Finite Group Databasebeta

← #14763765

Subgroups — #14763765

Order 2816.

1014 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic
2C2×#10622612C211yesmaximal, characteristic
3#13069573C212yesmaximal, complemented
4#13069539C212yesmaximal, complemented
5#13069047C212yesmaximal
6#13069037C212yesmaximal
7#13068628C212yesmaximal, complemented
8#13068618C212yesmaximal, complemented
9C11×#2314C211yesmaximal, characteristic
10C2×C11×#117C2211yescharacteristic
11C2×#66977C2212yes—
12C22×#4318C2211yescharacteristic
13C23×C11⋊C8C2211yescharacteristic
14#10623049—24no—
15#10623049C418yescomplemented
16C2×#66942—22no—
17C2×#66932—22no—
18C2×#66923C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C2×C4×Dic22C2212yes—
21C11×#388—22no—
22C11×#387—22no—
23C11×#384C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C11×#380C2212yes—
26C4×C11×C4⋊C4C2212yes—
27#10622612—24no—
28C2×#66874C2212yes—
29C2×#66874C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×C4⋊(C11⋊C8)C2212yes—
33C2×C4⋊(C11⋊C8)C2212yes—
34#10622167C2212yes—
35#10622167C2212yes—
36#10622167C2212yes—
37#10622167C2212yes—
38C23×C4×C11C2311yescharacteristic
39C22×Dic22C2312yes—
40C11×#117C2×C414yes—
41C11×#117D414yes—
42C2×C11×C4⋊C4—22no—
43C2×C11×C4⋊C4D412yes—
44C2×C11×C4⋊C4C2312yes—
45C2×C11×C4⋊C4C2312yes—
46C2×C11×C22⋊C4—22no—
47C2×C11×C22⋊C4D412yes—
48C2×C42×C11—22no—
49C2×C42×C11C2311yescharacteristic
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—22no—
52C2×C4⋊Dic11—22no—
53C2×C4⋊Dic11C2312yes—
54#66977—24no—
55#66977C2×C418yes—
56C2×Dic11⋊C4—22no—
57C2×Dic11⋊C4—22no—
58C2×Dic11⋊C4—22no—
59C2×C4×Dic11—22no—
60C2×#4318—22no—
61C2×#4318—41no—
62C2×#4318—41no—
63C22×C11⋊C8—22no—
64C22×C11⋊C8—41no—
65C22×C11⋊C8—41no—
66C22×C11⋊C8C2312yes—
67C22×C11⋊C8C2312yes—
68#66942—216no—
69#66932—216no—
70#66923—22no—
71#66923C2×C414yes—
72#66922—22no—
73#66922C2×C414yes—
74C4×Dic22—24no—
75C4×Dic22C2×C418yes—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79#66874—42no—
80#66874—42no—
81#66874—42no—
82#66874—42no—
83C4⋊(C11⋊C8)—24no—
84C4⋊(C11⋊C8)—24no—
85#21898—111nomaximal, Sylow
86C24×C11C2×D411yescharacteristic
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11C22×C412yes—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D412yes—
97C22×C4×C11C2×D412yes—
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—22no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22—22no—
104C2×Dic22—22no—
105C2×Dic22—22no—
106C2×Dic22C22×C414yes—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—82no—
112C11×C4⋊C4C22⋊C418yes—
113C11×C22⋊C4—82no—
114C11×C22⋊C4C22⋊C418yes—
115C42×C11—82no—
116C42×C11C22×C412yes—
117C42×C11C22×C412yes—
118C42×C11C2×D412yes—
119C42×C11C2×D412yes—
120C22⋊Dic11—28no—
121C4⋊Dic11—28no—
122C4⋊Dic11—22no—
123C4⋊Dic11C22×C414yes—
124Dic11⋊C4—28no—
125Dic11⋊C4—28no—
126Dic11⋊C4—28no—
127C4×Dic11—28no—
