Finite Group Databasebeta

← #14652902

Subgroups — #14652902

Order 2816.

742 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
1#13076917C211yesmaximal, characteristic
2C2×#10622105C212yesmaximal, complemented
3C2×#10622108C212yesmaximal
4C4×C11⋊#95C211yesmaximal, characteristic, complemented
5C11×#1797C211yesmaximal, characteristic, complemented
6C22×C42×C11C2211yescharacteristic
7C2×#66983C2211yescharacteristic
8C2×#66977C2211yescharacteristic
9C22×C4×Dic11—21no—
10C2×#66928C411yescharacteristic, complemented
11C2×C11×C4⋊C8—21no—
12C2×C11×C22⋊C8C2212yes—
13#10622826—21no—
14#10622826—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2212yes—
17#10622553—21no—
18#10622553—21no—
19#10622552C411yescharacteristic, complemented
20#10622549C411yescharacteristic, complemented
21#10622542C411yescharacteristic, complemented
22C11×#336—21no—
23#10622108—24no—
24#10622105—24no—
25C23×C4×C11D411yescharacteristic
26C23×C4×C11D411yescharacteristic
27C23×C4×C11C2311yescharacteristic
28C22×C22⋊D11—21no—
29C23×Dic11—22no—
30C22×D44C2×C411yescharacteristic
31C22×Dic22C2×C411yescharacteristic
32C22×C8×C11—22no—
33C2×C42×C11—42no—
34C2×C42×C11C2×C411yescharacteristic
35C2×C42×C11C2×C411yescharacteristic
36C2×C42×C11D411yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×C22⋊Dic11—21no—
39#66983—22no—
40#66983—22no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×(C2×D11)⋊C4—21no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11C2×C411yescharacteristic
47C2×C4⋊Dic11C2×C411yescharacteristic
48#66977—22no—
49#66977—22no—
50C2×Dic11⋊C4—21no—
51C2×C4×Dic11—24no—
52C2×C4×Dic11—42no—
53C2×C4×Dic11—42no—
54#66928—42no—
55C11×C4⋊C8—42no—
56C11×C22⋊C8—22no—
57C11×C22⋊C8—22no—
58C11⋊#95—24no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—21no—
63C11⋊#95—22no—
64C11⋊#95D414yes—
65#9713—111nomaximal, Sylow
66C24×C11C2×D411yescharacteristic
67C23×D11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—22no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11C22⋊C411yescharacteristic
78C22×C4×C11C22⋊C411yescharacteristic
79C22×C4×C11C22⋊C411yescharacteristic
80C22×C4×C11C22⋊C411yescharacteristic
81C22×C4×C11C22×C411yescharacteristic
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D412yes—
84C22×C4×C11#4112yes—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C2×C22⋊D11—41no—
88C2×C22⋊D11—41no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—24no—
95C22×Dic11—42no—
96C22×Dic11—42no—
97C22×Dic11—42no—
98C22×Dic11—42no—
99C2×D44—22no—
100C2×D44—41no—
101C2×D44—41no—
102C2×Dic22—22no—
103C2×Dic22—41no—
104C2×Dic22—41no—
105C2×C8×C11—42no—
106C2×C8×C11—42no—
107C2×C8×C11—42no—
108C42×C11—22no—
109C42×C11—22no—
110C42×C11—41no—
111C42×C11—41no—
112C22⋊Dic11—42no—
113(C2×D11)⋊C4—42no—
114(C2×D11)⋊C4—42no—
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117(C2×D11)⋊C4—41no—
118(C2×D11)⋊C4—41no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—48no—
124#2850—111no—
125#1797D1111yescharacteristic, complemented
126C2×#328—112no—
127C2×#327—112no—
128C4×#95—111no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—21no—
133C23×C11C2×C22⋊C411yescharacteristic
