Finite Group Databasebeta

← #14737664

Subgroups — #14737664

Order 2816.

870 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078092C212yesmaximal, complemented
2C8×#4339C211yesmaximal, characteristic, complemented
3#13067973C214yesmaximal, complemented
4#13067968C214yesmaximal, complemented
5#13067375C211yesmaximal, characteristic, complemented
6#13067284C212yesmaximal, complemented
7C2×C11×#493C211yesmaximal, characteristic, complemented
8C22×C11×D8—22no—
9C2×C11×#127C2212yes—
10C2×#66985—22no—
11C4×#4339C2211yescharacteristic
12C11×#493—21no—
13C11×#493—21no—
14C11×#493C2214yes—
15C2×C4×C8×C11C2211yescharacteristic
16#10622828—22no—
17C8×C22⋊D11—22no—
18#10622688—22no—
19#10622688C2214yescomplemented
20#10622685—22no—
21#10622685C2214yescomplemented
22#10622538C2211yescharacteristic
23#10622537C2212yes—
24C8×D44C2212yescomplemented
25#10622298—21no—
26C4×C8×D11—21no—
27C8×Dic22C2212yescomplemented
28#10622182C2218yescomplemented
29#10622096C2214yescomplemented
30C22×D4×C11—22no—
31C22×D4×C11—22no—
32C22×D4×C11—22no—
33C2×#4339D411yescharacteristic
34C2×C11×D8—24no—
35C2×C11×D8—24no—
36C2×C11×D8—48no—
37C22×C8×C11D412yes—
38C11×#127—22no—
39C11×#127—22no—
40C11×#127—22no—
41C11×#127C2314yes—
42C2×C42×C11C2311yescharacteristic
43C2×#4324—24no—
44#66985—48no—
45C2×#4323—24no—
46C4×C22⋊D11—21no—
47C4×C22⋊D11—21no—
48#66979D411yescharacteristic
49C2×#4318—22no—
50C2×C8×D11—22no—
51C4×D44D411yescharacteristic
52C4×D44C2311yescharacteristic
53#66925—21no—
54C42×D11—21no—
55C4×Dic22D411yescharacteristic
56C4×Dic22C2311yescharacteristic
57C4×C8×C11D411yescharacteristic
58C4×C8×C11D411yescharacteristic
59C4×C8×C11C2312yes—
60#66896—24no—
61#66896—24no—
62C22⋊(C11⋊C8)—21no—
63(C2×D11)⋊C8—22no—
64Dic11⋊C8—22no—
65C8×Dic11—22no—
66C4⋊(C11⋊C8)—22no—
67C4⋊(C11⋊C8)C2314yes—
68C4⋊(C11⋊C8)C2312yes—
69C4×C11⋊C8—21no—
70#19267—111nomaximal, Sylow
71C24×C11—42no—
72C2×D4×C11—24no—
73C2×D4×C11—24no—
74C2×D4×C11—24no—
75C2×D4×C11—48no—
76C2×D4×C11—42no—
77C2×D4×C11—42no—
78C2×D4×C11—42no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—84no—
82C22×C4×C11C2×D411yescharacteristic
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C2×C22⋊D11—21no—
86#4339—22no—
87#4339D814yescomplemented
88C2×D44C2×D411yescharacteristic
89C2×C4×D11—21no—
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×Dic22C2×D411yescharacteristic
93C11×D8—48no—
94C11×D8—48no—
95C2×C8×C11—24no—
96C2×C8×C11C2×D412yes—
97C2×C8×C11C2×D412yes—
98C42×C11C2×D411yescharacteristic
99C42×C11C2×D411yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11C2411yescharacteristic
102C22⋊Dic11—21no—
103#4324—48no—
104#4323—48no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107C4⋊Dic11C2×D411yescharacteristic
108C4⋊Dic11C2×D411yescharacteristic
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111C4×Dic11—21no—
112C4×Dic11—21no—
113C4×Dic11—21no—
114#4318—44no—
