Finite Group Databasebeta

← #14916662

Subgroups — #14916662

Order 2816.

1910 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#125C211yesmaximal, characteristic
2#13071802C211yesmaximal, characteristic, complemented
3#13071801C212yesmaximal, complemented
4#13071720C214yesmaximal, complemented
5#13071492C214yesmaximal
6#13071490C214yesmaximal
7#13071421C214yesmaximal, complemented
8#13071414C214yesmaximal, complemented
9#13071215C214yesmaximal
10#13071009C212yesmaximal
11C11×#2382C211yesmaximal, characteristic, complemented
12C2×C11×#125C2211yescharacteristic
13D11×#125C4116yescomplemented
14C2×C4⋊C4×D11C2212yes—
15C2×C4⋊C4×D11C2214yes—
16C2×#66943C2212yes—
17C2×#66942C2214yes—
18C2×C42×D11C2211yescharacteristic
19C2×#66923C2211yescharacteristic
20C11×#389C2214yes—
21C11×#387C2214yes—
22C11×#387C2214yes—
23C11×#382C2212yes—
24#10622600C2214yes—
25#10622600C2212yes—
26#10622600C2212yes—
27#10622598C2214yes—
28#10622594C2214yes—
29#10622594C2214yes—
30#10622591C2214yes—
31#10622591C2214yes—
32#10622591C2214yes—
33C4⋊C4×Dic11C2212yes—
34C4⋊C4×Dic11C2214yes—
35C4⋊C4×Dic11C2212yes—
36#10622585C2214yes—
37C4×(C2×D11)⋊C4C2214yes—
38#10622549C2212yes—
39C4×C4⋊Dic11C2214yes—
40#10622546C2214yes—
41C4×Dic11⋊C4C2214yes—
42#10622280C2214yes—
43#10622279C2214yes—
44#10622279C2214yes—
45#10622277C2214yes—
46#10622268C2214yes—
47#10622268C2214yes—
48#10622268C2214yes—
49#10622267C2214yes—
50#10622267C2214yes—
51#10622266C2214yes—
52#10622266C2214yes—
53#10622265C2214yes—
54#10622264C2214yes—
55#10622262C2214yes—
56#10622261C2214yes—
57#10622260C2214yes—
58C22×C4×D11C2311yescharacteristic
59C22×C4×D11C2312yes—
60C22×C4×D11C2314yes—
61C11×#125C2×C418yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2314yes—
68C2×C42×C11C2311yescharacteristic
69C2×(C2×D11)⋊C4C2314yes—
70C2×(C2×D11)⋊C4C2314yes—
71C2×C4⋊Dic11C2312yes—
72C2×C4⋊Dic11C2314yes—
73C2×C4⋊Dic11C2312yes—
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2314yes—
76C2×Dic11⋊C4C2314yes—
77C2×Dic11⋊C4C2314yes—
78C2×Dic11⋊C4C2314yes—
79C2×Dic11⋊C4C2314yes—
80C2×Dic11⋊C4C2314yes—
81C2×C4×Dic11C2314yes—
82C2×C4×Dic11C2314yes—
83C2×C4×Dic11C2314yes—
84C2×C4×Dic11C2314yes—
85C2×C4×Dic11C2314yes—
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2312yes—
88C4⋊C4×D11C2×C4132yes—
89C4⋊C4×D11C2×C4116yes—
90#66943C2×C4116yes—
91#66942C2×C4132yes—
92C42×D11C2×C418yes—
93#66923C2×C418yes—
94C11×#95C2314yes—
95C11×#95C2314yes—
96C11×#95C2314yes—
97C11×#95C2314yes—
98C11⋊#95C2314yes—
99C11⋊#95C2314yes—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2314yes—
103C11⋊#95C2314yes—
104C11⋊#95C2314yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2314yes—
110#34372—111nomaximal, Sylow
111C23×D11C2411yescharacteristic
112C22×C4×C11C2414yes—
113C22×C4×C11C2414yes—
114C22×C4×C11C2411yescharacteristic
115C22×C4×C11C2414yes—
116C22×C4×C11C2412yes—
117C22×Dic11C2414yes—
118C22×Dic11C2414yes—
119C22×Dic11C2411yescharacteristic
120C22×Dic11C2412yes—
121C22×Dic11C2414yes—
122C2×C4×D11—22no—
123C2×C4×D11—22no—
124C2×C4×D11—44no—
125C2×C4×D11—42no—
126C2×C4×D11—44no—
127C2×C4×D11—42no—
128C2×C4×D11C22×C414yes—
129C2×C4×D11C22×C418yes—
130C2×C4×D11C22×C4116yes—
