Finite Group Databasebeta

← #14770839

Subgroups — #14770839

Order 2816.

990 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66899C211yesmaximal, characteristic
2#13071487C211yesmaximal, characteristic
3Q8×C22⋊Dic11C211yesmaximal, characteristic
4#13069303C212yesmaximal, complemented
5#13069260C212yesmaximal, complemented
6#13068868C212yesmaximal, complemented
7#13068703C211yesmaximal, characteristic
8#13068643C211yesmaximal, characteristic
9#13068448C212yesmaximal, complemented
10#13068395C211yesmaximal, characteristic
11C11×#1787C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C2×Q8×Dic11C2212yes—
14C22×C4⋊Dic11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×#66930—21no—
17C2×C11×#103C2212yes—
18C2×C11×#103C2212yes—
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2211yescharacteristic
21#10622843—22no—
22#10622843C2212yes—
23C2×#66899C418yescomplemented
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28#10622825—21no—
29#10622825C2211yescharacteristic
30C4×C22⋊Dic11—21no—
31C4×C22⋊Dic11C2211yescharacteristic
32C2×#66879C2212yes—
33C4⋊C4×Dic11C2212yes—
34#10622586C2212yes—
35C2×#66871C2212yes—
36#10622556—21no—
37#10622267—22no—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42C22×Q8×C11—21no—
43C22×Q8×C11—22no—
44C22×Q8×C11—24no—
45C22×Q8×C11—42no—
46C22×Q8×C11C2×C414yes—
47C22×Q8×C11C2311yescharacteristic
48C22×Q8×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C22×C8×C11C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—21no—
55C2×C22⋊Dic11—21no—
56C2×C22⋊Dic11D411yescharacteristic
57C2×C22⋊Dic11D411yescharacteristic
58Q8×Dic11—24no—
59Q8×Dic11—42no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2×C414yes—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2311yescharacteristic
67C2×Dic11⋊C4—22no—
68C2×C4×Dic11—22no—
69C2×C4×Dic11—22no—
70C2×C4×Dic11C2312yes—
71C22×C11⋊C8—42no—
72C22×C11⋊C8C2×C414yes—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75#66930—44no—
76C11×#103—24no—
77C11×#103—42no—
78C11×C22⋊C8—22no—
79C11×#95—21no—
80#66899C2×C414yes—
81#66899C2×C414yes—
82#66899C2×C414yes—
83#66899C2×C414yes—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90#66879—42no—
91#66871—42no—
92#22563—111nomaximal, Sylow
93C24×C11C2×D411yescharacteristic
94C2×Q8×C11—24no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—22no—
98C2×Q8×C11—28no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—44no—
102C2×Q8×C11—44no—
103C2×Q8×C11—48no—
104C2×Q8×C11C22×C412yes—
105C2×Q8×C11C22×C412yes—
106C2×Q8×C11#4114yes—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—44no—
114C22×C4×C11C22×C412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C22×Dic11—24no—
119C22×Dic11—21no—
120C22×Dic11—21no—
121C22×Dic11—22no—
122C22×Dic11—42no—
123C22×Dic11—42no—
124C22×Dic11C2×D412yes—
125C22×Dic11C2×D412yes—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C2×C8×C11—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C22⋊C4—42no—
132C22⋊Dic11—22no—
133C22⋊Dic11—22no—
134C22⋊Dic11—42no—
135C4⋊Dic11—24no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—44no—
141C4⋊Dic11C22×C412yes—
142C4⋊Dic11C22×C412yes—
143Dic11⋊C4—44no—
144C4×Dic11—22no—
145C4×Dic11—22no—
146C4×Dic11—44no—
147C4×Dic11—44no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—44no—
151C2×C11⋊C8C22×C412yes—
152C2×C11⋊C8C22×C412yes—
153C22×#103—111no—
154#2344—111no—
155Q8×C22⋊C4—111no—
156#1935—112no—
157#1928—112no—
158#1863—112no—
159#1823—111no—
160#1808—111no—
161#1787D1111yescharacteristic
162#1763—112no—
163#1752—111no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11C4×D412yes—
167C23×C11AGL(1,ℤ/8)12yes—
168C23×C11#13712yes—
169C23×C11C22×D411yescharacteristic
170Q8×C11—22no—
171Q8×C11—24no—
172Q8×C11—22no—
173Q8×C11—22no—
174Q8×C11—48no—
175Q8×C11—42no—
176Q8×C11#11714yescomplemented
177C2×C4×C11—22no—
178C2×C4×C11—24no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—24no—
183C2×C4×C11—22no—
184C2×C4×C11—48no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11C4×D412yes—
190C2×C4×C11C23×C411yescharacteristic
191C2×C4×C11C2×#4112yes—
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)12yes—
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—48no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C8×C11—42no—
211C11⋊C8—22no—
212C11⋊C8—22no—
213C23×Q8C2×D1111yescharacteristic
214C23×C8—111no—
215C2×C4×Q8—112no—
216C2×#117—221no—
217C22×C4⋊C4—111no—
218C2×#107—112no—
219C2×#103—111no—
220C2×#103—111no—
221C2×#103—111no—
222C2×#103—111no—
223C2×#103—118no—
224C2×#103C2×D1112yes—
225C2×#103C2×D1112yes—
226C2×C22⋊C8C2×D1111yescharacteristic
227C2×#97—112no—
228#391—112no—
229#391—222no—
230#389—112no—
231#387—222no—
232#381—221no—
233#380—111no—
234#380—221no—
235#380C2×D1111yescharacteristic
236C4×C4⋊C4—112no—
237C4×C22⋊C4—111no—