128#4318—44no—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—22no—
134C2×C11⋊C8—22no—
135C2×C11⋊C8—44no—
136C2×#541—111no—
137C2×#424—111no—
138#2314D1111yescharacteristic
139#1989—112no—
140#1981—112no—
141#1894—112no—
142#1892—112no—
143#1805—112no—
144#1803—112no—
145C23×C11—21no—
146C23×C11—21no—
147C23×C11—22no—
148C23×C11—22no—
149C23×C11C2×C22⋊C412yes—
150C23×C11C22×D411yescharacteristic
151C2×C4×C11—21no—
152C2×C4×C11—21no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—42no—
162C2×C4×C11—42no—
163C2×C4×C11—42no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11C2×C22⋊C414yes—
168C2×C4×C11C2×C22⋊C412yes—
169C2×C4×C11C2×C22⋊C414yes—
170C2×C4×C11C23×C411yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11H(5,𝔽2)11yescharacteristic
173C2×C4×C11H(5,𝔽2)11yescharacteristic
174C2×C4×C112−1+411yescharacteristic
175C2×C4×C112−1+411yescharacteristic
176C2×Dic11—24no—
177C2×Dic11—24no—
178C2×Dic11—42no—
179C2×Dic11—42no—
180C2×Dic11—42no—
181C2×Dic11—42no—
182Dic22—24no—
183Dic22—24no—
184Dic22—42no—
185Dic22—42no—
186C11⋊C8—42no—
187C11⋊C8—42no—
188C22×M16—111no—
189C23×C8—111no—
190#541—118no—
191#541—224no—
192C2×C4⋊Q8—111no—
193C2×#126—222no—
194C2×#125—111no—
195C2×#125—222no—
196C2×C22⋊Q8—112no—
197C2×C4×Q8—112no—
198C2×#117C2×D1111yescharacteristic
199#424—224no—
200C2×C4⋊C8—112no—
201C2×C4⋊C8—112no—
202C2×#103—112no—
203C2×#103—112no—
204C2×#103—112no—
205C2×#103—112no—
206#388—22no—
207#387—22no—
208#384C2×D1111yescharacteristic
209#382C2×D1111yescharacteristic
210#380C2×D1112yes—
211C4×C4⋊C4C2×D1112yes—
212#340—112no—
213#340—112no—
214#340—112no—
215#340—112no—
216C22×C11—22no—
217C22×C11—24no—
218C22×C11—42no—
219C22×C11—41no—
220C22×C11—41no—
221C22×C11C22×C22⋊C411yescharacteristic
222C22×C11#53711yescharacteristic
223C22×C11#53711yescharacteristic
224C22×C11#57712yes—
225C22×C11#57812yes—
226C4×C11—22no—
227C4×C11—24no—
228C4×C11—24no—
229C4×C11—82no—
230C4×C11—82no—
231C4×C11#52011yescharacteristic
232C4×C11#52011yescharacteristic
233C4×C11#53511yescharacteristic
234C4×C11#53611yescharacteristic
235Dic11—44no—
236Dic11—44no—
237C22×Q8—112no—
238C23×C4C22×D1111yescharacteristic
239C2×M16—222no—
240C2×M16—441no—
241C2×M16—441no—
242C22×C8—112no—
243C22×C8—112no—
244C22×C8—222no—
245C22×C8—441no—
246C22×C8—441no—
247C4⋊Q8—114no—
248C4⋊Q8—222no—
249#126—2216no—
250#125—114no—
251#125—2216no—
252#125—222no—
253C22⋊Q8—118no—
254C22⋊Q8—224no—
255C4×Q8—118no—
256C4×Q8—224no—
257#117C4×D1114yes—
258#117D4414yes—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—222no—
262C2×C4⋊C4—222no—
263C2×C4⋊C4—222no—
264C2×C4⋊C4—222no—
265C2×C4⋊C4C22⋊D1112yes—
266C2×C4⋊C4C22×D1112yes—
267C2×C4⋊C4C22×D1112yes—
268C2×C22⋊C4—22no—
269C2×C22⋊C4—222no—
270C2×C22⋊C4C22⋊D1112yes—
271C2×C42—22no—
272C2×C42—222no—
273C2×C42C22×D1111yescharacteristic
274C2×C42C22×D1111yescharacteristic
275C4⋊C8—224no—
276C4⋊C8—224no—
