Finite Group Databasebeta

← #14759009

Subgroups — #14759009

Order 2816.

1434 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×#10623256C211yesmaximal, characteristic
2C2×D11×#97C211yesmaximal, characteristic, complemented
3#13071009C211yesmaximal, characteristic, complemented
4#13069590C211yesmaximal, characteristic, complemented
5#13069440C211yesmaximal, characteristic, complemented
6#13069439C211yesmaximal, characteristic, complemented
7#13069043C214yesmaximal, complemented
8#13068440C214yesmaximal, complemented
9C11×#1993C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13C22×C8×D11C2212yes—
14#10623256—24no—
15#10623256C418yescomplemented
16C2×#66948—21no—
17C2×#66948C2212yes—
18C2×#66946—21no—
19C2×#66946C2212yes—
20C2×#66927C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C2×#66885C2214yes—
25C2×#66879C2212yes—
26#10622600C2212yes—
27C4⋊C4×Dic11C2212yes—
28C2×#66873C2214yes—
29#10622549C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31D11×#97—24no—
32#10622279—21no—
33#10622277—21no—
34#10622264—21no—
35#10622261—21no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×#4343—28no—
40C2×#4343—48no—
41C22×D44—22no—
42C22×D44—21no—
43C22×D44—21no—
44C22×D44C2312yes—
45C22×C4×D11—22no—
46C22×C4×D11D411yescharacteristic
47C22×C4×D11D411yescharacteristic
48C22×C4×D11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11C2311yescharacteristic
56#67000—28no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11C2312yes—
61C2×C4×Dic11—22no—
62C2×C4×Dic11D411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11C2311yescharacteristic
65C22×C11⋊C8C2312yes—
66C2×C8×D11—24no—
67C2×C8×D11—24no—
68C2×C8×D11—24no—
69#66948—28no—
70#66948—24no—
71#66948C2×C418yes—
72#66946—28no—
73#66946—24no—
74#66946C2×C418yes—
75#66927—22no—
76#66927C2×C414yes—
77C42×D11C2×C414yes—
78C42×D11D414yes—
79C11×#97—22no—
80C11×#95—21no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—28no—
87#66879—24no—
88#66873—28no—
89#66867—22no—
90#21408—111nomaximal, Sylow
91C23×D11—22no—
92C23×D11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—44no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104#4343—432no—
105C2×D44—28no—
106C2×D44—24no—
107C2×D44—24no—
108C2×D44—22no—
109C2×D44—24no—
110C2×D44—24no—
111C2×D44—44no—
112C2×D44—44no—
113C2×D44—48no—
114C2×D44C22×C414yes—
115C2×C4×D11—28no—
116C2×C4×D11—24no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—42no—
120C2×C4×D11—48no—
121C2×C4×D11C22⋊C414yes—
122C2×C4×D11C22⋊C414yes—
123C2×C4×D11C22×C412yes—
124C2×C4×D11C2×D412yes—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11#4114yescomplemented
128C11×C4⋊C4—24no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4C22×C414yes—
132C42×C11C22×C412yes—
133C42×C11C2×D412yes—
134(C2×D11)⋊C4—28no—
135(C2×D11)⋊C4—28no—
136(C2×D11)⋊C4—44no—
137C4⋊Dic11—24no—
138C4×Dic11—44no—
139C4×Dic11C22⋊C414yes—
140C4×Dic11C22⋊C414yes—
141C4×Dic11C22×C412yes—
142C4×Dic11C2×D412yes—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8#4114yescomplemented
146C8×D11—216no—
147C2×#532—111no—
148C22×#97—111no—
149#2283—111no—
150#1993—111no—
