Finite Group Databasebeta

← #14644670

Subgroups — #14644670

Order 2816.

804 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
1C4×#66983C211yesmaximal, characteristic
2C2×#10622108C212yesmaximal
3C4×C11⋊#95C211yesmaximal, characteristic, complemented
4#13066496C212yesmaximal, complemented
5C11×#1749C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×C4×C22⋊D11—21no—
9C22×C4×Dic11—21no—
10C2×C4×D44C411yescharacteristic, complemented
11C2×C11×C22⋊C8C2212yes—
12C2×C11×#97—21no—
13#10622826—21no—
14#10622825C2211yescharacteristic
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17#10622553—21no—
18#10622552C411yescharacteristic, complemented
19C4×(C2×D11)⋊C4—21no—
20C4×C4⋊Dic11C411yescharacteristic, complemented
21#10622541C411yescharacteristic, complemented
22C11×#336—21no—
23#10622108C418yescomplemented
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C23×C4×C11C2311yescharacteristic
27C22×C22⋊D11—21no—
28C23×Dic11—22no—
29C22×D44C2×C411yescharacteristic
30C22×C4×D11—21no—
31C22×C8×C11—22no—
32C2×C42×C11—42no—
33C2×C42×C11C2×C411yescharacteristic
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C22⋊Dic11—21no—
38#66983—22no—
39#66983C2×C414yes—
40C4×C22⋊D11—44no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×C4⋊Dic11C2×C411yescharacteristic
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48C2×Dic11⋊C4—21no—
49C2×C4×Dic11—24no—
50C2×C4×Dic11—21no—
51C2×C4×Dic11—42no—
52C2×C4×Dic11—42no—
53C4×D44—42no—
54C11×C22⋊C8—22no—
55C11×C22⋊C8C2×C414yescomplemented
56C11×#97—42no—
57C11⋊#95—24no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—22no—
62C11⋊#95C2×C414yescomplemented
63#8218—111nomaximal, Sylow
64C24×C11C2×D411yescharacteristic
65C23×D11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11C22⋊C411yescharacteristic
76C22×C4×C11C22⋊C411yescharacteristic
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22×C411yescharacteristic
80C22×C4×C11C22×C412yes—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11#4112yes—
83C2×C22⋊D11—24no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—41no—
86C2×C22⋊D11—41no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—24no—
93C22×Dic11—42no—
94C22×Dic11—42no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C2×D44—21no—
98C2×D44—41no—
99C2×D44—41no—
100C2×D44C4212yescomplemented
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C2×C4×D11—42no—
104C2×C8×C11—24no—
105C2×C8×C11—42no—
106C2×C8×C11—42no—
107C42×C11—22no—
108C42×C11—22no—
109C42×C11—41no—
110C42×C11—41no—
111C22⋊Dic11—42no—
112(C2×D11)⋊C4—24no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116C4⋊Dic11—21no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11C4212yescomplemented
120Dic11⋊C4—42no—
121C4×Dic11—48no—
122C4×Dic11—42no—
123C4×#121—111no—
124#1749D1111yescharacteristic, complemented
125C2×#327—112no—
126C4×#95—111no—
127#1294—112no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11C2×C22⋊C411yescharacteristic
133C23×C11C4×D412yes—
134C23×C11AGL(1,ℤ/8)11yescharacteristic
135C23×C11AGL(1,ℤ/8)12yes—
136C23×C11#13711yescharacteristic
137C22×D11—22no—
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—21no—
154C2×C4×C11—21no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11—21no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—44no—
162C2×C4×C11#9912yes—
163C2×C4×C11#10412yes—
164C2×C4×C11#10412yes—
165C2×C4×C11C2×C4211yescharacteristic
166C2×C4×C11#11711yescharacteristic
167C2×C4×C11C4×D412yes—
168C22⋊D11—44no—
169C22⋊D11—44no—
170C2×Dic11—28no—
171C2×Dic11—22no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11—44no—
175C2×Dic11—44no—
176C2×Dic11—44no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—44no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186D44—42no—
187D44—42no—
188C4×D11—84no—
189C8×C11—44no—
190C2×#121—111no—
191C2×C4×D4—111no—
192C2×C4×D4—221no—
193C22×C42—221no—
194C22×C42C2×D1111yescharacteristic
195C2×C22⋊C8C2×D1112yes—
196C2×#97—21no—
197#390—111no—
198#389—111no—
199#388—221no—
200#386—221no—
201#380—111no—
202C4×C4⋊C4—111no—
203C4×C22⋊C4—221no—
204C2×#95—112no—
205C2×#95—221no—
206#336—21no—
207#327—118no—
208C22×C11—22no—
209C22×C11—22no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—22no—
213C22×C11—22no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11C4×C22⋊C411yescharacteristic
217C22×C11C2×#9911yescharacteristic
218C22×C11#41011yescharacteristic
219C22×C11#41711yescharacteristic
220C22×C11#41811yescharacteristic
221C22×C11C2×#10411yescharacteristic
222C22×C11C2×#10411yescharacteristic
223C22×C11#44012yes—
224C22×C11#44212yes—
225C2×D11—42no—
226C2×D11—42no—
227C2×D11—42no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C4×C11—21no—