134C23×C11#12112yes—
135C23×C11#13512yes—
136C23×C11AGL(1,ℤ/8)11yescharacteristic
137C23×C11#13711yescharacteristic
138C22×D11—41no—
139C22×D11—41no—
140C22×D11—41no—
141C22×D11—41no—
142C22×D11—41no—
143C22×D11—41no—
144C22×D11—41no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
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—21no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—44no—
163C2×C4×C11#9912yes—
164C2×C4×C11#10412yes—
165C2×C4×C11#10412yes—
166C2×C4×C11C4×D412yes—
167C2×C4×C11#12411yescharacteristic
168C2×C4×C11#12711yescharacteristic
169C22⋊D11—82no—
170C22⋊D11—82no—
171C2×Dic11—28no—
172C2×Dic11—44no—
173C2×Dic11—44no—
174C2×Dic11—44no—
175C2×Dic11—44no—
176C2×Dic11—44no—
177C2×Dic11—44no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—41no—
187D44—82no—
188Dic22—82no—
189C8×C11—82no—
190C2×#124—111no—
191C2×C22⋊Q8—111no—
192C2×#121—111no—
193C22×C42—221no—
194C22×C42C2×D1111yescharacteristic
195C2×C4⋊C8—21no—
196C2×C22⋊C8C2×D1112yes—
197#391—111no—
198#390—111no—
199#388—221no—
200#388—221no—
201#386—221no—
202#386—221no—
203#382—111no—
204C2×#95—112no—
205C2×#95—221no—
206#336—21no—
207#328—224no—
208#327—224no—
209C22×C11—22no—
210C22×C11—22no—
211C22×C11—22no—
212C22×C11—22no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11#39011yescharacteristic
218C22×C11C2×#9911yescharacteristic
219C22×C11#41011yescharacteristic
220C22×C11#41611yescharacteristic
221C22×C11#41711yescharacteristic
222C22×C11C2×#10411yescharacteristic
223C22×C11C2×#10411yescharacteristic
224C22×C11#46312yes—
225C22×C11#46412yes—
226C2×D11—81no—
227C2×D11—81no—
228C2×D11—81no—
229C2×D11—81no—
230C2×D11—81no—
231C2×D11—81no—
232C2×D11—81no—
233C4×C11—22no—
234C4×C11—21no—
235C4×C11—21no—
236C4×C11—22no—
237C4×C11—22no—
238C4×C11—22no—
239C4×C11—41no—
240Dic11—48no—
241Dic11—81no—
242Dic11—81no—
243Dic11—81no—
244C22×Q8—111no—
245C22×D4—111no—
246C22×D4—221no—
247C23×C4—222no—
248C23×C4D4411yescharacteristic
249C23×C4D4411yescharacteristic
250C23×C4C22×D1111yescharacteristic
251C22×C8—22no—
252#124—442no—
253C22⋊Q8—222no—
254C22⋊Q8—222no—
255#121—222no—
256#121—222no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C22⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C22⋊C4—221no—
264C2×C22⋊C4—221no—
265C2×C22⋊C4—221no—
266C2×C42—42no—
267C2×C42—224no—
268C2×C42—442no—
269C2×C42—442no—
270C2×C42C4×D1111yescharacteristic
271C2×C42C4×D1111yescharacteristic
272C2×C42C22⋊D1111yescharacteristic
273C2×C42C22⋊D1111yescharacteristic
274C4⋊C8—42no—
275C22⋊C8—22no—
276C22⋊C8—22no—
277#95—114no—
278#95—224no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—222no—
284C2×C11—22no—
285C2×C11—22no—
286C2×C11#150011yescharacteristic
287C2×C11#150111yescharacteristic
288C2×C11#150411yescharacteristic
289C2×C11#150911yescharacteristic
290C2×C11#196211yescharacteristic
291C2×C11#196411yescharacteristic
292C2×C11#198311yescharacteristic
293D11—161no—
294C24—221no—
295C24C2×D4411yescharacteristic
296C2×Q8—222no—
297C2×Q8—441no—
298C2×Q8—441no—
299C2×D4—222no—
300C2×D4—441no—
301C2×D4—441no—
302C2×D4—442no—
303C2×D4—442no—
304C2×D4—441no—
