Finite Group Databasebeta

← #14763571

Subgroups — #14763571

Order 2816.

1022 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic
3#13069584C211yesmaximal, characteristic, complemented
4#13069580C211yesmaximal, characteristic, complemented
5#13069435C211yesmaximal, characteristic, complemented
6#13069417C211yesmaximal, characteristic, complemented
7#13068928C212yesmaximal
8#13068923C212yesmaximal
9#13068628C212yesmaximal, complemented
10#13068618C212yesmaximal, complemented
11C11×#2317C211yesmaximal, characteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66977C2212yes—
16#10623049—24no—
17#10623049C418yescomplemented
18C2×#66942—22no—
19C2×#66932—22no—
20C2×#66923C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2212yes—
23C11×#389—22no—
24C11×#385—22no—
25C11×#384C2211yescharacteristic
26C11×#384C2211yescharacteristic
27C11×#382C2211yescharacteristic
28C11×#382C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622613—24no—
31C2×#66874C2212yes—
32C2×#66874C2212yes—
33C2×#66874C2212yes—
34C2×#66874C2212yes—
35C2×C4⋊(C11⋊C8)C2212yes—
36C2×#66867C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42C23×C4×C11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×Dic22C2312yes—
45C11×#117—42no—
46C11×#117C2×C414yes—
47C11×#117D414yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—42no—
52C2×C11×C4⋊C4D412yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2311yescharacteristic
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62C2×C22⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11C2312yes—
65#66977—24no—
66#66977C2×C418yes—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×C4×Dic11—22no—
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2312yes—
73#66942—216no—
74#66932—216no—
75#66923—22no—
76#66923C2×C414yescomplemented
77#66922—22no—
78#66922C2×C414yescomplemented
79C4×Dic22—24no—
80C4×Dic22C2×C418yescomplemented
81C11×#95—22no—
82C11×#95—22no—
83C22⋊(C11⋊C8)—24no—
84#66874—42no—
85#66874—42no—
86#66874—42no—
87#66874—42no—
88C4⋊(C11⋊C8)—24no—
89#66867—22no—
90C4×C11⋊C8—22no—
91#21873—111nomaximal, Sylow
92C24×C11C2×D411yescharacteristic
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—42no—
100C22×C4×C11—82no—
101C22×C4×C11C22×C412yes—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D412yes—
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—22no—
108C22×Dic11—22no—
109C2×Dic22—22no—
110C2×Dic22—22no—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22—22no—
114C2×Dic22C22×C414yes—
115C11×C4⋊C4—22no—
116C11×C4⋊C4—22no—
117C11×C4⋊C4—22no—
118C11×C4⋊C4—22no—
119C11×C4⋊C4—42no—
120C11×C4⋊C4—82no—
121C11×C4⋊C4—82no—
122C11×C4⋊C4C22⋊C418yes—
123C11×C22⋊C4—42no—
124C11×C22⋊C4C22⋊C418yes—
125C42×C11—42no—
126C42×C11C22×C412yes—
127C42×C11C22×C412yes—
128C42×C11C2×D412yes—
129C42×C11C2×D412yes—
130C22⋊Dic11—28no—
131C4⋊Dic11—28no—
132C4⋊Dic11—22no—
133C4⋊Dic11C22×C414yes—
134Dic11⋊C4—28no—
135Dic11⋊C4—28no—
136Dic11⋊C4—28no—
137C4×Dic11—28no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—22no—
