Finite Group Databasebeta

← #14763707

Subgroups — #14763707

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10622450C211yesmaximal, characteristic, complemented
3#13071012C211yesmaximal, characteristic, complemented
4#13069569C211yesmaximal, characteristic, complemented
5#13069543C211yesmaximal, characteristic, complemented
6#13069542C211yesmaximal, characteristic, complemented
7#13069053C214yesmaximal, complemented
8#13068625C214yesmaximal, complemented
9C11×#1988C211yesmaximal, characteristic, complemented
10C22×#4343—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000—21no—
13C22×#4313C2212yes—
14#10623256—24no—
15#10623256C418yescomplemented
16C2×#66948—21no—
17C2×#66948C2212yes—
18C2×#66946—21no—
19C2×#66946C2212yes—
20C2×#66927C2211yescharacteristic
21C2×C42×D11C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66885C2214yes—
25C2×Dic11⋊C8C2212yes—
26#10622600C2212yes—
27#10622590C2212yes—
28C2×#66873C2214yes—
29C4×(C2×D11)⋊C4—21no—
30C4×C4⋊Dic11C2211yescharacteristic
31#10622545—21no—
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622450—24no—
34#10622277—21no—
35#10622264—21no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C2×#4343—28no—
40C2×#4343—44no—
41C2×#4343—44no—
42C22×D44—22no—
43C22×D44—21no—
44C22×D44—21no—
45C22×D44C2312yes—
46C22×C4×D11—22no—
47C22×C4×D11D411yescharacteristic
48C22×C4×D11D411yescharacteristic
49C22×C4×D11C2311yescharacteristic
50C22×C8×C11C2312yes—
51C11×C4⋊Q8—22no—
52C11×C4⋊Q8C2×C414yes—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#67000—28no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×C4⋊Dic11C2312yes—
63C2×C4×Dic11—21no—
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11D411yescharacteristic
66C2×C4×Dic11C2311yescharacteristic
67C22×C11⋊C8C2312yes—
68C2×#4313—24no—
69C2×#4313—44no—
70#66948—28no—
71#66948—24no—
72#66948C2×C418yes—
73#66946—28no—
74#66946—24no—
75#66946C2×C418yes—
76#66927—22no—
77#66927C2×C414yes—
78C42×D11C2×C414yes—
79C42×D11D414yes—
80C11×C4⋊C8—22no—
81C11×#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86#66885—44no—
87Dic11⋊C8—24no—
88#66873—44no—
89C4⋊(C11⋊C8)—22no—
90#21891—111nomaximal, Sylow
91C23×D11—22no—
92C23×D11C2×D411yescharacteristic
93C2×Q8×C11—24no—
94C2×Q8×C11—42no—
95C2×Q8×C11—42no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105#4343—432no—
106C2×D44—28no—
107C2×D44—24no—
108C2×D44—24no—
109C2×D44—22no—
110C2×D44—24no—
111C2×D44—24no—
112C2×D44—44no—
113C2×D44—44no—
114C2×D44—44no—
115C2×D44—42no—
116C2×D44—42no—
117C2×D44C22×C414yes—
118C2×C4×D11—28no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—44no—
125C2×C4×D11—44no—
126C2×C4×D11C22⋊C414yes—
127C2×C4×D11C22⋊C414yes—
128C2×C4×D11C22×C412yes—
129C2×C4×D11C2×D412yes—
130C2×C8×C11—22no—
131C2×C8×C11—24no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4C22×C414yes—
137C42×C11—42no—
138C42×C11C22×C412yes—
139C42×C11C2×D412yes—
140(C2×D11)⋊C4—28no—
141(C2×D11)⋊C4—28no—
142(C2×D11)⋊C4—44no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4×Dic11—42no—
146C4×Dic11C22⋊C414yes—
147C4×Dic11C22⋊C414yes—
148C4×Dic11C22×C412yes—
149C4×Dic11C2×D412yes—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—24no—
152#4313—48no—
