Finite Group Databasebeta

← #14763501

Subgroups — #14763501

Order 2816.

1114 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic
3D11×#382C211yesmaximal, characteristic
4#13069589C211yesmaximal, characteristic, complemented
5#13069588C211yesmaximal, characteristic, complemented
6#13069437C211yesmaximal, characteristic, complemented
7#13068920C214yesmaximal
8#13068629C214yesmaximal, complemented
9C11×#1960C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999C2212yes—
12C2×Q8×Dic11C2212yes—
13#10623259—24no—
14#10623259C418yescomplemented
15C2×#66950—21no—
16C2×#66945—21no—
17C2×C4⋊C4×D11C2212yes—
18C2×#66943—21no—
19C2×#66940—21no—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#103C2214yes—
23C2×C11×#97C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C2×#66899C2214yes—
26C2×(C2×D11)⋊C8C2212yes—
27C2×Dic11⋊C8C2212yes—
28#10622590C2212yes—
29#10622549C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31#10622318—24no—
32D11×#95—21no—
33D11×#95—21no—
34#10622263—21no—
35#10622263—21no—
36#10622189C2214yes—
37#10622167C2214yes—
38C22×Q8×C11C2312yes—
39C22×C4×D11—22no—
40C22×C4×D11D411yescharacteristic
41C22×C4×D11D411yescharacteristic
42C22×C4×D11C2311yescharacteristic
43C22×Dic22—21no—
44C22×C8×C11C2312yes—
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8C2×C414yescomplemented
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4C2312yes—
50C2×C42×C11C2311yescharacteristic
51#66999—24no—
52#66999C2×C418yes—
53Q8×Dic11—24no—
54Q8×Dic11C2×C418yescomplemented
55C2×(C2×D11)⋊C4—22no—
56C2×C4⋊Dic11—21no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11C2312yes—
59C2×C4⋊Dic11C2312yes—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11C2311yescharacteristic
66C22×C11⋊C8C2312yes—
67#66950—28no—
68#66945—28no—
69C4⋊C4×D11—44no—
70#66943—28no—
71#66940—28no—
72C42×D11C2×C414yes—
73C42×D11D414yes—
74#66922—22no—
75#66922C2×C414yescomplemented
76C11×#103—44no—
77C11×#97—22no—
78C11×#95—21no—
79C11×#95—21no—
80#66899—44no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85(C2×D11)⋊C8—24no—
86Dic11⋊C8—24no—
87#66867—22no—
88#21866—111nomaximal, Sylow
89C23×D11C2×D411yescharacteristic
90C2×Q8×C11—22no—
91C2×Q8×C11—24no—
92C2×Q8×C11—24no—
93C2×Q8×C11C22×C414yes—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11C2×D411yescharacteristic
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C2×C4×D11—24no—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—42no—
108C2×C4×D11—44no—
109C2×C4×D11—44no—
110C2×C4×D11—44no—
111C2×C4×D11C22⋊C414yes—
112C2×C4×D11C22⋊C414yes—
113C2×C4×D11C22×C412yes—
114C2×C4×D11C2×D412yes—
115C2×Dic22—24no—
116C2×Dic22—44no—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C11×C4⋊C4—24no—
121C11×C4⋊C4—24no—
122C11×C4⋊C4—24no—
123C42×C11C22×C412yes—
124C42×C11C2×D412yes—
125(C2×D11)⋊C4—28no—
126C4⋊Dic11—28no—
127C4⋊Dic11—24no—
128C4⋊Dic11—22no—
129C4⋊Dic11—24no—
130C4⋊Dic11C22×C414yes—
131Dic11⋊C4—28no—
132Dic11⋊C4—44no—
