Finite Group Databasebeta

← #14763702

Subgroups — #14763702

Order 2816.

1162 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13071023C211yesmaximal, characteristic, complemented
3#13069571C212yesmaximal, complemented
4#13069546C212yesmaximal, complemented
5#13069054C212yesmaximal
6#13069049C212yesmaximal, complemented
7#13068622C212yesmaximal, complemented
8#13068617C212yesmaximal, complemented
9C2×C11×#423C211yesmaximal, characteristic, complemented
10C22×C11×M16C2212yes—
11C22×C42×C11C2211yescharacteristic
12C2×#66983C2211yescharacteristic
13C2×#66982—21no—
14C2×C4×C22⋊D11—21no—
15C2×#66979—21no—
16C2×#66977C2211yescharacteristic
17#10623010—24no—
18#10623010C418yescomplemented
19C2×#66929—21no—
20C2×#66928C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66925—21no—
23C2×#66923C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#423—24no—
26C2×C11×C4⋊C8C2212yes—
27C2×C11×C4⋊C8C2212yes—
28#10622825—21no—
29#10622825C2212yes—
30C2×#66885C2214yes—
31C2×#66880C2214yes—
32#10622549—21no—
33#10622548C2212yes—
34C4×C4⋊Dic11—21no—
35C4×C4⋊Dic11C2212yes—
36#10622189C2214yes—
37#10622189C2214yes—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11—21no—
42C22×D44C2311yescharacteristic
43C22×C4×D11—21no—
44C22×Dic22C2311yescharacteristic
45C2×C11×M16—24no—
46C2×C11×M16—44no—
47C22×C8×C11C2314yes—
48C2×C42×C11C2×C414yes—
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D414yes—
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—21no—
55C2×C22⋊Dic11—22no—
56#66983—22no—
57#66983C2×C414yes—
58#66982—28no—
59C4×C22⋊D11—28no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—21no—
64#66979—44no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2314yes—
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70#66977—22no—
71#66977C2×C414yes—
72C2×Dic11⋊C4—21no—
73C2×Dic11⋊C4—21no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×C4×Dic11—21no—
77C2×C4×Dic11—22no—
78#66929—28no—
79#66928—22no—
80#66928C2×C414yes—
81C4×D44—22no—
82C4×D44C2×C414yes—
83#66925—28no—
84#66923—22no—
85#66923C2×C414yes—
86C4×Dic22—22no—
87C4×Dic22C2×C414yes—
88C11×C4⋊C8—24no—
89C11×C4⋊C8—24no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92#66885—44no—
93#66880—44no—
94#21890—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C23×D11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—42no—
102C22×C4×C11C22⋊C414yes—
103C22×C4×C11C22⋊C414yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C2×C22⋊D11—24no—
113C2×C22⋊D11—44no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117C22×Dic11—24no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44C22×C412yes—
122C2×C4×D11—24no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×Dic22—21no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22C22×C412yes—
129C11×M16—48no—
130C2×C8×C11—24no—
131C2×C8×C11—24no—
132C2×C8×C11—24no—
133C42×C11C22⋊C414yes—
134C42×C11C22⋊C414yes—
135C42×C11C22×C412yes—
136C42×C11C22×C412yes—
137C42×C11C2×D412yes—
138C42×C11C2×D412yes—
139C22⋊Dic11—24no—
140C22⋊Dic11—44no—
141(C2×D11)⋊C4—24no—
142(C2×D11)⋊C4—24no—
143(C2×D11)⋊C4—24no—
144(C2×D11)⋊C4—24no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—24no—
148C4⋊Dic11—24no—
149C4⋊Dic11—44no—
150C4⋊Dic11—44no—
151C4⋊Dic11C22×C412yes—
152C4⋊Dic11C22×C412yes—
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156Dic11⋊C4—24no—
157C4×Dic11—24no—
