Finite Group Databasebeta

← #14764059

Subgroups — #14764059

Order 2816.

1090 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622739C211yesmaximal, characteristic
2#13070998C212yesmaximal
3#13068818C212yesmaximal, complemented
4#13068816C212yesmaximal, complemented
5#13068814C212yesmaximal, complemented
6#13068812C212yesmaximal, complemented
7#13068649C211yesmaximal, characteristic, complemented
8#13068647C212yesmaximal, complemented
9C11×#1809C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×#4318C2211yescharacteristic
13C2×#66945C2212yes—
14C2×#66945C2212yes—
15C2×C11×#107C2211yescharacteristic, complemented
16C2×C11×#106C2211yescharacteristic, complemented
17C11×#380C2212yes—
18#10622825C2212yes—
19#10622739C418yescomplemented
20C2×(C2×D11)⋊C8C2212yes—
21C2×(C2×D11)⋊C8C2212yes—
22C2×#66882C2211yescharacteristic, complemented
23C2×#66881C2211yescharacteristic, complemented
24#10622600C2212yes—
25#10622600C2212yes—
26C2×#66872C2212yescomplemented
27C2×#66871C2212yescomplemented
28#10622568—22no—
29C22⋊C4×Dic11—22no—
30#10622279—22no—
31#10622277—22no—
32C11×#340C2212yescomplemented
33#10622189C2212yescomplemented
34#10622167C2212yescomplemented
35#10622167C2212yescomplemented
36C24×D11D411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11D411yescharacteristic
39C22×C4×D11—41no—
40C22×C4×D11—41no—
41C22×C4×D11—41no—
42C22×C4×D11—41no—
43C22×C4×D11C2×C414yes—
44C22×C4×D11D412yes—
45C22×C4×D11Q814yes—
46C22×C4×D11C2312yes—
47C2×C11×M16—41no—
48C2×C11×M16—41no—
49C2×C11×M16C2×C414yes—
50C22×C8×C11C2311yescharacteristic
51C22×C8×C11C2311yescharacteristic
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2312yes—
54C2×C11×C22⋊C4—22no—
55C2×C22⋊Dic11—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×C4×Dic11—22no—
63C2×C4×Dic11—22no—
64C2×#4318—41no—
65C2×#4318—41no—
66C2×#4318C2×C414yes—
67C22×C11⋊C8C2312yes—
68#66945—42no—
69#66945—42no—
70#66945—42no—
71#66945—42no—
72C11×#107—41no—
73C11×#106—41no—
74C11×#95—22no—
75C11⋊#95—22no—
76C11⋊#95—22no—
77C11⋊#95—22no—
78(C2×D11)⋊C8C2×C418yes—
79(C2×D11)⋊C8C2×C418yes—
80#66882—41no—
81#66881—41no—
82#66872—42no—
83#66871—42no—
84#21943—111nomaximal, Sylow
85C24×C11C2×D411yescharacteristic
86C23×D11—41no—
87C23×D11—41no—
88C23×D11—42no—
89C23×D11—42no—
90C23×D11C4⋊C414yes—
91C23×D11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×Q812yes—
101C22×C4×C11C2411yescharacteristic
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—41no—
105C22×Dic11—41no—
106C22×Dic11C4⋊C414yes—
107C22×Dic11C2×D412yes—
108C2×C4×D11—22no—
109C2×C4×D11—22no—
110C2×C4×D11—22no—
111C2×C4×D11—22no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—44no—
115C2×C4×D11—44no—
116C2×C4×D11—44no—
117C2×C4×D11—44no—
118C2×C4×D11C4⋊C418yes—
119C2×C4×D11C22×C414yes—
120C2×C4×D11C2×Q814yes—
121C11×M16—44no—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—21no—
125C2×C8×C11—21no—
126C2×C8×C11C22×C412yes—
127C2×C8×C11C22×C412yes—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C22⋊C4—44no—
133C22⋊Dic11—44no—
134(C2×D11)⋊C4—44no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—44no—
137(C2×D11)⋊C4—44no—
138C4⋊Dic11—22no—
139C4⋊Dic11—22no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4×Dic11—44no—
143C4×Dic11—44no—
144#4318—44no—
145C2×C11⋊C8—22no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8C22×C414yes—