131C11×C4⋊C4—44no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—42no—
134C11×C4⋊C4C22×C4116yes—
135C11×C4⋊C4C22×C418yes—
136C42×C11—44no—
137C42×C11C22×C414yes—
138(C2×D11)⋊C4—28no—
139(C2×D11)⋊C4—28no—
140C4⋊Dic11—44no—
141C4⋊Dic11—42no—
142C4⋊Dic11—42no—
143C4⋊Dic11C22×C418yes—
144C4⋊Dic11C22×C4116yes—
145Dic11⋊C4—44no—
146Dic11⋊C4—44no—
147Dic11⋊C4C22×C4116yes—
148Dic11⋊C4C22×C4116yes—
149Dic11⋊C4C22×C4116yes—
150C4×Dic11—44no—
151C4×Dic11—44no—
152C4×Dic11—44no—
153C4×Dic11—44no—
154C4×Dic11—44no—
155C4×Dic11C22×C418yes—
156C4×Dic11C22×C414yes—
157C22×#125—111no—
158#2382—112no—
159#2382—111no—
160#2382D1111yescharacteristic, complemented
161#2371—114no—
162#2345—114no—
163#2345—114no—
164#2336—114no—
165#2336—114no—
166#2313—114no—
167#2283—112no—
168C23×C11C2511yescharacteristic
169C22×D11—22no—
170C22×D11—22no—
171C22×D11C23×C412yes—
172C22×D112−1+412yes—
173C22×D112−1+412yes—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—24no—
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—24no—
181C2×C4×C11—24no—
182C2×C4×C11—24no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11C23×C414yes—
187C2×C4×C11C23×C412yes—
188C2×C4×C11C23×C418yes—
189C2×Dic11—21no—
190C2×Dic11—21no—
191C2×Dic11—22no—
192C2×Dic11—22no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11C23×C412yes—
202C2×Dic11C23×C414yes—
203C2×Dic11C23×C418yes—
204C4×D11—28no—
205C4×D11—48no—
206C4×D11—416no—
207C2×#125—1116no—
208C2×#125—114no—
209C2×#125—112no—
210C2×#125—111no—
211C2×#125C2×D1111yescharacteristic
212C22×C4⋊C4—112no—
213C22×C4⋊C4—114no—
214C22×C42—111no—
215#389—114no—
216#389—114no—
217#389—114no—
218#389C2×D1114yes—
219#387—114no—
220#387—114no—
221#387—114no—
222#387—114no—
223#387—114no—
224#387—114no—
225#387—114no—
226#387—114no—
227#387—114no—
228#387—114no—
229#387—114no—
230#387—114no—
231#387—114no—
232#387—114no—
233#387C2×D1114yes—
234#387C2×D1114yes—
235#383—114no—
236#382—112no—
237#382C2×D1112yes—
238#381—114no—
239#380—114no—
240#380—112no—
241#380—112no—
242#380—114no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—112no—
245C4×C4⋊C4—114no—
246C4×C4⋊C4—114no—
247C4×C4⋊C4—114no—
248C4×C4⋊C4—114no—
249C4×C22⋊C4—114no—
250C4×C22⋊C4—114no—
251C4×C22⋊C4—114no—
252#376—114no—
253C22×C11C24×C411yescharacteristic
254C22×C11C2×2−1+411yescharacteristic
255C22×C11C2×2−1+411yescharacteristic
256C22×C11#58512yes—
257C22×C11#58512yes—
258C2×D11—24no—
259C2×D11—24no—
260C2×D11—22no—
261C2×D11—22no—
262C2×D11#51914yes—
263C4×C11—22no—
264C4×C11—28no—
265C4×C11—24no—
266C4×C11—44no—
267C4×C11—44no—
268Dic11—22no—
269Dic11—24no—
270Dic11—28no—
271Dic11—44no—
272Dic11—44no—
273C23×C4—111no—
274C23×C4—114no—
275C23×C4—112no—
276#125—1132no—
277#125—1116no—
278#125—118no—
279#125C4×D1118yes—
280C2×C4⋊C4—114no—
281C2×C4⋊C4—114no—
282C2×C4⋊C4—114no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—114no—
285C2×C4⋊C4—1116no—
286C2×C4⋊C4—1132no—
287C2×C4⋊C4—112no—
288C2×C4⋊C4—112no—
289C2×C4⋊C4—114no—
290C2×C4⋊C4—114no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1112yes—
294C2×C4⋊C4C22×D1114yes—
295C2×C4⋊C4C22×D1112yes—
296C2×C4⋊C4C22×D1114yes—
297C2×C22⋊C4—114no—
298C2×C22⋊C4—114no—