158C4×Dic11—44no—
159C2×#529—111no—
160C2×#423D1111yescharacteristic, complemented
161#2285—111no—
162#1989—112no—
163#1983—112no—
164#1895—112no—
165#1894—112no—
166#1803—112no—
167#1802—112no—
168C23×C11—22no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—22no—
172C23×C11C2×C22⋊C412yes—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—42no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—42no—
179C2×C4×C11—22no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—24no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—28no—
188C2×C4×C11—44no—
189C2×C4×C11C2×C22⋊C412yes—
190C2×C4×C11C2×C22⋊C412yes—
191C2×C4×C11C2×C22⋊C412yes—
192C2×C4×C11C2×C22⋊C412yes—
193C2×C4×C11C2×C22⋊C412yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11#13712yes—
196C2×C4×C11C23×C411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11H(5,𝔽2)12yes—
199C2×C4×C112−1+412yes—
200C22⋊D11—48no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—44no—
209C2×Dic11—44no—
210C2×Dic11—44no—
211D44—24no—
212D44—41no—
213D44—41no—
214C4×D11—48no—
215Dic22—24no—
216Dic22—41no—
217Dic22—41no—
218C8×C11—44no—
219C22×M16C2×D1112yes—
220#529—118no—
221#529—224no—
222C2×#126—221no—
223C2×#125—111no—
224C2×#124—111no—
225C2×#123—221no—
226C2×C22⋊Q8—111no—
227C2×#121—111no—
228C2×C4×Q8—111no—
229C2×C4×D4—111no—
230C2×C4×D4—221no—
231C2×#117—221no—
232C2×#117—221no—
233C22×C42C2×D1111yescharacteristic
234#423—24no—
235C2×C4⋊C8C2×D1112yes—
236C2×C4⋊C8C2×D1112yes—
237C2×#103—114no—
238C2×#102—114no—
239#384—112no—
240#382—221no—
241#380—112no—
242#380—221no—
243C4×C4⋊C4—112no—
244C4×C4⋊C4—221no—
245#340—114no—
246#340—114no—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—42no—
251C22×C11—42no—
252C22×C11C22×C22⋊C411yescharacteristic
253C22×C11#53712yes—
254C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11#57512yes—
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—82no—
261C2×D11—82no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11—22no—
266C4×C11#41714yes—
267C4×C11#52012yes—
268C4×C11#53511yescharacteristic
269C4×C11#53611yescharacteristic
270Dic11—42no—
271Dic11—42no—
272Dic11—42no—
273Dic11—84no—
274C22×Q8—111no—
275C22×D4—111no—
276C22×D4—221no—
277C23×C4—221no—
278C23×C4D4411yescharacteristic
279C23×C4D4411yescharacteristic
280C23×C4C22×D1111yescharacteristic
281C2×M16—24no—
282C2×M16—44no—
283C22×C8C22×D1114yes—
284#126—228no—
285#125—114no—
286#125—222no—
287#124—114no—
288#124—222no—
289#123—228no—
290C22⋊Q8—114no—
291C22⋊Q8—222no—
292#121—114no—
293#121—222no—
294C4×Q8—114no—
295C4×Q8—222no—
296C4×D4—114no—
297C4×D4—228no—
298C4×D4—222no—
299#117—228no—
300#117—444no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—114no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C22⋊C4—222no—
316C2×C42—221no—
317C2×C42—222no—
318C2×C42C4×D1114yes—
319C2×C42D4411yescharacteristic
320C2×C42D4411yescharacteristic
321C2×C42C22⋊D1114yes—
322C2×C42C22×D1111yescharacteristic
323C2×C42C22×D1111yescharacteristic
324C4⋊C8—24no—
325C4⋊C8—24no—
326#103—444no—
327#102—444no—
328#95—222no—
329#95—222no—
330C2×C11—42no—
331C2×C11#231111yescharacteristic
332C2×C11C2×#41711yescharacteristic
333C2×C11#289611yescharacteristic
334C2×C11#325112yes—
335C2×C11#325212yes—
336D11—82no—
337C24—221no—
338C24C2×D4411yescharacteristic
339C2×Q8—112no—
340C2×Q8—221no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×D4—112no—
