Finite Group Databasebeta

← #14763534

Subgroups — #14763534

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic
3#13071022C211yesmaximal, characteristic
4#13069590C211yesmaximal, characteristic, complemented
5#13069436C211yesmaximal, characteristic, complemented
6#13069435C211yesmaximal, characteristic, complemented
7#13068927C214yesmaximal
8#13068620C214yesmaximal, complemented
9C11×#1993C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—21no—
12C2×Q8×Dic11—21no—
13#10623259—24no—
14#10623259C418yescomplemented
15C2×#66950C2212yes—
16C2×#66945—21no—
17C2×#66945C2212yes—
18C2×#66943—21no—
19C2×#66940C2212yes—
20C2×C42×D11C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66880C2214yes—
26C2×Dic11⋊C8C2212yes—
27#10622589C2212yes—
28C2×#66874C2214yes—
29#10622549C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31#10622318—24no—
32#10622280—21no—
33#10622280—21no—
34#10622262—21no—
35#10622262—21no—
36C11×#340C2214yes—
37#10622167C2214yes—
38C22×Q8×C11—21no—
39C22×C4×D11D411yescharacteristic
40C22×C4×D11D411yescharacteristic
41C22×C4×D11C2311yescharacteristic
42C22×Dic22C2312yes—
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×C11C2311yescharacteristic
50#66999—28no—
51Q8×Dic11—28no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—22no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—22no—
57C2×C4⋊Dic11C2312yes—
58C2×Dic11⋊C4—22no—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×C4×Dic11—22no—
62C2×C4×Dic11—22no—
63C2×C4×Dic11D411yescharacteristic
64C2×C4×Dic11D411yescharacteristic
65C2×C4×Dic11C2311yescharacteristic
66C22×C11⋊C8C2312yes—
67#66950—24no—
68#66950C2×C418yes—
69#66945—28no—
70#66945—44no—
71#66943—28no—
72#66940—24no—
73#66940C2×C418yes—
74C42×D11C2×C414yes—
75C42×D11D414yes—
76#66922—22no—
77#66922C2×C414yes—
78C11×#97—22no—
79C11×#95—21no—
80C11×#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83(C2×D11)⋊C8—24no—
84#66880—44no—
85Dic11⋊C8—24no—
86#66874—44no—
87#66867—22no—
88#21870—111nomaximal, Sylow
89C23×D11C2×D411yescharacteristic
90C2×Q8×C11—24no—
91C2×Q8×C11—44no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2411yescharacteristic
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11C2×D411yescharacteristic
100C22×Dic11C2×D411yescharacteristic
101C22×Dic11C2×D411yescharacteristic
102C2×C4×D11—24no—
103C2×C4×D11—22no—
104C2×C4×D11—22no—
105C2×C4×D11—42no—
106C2×C4×D11C22⋊C414yes—
107C2×C4×D11C22⋊C414yes—
108C2×C4×D11C22×C412yes—
109C2×C4×D11C2×D412yes—
110C2×Dic22—22no—
111C2×Dic22—24no—
112C2×Dic22—24no—
113C2×Dic22C22×C414yes—
114C2×C8×C11—22no—
115C2×C8×C11—22no—
116C2×C8×C11—22no—
117C11×C4⋊C4—24no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—24no—
120C11×C4⋊C4C22×C414yes—
121C42×C11C22×C412yes—
122C42×C11C2×D412yes—
123(C2×D11)⋊C4—28no—
124(C2×D11)⋊C4—44no—
125C4⋊Dic11—28no—
126C4⋊Dic11—24no—
127C4⋊Dic11—24no—
128C4⋊Dic11—24no—
129Dic11⋊C4—28no—
130Dic11⋊C4—44no—
131Dic11⋊C4—44no—
