Finite Group Databasebeta

← #14736840

Subgroups — #14736840

Order 2816.

842 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C212yesmaximal, complemented
2#13077329C211yesmaximal, characteristic, complemented
3#13068092C214yesmaximal, complemented
4#13067968C214yesmaximal, complemented
5#13067364C211yesmaximal, characteristic, complemented
6#13067284C212yesmaximal, complemented
7C2×C11×#493C211yesmaximal, characteristic, complemented
8C22×C11×D8—21no—
9C22×C11×D8—21no—
10C2×C11×#127C2212yes—
11C2×#66954—21no—
12#10623008C2211yescharacteristic
13C11×#493—21no—
14C11×#493—21no—
15C11×#493C2212yes—
16C11×#493C2212yes—
17C2×C4×C8×C11C2211yescharacteristic
18#10622830—24no—
19#10622723—21no—
20#10622686—22no—
21#10622685C2218yescomplemented
22#10622683—22no—
23#10622538C2212yes—
24#10622537C2211yescharacteristic
25#10622301—21no—
26#10622301C2212yescomplemented
27C8×D44—21no—
28C8×D44C2212yescomplemented
29#10622182C2218yescomplemented
30#10622096C2212yescomplemented
31#10622095C2212yescomplemented
32C22×D4×C11—22no—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C2×#4339—21no—
36C2×C11×D8—22no—
37C2×C11×D8—22no—
38C2×C11×D8—22no—
39C2×C11×D8—22no—
40C2×C11×D8—44no—
41C2×C11×D8—44no—
42C22×C8×C11D411yescharacteristic
43C22×C8×C11D411yescharacteristic
44C11×#127—22no—
45C11×#127—22no—
46C11×#127—22no—
47C11×#127C2314yes—
48C2×C42×C11C2311yescharacteristic
49C2×#4323—28no—
50#66983—21no—
51#66983D412yes—
52C2×#4318—21no—
53#66954—44no—
54C2×#4313—22no—
55C2×C8×D11—22no—
56#66928—21no—
57#66927D411yescharacteristic
58C4×D44—21no—
59C4×D44C2312yes—
60#66922D411yescharacteristic
61C4×C8×C11D411yescharacteristic
62C4×C8×C11D411yescharacteristic
63C4×C8×C11C2311yescharacteristic
64C4×C8×C11C2311yescharacteristic
65#66896—28no—
66C22⋊(C11⋊C8)—22no—
67(C2×D11)⋊C8—22no—
68(C2×D11)⋊C8—22no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)C2312yes—
71C4⋊(C11⋊C8)C2314yes—
72C4×C11⋊C8—22no—
73#19187—111nomaximal, Sylow
74C24×C11—42no—
75C2×D4×C11—24no—
76C2×D4×C11—24no—
77C2×D4×C11—24no—
78C2×D4×C11—42no—
79C2×D4×C11—42no—
80C2×D4×C11—42no—
81C2×D4×C11—44no—
82C2×D4×C11—44no—
83C2×D4×C11—84no—
84C2×D4×C11—84no—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11#4111yescharacteristic
88C2×C22⋊D11—22no—
89#4339—42no—
90#4339—42no—
91C2×D44—21no—
92C2×D44—21no—
93C2×D44C2×D412yes—
94C2×C4×D11—22no—
95C2×Dic22—21no—
96C11×D8—44no—
97C11×D8—44no—
98C11×D8—44no—
99C11×D8—44no—
100C2×C8×C11—22no—
101C2×C8×C11D814yescomplemented
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C42×C11C2×D411yescharacteristic
107C42×C11C2×D411yescharacteristic
108C42×C11#4111yescharacteristic
109C42×C11C2411yescharacteristic
110#4323—88no—
111(C2×D11)⋊C4—22no—
112(C2×D11)⋊C4—22no—
113C4⋊Dic11—21no—
114C4⋊Dic11C2×D412yes—
115#4318—42no—
116C2×C11⋊C8—24no—
117C2×C11⋊C8—22no—