115C2×C11⋊C8—22no—
116C2×C11⋊C8—24no—
117C8×D11—44no—
118C2×#493D1111yescharacteristic, complemented
119#3038—112no—
120C8×#41—111no—
121#1668—114no—
122#1667—114no—
123#1567—111no—
124#1545—112no—
125C23×C11—44no—
126C23×C11—84no—
127C23×C11—84no—
128C23×C11—84no—
129C23×C11#12111yescharacteristic
130C22×D11—21no—
131D4×C11—44no—
132D4×C11—44no—
133D4×C11—48no—
134D4×C11—84no—
135D4×C11—84no—
136D4×C11—84no—
137D4×C11—84no—
138C2×C4×C11—22no—
139C2×C4×C11—22no—
140C2×C4×C11#12111yescharacteristic
141C2×C4×C11#12111yescharacteristic
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11C2×D812yes—
144C2×C4×C11#13512yes—
145C2×C4×C11C22×D411yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C2×C4×C11C2×#4111yescharacteristic
148C22⋊D11—24no—
149C2×Dic11—21no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152D44—21no—
153D44C2×D812yescomplemented
154C4×D11—24no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—21no—
158Dic22C2×D812yescomplemented
159C8×C11—22no—
160C8×C11AGL(1,ℤ/8)14yescomplemented
161C11⋊C8—44no—
162C11⋊C8—42no—
163C2×AGL(1,ℤ/8)—222no—
164C22×D8—22no—
165C2×#127C2×D1112yes—
166C4×#41—111no—
167#493—21no—
168#493—21no—
169#493C2×D1114yes—
170#460—114no—
171#460—222no—
172#459—114no—
173#459—222no—
174C8×Q8—112no—
175C8×D4—112no—
176C8×D4—222no—
177#431—111no—
178#431—221no—
179#423—112no—
180#418—222no—
181C2×C4×C8—221no—
182C2×C4×C8C2×D1111yescharacteristic
183#335—114no—
184#331—118no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—84no—
188C22×C11—84no—
189C22×C11—84no—
190C22×C11—168no—
191C22×C11#46612yes—
192C22×C11C2×#12111yescharacteristic
193C2×D11—22no—
194C2×D11—41no—
195C2×D11—41no—
196C4×C11—21no—
197C4×C11—21no—
198C4×C11#46612yes—
199C4×C11#47212yes—
200C4×C11C22×D811yescharacteristic
201C4×C11C2×#13511yescharacteristic
202C4×C11C2×AGL(1,ℤ/8)12yes—
203Dic11—22no—
204Dic11—41no—
205Dic11—41no—
206C2×#41—111no—
207C22×D4—22no—
208C22×D4—22no—
209C22×D4—22no—
210AGL(1,ℤ/8)—448no—
211C2×SD16—224no—
212C2×D8—24no—
213C2×D8—24no—
214C2×D8—48no—
215C2×D8—224no—
216C2×M16—222no—
217C22×C8—222no—
218C22×C8C22⋊D1112yes—
219#127—22no—
220#127—22no—
221#127—22no—
222#127C22×D1114yes—
223C4×Q8—111no—
224C4×Q8—111no—
225C4×D4—111no—
226C4×D4—111no—
227C4×D4—221no—
228C4×D4—221no—
229#117—111no—
230#117—221no—
231C2×C42—221no—
232C2×C42C22×D1111yescharacteristic
233C4⋊C8—112no—
234C4⋊C8—114no—
235C4⋊C8—222no—
236C4⋊C8—222no—
237#102—224no—
238#102—224no—
239C22⋊C8—221no—
240C22⋊C8—222no—
241C4×C8—222no—
242C4×C8—221no—
243C4×C8C22⋊D1111yescharacteristic
244C4×C8C22⋊D1111yescharacteristic
245C4×C8C22×D1112yes—
246C2×C11—22no—
247C2×C11—164no—
248C2×C11#303811yescharacteristic
249C2×C11C2×#46611yescharacteristic
250C2×C11C2×#47211yescharacteristic
251D11—42no—
252C24—42no—
253#41—114no—
254#41—222no—
255C2×Q8—111no—
256C2×D4—24no—
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—48no—