132C4×Dic11—28no—
133C4×Dic11—44no—
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—
143#2285—111no—
144#1993—111no—
145#1993D1111yescharacteristic, complemented
146#1960—111no—
147#1960—111no—
148#1873—114no—
149#1803—114no—
150C23×C11C22×D411yescharacteristic
151C22×D11—21no—
152C22×D11—21no—
153C22×D11—22no—
154C22×D11—22no—
155C22×D11C2×C22⋊C412yes—
156Q8×C11—48no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—24no—
160C2×C4×C11—44no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11C2×C22⋊C412yes—
165C2×C4×C11C2×C22⋊C412yes—
166C2×C4×C11C23×C411yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11H(5,𝔽2)12yes—
169C2×C4×C112−1+412yes—
170C2×Dic11—21no—
171C2×Dic11—21no—
172C2×Dic11—22no—
173C2×Dic11—24no—
174C2×Dic11—42no—
175C2×Dic11—42no—
176C2×Dic11—42no—
177C2×Dic11—42no—
178C2×Dic11—42no—
179C2×Dic11C2×C22⋊C412yes—
180C2×Dic11C2×C22⋊C412yes—
181C2×Dic11C2×C22⋊C412yes—
182C2×Dic11#13714yes—
183C4×D11—24no—
184C4×D11—24no—
185C4×D11—28no—
186C4×D11—44no—
187Dic22—28no—
188Dic22—44no—
189C8×C11—42no—
190C11⋊C8—42no—
191#533—118no—
192#533—224no—
193C2×C4⋊Q8—111no—
194C2×C4⋊Q8C2×D1111yescharacteristic
195C2×#125—221no—
196C2×C22⋊Q8—112no—
197C2×C22⋊Q8—221no—
198C2×C4×Q8—112no—
199C2×C4×Q8—221no—
200C2×#117—112no—
201C2×#117—221no—
202C22×C42—111no—
203#432—224no—
204C2×C4⋊C8—112no—
205C2×#103—114no—
206C2×#103—114no—
207C2×C22⋊C8—112no—
208C2×#97—111no—
209C2×#97C2×D1111yescharacteristic
210#384—112no—
211#382—111no—
212#382C2×D1111yescharacteristic
213#380—221no—
214#380—221no—
215C4×C4⋊C4—221no—
216C4×C4⋊C4—221no—
217#340—114no—
218#340C2×D1114yes—
219C22×C11C22×C22⋊C411yescharacteristic
220C22×C11#53511yescharacteristic
221C22×C11#53611yescharacteristic
222C22×C11C2×#13712yes—
223C22×C11#57512yes—
224C2×D11—22no—
225C2×D11—22no—
226C2×D11—22no—
227C2×D11—42no—
228C2×D11—42no—
229C4×C11—22no—
230C4×C11—22no—
231C4×C11—44no—
232C4×C11—82no—
233C4×C11#52012yes—
234C4×C11#53712yes—
235Dic11—22no—
236Dic11—22no—
237Dic11—44no—
238Dic11—82no—
239Dic11#41914yes—
240C22×Q8—21no—
241C22×Q8—112no—
242C23×C4—111no—
243C23×C4—111no—
244C23×C4—111no—
245C22×C8—112no—
246C22×C8C22×D1112yes—
247C4⋊Q8—22no—
248C4⋊Q8—114no—
249C4⋊Q8—222no—
250C4⋊Q8C4×D1114yes—
251#125—228no—
252C22⋊Q8—118no—
253C22⋊Q8—224no—
254C22⋊Q8—228no—
255C4×Q8—118no—
256C4×Q8—224no—
257C4×Q8—228no—
258#117—228no—
259#117—444no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—112no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4—222no—
267C2×C4⋊C4—222no—
268C2×C4⋊C4C22×D1112yes—
269C2×C4⋊C4C22×D1112yes—
270C2×C22⋊C4—222no—
271C2×C22⋊C4—222no—
272C2×C42—111no—
273C2×C42—111no—
274C2×C42—111no—
275C2×C42—114no—
276C2×C42—114no—
277C2×C42—222no—
278C2×C42—222no—
279C2×C42C22×D1111yescharacteristic
280C4⋊C8—224no—
281#103—444no—
282#103—444no—
283C22⋊C8—224no—
284#97—22no—
285#97—222no—
286#95—21no—
287#95—21no—
288#95—221no—
289#95—221no—
290C2×C11#231111yescharacteristic
