Finite Group Databasebeta

← #14719711

Subgroups — #14719711

Order 2816.

1174 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623077C211yesmaximal, characteristic
2#13077699C212yesmaximal, complemented
3#13066955C214yesmaximal, complemented
4#13066947C214yesmaximal, complemented
5#13066937C211yesmaximal, characteristic, complemented
6#13066928C212yesmaximal, complemented
7C11×#1460C211yesmaximal, characteristic, complemented
8C22×#4341C411yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×D4×Dic11C411yescharacteristic
11C2×C4×C22⋊D11C412yes—
12C22×Dic11⋊C4C412yes—
13#10623077—24no—
14#10623077—24no—
15C2×C4⋊C4×D11C411yescharacteristic
16C2×#66940C411yescharacteristic
17C2×(C22⋊D11)⋊C4C2212yes—
18C2×#66930C2212yes—
19C2×#66925C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C11×#431C2212yes—
22#10622538C2212yes—
23#10622444—24no—
24#10622332C2218yes—
25#10622292—24no—
26C11×#323C2214yes—
27#10622163C2214yes—
28#10622107C2214yes—
29#10622106C2214yes—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C412yes—
32C22×C22⋊D11C2×C412yes—
33C23×Dic11C2×C412yes—
34C23×Dic11C2×C412yes—
35C2×#4341—24no—
36C2×#4341—24no—
37C2×#4341—24no—
38C22×C4×D11C2×C411yescharacteristic
39C22×C4×D11C2×C412yes—
40C22×Dic22C2×C411yescharacteristic
41C4×D4×C11—22no—
42C4×D4×C11—22no—
43C2×C11×C4⋊C4C2×C411yescharacteristic
44C2×C11×C22⋊C4C2312yes—
45C2×C42×C11C2311yescharacteristic
46C2×C22⋊Dic11C2×C412yes—
47D4×Dic11—24no—
48C4×C22⋊D11—24no—
49C4×C22⋊D11—24no—
50C2×(C2×D11)⋊C4C2×C411yescharacteristic
51C2×(C2×D11)⋊C4C2311yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×Dic11⋊C4—24no—
54C2×Dic11⋊C4—24no—
55C2×Dic11⋊C4C2×C411yescharacteristic
56C2×Dic11⋊C4C2×C412yes—
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2×C412yes—
59C2×Dic11⋊C4C2311yescharacteristic
60C2×C4×Dic11C2×C411yescharacteristic
61C2×C4×Dic11C2×C412yes—
62C2×C4×Dic11C2312yes—
63C4⋊C4×D11—24no—
64#66940—24no—
65(C22⋊D11)⋊C4—28no—
66#66930—28no—
67#66925—22no—
68#66925—22no—
69C4×Dic22D414yes—
70C4×Dic22D414yes—
71C11×C4⋊C8—22no—
72C11×C22⋊C8C2314yes—
73C4×C8×C11—22no—
74C22⋊(C11⋊C8)C2314yes—
75#66879—28no—
76Dic11⋊C8—28no—
77C4⋊(C11⋊C8)—22no—
78C4×C11⋊C8—22no—
79#17372—111nomaximal, Sylow
80C24×C11C22×C412yes—
81C23×D11C22×C411yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—22no—
84C2×D4×C11M1614yes—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—82no—
88C22×C4×C11C22×C412yes—
89C22×C4×C11C22×C411yescharacteristic
90C22×C4×C11C22×C411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C2×C22⋊D11—24no—
93C2×C22⋊D11—24no—
94C2×C22⋊D11—24no—
95C22×Dic11—24no—
96C22×Dic11—24no—
97C22×Dic11—24no—
98C22×Dic11—24no—
99C22×Dic11—82no—
100C22×Dic11C22×C412yes—
101C22×Dic11C22×C411yescharacteristic
102C22×Dic11C22×C411yescharacteristic
103C22×Dic11C22×C411yescharacteristic
104C22×Dic11C22×C412yes—
105#4341—232no—
106C2×C4×D11—24no—
107C2×C4×D11—22no—
108C2×C4×D11—22no—
109C2×C4×D11—82no—
110C2×C4×D11M1614yes—
111C2×Dic22—22no—
112C2×Dic22—22no—
113C2×Dic22C22⋊C414yes—
114C2×C8×C11—24no—
115C11×C4⋊C4—22no—
116C11×C22⋊C4—24no—
117C42×C11C2×D412yes—
118C42×C11C2×D412yes—
119C22⋊Dic11—24no—
120(C2×D11)⋊C4—21no—