153C2×#532—111no—
154C2×#423—111no—
155#2283—111no—
156#1988—111no—
157#1988D1111yescharacteristic, complemented
158#1982—111no—
159#1982—111no—
160#1895—114no—
161#1804—114no—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—21no—
165C22×D11—21no—
166C22×D11—22no—
167C22×D11—24no—
168C22×D11—44no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—44no—
172C22×D11C2×C22⋊C412yes—
173Q8×C11—48no—
174C2×C4×C11—22no—
175C2×C4×C11—24no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11C2×C22⋊C412yes—
182C2×C4×C11C2×C22⋊C412yes—
183C2×C4×C11AGL(1,ℤ/8)12yes—
184C2×C4×C11AGL(1,ℤ/8)12yes—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11H(5,𝔽2)12yes—
188C2×C4×C112−1+412yes—
189C2×Dic11—22no—
190C2×Dic11—21no—
191C2×Dic11—21no—
192C2×Dic11—22no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11C2×C22⋊C412yes—
197C2×Dic11C2×C22⋊C412yes—
198C2×Dic11C2×C22⋊C412yes—
199D44—28no—
200D44—48no—
201D44—416no—
202D44—42no—
203D44—42no—
204D44—48no—
205C4×D11—24no—
206C4×D11—22no—
207C4×D11—22no—
208C4×D11—28no—
209C4×D11—44no—
210C4×D11—416no—
211C8×C11—42no—
212C11⋊C8—42no—
213C22×#41—221no—
214C22×M16—112no—
215#532—118no—
216#532—224no—
217C2×C4⋊Q8C2×D1111yescharacteristic
218C2×#127—111no—
219C2×#124—221no—
220C2×#121—112no—
221C2×#121—221no—
222C2×C4×D4—112no—
223C2×C4×D4—221no—
224C22×C42—111no—
225#423—224no—
226C2×C4⋊C8—112no—
227C2×C4⋊C8—111no—
228C2×C4⋊C8C2×D1111yescharacteristic
229C2×#102—114no—
230C2×#102—114no—
231#383—221no—
232#382—112no—
233#381—221no—
234#380—112no—
235C4×C4⋊C4—111no—
236C4×C4⋊C4C2×D1111yescharacteristic
237C4×C22⋊C4—221no—
238#376—221no—
239#340—114no—
240#340C2×D1114yes—
241C22×C11C22×C22⋊C411yescharacteristic
242C22×C11#53712yes—
243C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C22×C11#57512yes—
246C2×D11—22no—
247C2×D11—22no—
248C2×D11—22no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—84no—
255C2×D11—84no—
256C4×C11—22no—
257C4×C11—44no—
258C4×C11—82no—
259C4×C11#41814yes—
260C4×C11#52012yes—
261C4×C11#53511yescharacteristic
262C4×C11#53611yescharacteristic
263Dic11—22no—
264Dic11—22no—
265Dic11—22no—
266Dic11—82no—
267C2×#41—228no—
268C2×#41—444no—
269C2×#41—444no—
270C22×Q8—21no—
271C22×D4—112no—
272C22×D4—222no—
273C22×D4—221no—
274C22×D4—221no—
275C23×C4—111no—
276C23×C4—111no—
277C23×C4—111no—
278C23×C4—222no—
279C2×M16—224no—
280C2×M16—444no—
281C22×C8—112no—
282C22×C8C22×D1112yes—
283C4⋊Q8—22no—
284C4⋊Q8C4×D1114yes—
285#127—114no—
286#127—222no—
287#124—228no—
288#121—118no—
289#121—224no—
290#121—228no—
291C4×D4—118no—
292C4×D4—224no—
293C4×D4—228no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—112no—
296C2×C4⋊C4C22×D1112yes—
297C2×C4⋊C4C22×D1112yes—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C22⋊C4—222no—
301C2×C42—21no—
302C2×C42—111no—
303C2×C42—111no—
304C2×C42—111no—
305C2×C42—114no—
306C2×C42—114no—
307C2×C42—221no—
308C2×C42C22×D1111yescharacteristic
309C4⋊C8—22no—
310C4⋊C8—224no—
311C4⋊C8—222no—
312#102—444no—
313#102—444no—
314#95—21no—
315#95—222no—
316#95—222no—
317#95—222no—
318#95—221no—
319C2×C11#231111yescharacteristic
320C2×C11C2×#41811yescharacteristic
321C2×C11#289611yescharacteristic
322C2×C11#325112yes—
323C2×C11#325112yes—
324D11—42no—
