Finite Group Databasebeta

← #14763756

Subgroups — #14763756

Order 2816.

1142 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623066C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic, complemented
3#13069573C212yesmaximal, complemented
4#13069543C212yesmaximal, complemented
5#13069052C212yesmaximal, complemented
6#13069042C212yesmaximal, complemented
7#13068623C212yesmaximal, complemented
8#13068613C212yesmaximal, complemented
9C11×#2314C211yesmaximal, characteristic, complemented
10C2×C11×#117C2211yescharacteristic
11C2×#66983C2212yes—
12C22×#4318C2211yescharacteristic
13C23×C11⋊C8C2211yescharacteristic
14#10623066—24no—
15#10623066C418yescomplemented
16C2×#66947—22no—
17C2×#66937—22no—
18C2×#66927C2211yescharacteristic
19C2×C4×D44C2212yes—
20C2×#66923C2211yescharacteristic
21C11×#388—22no—
22C11×#387—22no—
23C11×#384C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C11×#380C2212yes—
26C4×C11×C4⋊C4C2212yes—
27#10622612—24no—
28C2×#66873C2212yes—
29C2×#66873C2212yes—
30C2×#66873C2212yes—
31C2×#66873C2212yes—
32C2×C4⋊(C11⋊C8)C2212yes—
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—22no—
40C22×D44—22no—
41C22×D44C2312yes—
42C22×C4×D11—22no—
43C11×#117C2×C414yes—
44C11×#117D414yes—
45C2×C11×C4⋊C4—22no—
46C2×C11×C4⋊C4D412yes—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C11×C22⋊C4—22no—
50C2×C11×C22⋊C4D412yes—
51C2×C42×C11—22no—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54#66983—24no—
55#66983C2×C418yes—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×#4318—22no—
61C2×#4318—41no—
62C2×#4318—41no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8—41no—
65C22×C11⋊C8—41no—
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2312yes—
68#66947—216no—
69#66937—216no—
70#66927—22no—
71#66927C2×C414yes—
72C4×D44—24no—
73C4×D44C2×C418yes—
74#66923—22no—
75#66923C2×C414yes—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79#66873—42no—
80#66873—42no—
81#66873—42no—
82#66873—42no—
83C4⋊(C11⋊C8)—24no—
84C4⋊(C11⋊C8)—24no—
85#21897—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C23×D11—22no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11C22×C412yes—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2×D412yes—
99C22×C4×C11C2411yescharacteristic
100C2×C22⋊D11—28no—
101C2×C22⋊D11—82no—
102C2×C22⋊D11—82no—
103C22×Dic11—22no—
104C2×D44—28no—
105C2×D44—22no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—82no—
111C2×D44—82no—
112C2×D44C22×C414yes—
113C2×C4×D11—28no—
114C2×C4×D11—82no—
115C2×C4×D11—82no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—22no—
120C11×C4⋊C4—82no—
121C11×C4⋊C4C22⋊C418yes—
122C11×C22⋊C4—82no—
123C11×C22⋊C4C22⋊C418yes—
124C42×C11—82no—
125C42×C11C22×C412yes—
126C42×C11C22×C412yes—
127C42×C11C2×D412yes—
128C42×C11C2×D412yes—
129(C2×D11)⋊C4—28no—
130(C2×D11)⋊C4—28no—
131C4⋊Dic11—22no—
132C4⋊Dic11C22×C414yes—
133Dic11⋊C4—28no—
134#4318—44no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—44no—
142C2×#540—111no—
143C2×#424—111no—
144#2314D1111yescharacteristic, complemented
145#1989—112no—
146#1982—112no—
147#1895—112no—
148#1893—112no—
149#1804—112no—
