Finite Group Databasebeta

← #14719812

Subgroups — #14719812

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623092C211yesmaximal, characteristic
2#13077657C211yesmaximal, characteristic, complemented
3#13066979C214yesmaximal, complemented
4#13066962C214yesmaximal, complemented
5#13066939C212yesmaximal, complemented
6#13066928C212yesmaximal, complemented
7C11×#2972C211yesmaximal, characteristic, complemented
8C2×C4×D4×C11C2211yescharacteristic
9C2×#66991C411yescharacteristic
10C2×#66989C411yescharacteristic
11C2×#66982C2212yes—
12C2×#66977C2212yes—
13#10623092—24no—
14#10623092—24no—
15C2×#66950C411yescharacteristic
16C2×#66941C411yescharacteristic
17C2×#66938C412yes—
18C2×#66932C412yes—
19C2×#66925C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C8×D4×C11—24no—
22C11×#431C2212yes—
23C2×C11×C22⋊C8C2214yes—
24#10622820C2214yes—
25#10622625—24no—
26#10622538C2212yes—
27#10622107C2214yes—
28#10622107C2218yes—
29#10622106C2214yes—
30C22×D4×C11C2×C411yescharacteristic
31C23×C4×C11C2312yes—
32C22×C22⋊D11C2×C412yes—
33C22×C4×D11C2×C411yescharacteristic
34C22×Dic22C2×C411yescharacteristic
35C22×Dic22C2×C412yes—
36C22×C8×C11—24no—
37C4×D4×C11D414yes—
38C4×D4×C11D414yes—
39C2×C11×C4⋊C4C2×C411yescharacteristic
40C2×C11×C22⋊C4C2×C412yes—
41C2×C42×C11C2311yescharacteristic
42C2×C22⋊Dic11C2×C412yes—
43C2×C22⋊Dic11C2×C412yes—
44C2×C22⋊Dic11C2×C412yes—
45#66991—24no—
46#66989—24no—
47#66982—24no—
48#66982—24no—
49C2×(C2×D11)⋊C4C2×C411yescharacteristic
50C2×(C2×D11)⋊C4C2×C412yes—
51C2×(C2×D11)⋊C4C2311yescharacteristic
52C2×C4⋊Dic11C2×C411yescharacteristic
53C2×C4⋊Dic11C2×C412yes—
54#66977—24no—
55#66977—24no—
56C2×Dic11⋊C4C2×C411yescharacteristic
57C2×Dic11⋊C4C2×C412yes—
58C2×Dic11⋊C4C2312yes—
59C2×Dic11⋊C4C2311yescharacteristic
60C2×C4×Dic11C2×C412yes—
61C2×C4×Dic11C2×C411yescharacteristic
62C2×#4318—24no—
63#66950—24no—
64#66941—24no—
65#66938—28no—
66#66932—28no—
67#66925—22no—
68#66925—22no—
69C4×Dic22—22no—
70C4×Dic22—22no—
71C11×C4⋊C8—22no—
72C11×C22⋊C8—24no—
73C11×C22⋊C8C2314yes—
74C4×C8×C11—22no—
75C22⋊(C11⋊C8)—24no—
76C22⋊(C11⋊C8)C2314yes—
77C4⋊(C11⋊C8)—22no—
78C4×C11⋊C8—22no—
79#17388—111nomaximal, Sylow
80C24×C11C22×C412yes—
81C23×D11C22×C411yescharacteristic
82C2×D4×C11—24no—
83C2×D4×C11C22⋊C414yes—
84C22×C4×C11—82no—
85C22×C4×C11C22×C411yescharacteristic
86C22×C4×C11C22×C412yes—
87C22×C4×C11C22×C411yescharacteristic
88C22×C4×C11C2×D414yes—
89C22×C4×C11C2×D414yes—
90C22×C4×C11C2411yescharacteristic
91C2×C22⋊D11—24no—
92C2×C22⋊D11—82no—
93C22×Dic11C22×C412yes—
94C22×Dic11C22×C411yescharacteristic
95C22×Dic11C22×C411yescharacteristic
96C22×Dic11C22×C412yes—
97C22×Dic11C22×C411yescharacteristic
98C2×C4×D11—22no—
99C2×C4×D11—24no—
100C2×Dic22—22no—
101C2×Dic22—24no—
102C2×Dic22—24no—
103C2×Dic22—82no—
104C2×C8×C11—24no—
105C2×C8×C11—84no—
106C11×C4⋊C4C22⋊C414yes—
107C11×C22⋊C4C22⋊C418yes—
108C42×C11C2×D412yes—
109C42×C11C2×D412yes—
110C22⋊Dic11—24no—