325D11—84no—
326C24—111no—
327C24—222no—
328#41—4432no—
329C2×Q8—24no—
330C2×Q8—42no—
331C2×Q8—42no—
332C2×D4—114no—
333C2×D4—228no—
334C2×D4—224no—
335C2×D4—224no—
336C2×D4—222no—
337C2×D4—224no—
338C2×D4—224no—
339C2×D4—444no—
340C2×D4—444no—
341C2×D4—444no—
342C2×D4—442no—
343C2×D4—442no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—111no—
347C22×C4—111no—
348C22×C4—111no—
349C22×C4—114no—
350C22×C4—112no—
351C22×C4—112no—
352C22×C4—114no—
353C22×C4—228no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—442no—
360C22×C4—444no—
361C22×C4—444no—
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4C23×D1111yescharacteristic
365M16—448no—
366C2×C8—22no—
367C2×C8—24no—
368C2×C8—222no—
369C2×C8—224no—
370C4⋊C4—24no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4C2×C4×D1114yes—
377C22⋊C4—228no—
378C22⋊C4—228no—
379C22⋊C4—444no—
380C42—42no—
381C42—114no—
382C42—114no—
383C42—112no—
384C42—112no—
385C42—442no—
386C42C2×C4×D1112yes—
387C42D4×D1112yes—
388C11#2189111yescharacteristic, complemented, Sylow
389C23—112no—
390C23—221no—
391C23—221no—
392C23—222no—
393C23—222no—
394C23—224no—
395C23—442no—
396C23—442no—
397C23—444no—
398C23—444no—
399C23C2×D4×D1111yescharacteristic
400Q8—48no—
401D4—228no—
402D4—448no—
403D4—4416no—
404D4—442no—
405D4—448no—
406D4—442no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—112no—
415C2×C4—112no—
416C2×C4—112no—
417C2×C4—221no—
418C2×C4—221no—
419C2×C4—222no—
420C2×C4—222no—
421C2×C4—222no—
422C2×C4—224no—
423C2×C4—228no—
424C2×C4—222no—
425C2×C4—444no—
426C2×C4—4416no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4C22⋊C4×D1112yes—
431C2×C4C22⋊C4×D1112yes—
432C2×C4#6696412yes—
433C2×C4#6696712yes—
434C2×C4C22×C4×D1111yescharacteristic
435C2×C4C2×D4×D1111yescharacteristic
436C2×C4#6704012yes—
437C2×C4#6704212yes—
438C8—42no—
439C8—442no—
440C22—222no—
441C22—222no—
442C22—222no—
443C22—442no—
444C22—442no—
445C22—444no—
446C22—444no—
447C22—444no—
448C22—884no—
449C22—884no—
450C22C2×C22⋊C4×D1111yescharacteristic
451C22#1062316012yes—
452C22C2×#6696411yescharacteristic
453C22C2×#6696711yescharacteristic
454C22#1062330812yes—
455C4—22no—
456C4—44no—
457C4—82no—
458C4—222no—
459C4—222no—
460C4—222no—
461C4—882no—
462C4#1062238314yes—
463C4#1062310512yes—
464C4#1062320511yescharacteristic
465C4#1062325511yescharacteristic
466C2—442no—
467C2—884no—
468C2#1307120711yescharacteristic
469C2C2×#1062238311yescharacteristic
470C2#1307713411yescharacteristic
471C2#1307998012yes—
472C2#1307998112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1988C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1988D11
hypocenterC11#21891
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1988

Complements

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

NH ≅ G/Ntype
2. C2×#10622450C2semidirect
3. #13071012C2semidirect
4. #13069569C2semidirect
5. #13069543C2semidirect
6. #13069542C2semidirect
7. #13069053C2semidirect
8. #13068625C2semidirect
9. C11×#1988C2semidirect
15. #10623256C4semidirect
157. #1988D11semidirect
388. C11#21891semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106224502
#130710122
#130695692
#130695432
#130695422
#130690532
#130686252
C11×#19882
#2189111