150#1802—112no—
151C23×C11—21no—
152C23×C11—21no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11C2×C22⋊C412yes—
156C23×C11C22×D411yescharacteristic
157C22×D11—24no—
158C22×D11—42no—
159C22×D11—42no—
160C22×D11—42no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—42no—
164C2×C4×C11—21no—
165C2×C4×C11—21no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—22no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11C2×C22⋊C414yes—
181C2×C4×C11C2×C22⋊C412yes—
182C2×C4×C11C2×C22⋊C414yes—
183C2×C4×C11C23×C411yescharacteristic
184C2×C4×C11C22×D411yescharacteristic
185C2×C4×C11H(5,𝔽2)11yescharacteristic
186C2×C4×C11H(5,𝔽2)11yescharacteristic
187C2×C4×C112−1+411yescharacteristic
188C2×C4×C112−1+411yescharacteristic
189C22⋊D11—88no—
190C2×Dic11—24no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193D44—24no—
194D44—24no—
195D44—42no—
196D44—42no—
197D44—88no—
198C4×D11—88no—
199C11⋊C8—42no—
200C11⋊C8—42no—
201C22×M16—111no—
202C23×C8—111no—
203#540—118no—
204#540—224no—
205C2×#127—111no—
206C2×#125—111no—
207C2×#123—222no—
208C2×#121—112no—
209C2×#121—222no—
210C2×C4×D4—112no—
211C2×#117C2×D1111yescharacteristic
212#424—224no—
213C2×C4⋊C8—112no—
214C2×C4⋊C8—112no—
215C2×#102—112no—
216C2×#102—112no—
217C2×#102—112no—
218C2×#102—112no—
219#388—22no—
220#387—22no—
221#384C2×D1111yescharacteristic
222#382C2×D1111yescharacteristic
223#380C2×D1112yes—
224C4×C4⋊C4C2×D1112yes—
225#340—112no—
226#340—112no—
227#340—112no—
228#340—112no—
229C22×C11—22no—
230C22×C11—24no—
231C22×C11—42no—
232C22×C11—41no—
233C22×C11—41no—
234C22×C11C22×C22⋊C411yescharacteristic
235C22×C11#53711yescharacteristic
236C22×C11#53711yescharacteristic
237C22×C11#57612yes—
238C22×C11#57712yes—
239C2×D11—44no—
240C2×D11—44no—
241C2×D11—44no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—82no—
246C4×C11—22no—
247C4×C11—24no—
248C4×C11—24no—
249C4×C11—82no—
250C4×C11—82no—
251C4×C11#52011yescharacteristic
252C4×C11#52011yescharacteristic
253C4×C11#53511yescharacteristic
254C4×C11#53611yescharacteristic
255Dic11—44no—
256C22×D4—112no—
257C22×D4—222no—
258C22×D4—222no—
259C23×C4—222no—
260C23×C4C22×D1111yescharacteristic
261C2×M16—222no—
262C2×M16—441no—
263C2×M16—441no—
264C22×C8—112no—
265C22×C8—112no—
266C22×C8—222no—
267C22×C8—441no—
268C22×C8—441no—
269#127—114no—
270#127—222no—
271#125—114no—
272#125—222no—
273#123—2216no—
274#121—118no—
275#121—224no—
276#121—2216no—
277C4×D4—118no—
278C4×D4—224no—
279#117C4×D1114yes—
280#117D4414yes—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—222no—
284C2×C4⋊C4C22⋊D1112yes—
285C2×C4⋊C4C22×D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—22no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C22⋊C4C22⋊D1112yes—
291C2×C42—22no—
292C2×C42C22×D1111yescharacteristic
293C2×C42C22×D1111yescharacteristic
294C4⋊C8—224no—
295C4⋊C8—224no—
296#102—442no—
297#102—442no—
298#102—442no—
299#102—442no—
300#95—22no—
301#95—22no—
302#95—22no—
303C2×C11—42no—
304C2×C11#231111yescharacteristic
305C2×C11#289712yes—
306C2×C11#325712yes—
307C2×C11#325911yescharacteristic
308C2×C11#326011yescharacteristic
309D11—84no—
310C24—222no—
