Finite Group Databasebeta

← #14650460

Subgroups — #14650460

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077334C211yesmaximal, characteristic, complemented
2#13069441C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic, complemented
5#13066475C211yesmaximal, characteristic, complemented
6#13066446C211yesmaximal, characteristic, complemented
7C11×#3205C211yesmaximal, characteristic
8C11×#532C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#67001—21no—
11C11×#493C412yescomplemented
12C11×#486C412yescomplemented
13C11×#459—22no—
14C11×#447—22no—
15C11×#431C2211yescharacteristic
16#10622847—21no—
17C2×#66896—21no—
18C2×#66896—21no—
19#10622624—22no—
20#10622624—22no—
21#10622549C2211yescharacteristic
22#10622538C2211yescharacteristic
23#10622537C2211yescharacteristic
24C2×#66867C2211yescharacteristic
25#10622182—22no—
26#10622175—22no—
27C2×C11×#41—21no—
28C22×D4×C11—21no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C2×C11×D8—24no—
32C11×C4⋊Q8C2×C411yescharacteristic
33C11×#127—21no—
34C11×#127—21no—
35C11×#127—21no—
36C11×#127C2×C412yes—
37C11×#127C2×C411yescharacteristic
38C11×#124—21no—
39C11×#121—21no—
40C11×#121D412yes—
41C4×D4×C11—21no—
42C4×D4×C11D412yes—
43C2×C42×C11C2311yescharacteristic
44#67001—42no—
45#67001—42no—
46C2×C4⋊Dic11—21no—
47C2×#4318—22no—
48C2×#4318—21no—
49C22×C11⋊C8—22no—
50C22×C11⋊C8D411yescharacteristic
51C22×C11⋊C8D411yescharacteristic
52C11×C4⋊C8—21no—
53C11×#102—24no—
54C11×C22⋊C8—21no—
55C4×C8×C11C2×C412yes—
56#66896—42no—
57#66896—42no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C22⋊(C11⋊C8)—24no—
61C22⋊(C11⋊C8)—21no—
62C4⋊(C11⋊C8)—21no—
63C4⋊(C11⋊C8)—21no—
64C4⋊(C11⋊C8)D412yes—
65#66867—21no—
66#66867—21no—
67C4×C11⋊C8—21no—
68#9293—111nomaximal, Sylow
69C24×C11—41no—
70C11×#41—41no—
71C11×#41—41no—
72C11×#41—41no—
73C11×#41—41no—
74C2×Q8×C11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—21no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—22no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—82no—
89C2×D4×C11—82no—
90C2×D4×C11C22⋊C412yes—
91C22×C4×C11—22no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—41no—
96C11×D8—84no—
97C2×C8×C11—22no—
98C11×C4⋊C4—21no—
99C11×C4⋊C4C22⋊C412yes—
100C11×C22⋊C4—22no—
101C11×C22⋊C4—22no—
102C42×C11C22×C411yescharacteristic
103C42×C11C2×D411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C4⋊Dic11—41no—
107C4⋊Dic11—41no—
108#4318—44no—
109#4318—41no—
110#4318—41no—
111C2×C11⋊C8—21no—
112C2×C11⋊C8—21no—
113C2×C11⋊C8—22no—
114C2×C11⋊C8—21no—
115C2×C11⋊C8—21no—
116C2×C11⋊C8—21no—
117C2×C11⋊C8—44no—
118C2×C11⋊C8—41no—
119C2×C11⋊C8D812yescomplemented
120#3205D1111yescharacteristic
121#2932—111no—
122#1961—111no—
123#1545—111no—
124#1517—111no—
125#1286—111no—
126#1275—111no—
127C23×C11—22no—
128C23×C11—42no—
129C23×C11—82no—
130C23×C11—82no—
131C23×C11—81no—
132C23×C11—81no—
133C23×C11#12111yescharacteristic
134Q8×C11—41no—
135Q8×C11—41no—
136D4×C11—42no—
137D4×C11—44no—
138D4×C11—42no—
139D4×C11—42no—
140D4×C11—41no—
141D4×C11—42no—
142D4×C11—41no—
143D4×C11—42no—
144D4×C11—81no—
145D4×C11—82no—
146D4×C11—82no—
147D4×C11—82no—
148D4×C11—81no—
149D4×C11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11—41no—
153C2×C4×C11—42no—
154C2×C4×C11—42no—
155C2×C4×C11C2×C22⋊C411yescharacteristic
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12311yescharacteristic
161C2×C4×C11C2×D811yescharacteristic
162C2×C4×C11#13511yescharacteristic
163C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×Dic11—81no—
166C2×Dic11—81no—
167C2×Dic11—81no—
168C8×C11—42no—
169C11⋊C8—22no—
170C11⋊C8—42no—
171C11⋊C8—41no—
172C11⋊C8—81no—
173C2×#131—221no—
174#532C2×D1111yescharacteristic
175C2×#127C2×D1111yescharacteristic
176#493Dic1112yescomplemented
177#486Dic1112yescomplemented
178#459—22no—
179#447—22no—
180#435—222no—
181#435—222no—
182#431—111no—
183#431C2×D1111yescharacteristic
184#423—111no—
185C2×#102—221no—
186C2×#102—221no—
187#408—221no—
188C2×#97—111no—
189#382—111no—
190#331—222no—
191#327—222no—
192C22×C11—21no—
193C22×C11—21no—
194C22×C11—42no—
195C22×C11—42no—
196C22×C11—42no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11—82no—
200C22×C11—162no—
