Finite Group Databasebeta

← #14760468

Subgroups — #14760468

Order 2816.

954 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
1C2×#10622802C211yesmaximal, characteristic
2C2×Q16×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic
4#13071301C212yesmaximal
5#13069359C211yesmaximal, characteristic, complemented
6#13069295C212yesmaximal, complemented
7#13069036C212yesmaximal
8#13068646C211yesmaximal, characteristic
9#106×Dic11C211yesmaximal, characteristic, complemented
10#13068448C212yesmaximal, complemented
11C11×#1971C211yesmaximal, characteristic, complemented
12C22×C11×Q16C2211yescharacteristic
13C2×#66999C2212yes—
14C2×Q8×Dic11C2212yes—
15C22×#4313C2211yescharacteristic
16C22×C8×D11C2211yescharacteristic
17C2×#66925C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#103C2212yes—
20C2×C11×#97C2211yescharacteristic
21C11×#391C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2212yes—
24#10622802C418yescomplemented
25Q16×Dic11—24no—
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622600C2212yes—
31C4⋊C4×Dic11C2212yes—
32#10622541C2212yes—
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622321—24no—
35#10622283—22no—
36#10622282—22no—
37#10622265—22no—
38#10622260—22no—
39#10622189C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×Q8×C11C2312yes—
43C22×C4×D11C2311yescharacteristic
44C2×C11×Q16—22no—
45C2×C11×Q16—22no—
46C2×C11×Q16C2×C414yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66999—24no—
52#66999C2×C418yes—
53Q8×Dic11—24no—
54Q8×Dic11—24no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4D411yescharacteristic
58C2×(C2×D11)⋊C4D411yescharacteristic
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2312yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4D411yescharacteristic
65C2×Dic11⋊C4D411yescharacteristic
66C2×C4×Dic11—22no—
67C2×C4×Dic11—22no—
68C2×C4×Dic11C2311yescharacteristic
69C22×C11⋊C8C2311yescharacteristic
70C22×C11⋊C8C2311yescharacteristic
71C2×#4313—22no—
72C2×#4313—22no—
73C2×#4313C2×C414yes—
74C2×C8×D11—22no—
75C2×C8×D11—22no—
76C2×C8×D11—22no—
77#66925—22no—
78#66925—22no—
79C11×#106—22no—
80C11×#103—24no—
81C11×#97—22no—
82C11×#95—22no—
83C11×#95—22no—
84#66899—24no—
85#66899C2×C418yes—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66882—22no—
90#66881C2×C414yes—
91#66879—22no—
92C8×Dic11D414yes—
93C4×C11⋊C8—22no—
94#21537—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11C22×C414yes—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×C4×D11—21no—
113C2×C4×D11—21no—
114C2×C4×D11—21no—
115C2×C4×D11—21no—
116C2×C4×D11C22×C412yes—
117C2×C4×D11#4112yes—
118C11×Q16—28no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11C22×C412yes—
122C2×C8×C11C2×D412yes—
123C2×C8×C11#4112yes—
124C2×C8×C11#4112yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C42×C11—21no—
128C42×C11—21no—
129(C2×D11)⋊C4—22no—
130(C2×D11)⋊C4—22no—
131(C2×D11)⋊C4—28no—
132(C2×D11)⋊C4—82no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—22no—
136C4⋊Dic11—44no—
137C4⋊Dic11C22×C414yes—
138Dic11⋊C4—28no—
139Dic11⋊C4—22no—
140Dic11⋊C4—22no—
141Dic11⋊C4—82no—
142C4×Dic11—44no—
143C4×Dic11—82no—
144C4×Dic11C2×D412yes—