148C2×#407—111no—
149#2280—112no—
150#1854—112no—
151#1854—112no—
152#1854—112no—
153#1854—112no—
154#1809—112no—
155#1809—111no—
156#1809D1111yescharacteristic, complemented
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—22no—
160C23×C11—22no—
161C23×C11C2×C4⋊C412yes—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—22no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—22no—
169C22×D11—44no—
170C22×D11—48no—
171C22×D11—44no—
172C22×D11—48no—
173C22×D11—44no—
174C22×D11C2×C4⋊C414yes—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11C2×C4⋊C412yes—
188C2×C4×C11C23×C411yescharacteristic
189C2×C4×C11C22×Q811yescharacteristic
190C2×C4×C11H(5,𝔽2)11yescharacteristic
191C2×C4×C11H(5,𝔽2)11yescharacteristic
192C2×C4×C11H(5,𝔽2)11yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—44no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11C2×C4⋊C414yes—
204C4×D11—24no—
205C4×D11—24no—
206C4×D11—24no—
207C4×D11—24no—
208C4×D11—48no—
209C8×C11—22no—
210C8×C11—22no—
211C11⋊C8—24no—
212C24×C4—111no—
213C22×M16—111no—
214C22×M16C2×D1111yescharacteristic
215C2×#117—112no—
216C2×#117—112no—
217C2×#107—111no—
218C2×#107—112no—
219C2×#107C2×D1111yescharacteristic, complemented
220C2×#106—111no—
221C2×#106—112no—
222C2×#106C2×D1111yescharacteristic, complemented
223#407—118no—
224C2×C22⋊C8—112no—
225C2×C22⋊C8—112no—
226#381—222no—
227#380—112no—
228#380—112no—
229#380—112no—
230#380C2×D1112yes—
231#379—222no—
232C4×C22⋊C4—222no—
233C4×C22⋊C4—222no—
234#340—112no—
235#340—112no—
236#340—112no—
237#340C2×D1112yescomplemented
238C22×C11—22no—
239C22×C11—24no—
240C22×C11—41no—
241C22×C11—42no—
242C22×C11—41no—
243C22×C11C22×C4⋊C411yescharacteristic
244C22×C11#53411yescharacteristic
245C22×C11#53411yescharacteristic
246C22×C11#57512yes—
247C22×C11#57512yes—
248C2×D11—24no—
249C2×D11—24no—
250C2×D11—24no—
251C2×D11—416no—
252C2×D11—42no—
253C2×D11—42no—
254C2×D11—42no—
255C2×D11—42no—
256C4×C11—22no—
257C4×C11—82no—
258C4×C11—82no—
259C4×C11#51811yescharacteristic
260C4×C11#51811yescharacteristic
261C4×C11#54311yescharacteristic
262C4×C11#54311yescharacteristic
263Dic11—24no—
264Dic11—82no—
265Dic11—82no—
266C25—111no—
267C23×C4—111no—
268C23×C4—112no—
269C23×C4—114no—
270C23×C4—112no—
271C23×C4—114no—
272C23×C4—441no—
273C23×C4—441no—
274C23×C4—441no—
275C23×C4—441no—
276C23×C4C22×D1111yescharacteristic
277C2×M16—41no—
278C2×M16—41no—
279C2×M16—114no—
280C2×M16—441no—
281C2×M16—441no—
282C2×M16C4×D1114yes—
283C22×C8—112no—
284C22×C8C22×D1111yescharacteristic
285C22×C8C22×D1111yescharacteristic
286#117—442no—
287#117—442no—
288#117—442no—
289#117—442no—
290C2×C4⋊C4—112no—
291C2×C4⋊C4—112no—
292C2×C4⋊C4C22×D1112yes—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—22no—
295C2×C22⋊C4—222no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C22⋊C4—222no—
299C2×C22⋊C4—222no—
300C2×C42—222no—
301C2×C42—222no—
302#107—41no—
303#107—442no—
304#107—441no—
305#106—41no—
306#106—442no—
307#106—441no—
308C22⋊C8—118no—
309C22⋊C8—118no—
310#95—22no—
311#95—222no—
312#95—222no—
313#95—222no—
314C2×C11—42no—
315C2×C11#231511yescharacteristic
316C2×C11#291112yes—
317C2×C11#319711yescharacteristic
318C2×C11#319712yes—
319C2×C11#319711yescharacteristic
320D11—44no—
321C24—112no—
322C24—114no—
323C24—441no—
324C24—441no—
325C24—442no—
326C24—442no—
327C24D4×D1111yescharacteristic
