Finite Group Databasebeta

← #14756502

Subgroups — #14756502

Order 2816.

1338 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622828C211yesmaximal, characteristic
2C2×#10622828C211yesmaximal, characteristic
3C2×C4×#4318C211yesmaximal, characteristic, complemented
4#13071099C211yesmaximal, characteristic, complemented
5#13069316C214yesmaximal, complemented
6#13069302C214yesmaximal, complemented
7#13068335C211yesmaximal, characteristic, complemented
8#13068335C211yesmaximal, characteristic, complemented
9C2×C11×#390C211yesmaximal, characteristic
10C23×D4×C11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4—22no—
13C22×C42×C11C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C22×#4318C2211yescharacteristic
18C11×#390—22no—
19C11×#390C2212yes—
20C11×#390C2212yes—
21#10622828—24no—
22#10622828C418yescomplemented
23C2×#66896C2214yes—
24C2×#66896C2214yes—
25#10622823—22no—
26C4×Dic11⋊C4—22no—
27#10622541C2212yescomplemented
28#10622541C2212yescomplemented
29C4×#4318—24no—
30C2×#66867C2212yescomplemented
31C2×C4×C11⋊C8C2212yescomplemented
32#10622167C2214yescomplemented
33#10622167C2214yescomplemented
34C25×C11—21no—
35C22×D4×C11—22no—
36C22×D4×C11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11C2×C414yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—21no—
44C23×C4×C11D412yes—
45C23×C4×C11C2311yescharacteristic
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4—22no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—48no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11D412yes—
56C2×C42×C11C2311yescharacteristic
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—21no—
59C2×C22⋊Dic11—21no—
60#66979—22no—
61#66979—22no—
62#66979—22no—
63#66979C2×C414yes—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11—21no—
70C2×#4318—22no—
71C2×#4318—22no—
72C2×#4318—22no—
73C2×#4318—22no—
74C2×#4318C2×C414yes—
75C2×#4318D414yes—
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2312yes—
78#66896—28no—
79#66896C2×C4116yescomplemented
80C11⋊#95—22no—
81C11⋊#95—22no—
82#66867—24no—
83C4×C11⋊C8—24no—
84#21095—111nomaximal, Sylow
85C24×C11—24no—
86C24×C11—22no—
87C24×C11—44no—
88C24×C11—44no—
89C24×C11—42no—
90C24×C11—42no—
91C24×C11C2×D411yescharacteristic
92C2×D4×C11—28no—
93C2×D4×C11—28no—
94C2×D4×C11—24no—
95C2×D4×C11—22no—
96C2×D4×C11—22no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11—22no—
100C2×D4×C11—42no—
101C2×D4×C11—44no—
102C2×D4×C11—42no—
103C2×D4×C11—44no—
104C2×D4×C11C22×C414yes—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—44no—
110C22×C4×C11—42no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11#4112yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—22no—
122C22×Dic11—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—48no—
127C11×C22⋊C4—48no—
128C42×C11—24no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—21no—
133C22⋊Dic11—24no—
134C22⋊Dic11—42no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11C22×C414yes—
139Dic11⋊C4—44no—
140Dic11⋊C4—44no—
141C4×Dic11—24no—
142C4×Dic11—42no—
143#4318—28no—
144#4318—28no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8C22×C414yes—
150C2×C11⋊C8C2×D414yes—
151C2×#418—111no—
152C2×#418—111no—
153C2×C4×M16—111no—
154#2296—111no—
155C2×#390D1111yescharacteristic
156#1936—114no—
157#1934—114no—