305C2×D4—441no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—224no—
316C22×C4—224no—
317C22×C4—224no—
318C22×C4—221no—
319C22×C4—221no—
320C22×C4—221no—
321C22×C4—442no—
322C22×C4—442no—
323C22×C4—442no—
324C22×C4—442no—
325C22×C4(C2×D11)⋊C411yescharacteristic
326C22×C4(C2×D11)⋊C411yescharacteristic
327C22×C4(C2×D11)⋊C411yescharacteristic
328C22×C4(C2×D11)⋊C411yescharacteristic
329C22×C4C2×C4×D1111yescharacteristic
330C22×C4D4×D1112yes—
331C22×C4#434312yes—
332C22×C4C2×C22⋊D1111yescharacteristic
333C2×C8—42no—
334C2×C8—42no—
335C2×C8—42no—
336C4⋊C4—222no—
337C4⋊C4—222no—
338C4⋊C4—441no—
339C4⋊C4—441no—
340C22⋊C4—442no—
341C22⋊C4—442no—
342C22⋊C4—442no—
343C22⋊C4—442no—
344C22⋊C4—442no—
345C22⋊C4—441no—
346C22⋊C4—441no—
347C42—22no—
348C42—22no—
349C42—41no—
350C42—41no—
351C42—448no—
352C11#971311yescharacteristic, complemented, Sylow
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—441no—
358C23—441no—
359C23—441no—
360C23—441no—
361C23—441no—
362C23—441no—
363C23—441no—
364C23#6694812yes—
365C23#6695712yes—
366C23#6696111yescharacteristic
367C23#6696211yescharacteristic
368C23C2×(C2×D11)⋊C411yescharacteristic
369Q8—882no—
370D4—882no—
371D4—882no—
372D4—882no—
373C2×C4—24no—
374C2×C4—24no—
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—21no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—44no—
391C2×C4—228no—
392C2×C4—444no—
393C2×C4—444no—
394C2×C4—444no—
395C2×C4—444no—
396C2×C4—444no—
397C2×C4—444no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4#6687012yes—
408C2×C4#6688912yes—
409C2×C4#6688912yes—
410C2×C4#6694612yes—
411C2×C4#6699311yescharacteristic
412C2×C4#6700011yescharacteristic
413C8—82no—
414C22—22no—
415C22—22no—
416C22—21no—
417C22—21no—
418C22—22no—
419C22—21no—
420C22—21no—
421C22—22no—
422C22—881no—
423C22—881no—
424C22—881no—
425C22—881no—
426C22—881no—
427C22—881no—
428C22—881no—
429C22#1062245712yes—
430C22#1062245812yes—
431C22C2×#6687011yescharacteristic
432C22#1062260111yescharacteristic
433C22#1062261911yescharacteristic
434C22#1062272611yescharacteristic
435C22#1062274611yescharacteristic
436C22C2×#6688911yescharacteristic
437C22C2×#6688911yescharacteristic
438C4—22no—
439C4—22no—
440C4—22no—
441C4—21no—
442C4—22no—
443C4—21no—
444C4—41no—
445C4—448no—
446C4—881no—
447C4—881no—
448C4—881no—
449C2—22no—
450C2—22no—
451C2—1761no—
452C2#1306710311yescharacteristic
453C2#1306710811yescharacteristic
454C2#1306712111yescharacteristic
455C2#1306714211yescharacteristic
456C2#1306944311yescharacteristic
457C2#1306945111yescharacteristic
458C2#1306954611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1797C2
socleC23×C11C2×C22⋊C4
prime radicalC2×#66983C22
cosocleC23×C4×C11C23
hypercenter#1797D11
hypocenterC11#9713
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
2. C2×#10622105C2semidirect
4. C4×C11⋊#95C2semidirect
5. C11×#1797C2semidirect
10. C2×#66928C4semidirect
19. #10622552C4semidirect
20. #10622549C4semidirect
21. #10622542C4semidirect
125. #1797D11semidirect
352. C11#9713semidirect

Maximal subgroups

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

subgroupindex
#130769172
C2×#106221052
C2×#106221082
C4×C11⋊#952
C11×#17972
#971311