133C4×Dic11—28no—
134C4×Dic11C22⋊C414yes—
135C4×Dic11C22⋊C414yes—
136C4×Dic11C22×C412yes—
137C4×Dic11C2×D412yes—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×#533—111no—
142C2×#432—111no—
143C2×#382—111no—
144#1993—111no—
145#1993—111no—
146#1960—111no—
147#1960D1111yescharacteristic, complemented
148#1872—114no—
149#1805—114no—
150C23×C11C22×D411yescharacteristic
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—22no—
154C22×D11C2×C22⋊C412yes—
155C22×D11#13714yes—
156Q8×C11—28no—
157Q8×C11—44no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—24no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11C2×C22⋊C412yes—
167C2×C4×C11C2×C22⋊C412yes—
168C2×C4×C11C23×C411yescharacteristic
169C2×C4×C11C22×D411yescharacteristic
170C2×C4×C11H(5,𝔽2)12yes—
171C2×C4×C112−1+412yes—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—22no—
175C2×Dic11—22no—
176C2×Dic11—24no—
177C2×Dic11—44no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11C2×C22⋊C412yes—
182C2×Dic11C2×C22⋊C412yes—
183C2×Dic11C2×C22⋊C412yes—
184C4×D11—28no—
185C4×D11—24no—
186C4×D11—24no—
187C4×D11—44no—
188C4×D11—88no—
189Dic22—48no—
190C8×C11—42no—
191C11⋊C8—42no—
192#533—118no—
193#533—224no—
194C2×C4⋊Q8—111no—
195C2×C4⋊Q8C2×D1111yescharacteristic
196C2×#125—221no—
197C2×C22⋊Q8—112no—
198C2×C22⋊Q8—221no—
199C2×C4×Q8—112no—
200C2×C4×Q8—221no—
201C2×#117—221no—
202C22×C4⋊C4—112no—
203C22×C42—111no—
204#432—224no—
205C2×C4⋊C8—112no—
206C2×#103—114no—
207C2×#103C2×D1114yes—
208C2×C22⋊C8—112no—
209C2×#97—111no—
210C2×#97C2×D1111yescharacteristic
211#382—112no—
212#382—111no—
213#382—221no—
214#382—221no—
215#382C2×D1111yescharacteristic
216C2×#95—221no—
217C2×#95—221no—
218#340—114no—
219#340—114no—
220C22×C11C22×C22⋊C411yescharacteristic
221C22×C11#53511yescharacteristic
222C22×C11#53611yescharacteristic
223C22×C11C2×#13712yes—
224C22×C11#57512yes—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—24no—
228C2×D11—24no—
229C2×D11#41914yes—
230C4×C11—22no—
231C4×C11—22no—
232C4×C11—44no—
233C4×C11—82no—
234C4×C11#52012yes—
235C4×C11#53712yes—
236Dic11—22no—
237Dic11—22no—
238Dic11—22no—
239Dic11—44no—
240Dic11—82no—
241C22×Q8—221no—
242C22×Q8C22×D1112yes—
243C23×C4—111no—
244C23×C4—111no—
245C23×C4—111no—
246C23×C4—222no—
247C22×C8—112no—
248C22×C8C22×D1112yes—
249C4⋊Q8—22no—
250C4⋊Q8—114no—
251C4⋊Q8—222no—
252C4⋊Q8C4×D1114yescomplemented
253#125—228no—
254C22⋊Q8—118no—
255C22⋊Q8—228no—
256C22⋊Q8—224no—
257C4×Q8—118no—
258C4×Q8—228no—
259C4×Q8—224no—
260#117—228no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—112no—
264C2×C4⋊C4—112no—
265C2×C4⋊C4—222no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—221no—
268C2×C4⋊C4—222no—
269C2×C4⋊C4—444no—
270C2×C4⋊C4C22×D1112yes—
271C2×C22⋊C4—222no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—114no—
276C2×C42—114no—
277C2×C42—222no—
278C2×C42C22×D1111yescharacteristic
279C4⋊C8—224no—
280#103—44no—
281#103—444no—
282C22⋊C8—224no—
283#97—22no—
