Finite Group Databasebeta

← #14763281

Subgroups — #14763281

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622446C211yesmaximal, characteristic
3#13071012C211yesmaximal, characteristic
4#13069579C214yesmaximal, complemented
5#13069568C211yesmaximal, characteristic, complemented
6#13069567C211yesmaximal, characteristic, complemented
7#13069565C211yesmaximal, characteristic, complemented
8#13068710C214yesmaximal
9C11×#1987C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13#10623259—24no—
14#10623259C418yescomplemented
15C2×#66950—21no—
16C2×#66945C2212yes—
17C2×#66943C2212yes—
18C2×#66940—21no—
19C2×C42×D11C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×(C2×D11)⋊C8C2212yes—
24C2×C8×Dic11C2212yes—
25#10622600C2212yes—
26#10622590C2212yes—
27C4×(C2×D11)⋊C4—21no—
28C4×C4⋊Dic11C2211yescharacteristic
29#10622545—21no—
30C2×C4⋊(C11⋊C8)C2211yescharacteristic
31#10622446—24no—
32#10622277—21no—
33#10622264—21no—
34C11×#340C2214yes—
35#10622189C2214yes—
36#10622167C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11D411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×Dic22—21no—
43C22×C8×C11C2312yes—
44C11×C4⋊Q8—22no—
45C11×C4⋊Q8C2×C414yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4C2312yes—
48C2×C11×C4⋊C4C2312yes—
49C2×C42×C11—21no—
50C2×C42×C11C2311yescharacteristic
51#66999—28no—
52Q8×Dic11—28no—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2312yes—
58C2×C4⋊Dic11C2312yes—
59C2×Dic11⋊C4—22no—
60C2×C4×Dic11—22no—
61C2×C4×Dic11—21no—
62C2×C4×Dic11D411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11C2311yescharacteristic
65C22×C11⋊C8C2312yes—
66#66950—28no—
67#66945—24no—
68#66945C2×C418yes—
69#66943—24no—
70#66943C2×C418yes—
71#66940—28no—
72C42×D11C2×C414yes—
73C42×D11D414yes—
74#66922—22no—
75#66922C2×C414yes—
76C11×C4⋊C8—22no—
77C11×#95—21no—
78C11⋊#95—21no—
79C11⋊#95—22no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82(C2×D11)⋊C8—24no—
83C8×Dic11—24no—
84C4⋊(C11⋊C8)—22no—
85#21837—111nomaximal, Sylow
86C23×D11C2×D411yescharacteristic
87C2×Q8×C11—24no—
88C2×Q8×C11—44no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C22×Dic11—22no—
95C22×Dic11—22no—
96C22×Dic11C2×D411yescharacteristic
97C22×Dic11C2×D411yescharacteristic
98C22×Dic11C2×D411yescharacteristic
99C2×C4×D11—22no—
100C2×C4×D11—22no—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—42no—
104C2×C4×D11C22⋊C414yes—
105C2×C4×D11C22⋊C414yes—
106C2×C4×D11C22×C412yes—
107C2×C4×D11C2×D412yes—
108C2×Dic22—24no—
109C2×Dic22—42no—
110C2×Dic22—42no—
111C2×C8×C11—22no—
112C2×C8×C11—24no—
113C11×C4⋊C4—24no—
114C11×C4⋊C4—22no—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4C22×C414yes—
118C42×C11—42no—
119C42×C11C22×C412yes—
120C42×C11C2×D412yes—
121(C2×D11)⋊C4—28no—
122(C2×D11)⋊C4—44no—
123C4⋊Dic11—28no—
124C4⋊Dic11—24no—
125C4⋊Dic11—22no—
126C4⋊Dic11—22no—
127C4⋊Dic11—22no—
128C4⋊Dic11C22×C414yes—
129Dic11⋊C4—28no—
130C4×Dic11—28no—
131C4×Dic11—42no—
132C4×Dic11C22⋊C414yes—
133C4×Dic11C22⋊C414yes—
