Finite Group Databasebeta

← #14656251

Subgroups — #14656251

Order 2816.

582 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 582 conjugacy classes of subgroups — too many to draw. Only its 103 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#13079926C211yesmaximal, characteristic
2#13078090C212yesmaximal, complemented
3#13069551C211yesmaximal, characteristic, complemented
4#13067066C212yesmaximal, complemented
5C11×#1292C211yesmaximal, characteristic, complemented
6C2×#66962—22no—
7#10623008C2212yes—
8C2×C4×Dic22C2211yescharacteristic
9C11×#423C2212yes—
10C2×C11×C4⋊C8C2211yescharacteristic
11#10622746—22no—
12#10622728—22no—
13C2×C4×C11⋊C8C2211yescharacteristic
14#10622462—22no—
15#10622461—22no—
16#10622459—22no—
17#10622458—24no—
18#10622456—22no—
19#10622188—22no—
20#10622121—24no—
21C2×#4339—22no—
22C22×Dic22D411yescharacteristic
23C2×C11×M16—22no—
24C22×C8×C11D412yes—
25C2×C42×C11C2311yescharacteristic
26#66983—22no—
27#66983—22no—
28C2×C4⋊Dic11D411yescharacteristic
29C2×Dic11⋊C4—21no—
30C2×C4×Dic11—21no—
31C22×C11⋊C8—21no—
32#66962—44no—
33#66962—44no—
34C2×Dic44—24no—
35C2×D88—22no—
36C2×#4314—24no—
37#66928—22no—
38#66927D412yes—
39C4×D44—22no—
40C4×D44—22no—
41#66922D412yes—
42C4×Dic22—22no—
43C4×Dic22—22no—
44C11×C4⋊C8—22no—
45C11×C4⋊C8—22no—
46C11×C4⋊C8D414yes—
47#66885—24no—
48#66885—24no—
49#66882—22no—
50#66880—24no—
51C4×C11⋊C8—22no—
52#10255—111nomaximal, Sylow
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C2×C22⋊D11—42no—
57C22×Dic11—21no—
58C22×Dic11—21no—
59#4339—42no—
60#4339—42no—
61#4339—42no—
62#4339—42no—
63C2×D44—22no—
64C2×D44—22no—
65C2×D44—22no—
66C2×C4×D11—42no—
67C2×Dic22—22no—
68C2×Dic22—22no—
69C2×Dic22—21no—
70C2×Dic22—22no—
71C2×Dic22D812yescomplemented
72C11×M16—42no—
73C11×M16—42no—
74C2×C8×C11—24no—
75C2×C8×C11—22no—
76C2×C8×C11—42no—
77C42×C11C2×D412yes—
78C42×C11C2×D412yes—
79(C2×D11)⋊C4—42no—
80(C2×D11)⋊C4—42no—
81C4⋊Dic11—22no—
82C4⋊Dic11—22no—
83C4⋊Dic11—22no—
84Dic11⋊C4—42no—
85C4×Dic11—41no—
86C4×Dic11—41no—
87C2×C11⋊C8—22no—
88C2×C11⋊C8—41no—
89C2×C11⋊C8—41no—
90Dic44—48no—
91D88—82no—
92#4314—48no—
93#3245—111no—
94#3037—112no—
95#1984—111no—
96#1492—112no—
97#1292D1111yescharacteristic, complemented
98C23×C11#12111yescharacteristic
99C22×D11—42no—
100C2×C4×C11—21no—
101C2×C4×C11—21no—
102C2×C4×C11—41no—
103C2×C4×C11#12012yes—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11#12112yes—
106C2×C4×C11#12711yescharacteristic
107C2×C4×C11C2×D811yescharacteristic
108C2×C4×C11#13511yescharacteristic
109C2×C4×C11AGL(1,ℤ/8)12yes—
110C22⋊D11—82no—
111C22⋊D11—82no—
112C2×Dic11—22no—
113C2×Dic11—41no—
114C2×Dic11—41no—
115C2×Dic11—42no—
116C2×Dic11—41no—
117C2×Dic11—42no—
118D44—44no—
119D44—42no—
120D44—42no—
121D44—42no—
122D44—42no—
123C4×D11—82no—
124C4×D11—82no—
125Dic22—24no—
126Dic22—42no—
127Dic22—42no—
128Dic22—42no—
129C8×C11—44no—
130C8×C11—42no—
131C11⋊C8—42no—
132C2×#137—222no—
133#532—112no—
134C2×C4×Q8—111no—
135#474—222no—
136#466—222no—
137#464—224no—
138#462—222no—
139#460—222no—
140#459—222no—
141#423C2×D1112yes—
142C2×C4⋊C8C2×D1111yescharacteristic
143#417—222no—
144C2×C4×C8—111no—
145#336—222no—
146D4⋊C8—224no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11#39211yescharacteristic
150C22×C11#46611yescharacteristic
151C22×C11#46911yescharacteristic
152C2×D11—82no—
153C2×D11—82no—
