Finite Group Databasebeta

← #14735060

Subgroups — #14735060

Order 2816.

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

normal subgroups only

This group has 960 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
1#13079603C212yesmaximal, complemented
2#13079019C211yesmaximal, characteristic, complemented
3#13067939C214yesmaximal, complemented
4#13067909C214yesmaximal, complemented
5#13067243C211yesmaximal, characteristic, complemented
6#13067214C212yesmaximal, complemented
7C2×C11×#562C211yesmaximal, characteristic, complemented
8C11×#562—22no—
9C11×#562—24no—
10C11×#562C2214yes—
11C2×C11×#125C2211yescharacteristic
12C2×C11×#124C2212yes—
13C2×C11×#123—22no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×#121—22no—
16#10623008C2211yescharacteristic
17#10622840—22no—
18#10622830—22no—
19#10622682C2212yescomplemented
20#10622681—22no—
21#10622680C2212yescomplemented
22#10622671C2214yescomplemented
23#10622670—24no—
24#10622668C2214yescomplemented
25#10622579—22no—
26#10622539C2212yes—
27C4×#4318C2211yescharacteristic
28#10622181C2214yescomplemented
29#10622178C2218yescomplemented
30C22×Q8×C11D412yes—
31C22×D4×C11—22no—
32C22×D4×C11D412yes—
33C23×C4×C11—22no—
34C2×#4339—21no—
35C11×#125—22no—
36C11×#125D412yes—
37C11×#125C2312yes—
38C11×#124—22no—
39C11×#124—22no—
40C11×#124D414yes—
41C11×#124C2314yes—
42C11×#123—28no—
43C11×#123—28no—
44C11×C22⋊Q8—28no—
45C11×C22⋊Q8—28no—
46C11×#121—28no—
47C11×#121—28no—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4—22no—
54C2×C42×C11C2311yescharacteristic
55C2×#4325—24no—
56C2×#4323—24no—
57#66983—22no—
58C2×#4318—21no—
59#66928—21no—
60#66927C2311yescharacteristic
61C4×D44—22no—
62#66922C2311yescharacteristic
63#66899—24no—
64#66896—24no—
65C22⋊(C11⋊C8)—22no—
66#66874—24no—
67#66873—24no—
68C4⋊(C11⋊C8)—22no—
69#66867C2312yes—
70#66867C2314yes—
71C4×C11⋊C8—21no—
72#19001—111nomaximal, Sylow
73C24×C11—22no—
74C2×Q8×C11—22no—
75C2×Q8×C11—82no—
76C2×Q8×C11C2×D414yes—
77C2×D4×C11—28no—
78C2×D4×C11—22no—
79C2×D4×C11—82no—
80C2×D4×C11—84no—
81C2×D4×C11C2×D414yes—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—28no—
85C22×C4×C11—84no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D412yes—
88C2×C22⋊D11—41no—
89#4339—44no—
90C2×D44—21no—
91C2×D44—22no—
92C2×C4×D11—41no—
93C2×Dic22—21no—
94C11×C4⋊C4—28no—
95C11×C4⋊C4—24no—
96C11×C4⋊C4—22no—
97C11×C4⋊C4—24no—
98C11×C4⋊C4C2×D414yes—
99C11×C22⋊C4—28no—
100C11×C22⋊C4—24no—
101C11×C22⋊C4—24no—
102C11×C22⋊C4—24no—
103C11×C22⋊C4—24no—
104C42×C11C2×D411yescharacteristic
105C42×C11C2×D412yes—
106C42×C11C2411yescharacteristic
107#4325—84no—
108#4323—84no—
109(C2×D11)⋊C4—42no—
110C4⋊Dic11—22no—
111#4318—42no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8—24no—
114C2×#562D1111yescharacteristic, complemented
115#3213—112no—
116#3142—111no—
117#1662—114no—
118#1656—114no—
119#1534—111no—
120#1527—112no—
121C23×C11—24no—
122C23×C11—44no—
123C23×C11—44no—
124C23×C11—44no—
125C23×C11#12011yescharacteristic
126C22×D11—41no—
127Q8×C11—44no—
128Q8×C11—82no—
129D4×C11—44no—
130D4×C11—82no—
131D4×C11—88no—
132C2×C4×C11—22no—
133C2×C4×C11—24no—
134C2×C4×C11—24no—
135C2×C4×C11—42no—
136C2×C4×C11—44no—
137C2×C4×C11—44no—
138C2×C4×C11—88no—
139C2×C4×C11#12012yes—
140C2×C4×C11#12011yescharacteristic
141C2×C4×C11C22×D412yes—
142C2×C4×C11C22×D411yescharacteristic
143C22⋊D11—82no—
144C2×Dic11—41no—
145D44—44no—
146D44—42no—
147C4×D11—82no—
148Dic22—42no—
149C11⋊C8—42no—
150C11⋊C8—44no—
151#562—22no—
152#562—24no—
153#562C2×D1114yes—
154#532—111no—
155C2×#125C2×D1111yescharacteristic
156C2×#124C2×D1112yes—
157C2×#123—22no—
158C2×C22⋊Q8—22no—
159C2×#121—22no—
160#496—114no—
161#491—112no—
162#490—112no—
163#489—114no—
164#488—222no—
165#463—224no—
166#448—222no—
167#447—222no—