134C4×Dic11C22×C412yes—
135C4×Dic11C2×D412yes—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—24no—
138C2×#533—111no—
139C2×#431—111no—
140#2283—111no—
141#1991—114no—
142#1988—111no—
143#1988—111no—
144#1987—111no—
145#1987D1111yescharacteristic, complemented
146#1825—114no—
147C23×C11C22×D411yescharacteristic
148C22×D11—22no—
149C22×D11—21no—
150C22×D11—21no—
151C22×D11—22no—
152C22×D11C2×C22⋊C412yes—
153Q8×C11—48no—
154C2×C4×C11—22no—
155C2×C4×C11—24no—
156C2×C4×C11—44no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—42no—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C2×C22⋊C412yes—
162C2×C4×C11#13512yes—
163C2×C4×C11#13512yes—
164C2×C4×C11C23×C411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C112−1+412yes—
167C2×C4×C112−1+412yes—
168C2×Dic11—22no—
169C2×Dic11—21no—
170C2×Dic11—21no—
171C2×Dic11—22no—
172C2×Dic11—24no—
173C2×Dic11—42no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11C2×C22⋊C412yes—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11C2×C22⋊C412yes—
181C4×D11—24no—
182C4×D11—22no—
183C4×D11—22no—
184C4×D11—28no—
185C4×D11—44no—
186Dic22—48no—
187C8×C11—42no—
188C11⋊C8—42no—
189#533—118no—
190#533—224no—
191C2×C4⋊Q8—111no—
192C2×C4⋊Q8C2×D1111yescharacteristic
193C2×#125—112no—
194C2×C22⋊Q8—221no—
195C2×C22⋊Q8—221no—
196C2×C4×Q8—221no—
197C2×C4×Q8—221no—
198C2×#117—112no—
199C22×C42—111no—
200#431—224no—
201C2×C4⋊C8—111no—
202C2×C4⋊C8C2×D1111yescharacteristic
203C2×C22⋊C8—112no—
204C2×C4×C8—112no—
205#383—221no—
206#382—112no—
207#381—221no—
208#380—112no—
209C4×C4⋊C4—111no—
210C4×C4⋊C4C2×D1111yescharacteristic
211C4×C22⋊C4—221no—
212#376—221no—
213#340—114no—
214#340—114no—
215#340—114no—
216#340C2×D1114yes—
217C22×C11C22×C22⋊C411yescharacteristic
218C22×C11#53612yes—
219C22×C11C2×#13511yescharacteristic
220C22×C11C2×#13511yescharacteristic
221C22×C11#57512yes—
222C2×D11—22no—
223C2×D11—22no—
224C2×D11—22no—
225C2×D11—42no—
226C2×D11—42no—
227C4×C11—22no—
228C4×C11—44no—
229C4×C11—82no—
230C4×C11#41614yes—
231C4×C11#51912yes—
232C4×C11#53611yescharacteristic
233C4×C11#53611yescharacteristic
234Dic11—22no—
235Dic11—22no—
236Dic11—22no—
237Dic11—44no—
238Dic11—82no—
239C22×Q8—21no—
240C22×Q8—221no—
241C23×C4—111no—
242C23×C4—111no—
243C23×C4—111no—
244C22×C8—112no—
245C22×C8C22×D1112yes—
246C4⋊Q8—22no—
247C4⋊Q8—114no—
248C4⋊Q8—222no—
249C4⋊Q8C4×D1114yes—
250#125—118no—
251#125—224no—
252C22⋊Q8—228no—
253C22⋊Q8—228no—
254C4×Q8—228no—
255C4×Q8—228no—
256#117—118no—
257#117—224no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—112no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4C22×D1112yes—
265C2×C4⋊C4C22×D1112yes—
266C2×C22⋊C4—222no—
267C2×C22⋊C4—222no—
268C2×C42—21no—
269C2×C42—111no—
270C2×C42—111no—
271C2×C42—111no—
272C2×C42—114no—
273C2×C42—114no—
274C2×C42—222no—
275C2×C42—221no—
276C2×C42C22×D1111yescharacteristic
277C4⋊C8—22no—
278C4⋊C8—222no—
279C22⋊C8—224no—
280C4×C8—224no—
281#95—21no—
282#95—222no—
283#95—222no—
284#95—222no—
285#95—221no—
