Finite Group Databasebeta

← #14908087

Subgroups — #14908087

Order 2816.

748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622521C211yesmaximal, characteristic, complemented
2C22×#66890C211yesmaximal, characteristic, complemented
3#13079097C211yesmaximal, characteristic, complemented
4#13077467C211yesmaximal, characteristic, complemented
5#13070670C214yesmaximal, complemented
6#13070650C214yesmaximal, complemented
7#13070376C211yesmaximal, characteristic, complemented
8#13070321C211yesmaximal, characteristic, complemented
9C11×#2140C211yesmaximal, characteristic, complemented
10C22×C11×D8C2211yescharacteristic
11#10623336—21no—
12C2×#66985—21no—
13C2×#66957C2211yescharacteristic
14C22×D88C2211yescharacteristic
15#10623052—21no—
16C2×C11×M32C2211yescharacteristic
17C11×#427C2211yescharacteristic
18#10622768C2212yescomplemented
19#10622767—22no—
20#10622764C2212yescomplemented
21C2×#66890—24no—
22C2×#66890C2214yes—
23#10622714C2211yescharacteristic
24C22×C11⋊C16C2211yescharacteristic
25#10622614—21no—
26#10622521—24no—
27C2×#66864C2212yescomplemented
28C2×D176C2212yescomplemented
29#10622485C2214yescomplemented
30#10622482—22no—
31C11×#357C2214yescomplemented
32Dic11⋊C16C2214yescomplemented
33#10622130C2212yescomplemented
34#10622129C2212yescomplemented
35C22×D4×C11—21no—
36C2×#4339—21no—
37C22×D44—21no—
38C2×C11×D8—22no—
39C2×C11×D8—21no—
40C2×C11×D8—22no—
41C2×C11×D8C2312yes—
42C22×C8×C11C2311yescharacteristic
43C11×#117—21no—
44#67006—42no—
45#66993—22no—
46#66991—42no—
47#66989—22no—
48C2×#4324—22no—
49#66985—44no—
50C2×#4323—22no—
51#66979D411yescharacteristic
52C2×#4318D411yescharacteristic
53C2×Dic44C2311yescharacteristic
54#66957—22no—
55#66957—22no—
56C2×D88—21no—
57C2×D88—22no—
58C2×D88D414yescomplemented
59C2×D88C2311yescharacteristic
60C2×D88C2312yes—
61C2×#4314—21no—
62#66946—24no—
63C22⋊C4×D11—42no—
64C4×D44—42no—
65C11×M32—22no—
66C2×C11×C16C2312yes—
67C11×#107C2312yes—
68C11×#106—21no—
69#66890—28no—
70#66879D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16—22no—
73C2×C11⋊C16C2312yes—
74#66873—24no—
75#66864—24no—
76D176—24no—
77#33585—111nomaximal, Sylow
78C24×C11—41no—
79C23×D11—41no—
80C2×D4×C11—22no—
81C2×D4×C11—42no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C22×C4×C11C2×D411yescharacteristic
85C2×C22⋊D11—44no—
86C2×C22⋊D11—41no—
87#4339—42no—
88#4339—42no—
89C2×D44—24no—
90C2×D44—22no—
91C2×D44—21no—
92C2×D44—41no—
93C2×D44—42no—
94C2×C4×D11—44no—
95C2×C4×D11—41no—
96C2×Dic22—21no—
97C11×D8—22no—
98C11×D8—22no—
99C11×D8—42no—
100C2×C8×C11C2×D412yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11#4112yes—
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C22⋊C4—41no—
106C42×C11—41no—
107C22⋊Dic11—44no—
108C22⋊Dic11D812yes—
109#4324—44no—
110#4323—44no—
111(C2×D11)⋊C4—44no—
112C4⋊Dic11D812yes—
