Finite Group Databasebeta

← #14808043

Subgroups — #14808043

Order 2816.

1094 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×#10622706C211yesmaximal, characteristic, complemented
3#13076963C211yesmaximal, characteristic
4#13069814C214yesmaximal
5#13069578C211yesmaximal, characteristic, complemented
6#13069418C211yesmaximal, characteristic, complemented
7#13068881C214yesmaximal, complemented
8C4×(C2×D11)⋊C8C211yesmaximal, characteristic
9C2×C11×#498C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66999—21no—
13C2×#66999—21no—
14C2×Q8×Dic11—21no—
15#10623259—24no—
16#10623259—24no—
17C2×#66950C2212yes—
18C2×#66945—21no—
19C2×#66943—21no—
20C2×#66940C2212yes—
21C2×C42×D11C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#498—24no—
24C2×C11×#106C2214yes—
25C2×C4×C8×C11C2211yescharacteristic
26#10622843—21no—
27C2×(C2×D11)⋊C8C2212yes—
28C2×#66880C2214yes—
29#10622706—24no—
30#10622600—21no—
31#10622600C2212yes—
32#10622586—21no—
33#10622586C2212yes—
34C2×#66874C2214yes—
35#10622548C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622188C2212yes—
38#10622167C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×C4×D11D411yescharacteristic
42C22×C4×D11D411yescharacteristic
43C22×C4×D11C2311yescharacteristic
44C22×Dic22C2312yes—
45C22×C8×C11C2312yes—
46C11×C4⋊Q8—22no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8D414yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11C2311yescharacteristic
55#66999—28no—
56#66999—44no—
57Q8×Dic11—28no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C22×C11⋊C8C2312yes—
73#66950—24no—
74#66950—24no—
75#66945—28no—
76#66943—28no—
77#66940—24no—
78#66940—24no—
79C42×D11—22no—
80C42×D11—22no—
81#66922—22no—
82#66922D414yes—
83C11×#106—28no—
84C4×C8×C11—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87(C2×D11)⋊C8—24no—
88#66880—28no—
89#66874—28no—
90C4×C11⋊C8—22no—
91#25672—111nomaximal, Sylow
92C23×D11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C2×Q8×C11—42no—
97C2×Q8×C11—42no—
98C2×Q8×C11—42no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2411yescharacteristic
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108C22×Dic11C2×D411yescharacteristic
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—22no—
113C2×C4×D11—22no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11SD1614yes—
119C2×Dic22—22no—
120C2×Dic22—24no—
121C2×Dic22—24no—
122C2×Dic22C2×D414yes—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11#4114yes—
126C11×C4⋊C4—24no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4C2×D414yes—
132C42×C11C2×D412yes—
133C42×C11C2×D412yes—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—44no—
136C4⋊Dic11—28no—
137C4⋊Dic11—24no—
138C4⋊Dic11—24no—
139C4⋊Dic11—24no—
140C4⋊Dic11—42no—
141C4⋊Dic11—42no—
142Dic11⋊C4—28no—
143Dic11⋊C4—44no—
144C4×Dic11—28no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—22no—
152C2×#533—111no—
153C2×#498D1111yescharacteristic, complemented
154C2×#487—111no—
155#2857—111no—
156#2035—114no—
157#1990—111no—
158#1956—111no—
159#1865—114no—
160C4×C22⋊C8—111no—
161C23×C11C22×D411yescharacteristic
162C22×D11—21no—
163C22×D11—21no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—21no—
167C22×D11—21no—
168C22×D11C2×SD1612yes—
169Q8×C11—48no—
170Q8×C11—84no—
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×C11#12012yes—
178C2×C4×C11#12012yes—
179C2×C4×C11C2×SD1612yes—
180C2×C4×C11#13512yes—
181C2×C4×C11#13712yes—
182C2×C4×C11#13712yes—
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11C2×#4112yes—
186C2×C4×C112−1+412yes—
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—24no—
192C2×Dic11—21no—
193C2×Dic11—21no—
194C2×Dic11—21no—
195C2×Dic11—21no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11C2×SD1612yes—
202C4×D11—28no—
203C4×D11—42no—
204C4×D11—42no—
205C4×D11—44no—
206Dic22—28no—
207Dic22—44no—
208C8×C11—24no—
209C11⋊C8—42no—
210#533—224no—
211#533—224no—
212C2×C4⋊Q8—111no—
213C2×C4⋊Q8C2×D1111yescharacteristic
214C2×C4⋊Q8C2×D1111yescharacteristic
215C2×#125—221no—
216C2×C22⋊Q8—112no—
217C2×C22⋊Q8—221no—
218C2×C22⋊Q8—221no—
219C2×C4×Q8—112no—
220C2×C4×Q8—221no—
221C2×#117—221no—
222C22×C42—111no—
223#498—24no—
224#487—224no—
225C2×#106C2×D1114yes—
226C2×#103—114no—
227C2×#103—114no—
228C2×C22⋊C8—112no—
229C2×C4×C8—111no—
230C2×C4×C8C2×D1111yescharacteristic
231#391—221no—
232#389—112no—
233#389—221no—
234#384—111no—
235#380—112no—
236#380—221no—
237#340—114no—
238#336—112no—
239C22×C11C2×#12011yescharacteristic
240C22×C11#53211yescharacteristic
241C22×C11#53611yescharacteristic
242C22×C11C22×SD1611yescharacteristic
243C22×C11C2×#13511yescharacteristic