118#4313—44no—
119C8×D11—44no—
120#3205—112no—
121C2×#493D1111yescharacteristic, complemented
122#2931—111no—
123#1687—114no—
124#1667—114no—
125#1564—111no—
126#1545—112no—
127C23×C11—44no—
128C23×C11—84no—
129C23×C11—84no—
130C23×C11—84no—
131C23×C11#12111yescharacteristic
132C22×D11—22no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—48no—
136D4×C11—84no—
137D4×C11—84no—
138D4×C11—84no—
139D4×C11—84no—
140C2×C4×C11—22no—
141C2×C4×C11—22no—
142C2×C4×C11#12111yescharacteristic
143C2×C4×C11#12111yescharacteristic
144C2×C4×C11#12111yescharacteristic
145C2×C4×C11C2×D812yes—
146C2×C4×C11AGL(1,ℤ/8)12yes—
147C2×C4×C11C22×D411yescharacteristic
148C2×C4×C11C22×D411yescharacteristic
149C2×C4×C11C2×#4111yescharacteristic
150C22⋊D11—44no—
151C2×Dic11—22no—
152D44—24no—
153D44—42no—
154D44—42no—
155C4×D11—42no—
156C4×D11—42no—
157Dic22—42no—
158C8×C11—21no—
159C8×C11—21no—
160C8×C11C2×D812yes—
161C8×C11C2×D812yes—
162C11⋊C8—42no—
163C11⋊C8—44no—
164C22×D8—21no—
165C22×D8—21no—
166C2×#131—221no—
167#532—111no—
168C2×#127C2×D1112yes—
169#493—21no—
170#493—21no—
171#493—222no—
172#493C2×D1112yes—
173#493C2×D1112yes—
174#486—222no—
175#459—118no—
176#447—224no—
177#436—112no—
178#436—221no—
179C8×D4—112no—
180C8×D4—221no—
181#431—112no—
182#423—111no—
183#408—221no—
184C2×C4×C8C2×D1111yescharacteristic
185#335—112no—
186#334—112no—
187#331—118no—
188C22×C11—21no—
189C22×C11—21no—
190C22×C11—84no—
191C22×C11—84no—
192C22×C11—84no—
193C22×C11—168no—
194C22×C11#45912yes—
195C22×C11C2×#12111yescharacteristic
196C2×D11—42no—
197C2×D11—42no—
198C2×D11—42no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11#45912yes—
202C4×C11#47212yes—
203C4×C11C22×D811yescharacteristic
204C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
205C4×C11#57612yes—
206Dic11—42no—
207C2×#41—221no—
208C22×D4—22no—
209C22×D4—22no—
210C22×D4—22no—
211C2×D8—22no—
212C2×D8—22no—
213C2×D8—22no—
214C2×D8—22no—
215C2×D8—44no—
216C2×D8—44no—
217C2×D8—228no—
218#131—444no—
219C2×M16—221no—
220C2×M16—222no—
221C22×C8—222no—
222C22×C8C22⋊D1111yescharacteristic
223C22×C8C22⋊D1111yescharacteristic
224C4⋊Q8—111no—
225#127—22no—
226#127—22no—
227#127—22no—
228#127—111no—
229#127C22×D1114yes—
230#124—221no—
231#121—112no—
232#121—221no—
233C4×D4—112no—
234C4×D4—221no—
235C2×C42C22×D1111yescharacteristic
236C4⋊C8—112no—
237C4⋊C8—114no—
238C4⋊C8—221no—
239#102—228no—
240C22⋊C8—222no—
241C22⋊C8—222no—
242C22⋊C8—222no—
243C4×C8—222no—
244C4×C8C22⋊D1111yescharacteristic
245C4×C8C22⋊D1111yescharacteristic
246C4×C8C22×D1111yescharacteristic
247C4×C8C22×D1111yescharacteristic
248C2×C11—22no—
249C2×C11—164no—
250C2×C11C2×#45911yescharacteristic
251C2×C11#305811yescharacteristic
252C2×C11C2×#47211yescharacteristic
253D11—82no—
254C24—42no—
255#41—442no—
256#41—442no—
257C2×Q8—221no—
258C2×D4—24no—