154C2×D11—82no—
155C4×C11—21no—
156C4×C11—22no—
157C4×C11#44712yes—
158C4×C11#44912yes—
159C4×C11#45511yescharacteristic
160C4×C11#45611yescharacteristic
161Dic11—42no—
162Dic11—82no—
163Dic11—81no—
164C2×#41—222no—
165C22×Q8—111no—
166#137—444no—
167#137—444no—
168C2×Q16—224no—
169C2×SD16—224no—
170C2×D8—222no—
171C2×M16—22no—
172C22×C8—221no—
173C22×C8D4412yes—
174C4⋊Q8—112no—
175#127—112no—
176#124—222no—
177#121—222no—
178#121—222no—
179C4×Q8—222no—
180C4×Q8—222no—
181C4×D4—222no—
182C4×D4—222no—
183C2×C4⋊C4—111no—
184C2×C4⋊C4—221no—
185C2×C42—221no—
186C2×C42C22×D1111yescharacteristic
187#107—222no—
188C4⋊C8—22no—
189C4⋊C8—22no—
190C4⋊C8D4414yes—
191#103—224no—
192#102—224no—
193#102—224no—
194C4×C8—222no—
195C2×C11—21no—
196C2×C11—21no—
197C2×C11#199911yescharacteristic
198C2×C11#200711yescharacteristic
199C2×C11#201711yescharacteristic
200D11—162no—
201#41—442no—
202#41—442no—
203#41—442no—
204#41—442no—
205C2×Q8—112no—
206C2×Q8—221no—
207C2×Q8—222no—
208C2×Q8—222no—
209C2×Q8—222no—
210C2×D4—222no—
211C2×D4—222no—
212C2×D4—222no—
213C2×D4—442no—
214C22×C4—221no—
215C22×C4—221no—
216C22×C4—442no—
217C22×C4C2×D4411yescharacteristic
218C22×C4D4×D1111yescharacteristic
219C22×C4#434311yescharacteristic
220Q16—448no—
221SD16—448no—
222D8—882no—
223M16—42no—
224M16—42no—
225C2×C8—22no—
226C2×C8—24no—
227C2×C8—42no—
228C2×C8—222no—
229C2×C8—441no—
230C2×C8—441no—
231C4⋊C4—222no—
232C4⋊C4—222no—
233C4⋊C4—222no—
234C4⋊C4—442no—
235C22⋊C4—442no—
236C22⋊C4—442no—
237C42—441no—
238C42—441no—
239C42C2×D4412yes—
240C42D4×D1112yes—
241C11#1025511yescharacteristic, complemented, Sylow
242C23—442no—
243C23#6694811yescharacteristic
244Q8—224no—
245Q8—442no—
246Q8—442no—
247Q8—442no—
248D4—444no—
249D4—442no—
250D4—442no—
251D4—442no—
252D4—442no—
253D4—882no—
254D4—882no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—41no—
258C2×C4—222no—
259C2×C4—441no—
260C2×C4—441no—
261C2×C4—442no—
262C2×C4—441no—
263C2×C4—442no—
264C2×C4—882no—
265C2×C4—882no—
266C2×C4#6692711yescharacteristic
267C2×C4#6693511yescharacteristic
268C2×C4#6693512yes—
269C2×C4#6694812yes—
270C2×C4D8×D1111yescharacteristic
271C2×C4#6696712yes—
272C2×C4#6697211yescharacteristic
273C8—42no—
274C8—44no—
275C8—442no—
276C22—21no—
277C22—21no—
278C22—882no—
279C22—882no—
280C22—882no—
281C22#1062228411yescharacteristic
282C22#1062247811yescharacteristic
283C22#1062249611yescharacteristic
284C4—21no—
285C4—22no—
286C4—442no—
287C4—882no—
288C4—881no—
289C4#1062235911yescharacteristic
290C4#1062236511yescharacteristic
291C4#1062238612yes—
292C4#1062242412yes—
293C2—21no—
294C2—21no—
295C2—1762no—
296C2#1306961511yescharacteristic
297C2#1306966511yescharacteristic
298C2#1306972111yescharacteristic
subgroupG/H
centerC22#10622284
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1292C2
socleC22×C11#392
prime radical#13079926C2
hypercenter#1292D11
hypocenterC11#10255
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1292

Complements

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

NH ≅ G/Ntype
2. #13078090C2semidirect
3. #13069551C2semidirect
4. #13067066C2semidirect
5. C11×#1292C2semidirect
71. C2×Dic22D8semidirect
97. #1292D11semidirect
241. C11#10255semidirect

Maximal subgroups

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

subgroupindex
#130799262
#130780902
#130695512
#130670662
C11×#12922
#1025511