Finite Group Databasebeta

← #14735058

Subgroups — #14735058

Order 2816.

960 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 960 conjugacy classes of subgroups — too many to draw. Only its 155 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×#10623231C211yesmaximal, characteristic, complemented
2#13079599C212yesmaximal, complemented
3#13067937C214yesmaximal, complemented
4#13067908C214yesmaximal, complemented
5#13067243C211yesmaximal, characteristic, complemented
6#13067213C212yesmaximal, complemented
7C11×#3142C211yesmaximal, characteristic, complemented
8C11×#532C2211yescharacteristic
9C2×C11×#125C2211yescharacteristic
10#10623231—22no—
11#10623231—24no—
12#10623231C2214yes—
13C2×#66949—22no—
14C2×#66948—22no—
15C2×#66947—22no—
16C2×#66928C2212yes—
17C11×#491C2212yescomplemented
18C11×#490C2212yescomplemented
19C11×#488—22no—
20C11×#417—22no—
21C4×C11×M16C2211yescharacteristic
22#10622702C2214yescomplemented
23#10622687C2214yescomplemented
24#10622653—22no—
25#10622649—22no—
26#10622629—24no—
27#10622539C2212yes—
28#10622181C2214yescomplemented
29#10622102C2218yescomplemented
30C2×C11×#41—21no—
31C22×D44—22no—
32C22×D44D412yes—
33C22×C4×D11—22no—
34C22×Dic22D412yes—
35C2×C11×M16—21no—
36C11×C4⋊Q8C2311yescharacteristic
37C11×#127C2311yescharacteristic
38C11×#125—22no—
39C11×#125D412yes—
40C11×#125C2312yes—
41C11×#124—21no—
42C11×#121—22no—
43C4×D4×C11—22no—
44C2×C11×C4⋊C4—22no—
45C2×C11×C4⋊C4D412yes—
46C2×C42×C11C2311yescharacteristic
47C2×#4324—24no—
48C2×#4323—24no—
49C2×(C2×D11)⋊C4—22no—
50C2×(C2×D11)⋊C4—22no—
51C2×(C2×D11)⋊C4—22no—
52C2×Dic11⋊C4—22no—
53#66949—28no—
54#66949—28no—
55#66948—28no—
56#66948—28no—
57#66947—28no—
58#66947—28no—
59#66928—22no—
60#66928—22no—
61#66928D414yes—
62#66928C2314yes—
63C11×#103—24no—
64C11×#102—24no—
65C11×#97C2312yes—
66C4×C8×C11—21no—
67C22⋊(C11⋊C8)—22no—
68#66874—24no—
69#66873—24no—
70C4⋊(C11⋊C8)—22no—
71#66867C2314yes—
72#19001—111nomaximal, Sylow
73C23×D11—22no—
74C11×#41—44no—
75C2×Q8×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—41no—
79C22×C4×C11—22no—
80C22×C4×C11—41no—
81C22×C4×C11C2×D411yescharacteristic
82C22×C4×C11C2×D412yes—
83C22×Dic11—22no—
84C2×D44—28no—
85C2×D44—22no—
86C2×D44—82no—
87C2×D44—84no—
88C2×D44C2×D414yes—
89C2×C4×D11—28no—
90C2×C4×D11—84no—
91C2×Dic22—22no—
92C2×Dic22—82no—
93C2×Dic22C2×D414yes—
94C11×M16—42no—
95C2×C8×C11—22no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4—24no—
99C11×C4⋊C4—22no—
100C11×C4⋊C4C2×D414yes—
101C11×C22⋊C4—42no—
102C42×C11C2×D412yes—
103C42×C11C2×D411yescharacteristic
104C42×C11C2411yescharacteristic
105#4324—84no—
106#4323—84no—
107(C2×D11)⋊C4—28no—
108(C2×D11)⋊C4—24no—
109(C2×D11)⋊C4—24no—
110(C2×D11)⋊C4—24no—
111(C2×D11)⋊C4—24no—
112Dic11⋊C4—28no—
113C2×C11⋊C8—24no—
114C2×#562—111no—
115#3213—112no—
116#3142D1111yescharacteristic, complemented
117#1662—114no—
118#1656—114no—
119#1534—111no—
120#1527—112no—
121C23×C11—41no—
122C23×C11#12011yescharacteristic
123C22×D11—24no—
124C22×D11—44no—
125C22×D11—44no—
126C22×D11—44no—
127Q8×C11—42no—
128D4×C11—44no—
129D4×C11—42no—
130D4×C11—82no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—42no—
134C2×C4×C11—44no—
135C2×C4×C11—41no—
136C2×C4×C11—82no—
137C2×C4×C11#12011yescharacteristic
138C2×C4×C11#12012yes—
139C2×C4×C11C22×D412yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×Dic11—24no—
142C2×Dic11—44no—
143D44—44no—
144D44—82no—
145D44—88no—
146C4×D11—88no—
147Dic22—44no—
148Dic22—82no—
149C8×C11—42no—
150C11⋊C8—44no—
151#562—114no—
152#562—224no—
153#562—222no—
154#532C2×D1111yescharacteristic
155C2×#125C2×D1111yescharacteristic
156C2×#124—112no—
157C2×#123—222no—
158C2×C22⋊Q8—222no—
159C2×#121—222no—
160#496—114no—
161#491C2×D1112yescomplemented
162#490C2×D1112yescomplemented
163#489—114no—
164#488—22no—