151#1993D1111yescharacteristic, complemented
152#1961—111no—
153#1961—111no—
154#1893—114no—
155#1762—114no—
156C23×C11C22×D411yescharacteristic
157C22×D11—21no—
158C22×D11—21no—
159C22×D11—22no—
160C22×D11—24no—
161C22×D11—42no—
162C22×D11—42no—
163C22×D11—44no—
164C22×D11—44no—
165C22×D11C2×C22⋊C412yes—
166C22×D11AGL(1,ℤ/8)14yes—
167Q8×C11—48no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—44no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11C2×C22⋊C412yes—
176C2×C4×C11C2×C22⋊C412yes—
177C2×C4×C11C23×C411yescharacteristic
178C2×C4×C11C22×D411yescharacteristic
179C2×C4×C11C2×#4112yes—
180C2×C4×C11C2×#4112yes—
181C2×Dic11—21no—
182C2×Dic11—21no—
183C2×Dic11—22no—
184C2×Dic11—22no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11C2×C22⋊C412yes—
189C2×Dic11C2×C22⋊C412yes—
190C2×Dic11C2×C22⋊C412yes—
191D44—28no—
192D44—48no—
193D44—48no—
194D44—416no—
195D44—44no—
196C4×D11—28no—
197C4×D11—24no—
198C4×D11—24no—
199C4×D11—44no—
200C4×D11—416no—
201C8×C11—24no—
202C11⋊C8—24no—
203C22×#41—221no—
204C23×C8—112no—
205#532—118no—
206#532—224no—
207C2×C4⋊Q8C2×D1111yescharacteristic
208C2×#127—111no—
209C2×#124—221no—
210C2×#121—112no—
211C2×#121—221no—
212C2×C4×D4—112no—
213C2×C4×D4—221no—
214C22×C42—111no—
215C2×#102—114no—
216C2×#102—114no—
217C2×#97—112no—
218C2×#97—111no—
219C2×#97—224no—
220C2×#97C2×D1111yescharacteristic
221#383—221no—
222#382—111no—
223#382C2×D1111yescharacteristic
224#381—221no—
225#380—112no—
226C4×C4⋊C4—112no—
227C4×C22⋊C4—221no—
228#376—221no—
229#340—114no—
230#340C2×D1114yes—
231C22×C11C22×C22⋊C411yescharacteristic
232C22×C11#53211yescharacteristic
233C22×C11#53211yescharacteristic
234C22×C11C2×AGL(1,ℤ/8)12yes—
235C22×C11#57512yes—
236C2×D11—22no—
237C2×D11—24no—
238C2×D11—24no—
239C2×D11—22no—
240C2×D11—44no—
241C2×D11—44no—
242C2×D11—44no—
243C2×D11—84no—
244C2×D11—84no—
245C2×D11#41814yes—
246C4×C11—22no—
247C4×C11—22no—
248C4×C11—44no—
249C4×C11—82no—
250C4×C11C4×#4112yes—
251C4×C11#52512yes—
252Dic11—22no—
253Dic11—22no—
254Dic11—22no—
255Dic11—82no—
256C2×#41—228no—
257C2×#41—448no—
258C22×Q8—21no—
259C22×D4—112no—
260C22×D4—222no—
261C22×D4—221no—
262C22×D4—221no—
263C23×C4—111no—
264C23×C4—111no—
265C23×C4—111no—
266C23×C4—222no—
267C22×C8—112no—
268C22×C8—224no—
269C22×C8—224no—
270C22×C8—224no—
271C22×C8C22×D1112yes—
272C4⋊Q8—22no—
273C4⋊Q8C4×D1114yes—
274#127—114no—
275#127—222no—
276#124—228no—
277#121—118no—
278#121—224no—
279#121—228no—
280C4×D4—118no—
281C4×D4—224no—
282C4×D4—228no—
283C2×C4⋊C4—21no—
284C2×C4⋊C4—112no—
285C2×C4⋊C4C22×D1112yes—
286C2×C4⋊C4C22×D1112yes—
287C2×C22⋊C4—222no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—222no—
290C2×C42—111no—
291C2×C42—111no—
292C2×C42—111no—
293C2×C42—114no—
294C2×C42—114no—
295C2×C42—222no—
296C2×C42C22×D1111yescharacteristic
297#102—228no—
298#102—228no—
299#97—22no—
300#97—224no—
301#97—222no—
302#95—21no—
303#95—21no—
304#95—222no—
305#95—222no—
306#95—221no—
307#95—221no—
308C2×C11#229711yescharacteristic
309C2×C11C2×#41811yescharacteristic
310C2×C11#289611yescharacteristic
311C2×C11#318012yes—
312C2×C11#318012yes—
313D11—24no—
