Finite Group Databasebeta

← #14721592

Subgroups — #14721592

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082380C211yesmaximal, characteristic
2#13077657C211yesmaximal, characteristic, complemented
3#13067175C212yesmaximal, complemented
4#13067144C214yesmaximal, complemented
5#13067131C214yesmaximal, complemented
6#13067110C212yesmaximal, complemented
7C11×#2357C211yesmaximal, characteristic, complemented
8C2×#67037—21no—
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66983C2214yes—
11#10623086C414yescomplemented
12#10623085—24no—
13D4×D44C414yescomplemented
14#10623041—21no—
15#10623024—22no—
16#10623008C2212yes—
17C11×#390—21no—
18C11×#388—22no—
19C11×#382C2211yescharacteristic, complemented
20C11×#381C2212yescomplemented
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4C2211yescharacteristic, complemented
23C4×C11×C22⋊C4C2212yescomplemented
24#10622820C2214yescomplemented
25#10622625—24no—
26#10622538C2212yescomplemented
27#10622089C2214yescomplemented
28#10622089C2214yescomplemented
29#10622089C2218yescomplemented
30C22×D4×C11D411yescharacteristic
31C23×C4×C11C2312yes—
32C22×C22⋊D11—24no—
33#67037—44no—
34#67037—44no—
35C2×#4341—24no—
36C2×D4×D11—24no—
37C2×#4339—22no—
38C22×D44C2×C414yes—
39C4×D4×C11C2×C414yes—
40C4×D4×C11D414yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C22⋊C4—22no—
45C2×C11×C22⋊C4—22no—
46C2×C11×C22⋊C4D412yes—
47C2×C42×C11—21no—
48C2×C42×C11—22no—
49C2×C42×C11C2311yescharacteristic
50#66983—22no—
51#66983—24no—
52#66983—24no—
53#66983C2×C418yes—
54#66983C2314yes—
55C2×(C2×D11)⋊C4—24no—
56C2×C4⋊Dic11C2×C414yes—
57C2×#4318—24no—
58#66950—24no—
59#66948—24no—
60#66939—28no—
61#66935—28no—
62#66928—22no—
63#66927C2×C412yes—
64C4×D44—22no—
65C4×D44C2×C414yes—
66#66922C2×C412yes—
67C11×#95—22no—
68C11×#95—21no—
69C11×#95C2311yescharacteristic
70C11×#95C2312yes—
71C11×#95C2311yescharacteristic
72C22⋊(C11⋊C8)—24no—
73C22⋊(C11⋊C8)C2314yes—
74C4⋊(C11⋊C8)—22no—
75C4×C11⋊C8—22no—
76#17626—111nomaximal, Sylow
77C24×C11C2×D412yes—
78C23×D11—24no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11C22⋊C414yes—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—21no—
85C22×C4×C11—82no—
86C22×C4×C11C22×C414yes—
87C22×C4×C11C2×D412yes—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D414yes—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2411yescharacteristic
92C2×C22⋊D11—28no—
93C2×C22⋊D11—24no—
94C2×C22⋊D11—48no—
95C2×C22⋊D11—48no—
96C22×Dic11—24no—
97#4341—416no—
98D4×D11—416no—
99#4339—44no—
100#4339—44no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—24no—
104C2×D44—84no—
105C2×D44C22×C414yes—
106C2×C4×D11—24no—
107C2×Dic22—22no—
108C11×C4⋊C4—42no—
109C11×C4⋊C4—42no—
110C11×C4⋊C4C22⋊C414yes—
111C11×C22⋊C4—44no—
112C11×C22⋊C4—82no—
113C11×C22⋊C4C22⋊C418yes—
114C42×C11—42no—
115C42×C11—82no—
116C42×C11C22×C412yes—
117C42×C11C2×D412yes—
118(C2×D11)⋊C4—24no—
119(C2×D11)⋊C4—28no—
120(C2×D11)⋊C4—24no—
121C4⋊Dic11—22no—
122C4⋊Dic11—24no—
123C4⋊Dic11C22×C414yes—
124#4318—84no—
125C2×C11⋊C8—24no—
126#3496—111no—
127#2975—111no—
128#2357D1111yescharacteristic, complemented
