Finite Group Databasebeta

← #14760460

Subgroups — #14760460

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×#10622481C211yesmaximal, characteristic
2C2×#10622486C211yesmaximal, characteristic, complemented
3C2×#10622321C211yesmaximal, characteristic
4#13071296C212yesmaximal
5#13069487C211yesmaximal, characteristic, complemented
6#13069291C212yesmaximal, complemented
7#13069038C212yesmaximal
8#13068650C211yesmaximal, characteristic
9#106×Dic11C211yesmaximal, characteristic, complemented
10#13068445C212yesmaximal, complemented
11C11×#1944C211yesmaximal, characteristic, complemented
12C22×Dic44C2211yescharacteristic
13C22×#4313C2211yescharacteristic
14C22×C8×D11C2211yescharacteristic
15C2×#66950C2212yes—
16C2×#66940C2212yes—
17C2×#66925C2211yescharacteristic
18C2×C11×#107C2211yescharacteristic
19C2×C11×#106C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C11×#389C2212yes—
22C2×#66881C2211yescharacteristic
23C2×#66880C2212yes—
24C2×#66879C2211yescharacteristic
25C2×C8×Dic11C2211yescharacteristic
26#10622603—22no—
27#10622600C2212yes—
28C4⋊C4×Dic11C2212yes—
29#10622586—22no—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32#10622542C2212yes—
33C2×C4×C11⋊C8C2211yescharacteristic
34#10622486—24no—
35#10622481C418yescomplemented
36#10622321—24no—
37#10622282—22no—
38#10622267—22no—
39C11×#340C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C22×C4×D11C2311yescharacteristic
43C22×Dic22C2312yes—
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2311yescharacteristic
46C2×C11×C4⋊C4—22no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11C2311yescharacteristic
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×(C2×D11)⋊C4D411yescharacteristic
53C2×(C2×D11)⋊C4D411yescharacteristic
54C2×C4⋊Dic11—22no—
55C2×C4⋊Dic11C2312yes—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4D411yescharacteristic
58C2×Dic11⋊C4D411yescharacteristic
59C2×C4×Dic11—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11C2311yescharacteristic
62C22×C11⋊C8C2311yescharacteristic
63C22×C11⋊C8C2311yescharacteristic
64C2×Dic44—22no—
65C2×Dic44—22no—
66C2×Dic44C2×C414yes—
67C2×#4313—22no—
68C2×#4313—22no—
69C2×#4313C2×C414yes—
70C2×C8×D11—22no—
71C2×C8×D11—22no—
72C2×C8×D11—22no—
73#66950—24no—
74#66950C2×C418yes—
75#66940—24no—
76#66940—24no—
77#66925—22no—
78#66925—22no—
79C11×#107—22no—
80C11×#106C2×C414yes—
81C11×#97—22no—
82C11×#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66881—22no—
88#66880—24no—
89#66879—22no—
90C8×Dic11D414yes—
91#66874—24no—
92#66874C2×C418yes—
93C4×C11⋊C8—22no—
94#21537—111nomaximal, Sylow
95C23×D11C2×D411yescharacteristic
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—22no—
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C2×C4×D11—21no—
107C2×C4×D11—21no—
108C2×C4×D11—21no—
109C2×C4×D11—21no—
110C2×C4×D11C22×C412yes—
111C2×C4×D11#4112yes—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22C22×C414yes—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11C22×C412yes—
121C2×C8×C11C2×D412yes—
122C2×C8×C11#4112yes—
123C2×C8×C11#4112yes—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—82no—
128C11×C4⋊C4C22×C414yes—
129C42×C11—21no—
130C42×C11—21no—
131(C2×D11)⋊C4—22no—
132(C2×D11)⋊C4—22no—
133(C2×D11)⋊C4—28no—
134(C2×D11)⋊C4—82no—
135C4⋊Dic11—28no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138Dic11⋊C4—22no—
139Dic11⋊C4—22no—
140Dic11⋊C4—44no—
141C4×Dic11—44no—
142C4×Dic11—82no—
143C4×Dic11C2×D412yes—
144C4×Dic11#4112yes—
145C2×C11⋊C8—21no—
146C2×C11⋊C8—21no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8C22×C412yes—
150C2×C11⋊C8C2×D412yes—
151Dic44—28no—
152#4313—28no—
153C8×D11—28no—
154C2×#470—111no—
155C2×C4×Q16—111no—
156C2×#405—111no—
157#2323—112no—
158#1971—111no—
159#1944D1111yescharacteristic, complemented
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—
171C2×C4×C11—24no—