111C22⋊Dic11—24no—
112C22⋊Dic11—24no—
113(C2×D11)⋊C4—22no—
114(C2×D11)⋊C4—24no—
115(C2×D11)⋊C4—21no—
116(C2×D11)⋊C4—21no—
117C4⋊Dic11—22no—
118C4⋊Dic11—24no—
119Dic11⋊C4—22no—
120Dic11⋊C4—24no—
121Dic11⋊C4—22no—
122Dic11⋊C4—22no—
123Dic11⋊C4—21no—
124Dic11⋊C4—21no—
125C4×Dic11—24no—
126C4×Dic11—22no—
127#4318—84no—
128C2×C11⋊C8—24no—
129C2×#542—111no—
130#2975—111no—
131#2972D1111yescharacteristic, complemented
132#1472—114no—
133#1468—114no—
134#1461—112no—
135#1458—112no—
136C23×C11—24no—
137C23×C11—42no—
138C23×C11—42no—
139C23×C11C2×C22⋊C414yes—
140C23×C11C23×C411yescharacteristic
141C22×D11—21no—
142C22×D11—22no—
143C22×D11—41no—
144C22×D11—41no—
145D4×C11—28no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11—42no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11C2×C22⋊C412yes—
152C2×C4×C11C2×C22⋊C414yes—
153C2×C4×C11C2×C22⋊C412yes—
154C2×C4×C11#13114yes—
155C2×C4×C11C22×D411yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C22⋊D11—84no—
158C2×Dic11—21no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—21no—
162C2×Dic11—21no—
163C2×Dic11—24no—
164C2×Dic11—22no—
165C2×Dic11—41no—
166C2×Dic11—42no—
167C2×Dic11—41no—
168C4×D11—44no—
169Dic22—44no—
170Dic22—84no—
171C8×C11—44no—
172C11⋊C8—44no—
173#542—224no—
174#542—224no—
175C2×C4⋊Q8—111no—
176C2×#126—112no—
177C2×#124—111no—
178C2×#124—112no—
179C2×#123—112no—
180C2×C22⋊Q8—112no—
181C2×C22⋊Q8—111no—
182C2×#121—111no—
183C2×C4×Q8—111no—
184C2×C4×D4C2×D1111yescharacteristic
185C2×#117—111no—
186#436—224no—
187C8×D4—24no—
188#431—112no—
189#431C2×D1112yes—
190#407—114no—
191C2×C22⋊C8C2×D1114yes—
192#324—114no—
193#324—118no—
194#323—114no—
195C22×C11—21no—
196C22×C11—21no—
197C22×C11—24no—
198C22×C11—24no—
199C22×C11—24no—
200C22×C11—84no—
201C22×C11C22×C22⋊C411yescharacteristic
202C22×C11C2×#13112yes—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—82no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—24no—
210C4×C11—22no—
211C4×C11#40814yes—
212Dic11—42no—
213Dic11—41no—
214Dic11—41no—
215Dic11—42no—
216Dic11—41no—
217C22×Q8—111no—
218C22×Q8—112no—
219C22×D4—112no—
220C22×D4C4×D1111yescharacteristic
221C23×C4—111no—
222C23×C4C22×D1112yes—
223C2×M16—224no—
224C22×C8—24no—
225C4⋊Q8—224no—
226#126—228no—
227#124—224no—
228#124—228no—
229#123—224no—
230#123—224no—
231C22⋊Q8—224no—
232C22⋊Q8—224no—
233C22⋊Q8—224no—
234#121—224no—
235C4×Q8—222no—
236C4×Q8—222no—
237C4×D4D4414yes—
238C4×D4C22⋊D1114yes—
239#117—222no—
240#117—222no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—112no—
244C2×C4⋊C4—112no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—112no—
247C2×C4⋊C4C4×D1111yescharacteristic
248C2×C22⋊C4—112no—
249C2×C22⋊C4—112no—
250C2×C22⋊C4—112no—
251C2×C22⋊C4—111no—
252C2×C22⋊C4—112no—
253C2×C22⋊C4—111no—
254C2×C22⋊C4C4×D1112yes—
255C2×C42—111no—
256C2×C42—112no—
257C2×C42C22×D1111yescharacteristic
258C4⋊C8—22no—
259C4⋊C8—222no—
260C22⋊C8—24no—
261C22⋊C8—114no—
262C22⋊C8—224no—