129#1517—112no—
130#1510—114no—
131#1507—114no—
132#1502—112no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—42no—
136C23×C11—42no—
137C23×C11C2×C22⋊C414yes—
138C23×C11C22×D411yescharacteristic
139C22×D11—24no—
140C22×D11—48no—
141C22×D11—84no—
142C22×D11—84no—
143D4×C11—28no—
144C2×C4×C11—22no—
145C2×C4×C11—44no—
146C2×C4×C11—42no—
147C2×C4×C11—41no—
148C2×C4×C11—44no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—42no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—42no—
158C2×C4×C11C2×C22⋊C412yes—
159C2×C4×C11C2×C22⋊C414yes—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11AGL(1,ℤ/8)12yes—
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11C23×C411yescharacteristic
164C2×C4×C11C22×D411yescharacteristic
165C22⋊D11—416no—
166C22⋊D11—44no—
167C22⋊D11—44no—
168C2×Dic11—24no—
169C2×Dic11—48no—
170D44—44no—
171D44—44no—
172D44—82no—
173D44—84no—
174C4×D11—48no—
175Dic22—44no—
176C11⋊C8—44no—
177C2×H(5,𝔽2)—221no—
178#547—114no—
179#546—224no—
180D42—114no—
181#537—221no—
182#534—222no—
183#532—112no—
184C2×#121—114no—
185C2×C4×D4C2×D1111yescharacteristic
186#436—224no—
187#431—112no—
188#407—114no—
189#390—21no—
190#388—22no—
191#382C2×D1111yescharacteristic, complemented
192#381C2×D1112yescomplemented
193C4×C4⋊C4—21no—
194C4×C4⋊C4C2×D1111yescharacteristic, complemented
195C4×C22⋊C4C2×D1112yescomplemented
196#327—114no—
197#327—114no—
198#327—118no—
199C22×C11—21no—
200C22×C11—21no—
201C22×C11—24no—
202C22×C11—24no—
203C22×C11—24no—
204C22×C11—82no—
205C22×C11—82no—
206C22×C11C22×C22⋊C411yescharacteristic
207C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
208C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
209C2×D11—44no—
210C2×D11—44no—
211C2×D11—44no—
212C2×D11—168no—
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—24no—
216C4×C11—22no—
217C4×C11—42no—
218C4×C11—81no—
219C4×C11—82no—
220C4×C11#41814yes—
221Dic11—44no—
222H(5,𝔽2)—444no—
223H(5,𝔽2)—444no—
224C2×#41—224no—
225C2×#41—222no—
226C22×D4—114no—
227C22×D4—224no—
228C22×D4—224no—
229C22×D4C22⋊D1111yescharacteristic
230C23×C4C22×D1112yes—
231C2×M16—224no—
232C4⋊Q8—112no—
233#127—112no—
234#124—222no—
235#123—228no—
236C22⋊Q8—224no—
237#121—118no—
238#121—114no—
239#121—224no—
240#121—224no—
241#121—222no—
242#121—224no—
243#120—228no—
244C4×D4—114no—
245C4×D4—222no—
246C4×D4C4×D1114yes—
247C4×D4D4414yes—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—114no—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C22⋊C4—22no—
253C2×C22⋊C4—22no—
254C2×C22⋊C4—224no—
255C2×C22⋊C4C22⋊D1112yes—
256C2×C42—21no—
257C2×C42—22no—
258C2×C42C22×D1111yescharacteristic
259C4⋊C8—222no—
260C22⋊C8—114no—
261C22⋊C8—224no—
262C4×C8—222no—
263#95—22no—
264#95—21no—
265#95C22×D1111yescharacteristic
266#95C22×D1112yes—
267#95C22×D1111yescharacteristic
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—44no—
271C2×C11#288311yescharacteristic
272C2×C11C2×#41811yescharacteristic
273C2×C11#290111yescharacteristic
274D11—84no—
275C24—224no—
276C24C2×C22⋊D1112yes—
277#41—4416no—
278#41—444no—
279#41—444no—
280C2×Q8—222no—
281C2×D4—22no—