158#1736—111no—
159#1736—111no—
160C23×C11—22no—
161C23×C11—22no—
162C23×C11—24no—
163C23×C11—416no—
164C23×C11—42no—
165C23×C11—42no—
166C23×C11—44no—
167C23×C11—44no—
168C23×C11—48no—
169C23×C11—84no—
170C23×C11—84no—
171C23×C11—88no—
172C23×C11C4×D412yes—
173C23×C11#12112yes—
174C23×C11#12412yes—
175C23×C11C22×D411yescharacteristic
176D4×C11—24no—
177D4×C11—24no—
178D4×C11—42no—
179D4×C11—42no—
180D4×C11—48no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—48no—
187C2×C4×C11—42no—
188C2×C4×C11—44no—
189C2×C4×C11—84no—
190C2×C4×C11#11714yes—
191C2×C4×C11C4×D414yes—
192C2×C4×C11C4×D412yes—
193C2×C4×C11#12112yes—
194C2×C4×C11#12314yes—
195C2×C4×C11#12412yes—
196C2×C4×C11#12614yes—
197C2×C4×C11AGL(1,ℤ/8)14yes—
198C2×C4×C11C23×C411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×Dic11—24no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C11⋊C8—24no—
211C11⋊C8—24no—
212C23×D4C2×D1111yescharacteristic
213C22×M16—111no—
214C22×M16—111no—
215C2×#117—111no—
216C2×#117—111no—
217C22×C4⋊C4C2×D1111yescharacteristic
218C22×C22⋊C4—22no—
219C22×C42C2×D1111yescharacteristic
220#418—118no—
221#418—224no—
222C2×#102—114no—
223C2×#102—114no—
224C4×M16—224no—
225C2×#97—112no—
226C2×C4×C8—112no—
227#390—22no—
228#390C2×D1112yes—
229#390C2×D1112yes—
230#389—112no—
231#389—112no—
232#385—222no—
233C4×C4⋊C4—222no—
234#340—114no—
235#340—114no—
236C22×C11—22no—
237C22×C11—22no—
238C22×C11—24no—
239C22×C11—24no—
240C22×C11—48no—
241C22×C11—44no—
242C22×C11—816no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—84no—
246C22×C11#38814yes—
247C22×C11C2×C4×D411yescharacteristic
248C22×C11C2×#12111yescharacteristic
249C22×C11C2×#12411yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)12yes—
251C22×C11#57512yes—
252C4×C11—24no—
253C4×C11—42no—
254C4×C11—82no—
255C4×C11#38814yes—
256C4×C11C2×#11711yescharacteristic
257C4×C11C2×C4×D411yescharacteristic
258C4×C11C2×#12311yescharacteristic
259C4×C11C2×#12611yescharacteristic
260Dic11—44no—
261Dic11—82no—
262C25—21no—
263C22×D4—22no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—22no—
267C22×D4—22no—
268C22×D4—21no—
269C22×D4C4×D1114yes—
270C22×D4C22×D1112yes—
271C23×C4—21no—
272C23×C4C22⋊D1112yes—
273C23×C4C22×D1111yescharacteristic
274C2×M16—114no—
275C2×M16—114no—
276C2×M16—222no—
277C2×M16—222no—
278C2×M16—222no—
279C2×M16—222no—
280C22×C8—112no—
281C22×C8—112no—
282#117—114no—
283#117—222no—
284#117—222no—
285#117—222no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—24no—
295C2×C22⋊C4—24no—
296C2×C22⋊C4—48no—
297C2×C22⋊C4—221no—
298C2×C22⋊C4—221no—
299C2×C42—22no—
300C2×C42—22no—
301C2×C42—221no—
302C2×C42—221no—
303C2×C42C22⋊D1112yes—
304C2×C42C22×D1111yescharacteristic
305C2×C42C22×D1111yescharacteristic
306#102—1116no—
307#102—228no—
308#97—224no—
309C4×C8—224no—
310#95—222no—
311#95—222no—
312C2×C11—24no—
313C2×C11—84no—
314C2×C11C2×#38811yescharacteristic
315C2×C11C4×AGL(1,ℤ/8)12yes—
316C2×C11#305512yes—
317C2×C11#313811yescharacteristic
318C2×C11#314011yescharacteristic
319C24—24no—
320C24—22no—
321C24—44no—
322C24—44no—
323C24—42no—
324C24—42no—
325C24C2×C22⋊D1111yescharacteristic
326C2×D4—28no—
327C2×D4—28no—
328C2×D4—24no—
329C2×D4—22no—
330C2×D4—22no—
331C2×D4—22no—
332C2×D4—22no—
333C2×D4—22no—
334C2×D4—44no—