344C2×D4—224no—
345C2×D4—222no—
346C2×D4—222no—
347C2×D4—221no—
348C2×D4—444no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—42no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—224no—
358C22×C4—224no—
359C22×C4—442no—
360C22×C4—442no—
361C22×C4(C2×D11)⋊C414yes—
362C22×C4(C2×D11)⋊C414yes—
363C22×C4C2×C4×D1112yes—
364C22×C4C2×D4411yescharacteristic
365C22×C4C2×D4411yescharacteristic
366C22×C4C2×D4411yescharacteristic
367C22×C4C2×D4411yescharacteristic
368C22×C4C2×D4411yescharacteristic
369C22×C4C2×C22⋊D1112yes—
370C22×C4C23×D1111yescharacteristic
371M16—48no—
372C2×C8—24no—
373C2×C8—24no—
374C2×C8—24no—
375C4⋊C4—112no—
376C4⋊C4—112no—
377C4⋊C4—224no—
378C4⋊C4—224no—
379C4⋊C4—224no—
380C4⋊C4—224no—
381C4⋊C4—221no—
382C4⋊C4—221no—
383C4⋊C4—224no—
384C4⋊C4—224no—
385C4⋊C4—444no—
386C4⋊C4—444no—
387C22⋊C4—224no—
388C22⋊C4—224no—
389C22⋊C4—224no—
390C22⋊C4—224no—
391C22⋊C4—224no—
392C22⋊C4—444no—
393C42—224no—
394C42—444no—
395C42(C2×D11)⋊C414yes—
396C42(C2×D11)⋊C414yes—
397C42C2×C4×D1112yes—
398C42C2×C4×D1112yes—
399C42C2×C22⋊D1112yes—
400C42C2×C22⋊D1112yes—
401C11#2189011yescharacteristic, complemented, Sylow
402C23—21no—
403C23—21no—
404C23—22no—
405C23—22no—
406C23—222no—
407C23—441no—
408C23—441no—
409C23—442no—
410C23—442no—
411C23C2×(C2×D11)⋊C412yes—
412C23C22×D4411yescharacteristic
413Q8—224no—
414Q8—441no—
415Q8—441no—
416D4—224no—
417D4—448no—
418D4—441no—
419D4—441no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—28no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—44no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—448no—
438C2×C4—444no—
439C2×C4—444no—
440C2×C4—444no—
441C2×C4#6696112yes—
442C2×C4#6696212yes—
443C2×C4C2×(C2×D11)⋊C412yes—
444C2×C4C2×(C2×D11)⋊C412yes—
445C2×C4C2×(C2×D11)⋊C412yes—
446C2×C4C2×(C2×D11)⋊C412yes—
447C2×C4C2×(C2×D11)⋊C412yes—
448C2×C4C22×C4×D1111yescharacteristic
449C2×C4#6703712yes—
450C2×C4#6704012yes—
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—44no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—42no—
457C22—42no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22—882no—
462C22—882no—
463C22#1062304112yes—
464C22C2×#6696111yescharacteristic
465C22C2×#6696211yescharacteristic
466C22#1062327912yes—
467C22C22×(C2×D11)⋊C411yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—442no—
473C4—442no—
474C4—442no—
475C4—884no—
476C4#1062274614yes—
477C4#1062303512yes—
478C4#1062333611yescharacteristic
479C4#1062334711yescharacteristic
480C2—42no—
481C2—882no—
482C2#1307120911yescharacteristic
483C2C2×#1062274611yescharacteristic
484C2#1307713611yescharacteristic
485C2#1307997912yes—
486C2#1307999012yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#423C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
cosocleC22×C4×C11C24
hypercenterC2×#423D11
hypocenterC11#21890
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#423

Complements

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

NH ≅ G/Ntype
2. #13071023C2semidirect
3. #13069571C2semidirect
4. #13069546C2semidirect
6. #13069049C2semidirect
7. #13068622C2semidirect
8. #13068617C2semidirect
9. C2×C11×#423C2semidirect
18. #10623010C4semidirect
160. C2×#423D11semidirect
401. C11#21890semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130710232
#130695712
#130695462
#130690542
#130690492
#130686222
#130686172
C2×C11×#4232
#2189011