165#463—224no—
166#448—222no—
167#447—222no—
168#432—112no—
169#417—22no—
170C4×M16C2×D1111yescharacteristic
171#330—114no—
172#329—118no—
173C22×C11—22no—
174C22×C11—81no—
175C22×C11—82no—
176C22×C11#45412yes—
177C22×C11C2×#12011yescharacteristic
178C2×D11—44no—
179C2×D11—44no—
180C2×D11—44no—
181C2×D11—88no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—44no—
187C4×C11—81no—
188Dic11—44no—
189C2×#41—21no—
190C22×Q8—112no—
191C22×D4—112no—
192C22×D4—222no—
193C23×C4—222no—
194C2×SD16—224no—
195C2×D8—224no—
196C2×M16—21no—
197C4⋊Q8C22×D1111yescharacteristic
198#127C22×D1111yescharacteristic
199#125—22no—
200#125C22⋊D1112yes—
201#125C22×D1112yes—
202#124—21no—
203#124—114no—
204#124—114no—
205#124—222no—
206#124—222no—
207#123—228no—
208#123—228no—
209C22⋊Q8—228no—
210C22⋊Q8—228no—
211#121—22no—
212#121—228no—
213#121—228no—
214C4×D4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—222no—
217C2×C4⋊C4C22⋊D1112yes—
218C2×C22⋊C4—222no—
219C2×C22⋊C4—222no—
220C2×C22⋊C4—222no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—222no—
223#103—24no—
224#103—224no—
225#102—24no—
226#102—224no—
227C22⋊C8—222no—
228#97—114no—
229#97C22×D1112yes—
230C4×C8—21no—
231C2×C11—22no—
232C2×C11—161no—
233C2×C11C2×#45411yescharacteristic
234C2×C11#301912yes—
235D11—84no—
236C24—222no—
237#41—44no—
238C2×Q8—21no—
239C2×Q8—114no—
240C2×Q8—222no—
241C2×Q8—882no—
242C2×D4—22no—
243C2×D4—21no—
244C2×D4—41no—
245C2×D4—114no—
246C2×D4—228no—
247C2×D4—222no—
248C2×D4—882no—
249C2×D4—884no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—228no—
253C22×C4—222no—
254C22×C4—884no—
255C22×C4D4×D1112yes—
256C22×C4C2×C22⋊D1111yescharacteristic
257SD16—884no—
258D8—884no—
259M16—42no—
260C2×C8—22no—
261C2×C8—224no—
262C4⋊C4—24no—
263C4⋊C4—22no—
264C4⋊C4—24no—
265C4⋊C4—22no—
266C4⋊C4—228no—
267C4⋊C4C2×C22⋊D1114yes—
268C22⋊C4—42no—
269C22⋊C4—228no—
270C22⋊C4—224no—
271C22⋊C4—224no—
272C22⋊C4—224no—
273C22⋊C4—224no—
274C42D4×D1112yes—
275C42C2×C22⋊D1111yescharacteristic
276C42C23×D1111yescharacteristic
277C11#1900111yescharacteristic, complemented, Sylow
278C23—41no—
279C23—224no—
280C23—444no—
281C23—444no—
282C23—444no—
283C23#6699011yescharacteristic
284Q8—42no—
285Q8—444no—
286Q8—882no—
287D4—44no—
288D4—42no—
289D4—82no—
290D4—444no—
291D4—882no—
292D4—888no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—41no—
298C2×C4—82no—
299C2×C4—224no—
300C2×C4—444no—
301C2×C4—888no—
302C2×C4#6699011yescharacteristic
303C2×C4#6699012yes—
304C2×C4C2×D4×D1112yes—
305C2×C4C22×C22⋊D1111yescharacteristic
306C8—42no—
307C8—444no—
308C22—22no—
309C22—81no—
310C22—82no—
311C22—444no—
312C22—444no—
313C22—444no—
314C22—888no—
315C22#1062267512yes—
316C22C2×#6699011yescharacteristic
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—44no—
322C4—81no—
323C4—444no—
324C2—22no—
325C2—161no—
326C2—884no—
327C2C2×#1062267511yescharacteristic
328C2#1307797112yes—
subgroupG/H
centerC22C2×#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3142C2
socleC22×C11C2×#120
hypercenter#3142D11
hypocenterC11#19001
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3142

Complements

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

NH ≅ G/Ntype
1. C2×#10623231C2semidirect
2. #13079599C2semidirect
3. #13067937C2semidirect
4. #13067908C2semidirect
5. #13067243C2semidirect
6. #13067213C2semidirect
7. C11×#3142C2semidirect
17. C11×#491C22semidirect
18. C11×#490C22semidirect
22. #10622702C22semidirect
23. #10622687C22semidirect
28. #10622181C22semidirect
29. #10622102C22semidirect
116. #3142D11semidirect
161. #491C2×D11semidirect
162. #490C2×D11semidirect
277. C11#19001semidirect

Maximal subgroups

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

subgroupindex
C2×#106232312
#130795992
#130679372
#130679082
#130672432
#130672132
C11×#31422
#1900111