113C4×Dic11C2×D412yes—
114#4318—22no—
115C2×C11⋊C8C2×D412yes—
116Dic44—21no—
117Dic44—21no—
118D88—24no—
119D88—21no—
120D88—22no—
121D88—21no—
122D88C2×D414yes—
123#4314—42no—
124C11×C16—22no—
125C11⋊C16—22no—
126C2×#509—111no—
127C22×D16—111no—
128#3155—111no—
129#2948—111no—
130#2210—114no—
131#2206—114no—
132#2151—111no—
133#2140D1111yescharacteristic, complemented
134#2138—111no—
135C23×C11—42no—
136C23×C11—82no—
137C23×C11—162no—
138C23×C11C2×D811yescharacteristic
139C22×D11—42no—
140C22×D11—44no—
141C22×D11—41no—
142C22×D11—162no—
143D4×C11—42no—
144D4×C11—42no—
145D4×C11—82no—
146C2×C4×C11—42no—
147C2×C4×C11#12112yes—
148C2×C4×C11C2×D811yescharacteristic
149C2×C4×C11AGL(1,ℤ/8)12yes—
150C2×C4×C11C22×D411yescharacteristic
151C22⋊D11—82no—
152C22⋊D11—164no—
153C2×Dic11—41no—
154C2×Dic11C2×D814yes—
155D44—24no—
156D44—41no—
157D44—42no—
158D44—41no—
159D44—44no—
160C4×D11—82no—
161C4×D11—164no—
162Dic22—41no—
163Dic22—41no—
164C8×C11#12112yes—
165C8×C11C22×D411yescharacteristic
166C8×C11C2×#4111yescharacteristic
167C11⋊C8—22no—
168C2×AGL(1,ℤ/8)—221no—
169C2×#135—111no—
170C22×D8—111no—
171C22×D8C2×D1111yescharacteristic
172#535—221no—
173#518—221no—
174#509—224no—
175C2×SD32—112no—
176C2×D16—114no—
177C2×D16—112no—
178C2×D16—224no—
179C2×M32C2×D1111yescharacteristic
180C22×C16—111no—
181#496—222no—
182#495—112no—
183#493—112no—
184#442—222no—
185C4×D8—114no—
186#427C2×D1111yescharacteristic
187#418—221no—
188#405—111no—
189C4⋊C16—114no—
190#358—112no—
191#357—112no—
192#357C2×D1114yescomplemented
193C22×C11—22no—
194C22×C11—84no—
195C22×C11—82no—
196C22×C11—164no—
197C22×C11#45912yes—
198C22×C11C22×D811yescharacteristic
199C2×D11—44no—
200C2×D11—84no—
201C2×D11—82no—
202C2×D11—81no—
203C2×D11—164no—
204C4×C11—82no—
205C4×C11#45912yes—
206C4×C11C2×#12111yescharacteristic
207C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
208Dic11—24no—
209Dic11—81no—
210C2×#41—221no—
211C22×D4—21no—
212C22×D4—221no—
213AGL(1,ℤ/8)—444no—
214#135—222no—
215#135—222no—
216C2×Q16—111no—
217C2×SD16—222no—
218C2×SD16—221no—
219C2×D8—22no—
220C2×D8—22no—
221C2×D8—21no—
222C2×D8—114no—
223C2×D8—112no—
224C2×D8—111no—
225C2×D8—222no—
226C2×D8—222no—
227C2×D8—221no—
228C2×D8C22×D1112yes—
229C2×M16—111no—
230C22×C8C22×D1111yescharacteristic
231#127—222no—
232#124—222no—
233#121—442no—
234#120—442no—
235C4×D4—224no—
236C4×D4—442no—
237#117—21no—
238#117—111no—
239C2×C22⋊C4—442no—
240SD32—224no—
241D16—224no—
242D16—228no—
243M32—22no—
244C2×C16—112no—
245C2×C16—222no—
246C2×C16C22×D1112yes—
247#107C22×D1112yes—
248#106—21no—
249#102—224no—
250#97—112no—
251C4×C8—112no—
252C2×C11—22no—
253C2×C11—162no—
254C2×C11C2×#45911yescharacteristic
255C2×C11#341512yes—
256D11—84no—
257D11—161no—
258C24—41no—
259C24—441no—
260#41—442no—
261#41—442no—
262C2×Q8—221no—