238C4×C22⋊C4—221no—
239#340—112no—
240#340—112no—
241#340—112no—
242#336—112no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11—24no—
246C22×C11—24no—
247C22×C11#44014yes—
248C22×C11C2×C4×D411yescharacteristic
249C22×C11#54612yes—
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11#57812yes—
253C4×C11—22no—
254C4×C11—24no—
255C4×C11—42no—
256C4×C11—82no—
257C4×C11C2×#11711yescharacteristic
258C4×C11#51811yescharacteristic
259C4×C11#55112yes—
260Dic11—42no—
261Dic11—42no—
262Dic11—42no—
263Dic11—42no—
264Dic11—82no—
265C22×Q8—21no—
266C22×Q8—22no—
267C22×Q8—24no—
268C22×Q8—42no—
269C22×Q8C4×D1114yes—
270C22×Q8C22×D1111yescharacteristic
271C22×Q8C22×D1111yescharacteristic
272C23×C4—21no—
273C23×C4—221no—
274C23×C4C22×D1111yescharacteristic
275C22×C8—111no—
276C22×C8—111no—
277C22×C8—114no—
278C22×C8—442no—
279C22×C8C22×D1112yes—
280C4×Q8—224no—
281C4×Q8—442no—
282#117—444no—
283C2×C4⋊C4—114no—
284C2×C4⋊C4—111no—
285C2×C4⋊C4—111no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—221no—
288C2×C4⋊C4—222no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4C22×D1112yes—
292C2×C22⋊C4—21no—
293C2×C22⋊C4—111no—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—221no—
296C2×C42—112no—
297C2×C42—222no—
298C2×C42—222no—
299#107—442no—
300#103—24no—
301#103—42no—
302#103—114no—
303#103—114no—
304#103—114no—
305#103—114no—
306C22⋊C8—22no—
307#97—442no—
308#95—21no—
309#95—112no—
310#95—222no—
311#95—222no—
312#95—222no—
313#95—222no—
314#95—221no—
315C2×C11—24no—
316C2×C11#234211yescharacteristic
317C2×C11C2×#44011yescharacteristic
318C2×C11#295011yescharacteristic
319C2×C11#330812yes—
320C2×C11#331212yes—
321C24D4×D1111yescharacteristic
322C2×Q8—24no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—22no—
326C2×Q8—28no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8—44no—
330C2×Q8—44no—
331C2×Q8—48no—
332C2×Q8C2×C4×D1112yes—
333C2×Q8C2×C4×D1112yes—
334C2×Q8#434114yes—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—44no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—224no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4—222no—
348C22×C4—442no—
349C22×C4—442no—
350C22×C4C2×C4×D1112yes—
351C22×C4D4×D1111yescharacteristic
352C22×C4#434112yes—
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—22no—
356C2×C8—22no—
357C2×C8—112no—
358C2×C8—112no—
359C2×C8—222no—
360C2×C8—222no—
361C2×C8—444no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—112no—
365C4⋊C4—112no—
366C4⋊C4—224no—
367C4⋊C4—221no—
368C4⋊C4—221no—
369C4⋊C4—222no—
370C4⋊C4—222no—
371C4⋊C4—444no—
372C4⋊C4—444no—
373C22⋊C4—42no—
374C22⋊C4—222no—
375C22⋊C4—222no—
376C22⋊C4—442no—
377C42—222no—
378C42—222no—
379C42—444no—
380C42—444no—
381C11#2256311yescharacteristic, complemented, Sylow
382C23—22no—
383C23—22no—
384C23(C22⋊D11)⋊C412yes—
385C23#6696712yes—
386C23#6697112yes—
387C23C2×D4×D1111yescharacteristic
388Q8—22no—
389Q8—24no—
390Q8—22no—
391Q8—22no—
392Q8—48no—
393Q8—42no—
394Q8#6693014yescomplemented
395C2×C4—22no—
396C2×C4—24no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—24no—
401C2×C4—22no—
402C2×C4—48no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—222no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—441no—
416C2×C4—441no—
417C2×C4—441no—
418C2×C4—441no—
419C2×C4—448no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4(C22⋊D11)⋊C412yes—
424C2×C4C22×C4×D1111yescharacteristic
425C2×C4C2×#434112yes—
426C2×C4C2×#434111yescharacteristic
427C2×C4#6703712yes—
428C8—42no—
429C8—222no—
430C8—222no—
431C22—24no—
432C22—24no—
433C22—22no—
434C22—22no—
435C22#1062243014yes—
436C22C2×(C22⋊D11)⋊C411yescharacteristic
437C22#1062312212yes—
438C22C2×#6696711yescharacteristic
439C22C2×#6697111yescharacteristic
440C22#1062331012yes—
441C4—22no—
442C4—24no—
443C4—42no—
444C4—82no—
445C4—442no—
446C4—442no—
447C4—442no—
448C4—442no—
449C4—882no—
450C4C2×#6693011yescharacteristic
451C4#1062301711yescharacteristic
452C4#1062311812yes—
453C2—24no—
454C2#1307146711yescharacteristic
455C2C2×#1062243011yescharacteristic
456C2#1307748011yescharacteristic
457C2#1308061112yes—
458C2#1308067112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1787C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1787D11
hypocenterC11#22563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1787

Complements

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

NH ≅ G/Ntype
4. #13069303C2semidirect
5. #13069260C2semidirect
6. #13068868C2semidirect
9. #13068448C2semidirect
23. C2×#66899C4semidirect
176. Q8×C11#117semidirect
381. C11#22563semidirect
394. Q8#66930semidirect

Maximal subgroups

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

subgroupindex
C22×#668992
#130714872
Q8×C22⋊Dic112
#130693032
#130692602
#130688682
#130687032
#130686432
#130684482
#130683952
C11×#17872
#2256311