286C2×C11#231011yescharacteristic
287C2×C11C2×#41611yescharacteristic
288C2×C11#289611yescharacteristic
289C2×C11#323312yes—
290C2×C11#323312yes—
291D11—42no—
292C24—111no—
293C2×Q8—24no—
294C2×Q8—44no—
295C2×Q8—224no—
296C2×Q8—442no—
297C2×Q8—442no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—114no—
304C22×C4—112no—
305C22×C4—112no—
306C22×C4—114no—
307C22×C4—222no—
308C22×C4—222no—
309C22×C4—222no—
310C22×C4—222no—
311C22×C4—222no—
312C22×C4—222no—
313C22×C4—442no—
314C22×C4D4×D1111yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4C23×D1111yescharacteristic
317C2×C8—22no—
318C2×C8—24no—
319C2×C8—222no—
320C2×C8—224no—
321C4⋊C4—24no—
322C4⋊C4—22no—
323C4⋊C4—22no—
324C4⋊C4—22no—
325C4⋊C4—114no—
326C4⋊C4—228no—
327C4⋊C4—228no—
328C4⋊C4—224no—
329C4⋊C4—222no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4C2×C4×D1114yes—
333C22⋊C4—228no—
334C22⋊C4—444no—
335C42—42no—
336C42—114no—
337C42—114no—
338C42—112no—
339C42—112no—
340C42—228no—
341C42—442no—
342C42C2×C4×D1112yes—
343C42D4×D1112yes—
344C11#2183711yescharacteristic, complemented, Sylow
345C23—112no—
346C23—221no—
347C23—221no—
348C23—222no—
349C23—222no—
350C23C2×D4×D1111yescharacteristic
351Q8—48no—
352Q8—448no—
353C2×C4—22no—
354C2×C4—24no—
355C2×C4—44no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—112no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—221no—
363C2×C4—221no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—224no—
368C2×C4—228no—
369C2×C4—222no—
370C2×C4—224no—
371C2×C4—444no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—442no—
375C2×C4—442no—
376C2×C4—442no—
377C2×C4C22⋊C4×D1112yes—
378C2×C4C22⋊C4×D1112yes—
379C2×C4#6696912yes—
380C2×C4#6697212yes—
381C2×C4C22×C4×D1111yescharacteristic
382C2×C4C2×D4×D1111yescharacteristic
383C2×C4#6704012yes—
384C2×C4#6704312yes—
385C8—42no—
386C8—442no—
387C22—222no—
388C22—222no—
389C22—222no—
390C22—442no—
391C22—442no—
392C22C2×C22⋊C4×D1111yescharacteristic
393C22#1062315912yes—
394C22C2×#6696911yescharacteristic
395C22C2×#6697211yescharacteristic
396C22#1062330412yes—
397C4—22no—
398C4—44no—
399C4—82no—
400C4—222no—
401C4—222no—
402C4—222no—
403C4—444no—
404C4—882no—
405C4#1062241714yes—
406C4#1062310312yes—
407C4#1062320611yescharacteristic
408C4#1062325511yescharacteristic
409C2—442no—
410C2#1307119911yescharacteristic
411C2C2×#1062241711yescharacteristic
412C2#1307713011yescharacteristic
413C2#1307979412yes—
414C2#1307980012yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1987C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1987D11
hypocenterC11#21837
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
4. #13069579C2semidirect
5. #13069568C2semidirect
6. #13069567C2semidirect
7. #13069565C2semidirect
9. C11×#1987C2semidirect
14. #10623259C4semidirect
145. #1987D11semidirect
344. C11#21837semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106224462
#130710122
#130695792
#130695682
#130695672
#130695652
#130687102
C11×#19872
#2183711