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—112no—
335C22×C4—114no—
336C22×C4—114no—
337C22×C4—114no—
338C22×C4—118no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
344C22×C4—222no—
345C22×C4—444no—
346C22×C4—444no—
347C22×C4—444no—
348C22×C4—444no—
349C22×C4—442no—
350C22×C4—442no—
351C22×C4—441no—
352C22×C4—441no—
353C22×C4C2×C4×D1112yes—
354C22×C4D4×D1111yescharacteristic
355C22×C4Q8×D1112yes—
356C22×C4C23×D1111yescharacteristic
357M16—44no—
358M16—444no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—21no—
363C2×C8—114no—
364C2×C8—222no—
365C2×C8—222no—
366C2×C8C2×C4×D1112yes—
367C2×C8C2×C4×D1112yes—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C22⋊C4—44no—
377C22⋊C4—444no—
378C22⋊C4—444no—
379C22⋊C4—444no—
380C22⋊C4—444no—
381C22⋊C4—444no—
382C42—444no—
383C42—444no—
384C11#2194311yescharacteristic, complemented, Sylow
385C23—22no—
386C23—22no—
387C23—21no—
388C23—21no—
389C23—114no—
390C23—222no—
391C23—222no—
392C23—222no—
393C23—222no—
394C23—222no—
395C23—222no—
396C23—444no—
397C23—448no—
398C23—444no—
399C23—448no—
400C23—444no—
401C23C4⋊C4×D1112yes—
402C23C2×D4×D1111yescharacteristic
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—114no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—224no—
419C2×C4—224no—
420C2×C4—224no—
421C2×C4—224no—
422C2×C4—448no—
423C2×C4—444no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4C4⋊C4×D1112yes—
431C2×C4C22×C4×D1111yescharacteristic
432C2×C4#6703711yescharacteristic
433C2×C4#6703711yescharacteristic
434C2×C4C2×Q8×D1111yescharacteristic
435C2×C4#6704211yescharacteristic
436C2×C4#6704211yescharacteristic
437C8—22no—
438C8—22no—
439C8—224no—
440C22—22no—
441C22—24no—
442C22—41no—
443C22—42no—
444C22—41no—
445C22—224no—
446C22—224no—
447C22—224no—
448C22—4416no—
449C22—442no—
450C22—442no—
451C22—442no—
452C22—442no—
453C22C2×C4⋊C4×D1111yescharacteristic
454C22#1062313611yescharacteristic
455C22#1062313611yescharacteristic
456C22#1062330412yes—
457C22#1062330812yes—
458C4—22no—
459C4—82no—
460C4—82no—
461C4—224no—
462C4—882no—
463C4—882no—
464C4#1062301711yescharacteristic
465C4#1062305211yescharacteristic
466C4#1062316511yescharacteristic
467C4#1062316511yescharacteristic
468C2—42no—
469C2—444no—
470C2#1307122911yescharacteristic
471C2#1307720312yes—
472C2#1307945211yescharacteristic
473C2#1307945412yes—
474C2#1307945911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC24×D11D4
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#21943
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
3. #13068818C2semidirect
4. #13068816C2semidirect
5. #13068814C2semidirect
6. #13068812C2semidirect
7. #13068649C2semidirect
8. #13068647C2semidirect
9. C11×#1809C2semidirect
15. C2×C11×#107C22semidirect
16. C2×C11×#106C22semidirect
19. #10622739C4semidirect
22. C2×#66882C22semidirect
23. C2×#66881C22semidirect
26. C2×#66872C22semidirect
27. C2×#66871C22semidirect
32. C11×#340C22semidirect
33. #10622189C22semidirect
34. #10622167C22semidirect
35. #10622167C22semidirect
156. #1809D11semidirect
219. C2×#107C2×D11semidirect
222. C2×#106C2×D11semidirect
237. #340C2×D11semidirect
384. C11#21943semidirect

Maximal subgroups

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

subgroupindex
C2×#106227392
#130709982
#130688182
#130688162
#130688142
#130688122
#130686492
#130686472
C11×#18092
#2194311