Finite Group Databasebeta

← #14721593

Subgroups — #14721593

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#13077657C211yesmaximal, characteristic, complemented
2#13071589C211yesmaximal, characteristic, complemented
3#13067176C212yesmaximal, complemented
4#13067145C214yesmaximal, complemented
5#13067132C214yesmaximal, complemented
6#13067111C212yesmaximal, complemented
7C11×#3496C211yesmaximal, characteristic
8C2×C11×H(5,𝔽2)—21no—
9C11×#547C414yescomplemented
10C11×#546—24no—
11D42×C11C414yescomplemented
12C11×#537—21no—
13C11×#534—22no—
14C11×#532C2212yes—
15C2×C11×#121C2214yes—
16C2×C4×D4×C11C2211yescharacteristic
17#10622834—21no—
18#10622824C2212yescomplemented
19C4×C22⋊Dic11C2212yescomplemented
20#10622820C2214yescomplemented
21#10622625—24no—
22C4⋊C4×Dic11—21no—
23#10622564—22no—
24#10622549C2211yescharacteristic, complemented
25C4×C4⋊Dic11C2211yescharacteristic, complemented
26#10622538C2212yescomplemented
27#10622175C2214yescomplemented
28#10622175C2214yescomplemented
29#10622175C2218yescomplemented
30C11×H(5,𝔽2)—44no—
31C11×H(5,𝔽2)—44no—
32C2×C11×#41—24no—
33C2×C11×#41—22no—
34C22×D4×C11—24no—
35C22×D4×C11—24no—
36C22×D4×C11C2×C414yes—
37C22×D4×C11D411yescharacteristic
38C23×C4×C11C2312yes—
39C11×C4⋊Q8C2×C412yes—
40C11×#127C2×C412yes—
41C11×#124—22no—
42C11×#123—28no—
43C11×C22⋊Q8—24no—
44C11×#121—24no—
45C11×#121—24no—
46C11×#121—22no—
47C11×#121—24no—
48C11×#121C2×C418yes—
49C11×#121C2314yes—
50C11×#120—28no—
51C4×D4×C11—22no—
52C4×D4×C11C2×C414yes—
53C4×D4×C11C2×C414yes—
54C4×D4×C11D414yes—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4D411yescharacteristic
57C2×C11×C22⋊C4—24no—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—22no—
66C2×#4318—24no—
67C11⋊#95—21no—
68C11⋊#95—22no—
69C11⋊#95C2311yescharacteristic
70C11⋊#95C2311yescharacteristic
71C11⋊#95C2312yes—
72C22⋊(C11⋊C8)—24no—
73C22⋊(C11⋊C8)C2314yes—
74C4⋊(C11⋊C8)—22no—
75C4×C11⋊C8—22no—
76#17626—111nomaximal, Sylow
77C24×C11—24no—
78C24×C11C2×D412yes—
79C11×#41—416no—
80C11×#41—44no—
81C11×#41—44no—
82C2×Q8×C11—22no—
83C2×D4×C11—28no—
84C2×D4×C11—24no—
85C2×D4×C11—22no—
86C2×D4×C11—22no—
87C2×D4×C11—24no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—416no—
91C2×D4×C11—48no—
92C2×D4×C11—48no—
93C2×D4×C11—84no—
94C2×D4×C11C22⋊C414yes—
95C2×D4×C11C22×C414yes—
96C22×C4×C11—24no—
97C22×C4×C11—24no—
98C22×C4×C11—82no—
99C22×C4×C11C22×C414yes—
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D414yes—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2411yescharacteristic
105C22×Dic11—21no—
106C22×Dic11—22no—
107C22×Dic11—21no—
108C11×C4⋊C4—24no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4C22⋊C414yes—
111C11×C4⋊C4C22×C414yes—
112C11×C22⋊C4—28no—
113C11×C22⋊C4—24no—
114C11×C22⋊C4—24no—
115C11×C22⋊C4C22⋊C418yes—
116C42×C11C22×C412yes—
117C42×C11C2×D412yes—
118C22⋊Dic11—44no—
119C22⋊Dic11—82no—
120C4⋊Dic11—42no—
121C4⋊Dic11—42no—
122C4×Dic11—42no—
123C4×Dic11—82no—
124#4318—84no—
125C2×C11⋊C8—24no—