142C2×C11⋊C8—22no—
143C2×C11⋊C8—22no—
144C2×#541—111no—
145C2×#433—111no—
146#2317D1111yescharacteristic
147#1992—111no—
148#1991—111no—
149#1960—111no—
150#1956—111no—
151#1873—112no—
152#1872—112no—
153#1805—112no—
154#1803—112no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—22no—
159C23×C11C2×C22⋊C412yes—
160C23×C11C22×D411yescharacteristic
161C2×C4×C11—21no—
162C2×C4×C11—21no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—24no—
168C2×C4×C11—24no—
169C2×C4×C11—41no—
170C2×C4×C11—41no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—84no—
178C2×C4×C11C2×C22⋊C414yes—
179C2×C4×C11C2×C22⋊C412yes—
180C2×C4×C11C2×C22⋊C414yes—
181C2×C4×C11C23×C411yescharacteristic
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11H(5,𝔽2)12yes—
184C2×C4×C112−1+412yes—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191Dic22—24no—
192Dic22—24no—
193Dic22—42no—
194Dic22—42no—
195C11⋊C8—42no—
196C11⋊C8—42no—
197#541—118no—
198#541—224no—
199C2×C4⋊Q8—111no—
200C2×#126—222no—
201C2×#125—111no—
202C2×#125—222no—
203C2×C22⋊Q8—112no—
204C2×C4×Q8—112no—
205C2×#117C2×D1111yescharacteristic
206C2×#117C2×D1111yescharacteristic
207C22×C4⋊C4C2×D1111yescharacteristic
208#433—224no—
209C2×C4⋊C8—112no—
210C2×#103—112no—
211C2×#103—112no—
212C2×#103—112no—
213C2×#103—112no—
214C2×C22⋊C8—112no—
215C2×#97—111no—
216C2×C4×C8—111no—
217#389—22no—
218#385—22no—
219#384C2×D1111yescharacteristic
220#384C2×D1111yescharacteristic
221#382C2×D1111yescharacteristic
222#382C2×D1111yescharacteristic
223#340—112no—
224#340—112no—
225#340—112no—
226#340—112no—
227C22×C11—22no—
228C22×C11—24no—
229C22×C11—41no—
230C22×C11—41no—
231C22×C11—42no—
232C22×C11C22×C22⋊C411yescharacteristic
233C22×C11#53511yescharacteristic
234C22×C11#53611yescharacteristic
235C22×C11#57712yes—
236C22×C11#57812yes—
237C4×C11—22no—
238C4×C11—24no—
239C4×C11—24no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—81no—
243C4×C11—81no—
244C4×C11#52012yes—
245C4×C11#53712yes—
246Dic11—44no—
247Dic11—44no—
248C22×Q8—112no—
249C23×C4—21no—
250C23×C4C22×D1111yescharacteristic
251C22×C8—112no—
252C22×C8—112no—
253C4⋊Q8—114no—
254C4⋊Q8—222no—
255#126—2216no—
256#125—114no—
257#125—2216no—
258#125—222no—
259C22⋊Q8—118no—
260C22⋊Q8—224no—
261C4×Q8—118no—
262C4×Q8—224no—
263#117—42no—
264#117C4×D1114yes—
265#117D4414yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—112no—
271C2×C4⋊C4—222no—
272C2×C4⋊C4—222no—
273C2×C4⋊C4—222no—
274C2×C4⋊C4—222no—
275C2×C4⋊C4C22⋊D1112yes—
276C2×C4⋊C4C22×D1111yescharacteristic
277C2×C4⋊C4C22×D1111yescharacteristic
278C2×C4⋊C4C22×D1111yescharacteristic
279C2×C4⋊C4C22×D1111yescharacteristic
280C2×C22⋊C4—21no—
281C2×C22⋊C4—222no—
282C2×C22⋊C4C22⋊D1112yes—
283C2×C42—21no—
284C2×C42—222no—
285C2×C42C22×D1111yescharacteristic
286C2×C42C22×D1111yescharacteristic
287C4⋊C8—224no—
288#103—442no—
289#103—442no—
290#103—442no—
291#103—442no—
292C22⋊C8—224no—
293#97—222no—
294C4×C8—222no—
295#95—22no—
296#95—22no—
297C2×C11—42no—
298C2×C11#231111yescharacteristic
299C2×C11#289812yes—
300C2×C11#322211yescharacteristic