121(C2×D11)⋊C4—21no—
122(C2×D11)⋊C4—22no—
123C4⋊Dic11C22⋊C414yes—
124Dic11⋊C4—24no—
125Dic11⋊C4—24no—
126Dic11⋊C4—21no—
127Dic11⋊C4—21no—
128Dic11⋊C4—22no—
129Dic11⋊C4C22⋊C414yes—
130Dic11⋊C4C22⋊C414yes—
131C4×Dic11—24no—
132C4×Dic11—22no—
133C4×Dic11C2×D418yes—
134C2×C11⋊C8—24no—
135C2×#520—111no—
136#2983—112no—
137#1466—114no—
138#1464—114no—
139#1460—111no—
140#1460D1111yescharacteristic, complemented
141#1458—112no—
142C23×C11—22no—
143C23×C11—22no—
144C23×C11—42no—
145C23×C11—42no—
146C23×C11C2×M1614yes—
147C23×C11C23×C411yescharacteristic
148C22×D11—21no—
149C22×D11—21no—
150C22×D11—41no—
151C22×D11—41no—
152C22×D11C2×M1612yes—
153D4×C11—28no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11—82no—
159C2×C4×C11—82no—
160C2×C4×C11C2×C22⋊C411yescharacteristic
161C2×C4×C11C2×C22⋊C411yescharacteristic
162C2×C4×C11C2×C22⋊C412yes—
163C2×C4×C11C2×M1612yes—
164C2×C4×C11C2×M1612yes—
165C2×C4×C11C22×D412yes—
166C22⋊D11—216no—
167C2×Dic11—216no—
168C2×Dic11—21no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—21no—
172C2×Dic11—21no—
173C2×Dic11—21no—
174C2×Dic11—42no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—84no—
178C2×Dic11C2×C22⋊C414yes—
179C2×Dic11C2×C22⋊C414yes—
180C2×Dic11C2×M1612yes—
181C4×D11—28no—
182C4×D11—84no—
183Dic22—28no—
184C8×C11—44no—
185C11⋊C8—44no—
186C22×#41—111no—
187#520—224no—
188#520—224no—
189C2×C4×Q8—111no—
190C2×C4×Q8—111no—
191C2×C4×D4—111no—
192C2×C4×D4—112no—
193C2×C4×D4—112no—
194C2×C4×D4C2×D1111yescharacteristic
195C2×#117—112no—
196C2×#117—111no—
197C22×C4⋊C4—112no—
198C22×C4⋊C4—111no—
199#446—224no—
200#446—224no—
201#432—118no—
202#431—112no—
203#431C2×D1112yes—
204#324—114no—
205#323—114no—
206#323—114no—
207#323C2×D1114yes—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11—24no—
211C22×C11—44no—
212C22×C11—44no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11C22×C22⋊C411yescharacteristic
216C22×C11C22×M1611yescharacteristic
217C22×C11C22×M1611yescharacteristic
218C2×D11—22no—
219C2×D11—42no—
220C2×D11—41no—
221C2×D11—41no—
222C2×D11—42no—
223C4×C11—22no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—42no—
227C4×C11#40714yes—
228Dic11—24no—
229Dic11—22no—
230Dic11—24no—
231Dic11—41no—
232Dic11—41no—
233C2×#41—224no—
234C2×#41—224no—
235C2×#41—224no—
236C22×Q8—111no—
237C22×D4—112no—
238C22×D4C4×D1111yescharacteristic
239C23×C4—111no—
240C23×C4—112no—
241C23×C4—112no—
242C23×C4—112no—
243C23×C4C4×D1112yes—
244C4×Q8—114no—
245C4×Q8—114no—
246C4×Q8—224no—
247C4×D4—22no—
248C4×D4—22no—
249C4×D4—228no—
250C4×D4—224no—
251C4×D4—224no—
252C4×D4—224no—
253#117—228no—
254#117—222no—
255#117—222no—
256C2×C4⋊C4—112no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—112no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—112no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—224no—
263C2×C4⋊C4—224no—
264C2×C4⋊C4—224no—
265C2×C4⋊C4C4×D1111yescharacteristic
266C2×C22⋊C4—112no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4C22×D1112yes—
270C2×C42—112no—
271C2×C42—112no—
272C2×C42—111no—
273C2×C42C22×D1111yescharacteristic
274C4⋊C8—22no—
275C4⋊C8—228no—
276C4⋊C8—222no—
277C22⋊C8—114no—
278C22⋊C8C22×D1114yes—