260C2×D4—44no—
261C2×D4—44no—
262C2×D4—42no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—84no—
266C2×D4—111no—
267C2×D4—221no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4D4×D1111yescharacteristic
272C22×C4#434111yescharacteristic
273C22×C4C2×C22⋊D1111yescharacteristic
274SD16—448no—
275D8—48no—
276D8—48no—
277D8—448no—
278M16—444no—
279C2×C8—24no—
280C2×C8—224no—
281C2×C8—222no—
282C2×C8—444no—
283C2×C8C2×C22⋊D1112yes—
284C2×C8C2×C22⋊D1112yes—
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—221no—
288C4⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C42—221no—
293C42—221no—
294C42—221no—
295C42D4×D1111yescharacteristic
296C42#434111yescharacteristic
297C42C2×C22⋊D1111yescharacteristic
298C42C23×D1111yescharacteristic
299C11#1926711yescharacteristic, complemented, Sylow
300C23—44no—
301C23—84no—
302C23—84no—
303C23—84no—
304C23—221no—
305C23#6699111yescharacteristic
306Q8—112no—
307Q8—221no—
308D4—44no—
309D4—44no—
310D4—48no—
311D4—84no—
312D4—84no—
313D4—84no—
314D4—84no—
315D4—112no—
316D4—224no—
317D4—221no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—221no—
321C2×C4—224no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—442no—
325C2×C4—442no—
326C2×C4D8×D1112yes—
327C2×C4#6696512yes—
328C2×C4#6699111yescharacteristic
329C2×C4#6699111yescharacteristic
330C2×C4#6699111yescharacteristic
331C2×C4C2×D4×D1111yescharacteristic
332C2×C4C2×#434111yescharacteristic
333C2×C4C22×C22⋊D1111yescharacteristic
334C8—22no—
335C8—444no—
336C8—442no—
337C8#6698514yescomplemented
338C22—21no—
339C22—21no—
340C22—84no—
341C22—84no—
342C22—84no—
343C22—168no—
344C22—222no—
345C22—441no—
346C22—441no—
347C22#1062277012yes—
348C22C2×#6699111yescharacteristic
349C4—21no—
350C4—21no—
351C4—222no—
352C4—441no—
353C4—441no—
354C4#1062277012yes—
355C4#1062277312yes—
356C4C2×D8×D1111yescharacteristic
357C4C2×#6696511yescharacteristic
358C4C2×#6698512yes—
359C2—22no—
360C2—164no—
361C2—442no—
362C2#1307809211yescharacteristic
363C2C2×#1062277011yescharacteristic
364C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#493C2
socleC22×C11C2×#121
hypercenterC2×#493D11
hypocenterC11#19267
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. #13078092C2semidirect
2. C8×#4339C2semidirect
3. #13067973C2semidirect
4. #13067968C2semidirect
5. #13067375C2semidirect
6. #13067284C2semidirect
7. C2×C11×#493C2semidirect
19. #10622688C22semidirect
21. #10622685C22semidirect
24. C8×D44C22semidirect
27. C8×Dic22C22semidirect
28. #10622182C22semidirect
29. #10622096C22semidirect
87. #4339D8semidirect
118. C2×#493D11semidirect
153. D44C2×D8semidirect
158. Dic22C2×D8semidirect
160. C8×C11AGL(1,ℤ/8)semidirect
299. C11#19267semidirect
337. C8#66985semidirect

Maximal subgroups

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

subgroupindex
#130780922
C8×#43392
#130679732
#130679682
#130673752
#130672842
C2×C11×#4932
#1926711