Finite Group Databasebeta

← #14909738

Subgroups — #14909738

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079195C211yesmaximal, characteristic, complemented
2#13070883C212yesmaximal, complemented
3#13070852C212yesmaximal, complemented
4#13070668C214yesmaximal, complemented
5#13070533C212yesmaximal, complemented
6#13070528C212yesmaximal, complemented
7#13070419C211yesmaximal, characteristic, complemented
8C2×C11×#495C211yesmaximal, characteristic, complemented
9C22×C11×Q16C2211yescharacteristic
10C22×C11×SD16—21no—
11C22×C11×D8C2211yescharacteristic
12C2×C11×#124—21no—
13#10623008—21no—
14C11×#495—21no—
15C11×#495—21no—
16C11×#495C2212yes—
17C11×#495C2212yes—
18C2×C4×C8×C11C2211yescharacteristic
19C2×#66892C2214yescomplemented
20C2×#66890C2214yes—
21#10622728—21no—
22#10622728C2212yes—
23#10622308C2211yescharacteristic, complemented
24#10622307—21no—
25C4×D88—21no—
26C4×D88C2212yescomplemented
27#10622295C2211yescharacteristic, complemented
28#10622202C2214yescomplemented
29#10622200C2214yes—
30C22⋊(C11⋊C16)C2212yes—
31C4⋊(C11⋊C16)C2212yescomplemented
32#10622099C2212yescomplemented
33C22×Q8×C11—21no—
34C22×D4×C11—21no—
35C2×#4339—41no—
36C2×C11×Q16—21no—
37C2×C11×Q16—42no—
38C2×C11×Q16C2312yes—
39C2×C11×SD16—22no—
40C2×C11×SD16—22no—
41C2×C11×SD16—44no—
42C2×C11×D8—21no—
43C2×C11×D8—42no—
44C2×C11×D8C2312yes—
45C22×C8×C11D411yescharacteristic
46C22×C8×C11C2311yescharacteristic
47C11×#124—22no—
48C11×#124—22no—
49C11×#124—41no—
50C11×#124—41no—
51C2×C11×C22⋊C4—41no—
52C2×C11×C22⋊C4—41no—
53C2×C42×C11D411yescharacteristic
54#66983—22no—
55#66983—41no—
56C2×D88—21no—
57C2×D88C2312yes—
58#66928—41no—
59#66927—21no—
60C4×D44—22no—
61C4×D44—41no—
62#66922—21no—
63C4×C8×C11D411yescharacteristic
64C4×C8×C11D411yescharacteristic
65C4×C8×C11C2311yescharacteristic
66C4×C8×C11C2311yescharacteristic
67#66892—44no—
68#66890—44no—
69#66885—22no—
70#66885—22no—
71#66882—21no—
72#66882C2312yes—
73C2×C11⋊C16C2314yes—
74#33779—111nomaximal, Sylow
75C24×C11—41no—
76C2×Q8×C11—22no—
77C2×Q8×C11—42no—
78C2×Q8×C11—42no—
79C2×Q8×C11—41no—
80C2×D4×C11—22no—
81C2×D4×C11—42no—
82C2×D4×C11—42no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C22×C4×C11D811yescharacteristic
86C22×C4×C11D811yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C2×C22⋊D11—42no—
89#4339—84no—
90C2×D44—22no—
91C2×D44—41no—
92C2×D44—41no—
93C2×C4×D11—42no—
94C2×Dic22—41no—
95C11×Q16—24no—
96C11×Q16—42no—
97C11×SD16—44no—
98C11×SD16—44no—
99C11×D8—24no—
100C11×D8—42no—
101C2×C8×C11—22no—
102C2×C8×C11—22no—
103C2×C8×C11C2×D411yescharacteristic
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2411yescharacteristic
107C11×C22⋊C4—42no—
108C11×C22⋊C4—42no—
109C11×C22⋊C4—42no—
110C11×C22⋊C4—42no—
111C42×C11D811yescharacteristic
112C42×C11D811yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115(C2×D11)⋊C4—42no—
116(C2×D11)⋊C4—42no—
117C4⋊Dic11—22no—
118C4⋊Dic11—41no—
119D88—24no—
120D88—42no—
121C11⋊C16—24no—
122#3169—111no—
123C2×#495D1111yescharacteristic, complemented
124#2250—112no—
125#2243—112no—
126#2210—114no—
127#2185—112no—
128#2184—112no—
129#2163—111no—
130C23×C11—42no—
131C23×C11—82no—
132C23×C11—82no—
133C23×C11—82no—
134C23×C11C2×D811yescharacteristic
135C22×D11—42no—
136Q8×C11—42no—
137Q8×C11—42no—
138Q8×C11—82no—
139D4×C11—42no—
140D4×C11—42no—
141D4×C11—82no—
142C2×C4×C11—22no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—41no—
146C2×C4×C11—42no—
147C2×C4×C11—82no—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11C2×D811yescharacteristic
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C2×D811yescharacteristic
153C2×C4×C11C22×D411yescharacteristic
154C22⋊D11—84no—
155C2×Dic11—42no—
156D44—42no—
157D44—42no—
158D44—82no—
159D44—82no—
160C4×D11—84no—
161Dic22—82no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11AGL(1,ℤ/8)12yes—
165C8×C11H(5,𝔽2)12yes—
166C22×Q16C2×D1111yescharacteristic
167C22×SD16—21no—
168C22×D8C2×D1111yescharacteristic
169#532—221no—
170C2×#124—21no—
171C2×SD32—114no—
172C2×D16—114no—
173#500—111no—
174#495—21no—
175#495—21no—
176#495C2×D1112yes—
177#495C2×D1112yes—
178#493—111no—
179#486—221no—
180#466—112no—
181#466—221no—
182C4×D8—112no—
183C4×D8—221no—
184C2×C4×C8C2×D1111yescharacteristic
185C4⋊C16—112no—
186#358—114no—
187#357—114no—
188C22⋊C16—112no—
