Finite Group Databasebeta

← #14729837

Subgroups — #14729837

Order 2816.

1716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 171 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×#10623248C211yesmaximal, characteristic, complemented
2#13078703C212yesmaximal, complemented
3#13067730C214yesmaximal, complemented
4#13067668C214yesmaximal, complemented
5#13067330C211yesmaximal, characteristic, complemented
6#13067060C212yesmaximal, complemented
7C11×#3151C211yesmaximal, characteristic, complemented
8C22×D4×D11—22no—
9C2×C11×AGL(1,ℤ/8)—22no—
10C11×#532C2211yescharacteristic, complemented
11C2×C11×#127C2211yescharacteristic
12C2×#66991—22no—
13C2×#66990—22no—
14#10623248—22no—
15#10623248—24no—
16#10623248C2214yes—
17C2×C4×D44C2212yes—
18C11×#496—22no—
19C11×#493C2212yescomplemented
20C11×#492C2212yescomplemented
21C4×C11×M16C2211yescharacteristic, complemented
22#10622697C2214yescomplemented
23#10622685C2214yescomplemented
24#10622649—22no—
25#10622647—22no—
26#10622627—24no—
27#10622539C2212yescomplemented
28#10622182C2214yescomplemented
29#10622097C2218yescomplemented
30C24×D11—22no—
31C2×C11×#41—21no—
32C22×D4×C11—22no—
33C22×D4×C11D412yes—
34C22×C22⋊D11—24no—
35C2×D4×D11—28no—
36C2×D4×D11—28no—
37C2×D4×D11—416no—
38C22×D44D412yes—
39C22×C4×D11—22no—
40C11×AGL(1,ℤ/8)—48no—
41C2×C11×SD16—24no—
42C2×C11×D8—24no—
43C2×C11×M16—21no—
44C11×C4⋊Q8C2311yescharacteristic, complemented
45C11×#127—22no—
46C11×#127D412yes—
47C11×#127C2312yes—
48C11×#127C2311yescharacteristic, complemented
49C11×#124—21no—
50C11×#121—22no—
51C4×D4×C11—22no—
52C2×C42×C11C2311yescharacteristic
53C2×C22⋊Dic11—22no—
54#66991—28no—
55#66991—28no—
56#66990—28no—
57#66990—28no—
58C2×#4323—24no—
59C2×(C2×D11)⋊C4—22no—
60C2×C4⋊Dic11D412yes—
61C4×D44—22no—
62C4×D44—22no—
63C4×D44D414yes—
64C4×D44C2314yes—
65C11×#97—21no—
66C4×C8×C11C2312yescomplemented
67#66896—24no—
68C22⋊(C11⋊C8)—22no—
69#66873—24no—
70#66872—24no—
71C4⋊(C11⋊C8)C2314yescomplemented
72#66867—22no—
73#18524—111nomaximal, Sylow
74C24×C11—22no—
75C23×D11—22no—
76C23×D11—28no—
77C23×D11—416no—
78C23×D11—84no—
79C11×#41—44no—
80C2×Q8×C11—21no—
81C2×D4×C11—24no—
82C2×D4×C11—22no—
83C2×D4×C11—24no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—48no—
87C2×D4×C11—44no—
88C2×D4×C11—41no—
89C2×D4×C11C2×D414yes—
90C22×C4×C11—41no—
91C22×C4×C11C2×D412yes—
92C22×C4×C11C2×D411yescharacteristic
93C2×C22⋊D11—216no—
94C2×C22⋊D11—416no—
95C22×Dic11—22no—
96D4×D11—432no—
97D4×D11—416no—
98D4×D11—416no—
99C2×D44—28no—
100C2×D44—22no—
101C2×D44C2×D414yes—
102C2×C4×D11—24no—
103C2×C4×D11—24no—
104C2×C4×D11—48no—
105C11×SD16—48no—
106C11×D8—48no—
107C11×M16—24no—
108C2×C8×C11—22no—
109C11×C4⋊C4—22no—
110C11×C22⋊C4—42no—
111C42×C11C2×D412yes—
112C42×C11C2×D411yescharacteristic
113C42×C11C2411yescharacteristic
114C22⋊Dic11—28no—
115#4323—48no—
116(C2×D11)⋊C4—24no—
117(C2×D11)⋊C4—24no—
118C4⋊Dic11—22no—
119C4⋊Dic11C2×D414yes—
120C2×C11⋊C8—24no—
121C2×D42—111no—
122#3151D1111yescharacteristic, complemented
123#3109—112no—
124#1629—114no—
125#1619—114no—
126#1555—111no—
127#1490—112no—
128C23×C11—24no—
129C23×C11—48no—
130C23×C11—44no—
131C23×C11—41no—
132C23×C11#12011yescharacteristic
133C22×D11—28no—
134C22×D11—24no—
135C22×D11—432no—
136C22×D11—44no—
137C22×D11—44no—
138C22×D11—88no—
139C22×D11—832no—
140Q8×C11—42no—
141D4×C11—44no—
142D4×C11—48no—
143D4×C11—42no—
144D4×C11—48no—
145D4×C11—44no—
146D4×C11—82no—
147D4×C11—82no—
148C2×C4×C11—22no—
149C2×C4×C11—24no—
150C2×C4×C11—41no—
151C2×C4×C11—82no—
152C2×C4×C11#12012yes—
153C2×C4×C11#12011yescharacteristic
154C2×C4×C11C22×D412yes—
155C2×C4×C11C22×D411yescharacteristic
156C22⋊D11—432no—
157C2×Dic11—24no—
158C2×Dic11—44no—
159D44—28no—
160D44—24no—
161D44AGL(1,ℤ/8)18yescomplemented
162C4×D11—48no—
163C4×D11—48no—
164C8×C11—24no—