168#432—112no—
169#417—222no—
170C4×M16—111no—
171#330—114no—
172#329—118no—
173C22×C11—22no—
174C22×C11—44no—
175C22×C11—44no—
176C22×C11—44no—
177C22×C11—88no—
178C22×C11#45412yes—
179C22×C11C2×#12011yescharacteristic
180C2×D11—81no—
181C2×D11—82no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—22no—
185C4×C11—22no—
186C4×C11—44no—
187C4×C11—44no—
188Dic11—81no—
189C2×#41—221no—
190C22×Q8C22⋊D1112yes—
191C22×D4—22no—
192C22×D4C22⋊D1112yes—
193C23×C4—22no—
194C2×SD16—224no—
195C2×D8—224no—
196C2×M16—221no—
197C4⋊Q8—111no—
198#127—111no—
199#125—22no—
200#125C22⋊D1112yes—
201#125C22×D1112yes—
202#124—22no—
203#124—22no—
204#124—221no—
205#124C22⋊D1114yes—
206#124C22×D1114yes—
207#123—28no—
208#123—28no—
209C22⋊Q8—28no—
210C22⋊Q8—28no—
211#121—28no—
212#121—28no—
213#121—222no—
214C4×D4—222no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4C22⋊D1112yes—
218C2×C22⋊C4—22no—
219C2×C22⋊C4—22no—
220C2×C22⋊C4—22no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—222no—
223#103—224no—
224#103—224no—
225#102—224no—
226#102—224no—
227C22⋊C8—222no—
228#97—112no—
229#97—114no—
230C4×C8—221no—
231C2×C11—22no—
232C2×C11—84no—
233C2×C11C2×#45411yescharacteristic
234C2×C11#301912yes—
235D11—161no—
236C24—22no—
237#41—444no—
238C2×Q8—22no—
239C2×Q8—82no—
240C2×Q8—221no—
241C2×Q8C2×C22⋊D1114yes—
242C2×D4—28no—
243C2×D4—22no—
244C2×D4—82no—
245C2×D4—84no—
246C2×D4—221no—
247C2×D4—222no—
248C2×D4—441no—
249C2×D4C2×C22⋊D1114yes—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—28no—
253C22×C4—84no—
254C22×C4—441no—
255C22×C4C2×C22⋊D1111yescharacteristic
256C22×C4C2×C22⋊D1112yes—
257SD16—884no—
258D8—884no—
259M16—442no—
260C2×C8—222no—
261C2×C8—224no—
262C4⋊C4—28no—
263C4⋊C4—24no—
264C4⋊C4—22no—
265C4⋊C4—24no—
266C4⋊C4—222no—
267C4⋊C4C2×C22⋊D1114yes—
268C22⋊C4—28no—
269C22⋊C4—24no—
270C22⋊C4—24no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—442no—
274C42C2×C22⋊D1111yescharacteristic
275C42C2×C22⋊D1112yes—
276C42C23×D1111yescharacteristic
277C11#1900111yescharacteristic, complemented, Sylow
278C23—24no—
279C23—44no—
280C23—44no—
281C23—44no—
282C23—441no—
283C23#6700611yescharacteristic
284Q8—44no—
285Q8—82no—
286Q8—442no—
287D4—44no—
288D4—82no—
289D4—88no—
290D4—444no—
291D4—442no—
292D4—882no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—24no—
296C2×C4—42no—
297C2×C4—44no—
298C2×C4—44no—
299C2×C4—88no—
300C2×C4—441no—
301C2×C4—882no—
302C2×C4#6700611yescharacteristic
303C2×C4#6700612yes—
304C2×C4C22×C22⋊D1111yescharacteristic
305C2×C4C22×C22⋊D1112yes—
306C8—442no—
307C8—444no—
308C22—22no—
309C22—44no—
310C22—44no—
311C22—44no—
312C22—88no—
313C22—881no—
314C22—882no—
315C22#1062285812yes—
316C22C2×#6700611yescharacteristic
317C4—21no—
318C4—21no—
319C4—22no—
320C4—22no—
321C4—44no—
322C4—44no—
323C4—881no—
324C2—22no—
325C2—84no—
326C2—1761no—
327C2C2×#1062285811yescharacteristic
328C2#1307797312yes—
subgroupG/H
centerC22C2×#67006
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#562C2
socleC22×C11C2×#120
hypercenterC2×#562D11
hypocenterC11#19001
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#562

Complements

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

NH ≅ G/Ntype
1. #13079603C2semidirect
2. #13079019C2semidirect
3. #13067939C2semidirect
4. #13067909C2semidirect
5. #13067243C2semidirect
6. #13067214C2semidirect
7. C2×C11×#562C2semidirect
19. #10622682C22semidirect
21. #10622680C22semidirect
22. #10622671C22semidirect
24. #10622668C22semidirect
28. #10622181C22semidirect
29. #10622178C22semidirect
114. C2×#562D11semidirect
277. C11#19001semidirect

Maximal subgroups

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

subgroupindex
#130796032
#130790192
#130679392
#130679092
#130672432
#130672142
C2×C11×#5622
#1900111