201C22×C11—162no—
202C22×C11#38611yescharacteristic
203C22×C11#45911yescharacteristic
204C22×C11#46311yescharacteristic
205C4×C11—21no—
206C4×C11—21no—
207C4×C11—21no—
208C4×C11—21no—
209C4×C11—42no—
210C4×C11C4×D811yescharacteristic
211C4×C11#44211yescharacteristic
212C4×C11#44711yescharacteristic
213C4×C11#44911yescharacteristic
214Dic11—161no—
215C2×#41—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—21no—
219C2×D8—24no—
220#131—442no—
221#131—442no—
222C2×M16—222no—
223C2×M16—221no—
224C22×C8—111no—
225C22×C8—111no—
226C22×C8—222no—
227C4⋊Q8C2×Dic1111yescharacteristic
228#127—21no—
229#127—21no—
230#127—21no—
231#127C2×Dic1112yes—
232#127C2×Dic1111yescharacteristic
233#124—21no—
234#121—21no—
235#121C22⋊D1112yes—
236C4×D4—21no—
237C4×D4C22⋊D1112yes—
238C2×C4⋊C4—221no—
239C2×C42C22×D1111yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—112no—
242C4⋊C8—221no—
243C4⋊C8—221no—
244#102—24no—
245#102—442no—
246#102—442no—
247C22⋊C8—21no—
248C22⋊C8—224no—
249C22⋊C8—221no—
250#97—221no—
251#97—221no—
252C4×C8—221no—
253C4×C8C2×Dic1112yes—
254#95—221no—
255#95—221no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11—82no—
259C2×C11—162no—
260C2×C11#187911yescharacteristic
261C2×C11#190311yescharacteristic
262C2×C11#191011yescharacteristic
263C24—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268C2×Q8—21no—
269C2×D4—22no—
270C2×D4—21no—
271C2×D4—22no—
272C2×D4—21no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—82no—
283C2×D4—82no—
284C2×D4C22⋊Dic1112yes—
285C22×C4—22no—
286C22×C4—441no—
287C22×C4D4×D1111yescharacteristic
288C22×C4#434111yescharacteristic
289C22×C4C2×C22⋊D1111yescharacteristic
290D8—84no—
291M16—444no—
292M16—441no—
293M16—441no—
294C2×C8—22no—
295C2×C8—112no—
296C2×C8—221no—
297C2×C8—221no—
298C2×C8—221no—
299C2×C8—221no—
300C2×C8—221no—
301C2×C8—222no—
302C2×C8—444no—
303C2×C8—441no—
304C4⋊C4—21no—
305C4⋊C4—441no—
306C4⋊C4—441no—
307C4⋊C4C22⋊Dic1112yes—
308C22⋊C4—22no—
309C22⋊C4—22no—
310C42D4×D1111yescharacteristic
311C42#434111yescharacteristic
312C42C22×Dic1111yescharacteristic
313C42C2×C22⋊D1111yescharacteristic
314C11#929311yescharacteristic, complemented, Sylow
315C23—22no—
316C23—42no—
317C23—82no—
318C23—82no—
319C23—81no—
320C23—81no—
321C23#6699211yescharacteristic
322Q8—41no—
323Q8—41no—
324D4—42no—
325D4—44no—
326D4—42no—
327D4—42no—
328D4—41no—
329D4—42no—
330D4—41no—
331D4—42no—
332D4—81no—
333D4—82no—
334D4—82no—
335D4—82no—
336D4—81no—
337D4—81no—
338C2×C4—22no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—881no—
344C2×C4—881no—
345C2×C4—881no—
346C2×C4D8×D1111yescharacteristic
347C2×C4#6696411yescharacteristic
348C2×C4#6696411yescharacteristic
349C2×C4#6696511yescharacteristic
350C2×C4D4×Dic1111yescharacteristic
351C2×C4D4×Dic1111yescharacteristic
352C2×C4#6698811yescharacteristic
353C2×C4#6699011yescharacteristic
354C2×C4#6699211yescharacteristic
355C2×C4C2×C22⋊Dic1111yescharacteristic
356C8—42no—
357C8—222no—
358C8—442no—
359C8—441no—
360C8—881no—
361C22—21no—
362C22—21no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22—162no—
370C22—162no—
371C22#1062276311yescharacteristic
372C22#1062276611yescharacteristic
373C22#1062283311yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—42no—
379C4—1761no—
380C4D8×Dic1111yescharacteristic
381C4#1062276511yescharacteristic
382C4#1062276911yescharacteristic
383C4#1062277111yescharacteristic
384C2—21no—
385C2—21no—
386C2—82no—
387C2—162no—
388C2#1306896611yescharacteristic
389C2#1306909811yescharacteristic
390C2#1306914411yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3205C2
socleC22×C11#386
cosocleC2×C42×C11C23
hypercenter#3205D11
hypocenterC11#9293
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #13077334C2semidirect
2. #13069441C2semidirect
3. #13067284C2semidirect
4. #13067176C2semidirect
5. #13066475C2semidirect
6. #13066446C2semidirect
11. C11×#493C4semidirect
12. C11×#486C4semidirect
119. C2×C11⋊C8D8semidirect
176. #493Dic11semidirect
177. #486Dic11semidirect
314. C11#9293semidirect

Maximal subgroups

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

subgroupindex
#130773342
#130694412
#130672842
#130671762
#130664752
#130664462
C11×#32052
#929311