301C2×C11#322311yescharacteristic
302C2×C11#324212yes—
303C24C2×C22⋊D1111yescharacteristic
304C2×Q8—114no—
305C2×Q8—222no—
306C2×Q8—222no—
307C2×Q8—222no—
308C2×Q8—222no—
309C2×Q8—222no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—42no—
317C22×C4—82no—
318C22×C4—222no—
319C22×C4—222no—
320C22×C4C2×C4×D1112yes—
321C22×C4C2×D4412yes—
322C22×C4C2×C22⋊D1112yes—
323C22×C4C2×C22⋊D1112yes—
324C22×C4C2×C22⋊D1111yescharacteristic
325C22×C4C23×D1111yescharacteristic
326C2×C8—222no—
327C2×C8—222no—
328C2×C8—222no—
329C2×C8—222no—
330C2×C8—222no—
331C2×C8—222no—
332C4⋊C4—22no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—22no—
336C4⋊C4—42no—
337C4⋊C4—82no—
338C4⋊C4—82no—
339C4⋊C4—114no—
340C4⋊C4—228no—
341C4⋊C4—228no—
342C4⋊C4—228no—
343C4⋊C4—228no—
344C4⋊C4—222no—
345C4⋊C4(C2×D11)⋊C418yes—
346C22⋊C4—42no—
347C22⋊C4—228no—
348C22⋊C4(C2×D11)⋊C418yes—
349C42—42no—
350C42—228no—
351C42C2×C4×D1112yes—
352C42C2×C4×D1112yes—
353C42C2×D4412yes—
354C42C2×D4412yes—
355C11#2187311yescharacteristic, complemented, Sylow
356C23—21no—
357C23—21no—
358C23—22no—
359C23—22no—
360C23C2×(C2×D11)⋊C412yes—
361C23C22×C22⋊D1111yescharacteristic
362Q8—224no—
363Q8—224no—
364Q8—442no—
365Q8—442no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—22no—
371C2×C4—22no—
372C2×C4—24no—
373C2×C4—24no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—42no—
379C2×C4—42no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—84no—
383C2×C4—224no—
384C2×C4—224no—
385C2×C4—442no—
386C2×C4—442no—
387C2×C4—442no—
388C2×C4—442no—
389C2×C4C2×(C2×D11)⋊C414yes—
390C2×C4C2×(C2×D11)⋊C414yes—
391C2×C4C2×(C2×D11)⋊C412yes—
392C2×C4C22×C4×D1111yescharacteristic
393C2×C4C22×D4411yescharacteristic
394C2×C4#6703712yes—
395C2×C4#6704012yes—
396C8—442no—
397C8—442no—
398C22—22no—
399C22—24no—
400C22—42no—
401C22—41no—
402C22—41no—
403C22C22×(C2×D11)⋊C411yescharacteristic
404C22#1062333611yescharacteristic
405C22#1062334711yescharacteristic
406C22#1062336712yes—
407C22#1062336912yes—
408C4—22no—
409C4—24no—
410C4—24no—
411C4—81no—
412C4—81no—
413C4—81no—
414C4—81no—
415C4—444no—
416C4—444no—
417C4#1062303512yes—
418C4#1062304112yes—
419C2—42no—
420C2#1307120911yescharacteristic
421C2#1307714612yes—
422C2#1307968811yescharacteristic
423C2#1307969911yescharacteristic
424C2#1307988412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2317C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2317D11
hypocenterC11#21873
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2317

Complements

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

NH ≅ G/Ntype
3. #13069584C2semidirect
4. #13069580C2semidirect
5. #13069435C2semidirect
6. #13069417C2semidirect
9. #13068628C2semidirect
10. #13068618C2semidirect
17. #10623049C4semidirect
76. #66923C2×C4semidirect
78. #66922C2×C4semidirect
80. C4×Dic22C2×C4semidirect
355. C11#21873semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106226132
#130695842
#130695802
#130694352
#130694172
#130689282
#130689232
#130686282
#130686182
C11×#23172
#2187311