279#97—228no—
280C4×C8—22no—
281C4×C8—222no—
282C2×C11—21no—
283C2×C11—21no—
284C2×C11—44no—
285C2×C11C2×#40711yescharacteristic
286C2×C11#288411yescharacteristic
287C2×C11#288811yescharacteristic
288D11—42no—
289C24—111no—
290C24C2×C4×D1112yes—
291#41—2232no—
292C2×Q8—114no—
293C2×Q8—222no—
294C2×Q8—222no—
295C2×D4—22no—
296C2×D4—22no—
297C2×D4—224no—
298C2×D4—224no—
299C2×D4—224no—
300C2×D4#431314yes—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—82no—
304C22×C4—112no—
305C22×C4—111no—
306C22×C4—112no—
307C22×C4—114no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—224no—
311C22×C4—224no—
312C22×C4—224no—
313C22×C4—224no—
314C22×C4—224no—
315C22×C4—222no—
316C22×C4—222no—
317C22×C4—882no—
318C22×C4—882no—
319C22×C4C2×C4×D1112yes—
320C22×C4C2×C4×D1111yescharacteristic
321C22×C4C2×C4×D1111yescharacteristic
322C22×C4C23×D1111yescharacteristic
323C2×C8—24no—
324C2×C8—224no—
325C4⋊C4—22no—
326C4⋊C4—114no—
327C4⋊C4—114no—
328C4⋊C4—114no—
329C4⋊C4—224no—
330C4⋊C4—224no—
331C4⋊C4—221no—
332C4⋊C4—221no—
333C4⋊C4—222no—
334C22⋊C4—24no—
335C22⋊C4—224no—
336C22⋊C4—221no—
337C22⋊C4—221no—
338C22⋊C4—222no—
339C42—118no—
340C42—224no—
341C42—222no—
342C42D4×D1112yes—
343C42D4×D1112yes—
344C11#1737211yescharacteristic, complemented, Sylow
345C23—22no—
346C23—22no—
347C23—42no—
348C23—42no—
349C23—112no—
350C23—221no—
351C23—221no—
352C23—441no—
353C23—441no—
354C23C2×#431314yes—
355C23C22×C4×D1111yescharacteristic
356Q8—228no—
357D4—28no—
358D4—2216no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—82no—
364C2×C4—82no—
365C2×C4—114no—
366C2×C4—114no—
367C2×C4—112no—
368C2×C4—2216no—
369C2×C4—221no—
370C2×C4—222no—
371C2×C4—221no—
372C2×C4—222no—
373C2×C4—228no—
374C2×C4—221no—
375C2×C4—221no—
376C2×C4—442no—
377C2×C4—441no—
378C2×C4—441no—
379C2×C4—884no—
380C2×C4—884no—
381C2×C4C22⋊C4×D1111yescharacteristic
382C2×C4C22⋊C4×D1111yescharacteristic
383C2×C4C22⋊C4×D1112yes—
384C2×C4C2×#431312yes—
385C2×C4M16×D1112yes—
386C2×C4C2×D4×D1112yes—
387C8—44no—
388C8—444no—
389C22—21no—
390C22—21no—
391C22—24no—
392C22—44no—
393C22—44no—
394C22—42no—
395C22—42no—
396C22—222no—
397C22—442no—
398C22—442no—
399C22—441no—
400C22—441no—
401C22C2×C22⋊C4×D1111yescharacteristic
402C22C22×#431311yescharacteristic
403C22C2×M16×D1111yescharacteristic
404C4—22no—
405C4—21no—
406C4—21no—
407C4—42no—
408C4—222no—
409C4—224no—
410C4—224no—
411C4—441no—
412C4—441no—
413C4#1062233914yes—
414C2—21no—
415C2—21no—
416C2—44no—
417C2—442no—
418C2C2×#1062233911yescharacteristic
419C2#1307707811yescharacteristic
420C2#1307709211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1460C2
socleC22×C11C22×C22⋊C4
prime radicalC22×#4341C4
cosocleC22×C4×C11C24
hypercenter#1460D11
hypocenterC11#17372
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13077699C2semidirect
3. #13066955C2semidirect
4. #13066947C2semidirect
5. #13066937C2semidirect
6. #13066928C2semidirect
7. C11×#1460C2semidirect
140. #1460D11semidirect
344. C11#17372semidirect

Maximal subgroups

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

subgroupindex
C2×#106230772
#130776992
#130669552
#130669472
#130669372
#130669282
C11×#14602
#1737211