126#3496D1111yescharacteristic
127#2975—111no—
128#2357—111no—
129#1517—112no—
130#1510—114no—
131#1507—114no—
132#1502—112no—
133C23×C11—22no—
134C23×C11—22no—
135C23×C11—24no—
136C23×C11—42no—
137C23×C11—42no—
138C23×C11—48no—
139C23×C11—84no—
140C23×C11—84no—
141C23×C11C2×C22⋊C414yes—
142C23×C11C22×D411yescharacteristic
143Q8×C11—44no—
144D4×C11—28no—
145D4×C11—44no—
146D4×C11—416no—
147D4×C11—44no—
148D4×C11—44no—
149D4×C11—44no—
150D4×C11—82no—
151D4×C11—84no—
152C2×C4×C11—24no—
153C2×C4×C11—44no—
154C2×C4×C11—42no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—44no—
158C2×C4×C11—48no—
159C2×C4×C11—48no—
160C2×C4×C11C2×C22⋊C412yes—
161C2×C4×C11C2×C22⋊C414yes—
162C2×C4×C11C2×C22⋊C412yes—
163C2×C4×C11AGL(1,ℤ/8)12yes—
164C2×C4×C11AGL(1,ℤ/8)12yes—
165C2×C4×C11C23×C411yescharacteristic
166C2×C4×C11C22×D411yescharacteristic
167C2×Dic11—22no—
168C2×Dic11—41no—
169C2×Dic11—41no—
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—41no—
174C2×Dic11—41no—
175C2×Dic11—42no—
176C11⋊C8—44no—
177C2×H(5,𝔽2)—21no—
178#547Dic1114yescomplemented
179#546—24no—
180D42Dic1114yescomplemented
181#537—21no—
182#534—22no—
183#532C2×D1112yes—
184C2×#121C2×D1114yes—
185C2×C4×D4C2×D1111yescharacteristic
186#436—224no—
187#431—112no—
188#407—114no—
189#390—221no—
190#388—222no—
191#382—111no—
192#381—112no—
193C4×C4⋊C4—111no—
194C4×C4⋊C4—221no—
195C4×C22⋊C4—112no—
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—44no—
205C22×C11—44no—
206C22×C11—44no—
207C22×C11—82no—
208C22×C11—82no—
209C22×C11—168no—
210C22×C11C22×C22⋊C411yescharacteristic
211C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
212C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
213C4×C11—21no—
214C4×C11—21no—
215C4×C11—24no—
216C4×C11—22no—
217C4×C11—44no—
218C4×C11#41814yes—
219Dic11—42no—
220Dic11—81no—
221Dic11—82no—
222H(5,𝔽2)—44no—
223H(5,𝔽2)—44no—
224C2×#41—24no—
225C2×#41—22no—
226C22×D4—24no—
227C22×D4—24no—
228C22×D4C2×Dic1114yes—
229C22×D4C22⋊D1111yescharacteristic
230C23×C4C22×D1112yes—
231C2×M16—224no—
232C4⋊Q8C2×Dic1112yes—
233#127C2×Dic1112yes—
234#124—22no—
235#123—28no—
236C22⋊Q8—24no—
237#121—24no—
238#121—24no—
239#121—22no—
240#121—24no—
241#121C2×Dic1118yes—
242#121C22×D1114yes—
243#120—28no—
244C4×D4—22no—
245C4×D4C2×Dic1114yes—
246C4×D4C2×Dic1114yes—
247C4×D4C22⋊D1114yes—
248C2×C4⋊C4—221no—
249C2×C4⋊C4—221no—
250C2×C4⋊C4C2×Dic1114yes—
251C2×C4⋊C4C22⋊D1111yescharacteristic
252C2×C22⋊C4—24no—
253C2×C22⋊C4—222no—
254C2×C22⋊C4—222no—
255C2×C22⋊C4C22⋊D1112yes—
256C2×C42—221no—
257C2×C42—222no—
258C2×C42C22×D1111yescharacteristic
259C4⋊C8—222no—
260C22⋊C8—114no—
261C22⋊C8—224no—
262C4×C8—222no—
263#95—111no—
264#95—112no—
265#95—111no—
266#95—222no—
267#95—221no—
268C2×C11—21no—
269C2×C11—21no—
270C2×C11—44no—
271C2×C11—84no—
272C2×C11#288311yescharacteristic
273C2×C11C2×#41811yescharacteristic
274C2×C11#290111yescharacteristic
275C24—24no—
276C24C2×C22⋊D1112yes—
277#41—416no—
278#41—44no—
279#41—44no—
280C2×Q8—22no—
281C2×D4—28no—
