Finite Group Databasebeta

← #14763083

Subgroups — #14763083

Order 2816.

1366 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3#13071020C211yesmaximal, characteristic
4#13069540C211yesmaximal, characteristic, complemented
5#13069539C211yesmaximal, characteristic, complemented
6#13069538C211yesmaximal, characteristic, complemented
7#13069416C214yesmaximal, complemented
8#13068549C214yesmaximal
9C11×#1981C211yesmaximal, characteristic, complemented
10C22×Q8×D11C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997C2212yes—
13D11×C4⋊Q8—24no—
14D11×C4⋊Q8C418yescomplemented
15C2×C4⋊C4×D11—21no—
16C2×C4⋊C4×D11—21no—
17C2×#66941—21no—
18C2×#66941—21no—
19C2×#66925—21no—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#103C2214yes—
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66899C2214yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×#66880C2214yes—
28C2×C8×Dic11C2212yes—
29#10622600C2212yes—
30#10622589C2212yes—
31C2×#66874C2214yes—
32C4×C4⋊Dic11C2211yescharacteristic
33C4×Dic11⋊C4—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35#10622446—24no—
36#10622280—21no—
37#10622263—21no—
38C22×Q8×C11C2312yes—
39C2×Q8×D11—24no—
40C2×Q8×D11—44no—
41C2×Q8×D11—44no—
42C2×Q8×D11C2×C418yes—
43C22×C4×D11—22no—
44C22×C4×D11D411yescharacteristic
45C22×C4×D11D411yescharacteristic
46C22×C4×D11C2311yescharacteristic
47C22×Dic22—22no—
48C22×Dic22C2312yes—
49C22×C8×C11C2312yes—
50C11×C4⋊Q8—22no—
51C11×C4⋊Q8C2×C414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C42×C11—21no—
56C2×C42×C11C2311yescharacteristic
57#66997—24no—
58#66997C2×C418yes—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72C4⋊C4×D11—28no—
73C4⋊C4×D11—28no—
74#66941—28no—
75#66941—28no—
76#66925—44no—
77C42×D11C2×C414yes—
78C42×D11D414yes—
79#66922—22no—
80#66922C2×C414yes—
81C11×C4⋊C8—22no—
82C11×#103—44no—
83C11×#95—21no—
84#66899—44no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87(C2×D11)⋊C8—24no—
88#66880—44no—
89C8×Dic11—24no—
90#66874—44no—
91C4⋊(C11⋊C8)—22no—
92#21804—111nomaximal, Sylow
93C23×D11C2×D411yescharacteristic
94C2×Q8×C11—22no—
95C2×Q8×C11—24no—
96C2×Q8×C11—24no—
97C2×Q8×C11C22×C414yes—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2411yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11C2×D411yescharacteristic
106C22×Dic11C2×D411yescharacteristic
107C22×Dic11C2×D411yescharacteristic
108Q8×D11—416no—
109Q8×D11—48no—
110Q8×D11—48no—
111C2×C4×D11—24no—
112C2×C4×D11—28no—
113C2×C4×D11—22no—
114C2×C4×D11—22no—
115C2×C4×D11—48no—
116C2×C4×D11C22⋊C414yes—
117C2×C4×D11C22⋊C414yes—
118C2×C4×D11SD1614yes—
119C2×C4×D11Q1614yes—
120C2×C4×D11C22×C412yes—
121C2×C4×D11C2×D412yes—
122C2×Dic22—28no—
123C2×Dic22—22no—
124C2×Dic22—24no—
125C2×Dic22—24no—
126C2×Dic22—48no—
127C2×Dic22C22×C414yes—
128C2×C8×C11—22no—
129C2×C8×C11—24no—
130C11×C4⋊C4—24no—
131C11×C4⋊C4—24no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C42×C11—42no—
135C42×C11C22×C412yes—
136C42×C11C2×D412yes—
137(C2×D11)⋊C4—44no—
138C4⋊Dic11—24no—
139C4⋊Dic11—24no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142Dic11⋊C4—28no—
143Dic11⋊C4—28no—
144Dic11⋊C4—44no—
145Dic11⋊C4—44no—
146C4×Dic11—42no—
147C4×Dic11C22⋊C414yes—
148C4×Dic11C22⋊C414yes—
149C4×Dic11C22×C412yes—