284#97—222no—
285#95—21no—
286#95—21no—
287#95—222no—
288#95—222no—
289#95—221no—
290#95—221no—
291C2×C11#231111yescharacteristic
292C2×C11C2×#41911yescharacteristic
293C2×C11#289611yescharacteristic
294C2×C11#321512yes—
295C2×C11#323612yes—
296D11—24no—
297C24—111no—
298C2×Q8—22no—
299C2×Q8—24no—
300C2×Q8—24no—
301C2×Q8—224no—
302C2×Q8—444no—
303C2×Q8C2×C4×D1114yes—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—114no—
310C22×C4—112no—
311C22×C4—112no—
312C22×C4—114no—
313C22×C4—224no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—222no—
318C22×C4—442no—
319C22×C4—444no—
320C22×C4—444no—
321C22×C4—444no—
322C22×C4D4×D1111yescharacteristic
323C22×C4D4×D1111yescharacteristic
324C22×C4C23×D1111yescharacteristic
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C4⋊C4—24no—
332C4⋊C4—24no—
333C4⋊C4—24no—
334C4⋊C4—114no—
335C4⋊C4—228no—
336C4⋊C4—228no—
337C4⋊C4—224no—
338C4⋊C4—222no—
339C4⋊C4—224no—
340C4⋊C4—444no—
341C22⋊C4—228no—
342C42—114no—
343C42—114no—
344C42—112no—
345C42—112no—
346C42—228no—
347C42C2×C4×D1112yes—
348C42D4×D1112yes—
349C11#2186611yescharacteristic, complemented, Sylow
350C23—112no—
351C23—114no—
352C23—221no—
353C23—222no—
354C23—221no—
355C23C2×D4×D1111yescharacteristic
356Q8—28no—
357Q8—44no—
358Q8—448no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—112no—
368C2×C4—112no—
369C2×C4—112no—
370C2×C4—228no—
371C2×C4—221no—
372C2×C4—222no—
373C2×C4—222no—
374C2×C4—221no—
375C2×C4—224no—
376C2×C4—224no—
377C2×C4—224no—
378C2×C4—444no—
379C2×C4—444no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—888no—
384C2×C4C22⋊C4×D1112yes—
385C2×C4C22⋊C4×D1112yes—
386C2×C4C22×C4×D1111yescharacteristic
387C2×C4C2×D4×D1111yescharacteristic
388C2×C4#6703712yes—
389C2×C4#6704312yes—
390C8—42no—
391C8—442no—
392C22—114no—
393C22—224no—
394C22—224no—
395C22—222no—
396C22—222no—
397C22C2×C22⋊C4×D1111yescharacteristic
398C22#1062320611yescharacteristic
399C22#1062324611yescharacteristic
400C22D11×#13712yes—
401C22#1062330812yes—
402C4—22no—
403C4—22no—
404C4—44no—
405C4—82no—
406C4—222no—
407C4—222no—
408C4—222no—
409C4—444no—
410C4—882no—
411C4#1062307712yes—
412C4#1062313912yes—
413C2—224no—
414C2#1307120611yescharacteristic
415C2D11×#41911yescharacteristic
416C2#1307713411yescharacteristic
417C2#1307961412yes—
418C2#1307981712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1960C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1960D11
hypocenterC11#21866
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
4. #13069589C2semidirect
5. #13069588C2semidirect
6. #13069437C2semidirect
8. #13068629C2semidirect
9. C11×#1960C2semidirect
14. #10623259C4semidirect
46. C11×C4⋊Q8C2×C4semidirect
54. Q8×Dic11C2×C4semidirect
75. #66922C2×C4semidirect
147. #1960D11semidirect
252. C4⋊Q8C4×D11semidirect
349. C11#21866semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106223182
D11×#3822
#130695892
#130695882
#130694372
#130689202
#130686292
C11×#19602
#2186611