335C2×D4—44no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4C2×C4×D1114yes—
339C22×C4—24no—
340C22×C4—24no—
341C22×C4—22no—
342C22×C4—42no—
343C22×C4—44no—
344C22×C4—42no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4C2×C4×D1112yes—
348C22×C4#433912yes—
349C22×C4D4×D1112yes—
350C22×C4#434112yes—
351C22×C4#434112yes—
352C22×C4#434112yes—
353C22×C4C2×C22⋊D1112yes—
354C22×C4C2×C22⋊D1112yes—
355C22×C4C2×C22⋊D1111yescharacteristic
356C22×C4C23×D1111yescharacteristic
357M16—228no—
358M16—228no—
359C2×C8—114no—
360C2×C8—114no—
361C2×C8—222no—
362C2×C8—222no—
363C2×C8—222no—
364C2×C8—222no—
365C4⋊C4—22no—
366C4⋊C4—22no—
367C4⋊C4—42no—
368C4⋊C4—114no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—222no—
372C4⋊C4—444no—
373C4⋊C4—444no—
374C22⋊C4—48no—
375C22⋊C4—48no—
376C22⋊C4—224no—
377C22⋊C4—442no—
378C42—24no—
379C42—21no—
380C42—21no—
381C42—21no—
382C42—21no—
383C42—224no—
384C42—442no—
385C11#2109511yescharacteristic, complemented, Sylow
386C23—22no—
387C23—22no—
388C23—24no—
389C23—416no—
390C23—44no—
391C23—48no—
392C23—42no—
393C23—42no—
394C23—44no—
395C23—84no—
396C23—88no—
397C23—84no—
398C23C4×C22⋊D1112yes—
399C23#6698912yes—
400C23#6699212yes—
401C23C22×C22⋊D1111yescharacteristic
402D4—24no—
403D4—24no—
404D4—42no—
405D4—42no—
406D4—48no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—48no—
413C2×C4—44no—
414C2×C4—42no—
415C2×C4—84no—
416C2×C4—224no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4#6693014yes—
423C2×C4#6693214yes—
424C2×C4(C22⋊D11)⋊C414yes—
425C2×C4#6693614yes—
426C2×C4C4×C22⋊D1112yes—
427C2×C4#6698514yes—
428C2×C4#6698912yes—
429C2×C4#6699212yes—
430C2×C4C22×C4×D1111yescharacteristic
431C2×C4C2×#433911yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×#434111yescharacteristic
434C2×C4C2×#434111yescharacteristic
435C2×C4C2×#434111yescharacteristic
436C8—224no—
437C8—224no—
438C22—24no—
439C22—22no—
440C22—24no—
441C22—22no—
442C22—48no—
443C22—44no—
444C22—816no—
445C22—82no—
446C22—84no—
447C22—82no—
448C22#1062255814yes—
449C22C2×C4×C22⋊D1111yescharacteristic
450C22C2×#6698512yes—
451C22C2×#6698911yescharacteristic
452C22C2×#6699211yescharacteristic
453C22#1062335312yes—
454C4—24no—
455C4—42no—
456C4—82no—
457C4—444no—
458C4—882no—
459C4#1062255814yes—
460C4C2×#6693011yescharacteristic
461C4C2×#6693211yescharacteristic
462C4C2×(C22⋊D11)⋊C411yescharacteristic
463C4C2×#6693611yescharacteristic
464C2—24no—
465C2—84no—
466C2C2×#1062255811yescharacteristic
467C2C4×#6698512yes—
468C2#1307823112yes—
469C2#1307899011yescharacteristic
470C2#1307900211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#390C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC2×#390D11
hypocenterC11#21095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×C4×#4318C2semidirect
4. #13071099C2semidirect
5. #13069316C2semidirect
6. #13069302C2semidirect
7. #13068335C2semidirect
8. #13068335C2semidirect
22. #10622828C4semidirect
27. #10622541C22semidirect
28. #10622541C22semidirect
30. C2×#66867C22semidirect
31. C2×C4×C11⋊C8C22semidirect
32. #10622167C22semidirect
33. #10622167C22semidirect
79. #66896C2×C4semidirect
385. C11#21095semidirect

Maximal subgroups

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

subgroupindex
C2×#106228282
C2×C4×#43182
#130710992
#130693162
#130693022
#130683352
C2×C11×#3902
#2109511