282C2×D4—24no—
283C2×D4—22no—
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—24no—
288C2×D4—416no—
289C2×D4—48no—
290C2×D4—48no—
291C2×D4—84no—
292C2×D4C22⋊Dic1114yes—
293C2×D4C22×Dic1114yes—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—82no—
297C22×C4—221no—
298C22×C4—222no—
299C22×C4—221no—
300C22×C4C22×Dic1114yes—
301C22×C4C2×C22⋊D1112yes—
302C22×C4C2×C22⋊D1111yescharacteristic
303C22×C4C2×C22⋊D1114yes—
304C22×C4C2×C22⋊D1111yescharacteristic
305C22×C4C23×D1111yescharacteristic
306M16—884no—
307C2×C8—224no—
308C4⋊C4—24no—
309C4⋊C4—22no—
310C4⋊C4—442no—
311C4⋊C4—442no—
312C4⋊C4C22⋊Dic1114yes—
313C4⋊C4C22×Dic1114yes—
314C22⋊C4—28no—
315C22⋊C4—24no—
316C22⋊C4—24no—
317C22⋊C4—444no—
318C22⋊C4—882no—
319C22⋊C4C22⋊Dic1118yes—
320C42—442no—
321C42—882no—
322C42C22×Dic1112yes—
323C42C2×C22⋊D1112yes—
324C11#1762611yescharacteristic, complemented, Sylow
325C23—22no—
326C23—22no—
327C23—24no—
328C23—42no—
329C23—42no—
330C23—48no—
331C23—84no—
332C23—84no—
333C23C2×C22⋊Dic1114yes—
334C23C22×C22⋊D1111yescharacteristic
335Q8—44no—
336D4—28no—
337D4—44no—
338D4—416no—
339D4—44no—
340D4—44no—
341D4—44no—
342D4—82no—
343D4—84no—
344C2×C4—24no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—44no—
348C2×C4—41no—
349C2×C4—44no—
350C2×C4—48no—
351C2×C4—48no—
352C2×C4—222no—
353C2×C4—441no—
354C2×C4—441no—
355C2×C4—442no—
356C2×C4—442no—
357C2×C4—441no—
358C2×C4—441no—
359C2×C4—441no—
360C2×C4—442no—
361C2×C4#6698512yes—
362C2×C4#6698512yes—
363C2×C4C2×C22⋊Dic1112yes—
364C2×C4C2×C22⋊Dic1114yes—
365C2×C4C2×C22⋊Dic1112yes—
366C2×C4C23×Dic1111yescharacteristic
367C2×C4C22×C22⋊D1111yescharacteristic
368C8—444no—
369C22—21no—
370C22—21no—
371C22—24no—
372C22—24no—
373C22—24no—
374C22—44no—
375C22—44no—
376C22—44no—
377C22—82no—
378C22—82no—
379C22—168no—
380C22C2×#6698511yescharacteristic
381C22C2×#6698511yescharacteristic
382C22C22×C22⋊Dic1111yescharacteristic
383C4—21no—
384C4—21no—
385C4—24no—
386C4—22no—
387C4—44no—
388C4—442no—
389C4—881no—
390C4—882no—
391C4#1062282814yes—
392C2—21no—
393C2—21no—
394C2—44no—
395C2—84no—
396C2#1307707711yescharacteristic
397C2C2×#1062282811yescharacteristic
398C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3496C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3496D11
hypocenterC11#17626
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #13077657C2semidirect
2. #13071589C2semidirect
3. #13067176C2semidirect
4. #13067145C2semidirect
5. #13067132C2semidirect
6. #13067111C2semidirect
9. C11×#547C4semidirect
11. D42×C11C4semidirect
18. #10622824C22semidirect
19. C4×C22⋊Dic11C22semidirect
20. #10622820C22semidirect
24. #10622549C22semidirect
25. C4×C4⋊Dic11C22semidirect
26. #10622538C22semidirect
27. #10622175C22semidirect
28. #10622175C22semidirect
29. #10622175C22semidirect
178. #547Dic11semidirect
180. D42Dic11semidirect
324. C11#17626semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130715892
#130671762
#130671452
#130671322
#130671112
C11×#34962
#1762611