291C2×C11C2×#41911yescharacteristic
292C2×C11#289611yescharacteristic
293C2×C11#321612yes—
294C2×C11#323712yes—
295D11—42no—
296C24—111no—
297C2×Q8—24no—
298C2×Q8—44no—
299C2×Q8—114no—
300C2×Q8—222no—
301C2×Q8—224no—
302C2×Q8—224no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—111no—
306C22×C4—111no—
307C22×C4—111no—
308C22×C4—114no—
309C22×C4—112no—
310C22×C4—112no—
311C22×C4—114no—
312C22×C4—224no—
313C22×C4—222no—
314C22×C4—222no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—442no—
318C22×C4D4×D1111yescharacteristic
319C22×C4D4×D1111yescharacteristic
320C22×C4C23×D1111yescharacteristic
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—22no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C4⋊C4—24no—
328C4⋊C4—22no—
329C4⋊C4—24no—
330C4⋊C4—228no—
331C4⋊C4—228no—
332C4⋊C4—224no—
333C4⋊C4—224no—
334C4⋊C4—224no—
335C4⋊C4—444no—
336C4⋊C4—444no—
337C4⋊C4C2×C4×D1114yes—
338C22⋊C4—228no—
339C22⋊C4—444no—
340C42—114no—
341C42—114no—
342C42—112no—
343C42—112no—
344C42—228no—
345C42—444no—
346C42C2×C4×D1112yes—
347C42D4×D1112yes—
348C11#2187011yescharacteristic, complemented, Sylow
349C23—112no—
350C23—221no—
351C23—222no—
352C23—222no—
353C23—221no—
354C23C2×D4×D1111yescharacteristic
355Q8—48no—
356Q8—228no—
357Q8—444no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—44no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—112no—
366C2×C4—114no—
367C2×C4—112no—
368C2×C4—112no—
369C2×C4—228no—
370C2×C4—221no—
371C2×C4—222no—
372C2×C4—221no—
373C2×C4—224no—
374C2×C4—224no—
375C2×C4—224no—
376C2×C4—444no—
377C2×C4—442no—
378C2×C4—442no—
379C2×C4—442no—
380C2×C4—442no—
381C2×C4—442no—
382C2×C4C22⋊C4×D1112yes—
383C2×C4C22⋊C4×D1112yes—
384C2×C4C22×C4×D1111yescharacteristic
385C2×C4C2×D4×D1111yescharacteristic
386C2×C4#6704012yes—
387C2×C4#6704212yes—
388C8—42no—
389C8—442no—
390C22—222no—
391C22—222no—
392C22—222no—
393C22—442no—
394C22—442no—
395C22C2×C22⋊C4×D1111yescharacteristic
396C22#1062320511yescharacteristic
397C22#1062325511yescharacteristic
398C22#1062330412yes—
399C22D11×#13712yes—
400C4—22no—
401C4—22no—
402C4—44no—
403C4—82no—
404C4—114no—
405C4—222no—
406C4—222no—
407C4—444no—
408C4—882no—
409C4#1062310512yes—
410C4#1062316012yes—
411C2—442no—
412C2#1307120711yescharacteristic
413C2D11×#41911yescharacteristic
414C2#1307713011yescharacteristic
415C2#1307962812yes—
416C2#1307983112yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1993C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1993D11
hypocenterC11#21870
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
4. #13069590C2semidirect
5. #13069436C2semidirect
6. #13069435C2semidirect
8. #13068620C2semidirect
9. C11×#1993C2semidirect
14. #10623259C4semidirect
145. #1993D11semidirect
348. C11#21870semidirect

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106223182
#130710222
#130695902
#130694362
#130694352
#130689272
#130686202
C11×#19932
#2187011