145C4×Dic11#4112yes—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8C22×C412yes—
151C2×C11⋊C8C2×D412yes—
152#4313—28no—
153C8×D11—28no—
154C2×#470—111no—
155C2×C4×Q16—111no—
156C2×#405—111no—
157#2323—112no—
158#1971D1111yescharacteristic, complemented
159#1944—111no—
160#1933—112no—
161#1892—112no—
162#1809—111no—
163C4×#106—111no—
164#1763—112no—
165C23×C11C22×D411yescharacteristic
166C22×D11—21no—
167C22×D11—21no—
168C22×D11—22no—
169C22×D11—22no—
170C22×D11C4×D412yes—
171Q8×C11—24no—
172Q8×C11—24no—
173Q8×C11—42no—
174Q8×C11—42no—
175C2×C4×C11—24no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11C23×C411yescharacteristic
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11C2×#4111yescharacteristic
191C2×Dic11—21no—
192C2×Dic11—21no—
193C2×Dic11—22no—
194C2×Dic11—22no—
195C2×Dic11—24no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11C4×D412yes—
202C2×Dic11#12112yes—
203C2×Dic11#12112yes—
204C4×D11—22no—
205C4×D11—22no—
206C4×D11—22no—
207C4×D11—22no—
208C8×C11—22no—
209C8×C11C4×D414yes—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C22×Q16C2×D1111yescharacteristic
213C22×M16—111no—
214C23×C8—111no—
215C2×C22⋊Q8—112no—
216C2×C4×Q8—112no—
217C2×#117—111no—
218#470—118no—
219C4×Q16—224no—
220C2×#107—111no—
221C2×#106—111no—
222C2×#106C2×D1111yescharacteristic
223C2×#103—112no—
224C2×#103—112no—
225C2×#103C2×D1112yes—
226#405—224no—
227C2×#97—111no—
228C2×#97C2×D1111yescharacteristic
229C2×C4×C8—111no—
230C2×C4×C8—111no—
231#391C2×D1112yes—
232#389—112no—
233#389—222no—
234#388—222no—
235#388—222no—
236#387—222no—
237#380—112no—
238C4×C4⋊C4—112no—
239#340—112no—
240#340—112no—
241#340—112no—
242C22×C11C2×C4×D411yescharacteristic
243C22×C11C2×#12111yescharacteristic
244C22×C11#53211yescharacteristic
245C22×C11#57712yes—
246C22×C11#57812yes—
247C2×D11—24no—
248C2×D11—22no—
249C2×D11—42no—
250C2×D11—41no—
251C2×D11—41no—
252C4×C11—41no—
253C4×C11—41no—
254C4×C11—44no—
255C4×C11—82no—
256C4×C11C2×C4×D411yescharacteristic
257C4×C11C4×#4111yescharacteristic
258C4×C11#52511yescharacteristic
259C4×C11#52911yescharacteristic
260Dic11—22no—
261Dic11—22no—
262Dic11—22no—
263Dic11—44no—
264Dic11—82no—
265C22×Q8C22×D1112yes—
266C23×C4—111no—
267C2×Q16—22no—
268C2×Q16—22no—
269C2×Q16C4×D1114yes—
270C2×M16—114no—
271C2×M16—222no—
272C2×M16—222no—
273C22×C8—111no—
274C22×C8—111no—
275C22×C8—222no—
276C22×C8—222no—
277C22×C8—222no—
278C22×C8C22×D1111yescharacteristic
279C22×C8C22×D1111yescharacteristic
280C22⋊Q8—118no—
281C22⋊Q8—224no—
282C4×Q8—224no—
283C4×Q8—224no—
284#117—222no—
285#117—222no—
286C2×C4⋊C4—112no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4—222no—
293C2×C4⋊C4C22×D1112yes—
294C2×C22⋊C4—111no—
295C2×C22⋊C4—111no—
296C2×C22⋊C4—222no—
297C2×C22⋊C4—222no—
298C2×C42—111no—
299C2×C42—222no—
300C2×C42—222no—
301C2×C42C22×D1111yescharacteristic
302#107—222no—
303#106—22no—
304#106—114no—
305#103—24no—
306#103—118no—
307#103—224no—
308#97—22no—
309#97—222no—
310C4×C8—114no—
311C4×C8—222no—
312#95—22no—
313#95—22no—
314#95—222no—
315#95—222no—
316#95—222no—
317C2×C11C4×#12111yescharacteristic
318C2×C11#294712yes—
319C2×C11#305911yescharacteristic
320C2×C11#306011yescharacteristic