282C2×D4—22no—
283C2×D4—114no—
284C2×D4—228no—
285C2×D4—224no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—224no—
289C2×D4—4416no—
290C2×D4—448no—
291C2×D4—448no—
292C2×D4—884no—
293C2×D4(C2×D11)⋊C414yes—
294C22×C4—21no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—82no—
298C22×C4—224no—
299C22×C4—224no—
300C22×C4C2×C4×D1114yes—
301C22×C4C2×D4414yes—
302C22×C4C2×C22⋊D1112yes—
303C22×C4C2×C22⋊D1111yescharacteristic
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C23×D1111yescharacteristic
306M16—884no—
307C2×C8—224no—
308C4⋊C4—42no—
309C4⋊C4—42no—
310C4⋊C4—114no—
311C4⋊C4—224no—
312C4⋊C4—222no—
313C4⋊C4(C2×D11)⋊C414yes—
314C22⋊C4—44no—
315C22⋊C4—82no—
316C22⋊C4—228no—
317C22⋊C4—224no—
318C22⋊C4—224no—
319C22⋊C4(C2×D11)⋊C418yes—
320C42—42no—
321C42—82no—
322C42C2×C4×D1112yes—
323C42C2×D4412yes—
324C11#1762611yescharacteristic, complemented, Sylow
325C23—22no—
326C23—22no—
327C23—42no—
328C23—42no—
329C23—224no—
330C23—448no—
331C23—884no—
332C23—884no—
333C23C2×(C2×D11)⋊C414yes—
334C23C22×C22⋊D1111yescharacteristic
335Q8—444no—
336D4—28no—
337D4—444no—
338D4—4416no—
339D4—444no—
340D4—444no—
341D4—444no—
342D4—884no—
343D4—882no—
344C2×C4—22no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—224no—
359C2×C4—448no—
360C2×C4—448no—
361C2×C4C2×(C2×D11)⋊C412yes—
362C2×C4C2×(C2×D11)⋊C414yes—
363C2×C4C2×(C2×D11)⋊C412yes—
364C2×C4#6700212yes—
365C2×C4#6700212yes—
366C2×C4C22×C4×D1111yescharacteristic
367C2×C4C22×D4411yescharacteristic
368C8—444no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—82no—
375C22—82no—
376C22—444no—
377C22—444no—
378C22—444no—
379C22—1768no—
380C22C22×(C2×D11)⋊C411yescharacteristic
381C22C2×#6700211yescharacteristic
382C22C2×#6700211yescharacteristic
383C4—21no—
384C4—21no—
385C4—24no—
386C4—22no—
387C4—42no—
388C4—81no—
389C4—82no—
390C4—444no—
391C4#1062261414yes—
392C2—21no—
393C2—21no—
394C2—44no—
395C2—884no—
396C2#1307707611yescharacteristic
397C2C2×#1062261411yescharacteristic
398C2#1307716411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2357C2
socleC22×C11C22×C22⋊C4
prime radical#13082380C2
cosocleC22×C4×C11C24
hypercenter#2357D11
hypocenterC11#17626
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2357

Complements

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

NH ≅ G/Ntype
2. #13077657C2semidirect
3. #13067175C2semidirect
4. #13067144C2semidirect
5. #13067131C2semidirect
6. #13067110C2semidirect
7. C11×#2357C2semidirect
11. #10623086C4semidirect
13. D4×D44C4semidirect
19. C11×#382C22semidirect
20. C11×#381C22semidirect
22. C4×C11×C4⋊C4C22semidirect
23. C4×C11×C22⋊C4C22semidirect
24. #10622820C22semidirect
26. #10622538C22semidirect
27. #10622089C22semidirect
28. #10622089C22semidirect
29. #10622089C22semidirect
128. #2357D11semidirect
191. #382C2×D11semidirect
192. #381C2×D11semidirect
194. C4×C4⋊C4C2×D11semidirect
195. C4×C22⋊C4C2×D11semidirect
324. C11#17626semidirect

Maximal subgroups

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

subgroupindex
#130823802
#130776572
#130671752
#130671442
#130671312
#130671102
C11×#23572
#1762611