165C11⋊C8—44no—
166C23×D4—222no—
167C2×AGL(1,ℤ/8)—22no—
168D42—114no—
169D42—224no—
170D42—222no—
171#532C2×D1111yescharacteristic, complemented
172C2×#127C2×D1111yescharacteristic
173C2×#121—222no—
174C2×#120—222no—
175C2×C4×D4—112no—
176#496—22no—
177#493C2×D1112yescomplemented
178#492C2×D1112yescomplemented
179#481—222no—
180#476—114no—
181#459—114no—
182#447—222no—
183#442—224no—
184#432—112no—
185C4×M16C2×D1111yescharacteristic, complemented
186#331—114no—
187D4⋊C8—118no—
188C22×C11—22no—
189C22×C11—48no—
190C22×C11—44no—
191C22×C11—88no—
192C22×C11—82no—
193C22×C11—81no—
194C22×C11#45312yes—
195C22×C11C2×#12011yescharacteristic
196C2×D11—28no—
197C2×D11—416no—
198C2×D11—44no—
199C2×D11—44no—
200C2×D11—832no—
201C4×C11—22no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11C2×AGL(1,ℤ/8)14yes—
206Dic11—44no—
207C25—222no—
208C2×#41—21no—
209C22×D4—22no—
210C22×D4—112no—
211C22×D4—228no—
212C22×D4—228no—
213C22×D4—224no—
214C22×D4—4416no—
215C22×D4C22⋊D1112yes—
216C23×C4—222no—
217AGL(1,ℤ/8)—48no—
218C2×SD16—24no—
219C2×D8—24no—
220C2×D8—224no—
221C2×M16—21no—
222C4⋊Q8C22×D1111yescharacteristic, complemented
223#127—22no—
224#127C22⋊D1112yes—
225#127C22×D1112yes—
226#127C22×D1111yescharacteristic, complemented
227#124—21no—
228#121—22no—
229#121—228no—
230#121—228no—
231#120—228no—
232#120—228no—
233C4×D4—22no—
234C4×D4—114no—
235C4×D4—114no—
236C4×D4—222no—
237C4×D4—222no—
238C2×C4⋊C4—112no—
239C2×C22⋊C4—222no—
240C2×C22⋊C4—222no—
241C2×C42C22×D1111yescharacteristic
242#106—224no—
243C4⋊C8—114no—
244#102—224no—
245#102—224no—
246C22⋊C8—222no—
247#97—21no—
248#97—222no—
249C4×C8C22×D1112yescomplemented
250C2×C11—22no—
251C2×C11—84no—
252C2×C11—161no—
253C2×C11#300312yes—
254C2×C11C2×#45311yescharacteristic
255D11—48no—
256C24—22no—
257C24—228no—
258C24—222no—
259C24—4416no—
260C24—884no—
261#41—44no—
262C2×Q8—21no—
263C2×D4—24no—
264C2×D4—22no—
265C2×D4—24no—
266C2×D4—22no—
267C2×D4—21no—
268C2×D4—48no—
269C2×D4—44no—
270C2×D4—41no—
271C2×D4—114no—
272C2×D4—228no—
273C2×D4—2216no—
274C2×D4—222no—
275C2×D4—4416no—
276C2×D4—4432no—
277C2×D4—4416no—
278C2×D4—4416no—
279C2×D4C2×C22⋊D1114yes—
280C22×C4—41no—
281C22×C4—222no—
282C22×C4—224no—
283C22×C4—224no—
284C22×C4—448no—
285C22×C4D4×D1112yes—
286C22×C4C2×C22⋊D1111yescharacteristic
287SD16—48no—
288D8—48no—
289D8—448no—
290M16—24no—
291C2×C8—22no—
292C2×C8—224no—
293C4⋊C4—22no—
294C4⋊C4—114no—
295C4⋊C4—222no—
296C22⋊C4—42no—
297C22⋊C4—228no—
298C22⋊C4—224no—
299C22⋊C4—224no—
300C42D4×D1112yes—
301C42C2×C22⋊D1111yescharacteristic
302C42C23×D1111yescharacteristic
303C11#1852411yescharacteristic, complemented, Sylow
304C23—24no—
305C23—48no—
306C23—44no—
307C23—41no—
308C23—228no—
309C23—224no—
310C23—444no—
311C23—4432no—
312C23—444no—
313C23—888no—
314C23—8832no—
315C23#6699011yescharacteristic
316Q8—42no—
317D4—44no—
318D4—48no—
319D4—42no—
320D4—48no—
321D4—44no—
322D4—82no—
323D4—82no—
324D4—118no—
325D4—228no—
326D4—224no—
327D4—4432no—
328C2×C4—22no—
329C2×C4—24no—
330C2×C4—41no—
331C2×C4—82no—
332C2×C4—224no—
333C2×C4—448no—
334C2×C4—444no—
335C2×C4—448no—
336C2×C4#6699011yescharacteristic
337C2×C4#6699012yes—
338C2×C4C2×D4×D1112yes—
339C2×C4C22×C22⋊D1111yescharacteristic
340C8—24no—
341C8—444no—
342C22—22no—
343C22—48no—
344C22—44no—
345C22—88no—
346C22—82no—
347C22—81no—
348C22—228no—
349C22—4416no—
350C22—444no—
351C22—444no—
352C22—8832no—
353C22#1062269012yes—
354C22C2×#6699011yescharacteristic
355C4—22no—
356C4—21no—
357C4—21no—
358C4—81no—
359C4—444no—
360C4D11×AGL(1,ℤ/8)14yes—
361C2—22no—
362C2—84no—
363C2—161no—
364C2—448no—
365C2#1307784112yes—
366C2C2×#1062269011yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3151C2
socleC22×C11C2×#120
hypercenter#3151D11
hypocenterC11#18524
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3151