244C22×C11C2×#13711yescharacteristic
245C22×C11C2×#13711yescharacteristic
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—41no—
250C2×D11—41no—
251C2×D11—41no—
252C2×D11—41no—
253C4×C11—44no—
254C4×C11—82no—
255C4×C11#44814yes—
256C4×C11#45214yes—
257C4×C11#54712yes—
258C4×C11#54812yes—
259Dic11—22no—
260Dic11—44no—
261Dic11—41no—
262Dic11—41no—
263Dic11—82no—
264C22×Q8—21no—
265C22×Q8—21no—
266C22×Q8—112no—
267C23×C4—111no—
268C23×C4—111no—
269C23×C4—111no—
270C22×C8—112no—
271C22×C8C22×D1112yes—
272C4⋊Q8—22no—
273C4⋊Q8—22no—
274C4⋊Q8—22no—
275C4⋊Q8—114no—
276C4⋊Q8—222no—
277C4⋊Q8C22⋊D1114yes—
278#125—228no—
279C22⋊Q8—224no—
280C22⋊Q8—228no—
281C22⋊Q8—224no—
282C22⋊Q8—444no—
283C4×Q8—224no—
284C4×Q8—228no—
285C4×Q8—224no—
286#117—228no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—221no—
293C2×C4⋊C4—221no—
294C2×C4⋊C4—222no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—221no—
297C2×C4⋊C4C22×D1112yes—
298C2×C4⋊C4C22×D1112yes—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C42—111no—
302C2×C42—111no—
303C2×C42—111no—
304C2×C42—222no—
305C2×C42—222no—
306C2×C42—222no—
307C2×C42C22×D1111yescharacteristic
308#106—28no—
309#103—228no—
310#103—228no—
311C22⋊C8—224no—
312C4×C8—22no—
313C4×C8—222no—
314#95—222no—
315#95—222no—
316C2×C11#243211yescharacteristic
317C2×C11C2×#44811yescharacteristic
318C2×C11C2×#45211yescharacteristic
319C2×C11#316711yescharacteristic
320C2×C11#318511yescharacteristic
321C2×C11#322911yescharacteristic
322C2×C11#323111yescharacteristic
323D11—42no—
324C24—111no—
325C2×Q8—24no—
326C2×Q8—42no—
327C2×Q8—42no—
328C2×Q8—42no—
329C2×Q8—42no—
330C2×Q8—42no—
331C2×Q8—114no—
332C2×Q8—222no—
333C2×Q8—224no—
334C2×Q8—224no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—111no—
338C22×C4—114no—
339C22×C4—111no—
340C22×C4—111no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—221no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—221no—
351C22×C4—222no—
352C22×C4D4×D1111yescharacteristic
353C22×C4D4×D1111yescharacteristic
354C22×C4C23×D1111yescharacteristic
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—222no—
358C2×C8—222no—
359C2×C8—222no—
360C2×C8#434314yes—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—42no—
366C4⋊C4—228no—
367C4⋊C4—228no—
368C4⋊C4—224no—
369C4⋊C4—224no—
370C4⋊C4—224no—
371C4⋊C4—444no—
372C4⋊C4—442no—
373C4⋊C4—442no—
374C4⋊C4C2×C22⋊D1114yes—
375C22⋊C4—228no—
376C22⋊C4—444no—
377C42—228no—
378C42—222no—
379C42—222no—
380C42—221no—
381C42—221no—
382C42D4×D1112yes—
383C42C2×C22⋊D1112yes—
384C11#2567211yescharacteristic, complemented, Sylow
385C23—112no—
386C23—221no—
387C23—221no—
388C23—221no—
389C23—221no—
390C23—221no—
391C23—221no—
392C23C2×D4×D1111yescharacteristic
393Q8—48no—
394Q8—84no—
395Q8—228no—
396Q8—444no—
397C2×C4—24no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—112no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—228no—
407C2×C4—221no—
408C2×C4—221no—
409C2×C4—221no—
410C2×C4—221no—
411C2×C4—221no—
412C2×C4—221no—
413C2×C4—224no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—444no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4SD16×D1112yes—
423C2×C4#6696812yes—
424C2×C4#6696812yes—
425C2×C4#6696912yes—
426C2×C4#6699012yes—
427C2×C4#6699012yes—
428C2×C4C2×D4×D1111yescharacteristic
429C2×C4C2×#434312yes—
430C2×C4#6704012yes—
431C2×C4C22×C22⋊D1111yescharacteristic
432C8—24no—
433C8—442no—
434C22—222no—
435C22—222no—
436C22—222no—
437C22—441no—
438C22—441no—
439C22—441no—
440C22—441no—
441C22#1062325511yescharacteristic
442C22#1062325611yescharacteristic
443C22C2×SD16×D1111yescharacteristic
444C22C2×#6696811yescharacteristic
445C22C2×#6696811yescharacteristic
446C22C2×#6696911yescharacteristic
447C22C2×#6699011yescharacteristic
448C4—44no—
449C4—82no—
450C4—222no—
451C4—441no—
452C4—441no—
453C4—444no—
454C4—882no—
455C4#1062278314yes—
456C4#1062278614yes—
457C4#1062325712yes—
458C4#1062334812yes—
459C2—442no—
460C2#1307224111yescharacteristic
461C2C2×#1062278311yescharacteristic
462C2C2×#1062278611yescharacteristic
463C2#1307917711yescharacteristic
464C2#1307936211yescharacteristic
465C2#1307976111yescharacteristic
466C2#1307977811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#498D11
hypocenterC11#25672
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. C2×#10622706C2semidirect
5. #13069578C2semidirect
6. #13069418C2semidirect
7. #13068881C2semidirect
9. C2×C11×#498C2semidirect
153. C2×#498D11semidirect
384. C11#25672semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106227062
#130769632
#130698142
#130695782
#130694182
#130688812
C4×(C2×D11)⋊C82
C2×C11×#4982
#2567211