172C2×C4×C11—21no—
173C2×C4×C11—21no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C2×#4111yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185C2×C4×C11C2×#4111yescharacteristic
186C2×C4×C11C2×#4111yescharacteristic
187C2×Dic11—21no—
188C2×Dic11—21no—
189C2×Dic11—22no—
190C2×Dic11—22no—
191C2×Dic11—24no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11C4×D412yes—
198C2×Dic11#12112yes—
199C2×Dic11#12112yes—
200C4×D11—22no—
201C4×D11—22no—
202C4×D11—22no—
203C4×D11—22no—
204Dic22—24no—
205Dic22—24no—
206Dic22—42no—
207Dic22—42no—
208C8×C11—22no—
209C8×C11C4×D414yes—
210C11⋊C8—22no—
211C11⋊C8—22no—
212C22×Q16—111no—
213C22×M16—111no—
214C23×C8—111no—
215C2×C22⋊Q8—112no—
216C2×C4×Q8—112no—
217C2×#117—111no—
218#470—118no—
219C4×Q16—224no—
220C2×#107C2×D1111yescharacteristic
221C2×#106—111no—
222C2×#106C2×D1111yescharacteristic
223C2×#103—112no—
224C2×#103—112no—
225C2×#103—112no—
226#405—224no—
227C2×#97—111no—
228C2×#97C2×D1111yescharacteristic
229C2×C4×C8—111no—
230C2×C4×C8—111no—
231#391—112no—
232#389—222no—
233#389C2×D1112yes—
234#388—222no—
235#388—222no—
236#387—222no—
237#380—112no—
238C4×C4⋊C4—112no—
239#340—112no—
240#340—112no—
241#340C2×D1112yes—
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—44no—
253C4×C11—41no—
254C4×C11—41no—
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×Q8—112no—
266C23×C4—111no—
267C2×Q16—114no—
268C2×Q16—222no—
269C2×Q16—222no—
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—22no—
287C2×C4⋊C4—111no—
288C2×C4⋊C4—111no—
289C2×C4⋊C4—112no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1112yes—
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—22no—
303#106—222no—
304#106C4×D1114yes—
305#103—118no—
306#103—224no—
307#103—224no—
308#97—22no—
309#97—222no—
310C4×C8—114no—
311C4×C8—222no—
312#95—22no—
313#95—222no—
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—114no—
325C2×Q8—222no—
326C2×Q8—222no—
327C2×Q8—222no—
328C2×Q8—222no—
329C2×Q8—222no—
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—228no—
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#434312yes—
360C2×C8#434312yes—
361C4⋊C4—22no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—82no—
365C4⋊C4—222no—
366C4⋊C4—222no—
367C4⋊C4—228no—
368C4⋊C4—222no—
369C4⋊C4—222no—
370C4⋊C4—444no—
371C4⋊C4C2×C4×D1114yes—
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—224no—
390Q8—224no—
391Q8—442no—
392Q8—442no—
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×#434311yescharacteristic
423C2×C4C2×#434311yescharacteristic
424C2×C4#41×D1111yescharacteristic
425C2×C4#41×D1111yescharacteristic
426C8—22no—
427C8—222no—
428C8—222no—
429C8#6694614yes—
430C22—222no—
431C22—224no—
432C22—441no—
433C22—442no—
434C22—441no—
435C22C4×D4×D1111yescharacteristic
436C22D11×#12111yescharacteristic
437C22#1062325611yescharacteristic
438C22#1062330612yes—
439C22#1062331012yes—
440C4—41no—
441C4—44no—
442C4—41no—
443C4—82no—
444C4—222no—
445C4—222no—
446C4—222no—
447C4—444no—
448C4—882no—
449C4C2×#6694611yescharacteristic
450C4C4×#434311yescharacteristic
451C4#1062315811yescharacteristic
452C4#1062322211yescharacteristic
453C2—442no—
454C2#1307112411yescharacteristic
455C2#1307745612yes—
456C2#1307826911yescharacteristic
457C2#1307827611yescharacteristic
458C2#1307928912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#21537
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
2. C2×#10622486C2semidirect
5. #13069487C2semidirect
6. #13069291C2semidirect
9. #106×Dic11C2semidirect
10. #13068445C2semidirect
11. C11×#1944C2semidirect
35. #10622481C4semidirect
159. #1944D11semidirect
382. C11#21537semidirect

Maximal subgroups

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

subgroupindex
C2×#106224812
C2×#106224862
C2×#106223212
#130712962
#130694872
#130692912
#130690382
#130686502
#106×Dic112
#130684452
C11×#19442
#2153711