321C2×C11#317812yes—
322D11—42no—
323C24—111no—
324C2×Q8—22no—
325C2×Q8—22no—
326C2×Q8—22no—
327C2×Q8—22no—
328C2×Q8—22no—
329C2×Q8C2×C4×D1114yes—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—111no—
333C22×C4—111no—
334C22×C4—111no—
335C22×C4—112no—
336C22×C4—112no—
337C22×C4—221no—
338C22×C4—221no—
339C22×C4—221no—
340C22×C4—221no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4D4×D1111yescharacteristic
344C22×C4D4×D1111yescharacteristic
345C22×C4C23×D1111yescharacteristic
346Q16—28no—
347M16—228no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—112no—
351C2×C8—112no—
352C2×C8—228no—
353C2×C8—221no—
354C2×C8—221no—
355C2×C8—221no—
356C2×C8—221no—
357C2×C8C2×C4×D1112yes—
358C2×C8D4×D1112yes—
359C2×C8#434112yes—
360C2×C8#434112yes—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—114no—
364C4⋊C4—222no—
365C4⋊C4—222no—
366C4⋊C4—228no—
367C4⋊C4—222no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—444no—
371C4⋊C4—882no—
372C22⋊C4—222no—
373C22⋊C4—222no—
374C22⋊C4—228no—
375C22⋊C4—882no—
376C42—21no—
377C42—21no—
378C42—112no—
379C42—112no—
380C42—444no—
381C42—882no—
382C11#2153711yescharacteristic, complemented, Sylow
383C23—112no—
384C23—221no—
385C23—222no—
386C23—222no—
387C23—221no—
388C23C2×D4×D1111yescharacteristic
389Q8—24no—
390Q8—24no—
391Q8—42no—
392Q8—42no—
393C2×C4—22no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—112no—
404C2×C4—112no—
405C2×C4—112no—
406C2×C4—221no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—221no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—224no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4C22×C4×D1111yescharacteristic
421C2×C4C2×D4×D1111yescharacteristic
422C2×C4C2×#434111yescharacteristic
423C2×C4C2×#434111yescharacteristic
424C2×C4#41×D1111yescharacteristic
425C2×C4#41×D1111yescharacteristic
426C8—22no—
427C8—222no—
428C8—222no—
429C8(C22⋊D11)⋊C414yes—
430C22—222no—
431C22—224no—
432C22—441no—
433C22—442no—
434C22—441no—
435C22C4×D4×D1111yescharacteristic
436C22D11×#12111yescharacteristic
437C22#1062324711yescharacteristic
438C22#1062330912yes—
439C22#1062331012yes—
440C4—41no—
441C4—44no—
442C4—41no—
443C4—82no—
444C4—222no—
445C4—222no—
446C4—222no—
447C4—444no—
448C4—882no—
449C4C2×(C22⋊D11)⋊C411yescharacteristic
450C4C4×#434111yescharacteristic
451C4#1062313711yescharacteristic
452C4#1062321111yescharacteristic
453C2—442no—
454C2#1307113211yescharacteristic
455C2#1307745812yes—
456C2#1307826911yescharacteristic
457C2#1307828011yescharacteristic
458C2#1307928112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1971C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1971D11
hypocenterC11#21537
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
2. C2×Q16×Dic11C2semidirect
5. #13069359C2semidirect
6. #13069295C2semidirect
9. #106×Dic11C2semidirect
10. #13068448C2semidirect
11. C11×#1971C2semidirect
24. #10622802C4semidirect
158. #1971D11semidirect
382. C11#21537semidirect

Maximal subgroups

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

subgroupindex
C2×#106228022
C2×Q16×Dic112
C2×#106223212
#130713012
#130693592
#130692952
#130690362
#130686462
#106×Dic112
#130684482
C11×#19712
#2153711