189#346—112no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—82no—
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—164no—
196C22×C11#50912yes—
197C22×C11C22×D811yescharacteristic
198C2×D11—82no—
199C2×D11—82no—
200C2×D11—82no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—21no—
206C4×C11—82no—
207C4×C11#53511yescharacteristic
208C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
209Dic11—82no—
210C2×#41—441no—
211C22×Q8—21no—
212C22×D4—21no—
213C2×Q16—21no—
214C2×Q16—42no—
215C2×Q16C22×D1112yes—
216C2×SD16—22no—
217C2×SD16—22no—
218C2×SD16—44no—
219C2×D8—21no—
220C2×D8—42no—
221C2×D8—112no—
222C2×D8—221no—
223C2×D8C22×D1112yes—
224C22×C8C22⋊D1111yescharacteristic
225C22×C8C22×D1111yescharacteristic
226C4⋊Q8—221no—
227#127—221no—
228#124—22no—
229#124—22no—
230#124—41no—
231#124—41no—
232#124—441no—
233#121—222no—
234#121—441no—
235C4×D4—222no—
236C4×D4—441no—
237C2×C22⋊C4—41no—
238C2×C22⋊C4—41no—
239C2×C42C22⋊D1111yescharacteristic
240SD32—444no—
241D16—444no—
242C2×C16—114no—
243#107—112no—
244#107—221no—
245#102—222no—
246#102—222no—
247C4×C8C22⋊D1111yescharacteristic
248C4×C8C22⋊D1111yescharacteristic
249C4×C8C22×D1111yescharacteristic
250C4×C8C22×D1111yescharacteristic
251C2×C11—22no—
252C2×C11—162no—
253C2×C11#320511yescharacteristic
254C2×C11C2×#50911yescharacteristic
255C2×C11#341411yescharacteristic
256D11—162no—
257C24—41no—
258#41—884no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—41no—
263C2×Q8—441no—
264C2×D4—22no—
265C2×D4—42no—
266C2×D4—42no—
267C2×D4—41no—
268C2×D4—222no—
269C2×D4—442no—
270C2×D4—441no—
271C2×D4—441no—
272C22×C4—41no—
273C22×C4—442no—
274C22×C4#432311yescharacteristic
275C22×C4#432311yescharacteristic
276C22×C4C2×C22⋊D1111yescharacteristic
277Q16—24no—
278Q16—42no—
279SD16—44no—
280SD16—44no—
281D8—24no—
282D8—42no—
283D8—224no—
284D8—442no—
285C2×C8—22no—
286C2×C8—22no—
287C2×C8C2×C22⋊D1111yescharacteristic
288C2×C8C2×C22⋊D1111yescharacteristic
289C2×C8C2×C22⋊D1111yescharacteristic
290C2×C8C23×D1111yescharacteristic
291C4⋊C4—222no—
292C4⋊C4—441no—
293C22⋊C4—42no—
294C22⋊C4—42no—
295C22⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—442no—
298C22⋊C4—442no—
299C42#432311yescharacteristic
300C42#432311yescharacteristic
301C42C2×C22⋊D1111yescharacteristic
302C42C2×C22⋊D1111yescharacteristic
303C16—224no—
304C11#3377911yescharacteristic, complemented, Sylow
305C23—42no—
306C23—82no—
307C23—82no—
308C23—82no—
309C23—442no—
310C23C2×#432311yescharacteristic
311Q8—42no—
312Q8—42no—
313Q8—82no—
314Q8—882no—
315D4—42no—
316D4—42no—
317D4—82no—
318D4—442no—
319D4—442no—
320D4—882no—
321D4—882no—
322D4—884no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—442no—
330C2×C4—884no—
331C2×C4C2×#432311yescharacteristic
332C2×C4C2×#432311yescharacteristic
333C2×C4C2×#432311yescharacteristic
334C2×C4C2×#432311yescharacteristic
335C2×C4C2×#432311yescharacteristic
336C2×C4C22×C22⋊D1111yescharacteristic
337C8—21no—
338C8—21no—
339C8#6698512yes—
340C8#6703712yes—
341C22—21no—
342C22—21no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—164no—
347C22—882no—
348C22—882no—
349C22—882no—
350C22#1062280612yes—
351C22C22×#432311yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—82no—
358C4—882no—
359C4C2×#6698511yescharacteristic
360C4#1062333611yescharacteristic
361C2—22no—
362C2—162no—
363C2—1762no—
364C2#1307953411yescharacteristic
365C2C2×#1062280611yescharacteristic
366C2#1308175011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#495C2
socleC22×C11C22×D8
hypercenterC2×#495D11
hypocenterC11#33779
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#495

Complements

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

NH ≅ G/Ntype
1. #13079195C2semidirect
2. #13070883C2semidirect
3. #13070852C2semidirect
4. #13070668C2semidirect
5. #13070533C2semidirect
6. #13070528C2semidirect
7. #13070419C2semidirect
8. C2×C11×#495C2semidirect
19. C2×#66892C22semidirect
23. #10622308C22semidirect
26. C4×D88C22semidirect
27. #10622295C22semidirect
28. #10622202C22semidirect
31. C4⋊(C11⋊C16)C22semidirect
32. #10622099C22semidirect
123. C2×#495D11semidirect
304. C11#33779semidirect

Maximal subgroups

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

subgroupindex
#130791952
#130708832
#130708522
#130706682
#130705332
#130705282
#130704192
C2×C11×#4952
#3377911