233C4×C11—21no—
234C4×C11—22no—
235C4×C11—22no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—41no—
239Dic11—48no—
240Dic11—42no—
241Dic11—81no—
242Dic11—81no—
243C22×D4—111no—
244C22×D4—221no—
245C23×C4—222no—
246C23×C4—221no—
247C23×C4D4411yescharacteristic
248C23×C4D4411yescharacteristic
249C23×C4C22×D1111yescharacteristic
250C22×C8—22no—
251#121—114no—
252#121—222no—
253C4×D4—442no—
254C4×D4—444no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—221no—
259C2×C22⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C42—42no—
265C2×C42—224no—
266C2×C42—221no—
267C2×C42—442no—
268C2×C42—442no—
269C2×C42C4×D1111yescharacteristic
270C2×C42C4×D1111yescharacteristic
271C2×C42C22⋊D1111yescharacteristic
272C2×C42C22⋊D1111yescharacteristic
273C22⋊C8—22no—
274C22⋊C8C4×D1114yescomplemented
275#97—42no—
276#95—114no—
277#95—224no—
278#95—221no—
279#95—221no—
280#95—222no—
281#95—221no—
282C2×C11—22no—
283C2×C11—22no—
284C2×C11#150411yescharacteristic
285C2×C11#150511yescharacteristic
286C2×C11#150711yescharacteristic
287C2×C11#150911yescharacteristic
288C2×C11C4×#9911yescharacteristic
289C2×C11C4×#10411yescharacteristic
290C2×C11#176211yescharacteristic
291D11—82no—
292C24—221no—
293C24C2×D4411yescharacteristic
294C2×D4—112no—
295C2×D4—224no—
296C2×D4—221no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—442no—
300C2×D4—441no—
301C2×D4—441no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—224no—
312C22×C4—224no—
313C22×C4—224no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4—442no—
320C22×C4—442no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4(C2×D11)⋊C411yescharacteristic
325C22×C4(C2×D11)⋊C411yescharacteristic
326C22×C4(C2×D11)⋊C411yescharacteristic
327C22×C4(C2×D11)⋊C411yescharacteristic
328C22×C4C2×C4×D1111yescharacteristic
329C22×C4C2×C4×D1112yes—
330C22×C4#433912yes—
331C22×C4C2×C22⋊D1111yescharacteristic
332C2×C8—24no—
333C2×C8—42no—
334C2×C8—42no—
335C4⋊C4—112no—
336C4⋊C4—221no—
337C4⋊C4—441no—
338C4⋊C4—441no—
339C4⋊C4—442no—
340C22⋊C4—224no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C42—22no—
346C42—22no—
347C42—41no—
348C42—41no—
349C42—448no—
350C42—442no—
351C11#821811yescharacteristic, complemented, Sylow
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—222no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23C4×D4412yes—
364C23#6696112yes—
365C23#6696111yescharacteristic
366C23#6696211yescharacteristic
367C23C2×(C2×D11)⋊C411yescharacteristic
368D4—442no—
369D4—442no—
370D4—444no—
371D4—444no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—44no—
390C2×C4—228no—
391C2×C4—222no—
392C2×C4—444no—
393C2×C4—444no—
394C2×C4—444no—
395C2×C4—444no—
396C2×C4—444no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—444no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—884no—
407C2×C4#6687012yes—
408C2×C4#6688912yes—
409C2×C4#6688912yes—
410C2×C4C42×D1111yescharacteristic
411C2×C4#6692511yescharacteristic
412C2×C4C4×C22⋊D1112yes—
413C8—44no—
414C22—21no—
415C22—21no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—442no—
423C22—442no—
424C22—442no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22#1062232312yes—
430C22#1062232412yes—
431C22C4×(C2×D11)⋊C411yescharacteristic
432C22C2×#6687011yescharacteristic
433C22#1062261911yescharacteristic
434C22#1062274411yescharacteristic
435C22#1062274611yescharacteristic
436C22C2×#6688911yescharacteristic
437C22C2×#6688911yescharacteristic
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—21no—
443C4—22no—
444C4—41no—
445C4—448no—
446C4—442no—
447C4—881no—
448C4—881no—
449C2—22no—
450C2—22no—
451C2—882no—
452C2#1306712111yescharacteristic
453C2#1306712511yescharacteristic
454C2#1306713311yescharacteristic
455C2#1306714211yescharacteristic
456C2C4×#6687011yescharacteristic
457C2C4×#6688911yescharacteristic
458C2#1306844211yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC2×C4×C11C2×C42
FrattiniC23×C4C22×D11
FittingC11×#1749C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1749D11
hypocenterC11#8218
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. C4×C11⋊#95C2semidirect
4. #13066496C2semidirect
5. C11×#1749C2semidirect
10. C2×C4×D44C4semidirect
18. #10622552C4semidirect
20. C4×C4⋊Dic11C4semidirect
21. #10622541C4semidirect
23. #10622108C4semidirect
55. C11×C22⋊C8C2×C4semidirect
62. C11⋊#95C2×C4semidirect
100. C2×D44C42semidirect
119. C4⋊Dic11C42semidirect
124. #1749D11semidirect
274. C22⋊C8C4×D11semidirect
351. C11#8218semidirect

Maximal subgroups

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

subgroupindex
C4×#669832
C2×#106221082
C4×C11⋊#952
#130664962
C11×#17492
#821811