150C4×Dic11C2×D412yes—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—24no—
153C22×C4⋊Q8—111no—
154C2×#431—111no—
155#2285—111no—
156#1981—111no—
157#1981—111no—
158#1981—111no—
159#1981D1111yescharacteristic, complemented
160#1956—114no—
161#1787—114no—
162C23×C11C22×D411yescharacteristic
163C22×D11—22no—
164C22×D11—22no—
165C22×D11C2×C22⋊C412yes—
166C22×D11C2×SD1612yes—
167C22×D11C2×Q1612yes—
168Q8×C11—28no—
169Q8×C11—42no—
170Q8×C11—42no—
171C2×C4×C11—22no—
172C2×C4×C11—24no—
173C2×C4×C11—44no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11C2×C22⋊C412yes—
178C2×C4×C11C2×C22⋊C412yes—
179C2×C4×C11C2×SD1612yes—
180C2×C4×C11C2×Q1612yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11H(5,𝔽2)12yes—
184C2×C4×C11H(5,𝔽2)12yes—
185C2×Dic11—22no—
186C2×Dic11—24no—
187C2×Dic11—44no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11C2×C22⋊C412yes—
192C2×Dic11C2×C22⋊C412yes—
193C2×Dic11C2×C22⋊C412yes—
194C2×Dic11C2×SD1612yes—
195C2×Dic11C2×Q1612yes—
196C2×Dic11#13714yes—
197C4×D11—24no—
198C4×D11—22no—
199C4×D11—22no—
200C4×D11—28no—
201C4×D11—416no—
202C4×D11#103116yescomplemented
203Dic22—28no—
204Dic22—416no—
205Dic22—42no—
206Dic22—42no—
207C8×C11—42no—
208C11⋊C8—42no—
209C23×Q8—112no—
210C2×C4⋊Q8—112no—
211C2×C4⋊Q8—118no—
212C2×C4⋊Q8—111no—
213C2×C4⋊Q8—221no—
214C2×C4⋊Q8—221no—
215C2×C4⋊Q8—224no—
216C2×C4⋊Q8C2×D1111yescharacteristic
217C2×#117—221no—
218C22×C4⋊C4—221no—
219C22×C4⋊C4—221no—
220C22×C42—111no—
221#431—224no—
222C2×C4⋊C8—111no—
223C2×C4⋊C8C2×D1111yescharacteristic
224C2×#103—114no—
225C2×#103—114no—
226C2×#103—114no—
227C2×#103C2×D1114yes—
228C2×C22⋊C8—112no—
229C2×C4×C8—112no—
230#384—112no—
231#382—221no—
232#380—112no—
233#380—221no—
234C4×C4⋊C4—111no—
235C4×C4⋊C4—221no—
236C4×C4⋊C4C2×D1111yescharacteristic
237C22×C11C22×C22⋊C411yescharacteristic
238C22×C11#53512yes—
239C22×C11C22×SD1611yescharacteristic
240C22×C11C22×Q1611yescharacteristic
241C22×C11C2×#13712yes—
242C2×D11—22no—
243C2×D11—22no—
244C2×D11—24no—
245C2×D11—24no—
246C2×D11C2×#10314yes—
247C4×C11—22no—
248C4×C11—44no—
249C4×C11—82no—
250C4×C11C2×#10314yes—
251C4×C11#51812yes—
252C4×C11#53511yescharacteristic
253C4×C11#53511yescharacteristic
254Dic11—22no—
255Dic11—44no—
256Dic11—82no—
257Dic11C2×#10314yes—
258Dic11#41914yes—
259C22×Q8—118no—
260C22×Q8—112no—
261C22×Q8—222no—
262C22×Q8—224no—
263C22×Q8—444no—
264C22×Q8—444no—
265C22×Q8C22×D1112yes—
266C23×C4—111no—
267C23×C4—111no—
268C23×C4—111no—
269C23×C4—222no—
270C22×C8—112no—
271C22×C8C22×D1112yes—
272C4⋊Q8—22no—
273C4⋊Q8—118no—
274C4⋊Q8—114no—
275C4⋊Q8—228no—
276C4⋊Q8—228no—
277C4⋊Q8—224no—
278C4⋊Q8—222no—
279C4⋊Q8C4×D1114yes—
280#117—444no—
281C2×C4⋊C4—21no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—228no—
285C2×C4⋊C4—228no—
286C2×C4⋊C4—222no—
287C2×C4⋊C4—222no—
288C2×C4⋊C4—221no—
289C2×C4⋊C4—221no—
290C2×C4⋊C4—222no—
291C2×C4⋊C4—222no—
292C2×C4⋊C4C22×D1112yes—
293C2×C22⋊C4—222no—
294C2×C42—21no—
295C2×C42—111no—
296C2×C42—111no—
297C2×C42—111no—
298C2×C42—114no—
299C2×C42—114no—
300C2×C42—221no—
301C2×C42C22×D1111yescharacteristic
302C4⋊C8—22no—
303C4⋊C8—222no—
304#103—44no—
305#103—444no—
306#103—444no—
307#103—444no—
308C22⋊C8—224no—
309C4×C8—224no—
310#95—21no—
311#95—222no—
312#95—221no—
313C2×C11#230911yescharacteristic