277#103—442no—
278#103—442no—
279#103—442no—
280#103—442no—
281#95—22no—
282#95—22no—
283#95—22no—
284C2×C11—42no—
285C2×C11#231111yescharacteristic
286C2×C11#289812yes—
287C2×C11#325812yes—
288C2×C11#326011yescharacteristic
289C2×C11#326111yescharacteristic
290C24C2×C22⋊D1111yescharacteristic
291C2×Q8—114no—
292C2×Q8—222no—
293C2×Q8—222no—
294C2×Q8—222no—
295C2×Q8—222no—
296C2×Q8—222no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4C2×C4×D1112yes—
306C22×C4C2×D4412yes—
307C22×C4C2×C22⋊D1111yescharacteristic
308C22×C4C2×C22⋊D1112yes—
309C22×C4C2×C22⋊D1112yes—
310C22×C4C23×D1111yescharacteristic
311M16—444no—
312C2×C8—222no—
313C2×C8—222no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8—444no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—22no—
322C4⋊C4—22no—
323C4⋊C4—82no—
324C4⋊C4—114no—
325C4⋊C4—228no—
326C4⋊C4—228no—
327C4⋊C4—228no—
328C4⋊C4—228no—
329C4⋊C4—222no—
330C4⋊C4(C2×D11)⋊C418yes—
331C22⋊C4—82no—
332C22⋊C4—228no—
333C22⋊C4(C2×D11)⋊C418yes—
334C42—82no—
335C42—228no—
336C42C2×C4×D1112yes—
337C42C2×C4×D1112yes—
338C42C2×D4412yes—
339C42C2×D4412yes—
340C11#2189811yescharacteristic, complemented, Sylow
341C23—21no—
342C23—21no—
343C23—22no—
344C23—22no—
345C23C2×(C2×D11)⋊C412yes—
346C23C22×C22⋊D1111yescharacteristic
347Q8—224no—
348Q8—224no—
349Q8—442no—
350Q8—442no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—224no—
368C2×C4—224no—
369C2×C4—442no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—442no—
373C2×C4C2×(C2×D11)⋊C414yes—
374C2×C4C2×(C2×D11)⋊C414yes—
375C2×C4C2×(C2×D11)⋊C412yes—
376C2×C4C22×C4×D1111yescharacteristic
377C2×C4C22×D4411yescharacteristic
378C2×C4#6704211yescharacteristic
379C2×C4#6704211yescharacteristic
380C2×C4#6704311yescharacteristic
381C2×C4#6704311yescharacteristic
382C8—442no—
383C8—442no—
384C22—22no—
385C22—24no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22C22×(C2×D11)⋊C411yescharacteristic
390C22#1062336411yescharacteristic
391C22#1062336411yescharacteristic
392C22#1062336712yes—
393C22#1062336912yes—
394C4—22no—
395C4—24no—
396C4—24no—
397C4—82no—
398C4—82no—
399C4—444no—
400C4—444no—
401C4#1062305411yescharacteristic
402C4#1062305411yescharacteristic
403C4#1062305611yescharacteristic
404C4#1062305711yescharacteristic
405C2—42no—
406C2#1307120411yescharacteristic
407C2#1307714612yes—
408C2#1308004212yes—
409C2#1308006211yescharacteristic
410C2#1308006611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2314C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2314D11
hypocenterC11#21898
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #13069573C2semidirect
4. #13069539C2semidirect
7. #13068628C2semidirect
8. #13068618C2semidirect
15. #10623049C4semidirect
340. C11#21898semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106226122
#130695732
#130695392
#130690472
#130690372
#130686282
#130686182
C11×#23142
#2189811