259C2×D4—24no—
260C2×D4—24no—
261C2×D4—44no—
262C2×D4—44no—
263C2×D4—42no—
264C2×D4—42no—
265C2×D4—42no—
266C2×D4—84no—
267C2×D4—84no—
268C2×D4—112no—
269C2×D4—222no—
270C2×D4—221no—
271C2×D4—221no—
272C22×C4—222no—
273C22×C4D4×D1111yescharacteristic
274C22×C4#434111yescharacteristic
275C22×C4C2×C22⋊D1111yescharacteristic
276D8—44no—
277D8—44no—
278D8—44no—
279D8—44no—
280D8—888no—
281M16—442no—
282M16—444no—
283C2×C8—22no—
284C2×C8—224no—
285C2×C8—222no—
286C2×C8—444no—
287C2×C8#432314yescomplemented
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C2×C8C2×C22⋊D1111yescharacteristic
291C2×C8C2×C22⋊D1111yescharacteristic
292C4⋊C4—112no—
293C4⋊C4—221no—
294C22⋊C4—222no—
295C22⋊C4—222no—
296C42D4×D1111yescharacteristic
297C42#434111yescharacteristic
298C42C2×C22⋊D1111yescharacteristic
299C42C23×D1111yescharacteristic
300C11#1918711yescharacteristic, complemented, Sylow
301C23—44no—
302C23—84no—
303C23—84no—
304C23—84no—
305C23—222no—
306C23#6699111yescharacteristic
307Q8—442no—
308D4—48no—
309D4—44no—
310D4—44no—
311D4—84no—
312D4—84no—
313D4—84no—
314D4—84no—
315D4—224no—
316D4—444no—
317D4—442no—
318D4—442no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—222no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4C2×#432312yes—
325C2×C4#6698512yes—
326C2×C4#6699111yescharacteristic
327C2×C4#6699111yescharacteristic
328C2×C4#6699111yescharacteristic
329C2×C4C2×D4×D1111yescharacteristic
330C2×C4C2×#434111yescharacteristic
331C2×C4C22×C22⋊D1111yescharacteristic
332C8—21no—
333C8—21no—
334C8—444no—
335C8—442no—
336C8C2×#432312yes—
337C8C2×#432312yes—
338C22—21no—
339C22—21no—
340C22—84no—
341C22—84no—
342C22—84no—
343C22—168no—
344C22—442no—
345C22—442no—
346C22—442no—
347C22#1062268512yes—
348C22C2×#6699111yescharacteristic
349C4—21no—
350C4—21no—
351C4—442no—
352C4#1062268512yes—
353C4#1062277312yes—
354C4#1062328812yes—
355C4C22×#432311yescharacteristic
356C4C2×#6698511yescharacteristic
357C2—22no—
358C2—164no—
359C2—882no—
360C2C2×#1062268511yescharacteristic
361C2#1307826011yescharacteristic
362C2C2×#1062277311yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#493C2
socleC22×C11C2×#121
hypercenterC2×#493D11
hypocenterC11#19187
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. #13079534C2semidirect
2. #13077329C2semidirect
3. #13068092C2semidirect
4. #13067968C2semidirect
5. #13067364C2semidirect
6. #13067284C2semidirect
7. C2×C11×#493C2semidirect
21. #10622685C22semidirect
26. #10622301C22semidirect
28. C8×D44C22semidirect
29. #10622182C22semidirect
30. #10622096C22semidirect
31. #10622095C22semidirect
101. C2×C8×C11D8semidirect
121. C2×#493D11semidirect
287. C2×C8#4323semidirect
300. C11#19187semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130773292
#130680922
#130679682
#130673642
#130672842
C2×C11×#4932
#1918711