263C2×D4—22no—
264C2×D4—42no—
265C2×D4—41no—
266C2×D4—42no—
267C2×D4—224no—
268C2×D4—222no—
269C2×D4—221no—
270C2×D4—444no—
271C2×D4—441no—
272C2×D4—441no—
273C2×D4—442no—
274C22×C4—444no—
275C22×C4—441no—
276C22×C4D4×D1111yescharacteristic
277Q16—221no—
278Q16—221no—
279SD16—444no—
280SD16—442no—
281D8—22no—
282D8—22no—
283D8—42no—
284D8—114no—
285D8—224no—
286D8—222no—
287D8—221no—
288D8—221no—
289D8—444no—
290M16—222no—
291C2×C8—112no—
292C2×C8#433912yes—
293C2×C8D4×D1111yescharacteristic
294C2×C8D4×D1112yes—
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—22no—
297C4⋊C4—112no—
298C22⋊C4—41no—
299C22⋊C4—112no—
300C22⋊C4—444no—
301C22⋊C4—444no—
302C42—41no—
303C42—112no—
304C16—22no—
305C16—222no—
306C11#3358511yescharacteristic, complemented, Sylow
307C23—42no—
308C23—82no—
309C23—162no—
310C23—442no—
311C23—444no—
312C23—441no—
313C23—1762no—
314C23D8×D1111yescharacteristic
315Q8—441no—
316Q8—441no—
317D4—42no—
318D4—42no—
319D4—82no—
320D4—224no—
321D4—441no—
322D4—442no—
323D4—441no—
324D4—444no—
325D4—882no—
326D4—1764no—
327C2×C4—42no—
328C2×C4—114no—
329C2×C4—441no—
330C2×C4—882no—
331C2×C4—1764no—
332C2×C4#6693712yes—
333C2×C4D8×D1111yescharacteristic
334C2×C4#6696712yes—
335C2×C4C2×D4×D1111yescharacteristic
336C8—222no—
337C8#6693712yes—
338C8C2×#433911yescharacteristic
339C8C2×D4×D1111yescharacteristic
340C22—22no—
341C22—82no—
342C22—84no—
343C22—164no—
344C22—444no—
345C22—884no—
346C22—881no—
347C22—882no—
348C22—1764no—
349C22#1062239912yes—
350C22C2×D8×D1111yescharacteristic
351C4—82no—
352C4—224no—
353C4—881no—
354C4#1062239912yes—
355C4C2×#6693711yescharacteristic
356C4C2×#6696711yescharacteristic
357C2—22no—
358C2—162no—
359C2—884no—
360C2—1761no—
361C2C2×#1062239911yescharacteristic
362C2#1308175612yes—
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2140C2
socleC22×C11C22×D8
hypercenter#2140D11
hypocenterC11#33585
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2140

Complements

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

NH ≅ G/Ntype
1. C2×#10622521C2semidirect
2. C22×#66890C2semidirect
3. #13079097C2semidirect
4. #13077467C2semidirect
5. #13070670C2semidirect
6. #13070650C2semidirect
7. #13070376C2semidirect
8. #13070321C2semidirect
9. C11×#2140C2semidirect
18. #10622768C22semidirect
20. #10622764C22semidirect
27. C2×#66864C22semidirect
28. C2×D176C22semidirect
29. #10622485C22semidirect
31. C11×#357C22semidirect
32. Dic11⋊C16C22semidirect
33. #10622130C22semidirect
34. #10622129C22semidirect
58. C2×D88D4semidirect
133. #2140D11semidirect
192. #357C2×D11semidirect
306. C11#33585semidirect

Maximal subgroups

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

subgroupindex
C2×#106225212
C22×#668902
#130790972
#130774672
#130706702
#130706502
#130703762
#130703212
C11×#21402
#3358511