314D11—84no—
315C24—111no—
316C24—222no—
317#41—4432no—
318C2×Q8—24no—
319C2×Q8—44no—
320C2×D4—114no—
321C2×D4—228no—
322C2×D4—224no—
323C2×D4—224no—
324C2×D4—222no—
325C2×D4—224no—
326C2×D4—224no—
327C2×D4—444no—
328C2×D4—444no—
329C2×D4—448no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—114no—
336C22×C4—112no—
337C22×C4—112no—
338C22×C4—114no—
339C22×C4—228no—
340C22×C4—224no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—442no—
345C22×C4—448no—
346C22×C4D4×D1111yescharacteristic
347C22×C4D4×D1111yescharacteristic
348C22×C4C23×D1111yescharacteristic
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—114no—
352C2×C8—2216no—
353C2×C8—222no—
354C2×C8—222no—
355C2×C8#434314yescomplemented
356C4⋊C4—24no—
357C4⋊C4—22no—
358C4⋊C4—24no—
359C4⋊C4—224no—
360C4⋊C4C2×C4×D1114yes—
361C22⋊C4—228no—
362C22⋊C4—228no—
363C22⋊C4—444no—
364C42—114no—
365C42—114no—
366C42—112no—
367C42—112no—
368C42—444no—
369C42C2×C4×D1112yes—
370C42D4×D1112yes—
371C11#2140811yescharacteristic, complemented, Sylow
372C23—112no—
373C23—114no—
374C23—221no—
375C23—222no—
376C23—221no—
377C23—224no—
378C23—442no—
379C23—444no—
380C23—444no—
381C23—442no—
382C23C2×D4×D1111yescharacteristic
383Q8—48no—
384D4—228no—
385D4—448no—
386D4—448no—
387D4—4416no—
388D4—444no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—24no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—112no—
397C2×C4—112no—
398C2×C4—112no—
399C2×C4—228no—
400C2×C4—221no—
401C2×C4—222no—
402C2×C4—222no—
403C2×C4—221no—
404C2×C4—224no—
405C2×C4—224no—
406C2×C4—444no—
407C2×C4—4416no—
408C2×C4—442no—
409C2×C4—442no—
410C2×C4—442no—
411C2×C4C22⋊C4×D1112yes—
412C2×C4C22⋊C4×D1112yes—
413C2×C4C22×C4×D1111yescharacteristic
414C2×C4C2×D4×D1111yescharacteristic
415C2×C4C2×#434312yes—
416C2×C4#41×D1112yes—
417C8—24no—
418C8—224no—
419C22—114no—
420C22—222no—
421C22—224no—
422C22—224no—
423C22—222no—
424C22—444no—
425C22—444no—
426C22—444no—
427C22—884no—
428C22—884no—
429C22C2×C22⋊C4×D1111yescharacteristic
430C22#1062319911yescharacteristic
431C22#1062325611yescharacteristic
432C22D11×AGL(1,ℤ/8)12yes—
433C22#1062330812yes—
434C4—22no—
435C4—22no—
436C4—44no—
437C4—82no—
438C4—222no—
439C4—222no—
440C4—222no—
441C4—882no—
442C4C4×#434312yes—
443C4#1062315812yes—
444C2—224no—
445C2—884no—
446C2#1307110511yescharacteristic
447C2D11×#41811yescharacteristic
448C2#1307713411yescharacteristic
449C2#1307931612yes—
450C2#1307931712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1993C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1993D11
hypocenterC11#21408
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
2. C2×D11×#97C2semidirect
3. #13071009C2semidirect
4. #13069590C2semidirect
5. #13069440C2semidirect
6. #13069439C2semidirect
7. #13069043C2semidirect
8. #13068440C2semidirect
9. C11×#1993C2semidirect
15. #10623256C4semidirect
127. C2×C8×C11#41semidirect
145. C2×C11⋊C8#41semidirect
151. #1993D11semidirect
355. C2×C8#4343semidirect
371. C11#21408semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×D11×#972
#130710092
#130695902
#130694402
#130694392
#130690432
#130684402
C11×#19932
#2140811