C2×C4#41×D1112yes—
432C8—24no—
433C8—224no—
434C22—114no—
435C22—222no—
436C22—222no—
437C22—222no—
438C22—222no—
439C22—222no—
440C22—222no—
441C22C2×C22⋊C4×D1111yescharacteristic
442C22D11×#12411yescharacteristic
443C22D11×C4⋊Q811yescharacteristic
444C22C2×#6696411yescharacteristic
445C22C2×#6696711yescharacteristic
446C22C2×#6696811yescharacteristic
447C22C2×#6697111yescharacteristic
448C4—44no—
449C4—82no—
450C4—114no—
451C4—222no—
452C4—222no—
453C4—444no—
454C4—882no—
455C4#1062238414yes—
456C4#1062241614yes—
457C4C4×Q8×D1112yes—
458C4D11×C22⋊Q812yes—
459C2—224no—
460C2D11×#39111yescharacteristic
461C2C2×#1062238411yescharacteristic
462C2C2×#1062241611yescharacteristic
463C2#1307898711yescharacteristic
464C2#1307899311yescharacteristic
465C2#1307915711yescharacteristic
466C2#1307915911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1990C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1990D11
hypocenterC11#21322
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. #13069583C2semidirect
5. #13069578C2semidirect
6. #13069577C2semidirect
7. #13069576C2semidirect
9. C11×#1990C2semidirect
15. #10623259C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
73. C2×#4313Q8semidirect
81. #66943C2×C4semidirect
86. #66922C2×C4semidirect
160. #1990D11semidirect
277. C4⋊Q8C4×D11semidirect
385. C11#21322semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×C4×#43132
D11×#3842
#130695832
#130695782
#130695772
#130695762
#130683342
C11×#19902
#2132211