314C2×C11C22×#10311yescharacteristic
315C2×C11C2×#41911yescharacteristic
316C2×C11#320612yes—
317C2×C11#320912yes—
318D11—24no—
319C24—111no—
320C2×Q8—22no—
321C2×Q8—24no—
322C2×Q8—24no—
323C2×Q8—114no—
324C2×Q8—228no—
325C2×Q8—222no—
326C2×Q8—224no—
327C2×Q8—224no—
328C2×Q8—448no—
329C2×Q8—4416no—
330C2×Q8—448no—
331C2×Q8—448no—
332C2×Q8C2×C4×D1114yes—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—111no—
336C22×C4—111no—
337C22×C4—114no—
338C22×C4—114no—
339C22×C4—114no—
340C22×C4—111no—
341C22×C4—114no—
342C22×C4—112no—
343C22×C4—112no—
344C22×C4—224no—
345C22×C4—228no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—448no—
351C22×C4D4×D1111yescharacteristic
352C22×C4D4×D1111yescharacteristic
353C22×C4C23×D1111yescharacteristic
354C2×C8—22no—
355C2×C8—24no—
356C2×C8—222no—
357C2×C8—224no—
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—22no—
361C4⋊C4—22no—
362C4⋊C4—228no—
363C4⋊C4—228no—
364C4⋊C4—224no—
365C4⋊C4—224no—
366C4⋊C4—222no—
367C4⋊C4—222no—
368C4⋊C4—444no—
369C4⋊C4—444no—
370C22⋊C4—444no—
371C42—42no—
372C42—114no—
373C42—114no—
374C42—112no—
375C42—112no—
376C42—442no—
377C42C2×C4×D1112yes—
378C42D4×D1112yes—
379C11#2180411yescharacteristic, complemented, Sylow
380C23—112no—
381C23—112no—
382C23—112no—
383C23—222no—
384C23—222no—
385C23C2×D4×D1111yescharacteristic
386Q8—28no—
387Q8—42no—
388Q8—42no—
389Q8—228no—
390Q8—4416no—
391Q8—442no—
392Q8—442no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—112no—
400C2×C4—112no—
401C2×C4—112no—
402C2×C4—112no—
403C2×C4—114no—
404C2×C4—1116no—
405C2×C4—112no—
406C2×C4—228no—
407C2×C4—222no—
408C2×C4—222no—
409C2×C4—224no—
410C2×C4—222no—
411C2×C4—224no—
412C2×C4—4416no—
413C2×C4—444no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4C22⋊C4×D1112yes—
418C2×C4C22⋊C4×D1112yes—
419C2×C4SD16×D1112yes—
420C2×C4Q16×D1112yes—
421C2×C4C22×C4×D1111yescharacteristic
422C2×C4C2×D4×D1111yescharacteristic
423C2×C4#6703712yes—
424C2×C4#6704212yes—
425C8—42no—
426C8—442no—
427C22—114no—
428C22—224no—
429C22—222no—
430C22—222no—
431C22—224no—
432C22C2×C22⋊C4×D1111yescharacteristic
433C22#1062313812yes—
434C22C2×SD16×D1111yescharacteristic
435C22C2×Q16×D1111yescharacteristic
436C22D11×#13712yes—
437C4—22no—
438C4—44no—
439C4—82no—
440C4—114no—
441C4—114no—
442C4—222no—
443C4—444no—
444C4—882no—
445C4D11×#10314yes—
446C4#1062307612yes—
447C4#1062320511yescharacteristic
448C4#1062324611yescharacteristic
449C2—224no—
450C2#1307119511yescharacteristic
451C2C2×D11×#10311yescharacteristic
452C2D11×#41911yescharacteristic
453C2#1307954012yes—
454C2#1307956312yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1981C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1981D11
hypocenterC11#21804
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1981

Complements

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

NH ≅ G/Ntype
4. #13069540C2semidirect
5. #13069539C2semidirect
6. #13069538C2semidirect
7. #13069416C2semidirect
9. C11×#1981C2semidirect
14. D11×C4⋊Q8C4semidirect
159. #1981D11semidirect
202. C4×D11#103semidirect
379. C11#21804semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106224462
#130710202
#130695402
#130695392
#130695382
#130694162
#130685492
C11×#19812
#2180411