299C2×C42—111no—
300C2×C42—112no—
301C2×C42—118no—
302C2×C42—114no—
303C2×C42—114no—
304C2×C42—114no—
305C2×C42—114no—
306C2×C42—114no—
307C2×C42C22×D1114yes—
308C2×C42C22×D1111yescharacteristic
309#95—114no—
310#95—114no—
311#95—114no—
312#95—114no—
313#95—114no—
314#95—114no—
315#95—114no—
316#95—114no—
317#95—114no—
318#95—114no—
319#95—114no—
320#95—114no—
321#95C22×D1114yes—
322#95C22×D1114yes—
323#95C22×D1114yes—
324#95C22×D1114yes—
325C2×C11C2×#51911yescharacteristic
326C2×C11#342812yes—
327C2×C11#355312yes—
328C2×C11#355311yescharacteristic
329C2×C11#355311yescharacteristic
330D11—24no—
331C24—111no—
332C22×C4—111no—
333C22×C4—112no—
334C22×C4—114no—
335C22×C4—114no—
336C22×C4—118no—
337C22×C4—1116no—
338C22×C4—114no—
339C22×C4—114no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—444no—
343C22×C4—442no—
344C22×C4—444no—
345C22×C4—442no—
346C22×C4C23×D1114yes—
347C22×C4C23×D1114yes—
348C22×C4C23×D1111yescharacteristic
349C22×C4C23×D1114yes—
350C22×C4C23×D1112yes—
351C4⋊C4—44no—
352C4⋊C4—42no—
353C4⋊C4—42no—
354C4⋊C4—1116no—
355C4⋊C4—1116no—
356C4⋊C4—1116no—
357C4⋊C4—1116no—
358C4⋊C4—118no—
359C4⋊C4—444no—
360C4⋊C4—444no—
361C4⋊C4—444no—
362C4⋊C4—442no—
363C4⋊C4—442no—
364C4⋊C4C2×C4×D1118yes—
365C4⋊C4C2×C4×D11116yes—
366C22⋊C4—228no—
367C22⋊C4—228no—
368C42—44no—
369C42—114no—
370C42—118no—
371C42—444no—
372C42—444no—
373C42—444no—
374C42—444no—
375C42—444no—
376C42C2×C4×D1114yes—
377C11#3437211yescharacteristic, complemented, Sylow
378C23—112no—
379C23—112no—
380C23—112no—
381C23—222no—
382C23—222no—
383C23C24×D1111yescharacteristic
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—112no—
397C2×C4—114no—
398C2×C4—118no—
399C2×C4—228no—
400C2×C4—222no—
401C2×C4—224no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—222no—
405C2×C4—224no—
406C2×C4—224no—
407C2×C4—224no—
408C2×C4—224no—
409C2×C4—224no—
410C2×C4—224no—
411C2×C4—224no—
412C2×C4—448no—
413C2×C4—4416no—
414C2×C4C22×C4×D1112yes—
415C2×C4C22×C4×D1114yes—
416C2×C4C22×C4×D1118yes—
417C22—114no—
418C22—224no—
419C22—222no—
420C22—222no—
421C22—224no—
422C22C23×C4×D1111yescharacteristic
423C22#1062345512yes—
424C22D11×2−1+411yescharacteristic
425C22D11×2−1+411yescharacteristic
426C22#1062345712yes—
427C4—22no—
428C4—28no—
429C4—24no—
430C4—44no—
431C4—44no—
432C4—222no—
433C4—224no—
434C4—228no—
435C4—444no—
436C4—444no—
437C2—224no—
438C2D11×#51911yescharacteristic
439C2#1308181612yes—
440C2#1308306712yes—
441C2#1308307111yescharacteristic
442C2#1308307311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2382C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2382D11
hypocenterC11#34372
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2382

Complements

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

NH ≅ G/Ntype
2. #13071802C2semidirect
3. #13071801C2semidirect
4. #13071720C2semidirect
7. #13071421C2semidirect
8. #13071414C2semidirect
11. C11×#2382C2semidirect
13. D11×#125C4semidirect
160. #2382D11semidirect
377. C11#34372semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1252
#130718022
#130718012
#130717202
#130714922
#130714902
#130714212
#130714142
#130712152
#130710092
C11×#23822
#3437211