Complements

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

NH ≅ G/Ntype
1. C2×#10623248C2semidirect
2. #13078703C2semidirect
3. #13067730C2semidirect
4. #13067668C2semidirect
5. #13067330C2semidirect
6. #13067060C2semidirect
7. C11×#3151C2semidirect
10. C11×#532C22semidirect
19. C11×#493C22semidirect
20. C11×#492C22semidirect
21. C4×C11×M16C22semidirect
22. #10622697C22semidirect
23. #10622685C22semidirect
27. #10622539C22semidirect
28. #10622182C22semidirect
29. #10622097C22semidirect
44. C11×C4⋊Q8C23semidirect
48. C11×#127C23semidirect
66. C4×C8×C11C23semidirect
71. C4⋊(C11⋊C8)C23semidirect
122. #3151D11semidirect
161. D44AGL(1,ℤ/8)semidirect
171. #532C2×D11semidirect
177. #493C2×D11semidirect
178. #492C2×D11semidirect
185. C4×M16C2×D11semidirect
222. C4⋊Q8C22×D11semidirect
226. #127C22×D11semidirect
249. C4×C8C22×D11semidirect
303. C11#18524semidirect

Maximal subgroups

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

subgroupindex
C2×#106232482
#130787032
#130677302
#130676682
#130673302
#130670602
C11×#31512
#1852411