263C22⋊C8C22×D1114yes—
264C4×C8—22no—
265C4×C8—222no—
266C2×C11—22no—
267C2×C11—44no—
268C2×C11C2×#40811yescharacteristic
269C2×C11#288311yescharacteristic
270C2×C11#288911yescharacteristic
271D11—81no—
272C24—111no—
273C24C2×C4×D1112yes—
274C2×Q8—224no—
275C2×Q8—222no—
276C2×Q8—224no—
277C2×Q8—882no—
278C2×D4—24no—
279C2×D4—224no—
280C2×D4—882no—
281C2×D4(C2×D11)⋊C414yes—
282C22×C4—82no—
283C22×C4—112no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—112no—
288C22×C4—224no—
289C22×C4—222no—
290C22×C4C2×C4×D1111yescharacteristic
291C22×C4C2×C4×D1112yes—
292C22×C4C2×C4×D1111yescharacteristic
293C22×C4C2×D4414yes—
294C22×C4C2×C22⋊D1114yes—
295C22×C4C23×D1111yescharacteristic
296M16—884no—
297C2×C8—24no—
298C2×C8—84no—
299C2×C8—224no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—224no—
303C4⋊C4—224no—
304C4⋊C4—221no—
305C4⋊C4—222no—
306C4⋊C4—221no—
307C4⋊C4—222no—
308C4⋊C4(C2×D11)⋊C414yes—
309C22⋊C4—224no—
310C22⋊C4—224no—
311C22⋊C4—224no—
312C22⋊C4—222no—
313C22⋊C4—224no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C22⋊C4(C2×D11)⋊C418yes—
317C42—222no—
318C42—224no—
319C42C2×D4412yes—
320C42C2×C22⋊D1112yes—
321C11#1738811yescharacteristic, complemented, Sylow
322C23—24no—
323C23—42no—
324C23—42no—
325C23—221no—
326C23—222no—
327C23—441no—
328C23—441no—
329C23C2×(C2×D11)⋊C414yes—
330C23C22×C4×D1111yescharacteristic
331Q8—444no—
332Q8—884no—
333D4—28no—
334D4—884no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—41no—
340C2×C4—222no—
341C2×C4—224no—
342C2×C4—221no—
343C2×C4—222no—
344C2×C4—221no—
345C2×C4—222no—
346C2×C4—221no—
347C2×C4—444no—
348C2×C4—442no—
349C2×C4—441no—
350C2×C4—441no—
351C2×C4#6695414yes—
352C2×C4C2×(C2×D11)⋊C412yes—
353C2×C4C2×(C2×D11)⋊C414yes—
354C2×C4C2×(C2×D11)⋊C412yes—
355C2×C4C22×D4411yescharacteristic
356C2×C4C22×C22⋊D1111yescharacteristic
357C8—44no—
358C8—444no—
359C22—21no—
360C22—21no—
361C22—24no—
362C22—24no—
363C22—24no—
364C22—84no—
365C22—441no—
366C22—441no—
367C22—441no—
368C22—882no—
369C22C2×#6695412yes—
370C22C22×(C2×D11)⋊C411yescharacteristic
371C4—21no—
372C4—21no—
373C4—24no—
374C4—22no—
375C4—441no—
376C4—442no—
377C4—442no—
378C4—441no—
379C4—441no—
380C4#1062272314yes—
381C2—22no—
382C2—44no—
383C2—881no—
384C2C2×#1062272311yescharacteristic
385C2#1307707611yescharacteristic
386C2#1307709811yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2972C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#66991C4
cosocleC22×C4×C11C24
hypercenter#2972D11
hypocenterC11#17388
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13077657C2semidirect
3. #13066979C2semidirect
4. #13066962C2semidirect
5. #13066939C2semidirect
6. #13066928C2semidirect
7. C11×#2972C2semidirect
131. #2972D11semidirect
321. C11#17388semidirect

Maximal subgroups

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

subgroupindex
C2×#106230922
#130776572
#130669792
#130669622
#130669392
#130669282
C11×#29722
#1738811