311C24C2×C22⋊D1111yescharacteristic
312C2×D4—114no—
313C2×D4—228no—
314C2×D4—228no—
315C2×D4—222no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—222no—
320C2×D4—882no—
321C2×D4—882no—
322C2×D4—882no—
323C2×D4—882no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—222no—
331C22×C4—228no—
332C22×C4—882no—
333C22×C4—882no—
334C22×C4C2×C4×D1112yes—
335C22×C4C2×D4412yes—
336C22×C4C2×C22⋊D1111yescharacteristic
337C22×C4C2×C22⋊D1112yes—
338C22×C4C2×C22⋊D1112yes—
339C22×C4C23×D1111yescharacteristic
340M16—444no—
341C2×C8—222no—
342C2×C8—222no—
343C2×C8—222no—
344C2×C8—222no—
345C2×C8—222no—
346C2×C8—222no—
347C2×C8—444no—
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—82no—
353C4⋊C4—114no—
354C4⋊C4—228no—
355C4⋊C4—222no—
356C4⋊C4(C2×D11)⋊C418yes—
357C22⋊C4—82no—
358C22⋊C4—228no—
359C22⋊C4—228no—
360C22⋊C4(C2×D11)⋊C418yes—
361C42—82no—
362C42C2×C4×D1112yes—
363C42C2×C4×D1112yes—
364C42C2×D4412yes—
365C42C2×D4412yes—
366C11#2189711yescharacteristic, complemented, Sylow
367C23—21no—
368C23—21no—
369C23—22no—
370C23—22no—
371C23—224no—
372C23—442no—
373C23—442no—
374C23—442no—
375C23—442no—
376C23—442no—
377C23—442no—
378C23C2×(C2×D11)⋊C412yes—
379C23C22×C22⋊D1111yescharacteristic
380D4—224no—
381D4—224no—
382D4—442no—
383D4—442no—
384D4—888no—
385D4—888no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—224no—
403C2×C4—442no—
404C2×C4—442no—
405C2×C4—888no—
406C2×C4C2×(C2×D11)⋊C414yes—
407C2×C4C2×(C2×D11)⋊C414yes—
408C2×C4C2×(C2×D11)⋊C412yes—
409C2×C4C22×C4×D1111yescharacteristic
410C2×C4C22×D4411yescharacteristic
411C2×C4#6704211yescharacteristic
412C2×C4#6704211yescharacteristic
413C2×C4#6704311yescharacteristic
414C2×C4#6704311yescharacteristic
415C8—442no—
416C8—442no—
417C22—22no—
418C22—24no—
419C22—42no—
420C22—41no—
421C22—41no—
422C22—444no—
423C22—444no—
424C22—444no—
425C22—882no—
426C22—882no—
427C22—882no—
428C22—882no—
429C22C22×(C2×D11)⋊C411yescharacteristic
430C22#1062336411yescharacteristic
431C22#1062336411yescharacteristic
432C22#1062336612yes—
433C22#1062336812yes—
434C4—22no—
435C4—24no—
436C4—24no—
437C4—82no—
438C4—82no—
439C4—444no—
440C4#1062305411yescharacteristic
441C4#1062305411yescharacteristic
442C4#1062305611yescharacteristic
443C4#1062305711yescharacteristic
444C2—42no—
445C2—884no—
446C2#1307120411yescharacteristic
447C2#1307713912yes—
448C2#1308002712yes—
449C2#1308005111yescharacteristic
450C2#1308005711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2314C2
socleC23×C11C22×D4
prime radicalC2×#10623066C2
cosocleC22×C4×C11C24
hypercenter#2314D11
hypocenterC11#21897
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#10622612C2semidirect
3. #13069573C2semidirect
4. #13069543C2semidirect
5. #13069052C2semidirect
6. #13069042C2semidirect
7. #13068623C2semidirect
8. #13068613C2semidirect
9. C11×#2314C2semidirect
15. #10623066C4semidirect
144. #2314D11semidirect
366. C11#21897semidirect

Maximal subgroups

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

subgroupindex
C2×#106230662
C2×#106226122
#130695732
#130695432
#130690522
#130690422
#130686232
#130686132
C11×#23142
#2189711