Finite Group Databasebeta

← #14656872

Subgroups — #14656872

Order 2816.

438 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 97 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#13076979C211yesmaximal, characteristic, complemented
2#13069444C211yesmaximal, characteristic
3#13067177C212yesmaximal
4#13066475C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C2×#66923—21no—
8C11×#431C2212yes—
9C43×C11C2211yescharacteristic
10#10622549C2212yes—
11#10622548—21no—
12#10622541—24no—
13C2×#66869—21no—
14C2×#66869—21no—
15#10622537C2211yescharacteristic
16#10622108—24no—
17C2×#4339—21no—
18C2×C42×C11—22no—
19C2×C42×C11D411yescharacteristic
20C2×C42×C11D411yescharacteristic
21C2×C42×C11C2311yescharacteristic
22#66983—22no—
23C2×C4⋊Dic11—24no—
24C2×C4⋊Dic11—22no—
25C2×Dic11⋊C4—24no—
26C2×#4318—21no—
27#66928—21no—
28#66927Q811yescharacteristic
29C4×D44—22no—
30#66923—42no—
31#66923—42no—
32#66922Q811yescharacteristic
33C11×C4⋊C8—22no—
34C11×C22⋊C8—22no—
35C4×C8×C11—22no—
36C11⋊#95—22no—
37C11⋊#95D414yes—
38#66869—42no—
39#66869—42no—
40C4⋊(C11⋊C8)—22no—
41#10364—111nomaximal, Sylow
42C22×C4×C11—21no—
43C22×C4×C11—21no—
44C22×C4×C11C2×D412yes—
45C22×C4×C11C2×D411yescharacteristic
46C2×C22⋊D11—41no—
47C22×Dic11—24no—
48#4339—41no—
49#4339—41no—
50#4339—41no—
51#4339—41no—
52C2×D44—21no—
53C2×D44—22no—
54C2×C4×D11—41no—
55C2×Dic22—21no—
56C2×C8×C11—42no—
57C42×C11—21no—
58C42×C11—21no—
59C42×C11—44no—
60C42×C11D812yes—
61C42×C11SD1612yes—
62C42×C11C2×Q811yescharacteristic
63C42×C11#4112yes—
64C42×C11#4111yescharacteristic
65(C2×D11)⋊C4—42no—
66C4⋊Dic11—22no—
67C4⋊Dic11—48no—
68C4⋊Dic11—42no—
69C4⋊Dic11—42no—
70Dic11⋊C4—48no—
71#4318—41no—
72#4318—41no—
73C2×C11⋊C8—41no—
74#2859—111no—
75#1962—111no—
76#1517—112no—
77#1286—112no—
78#1276D1111yescharacteristic, complemented
79C23×C11#12011yescharacteristic
80C22×D11—41no—
81C2×C4×C11—24no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—42no—
85C2×C4×C11—42no—
86C2×C4×C11C22⋊Q812yes—
87C2×C4×C11C22⋊Q811yescharacteristic
88C2×C4×C11#12411yescharacteristic
89C2×C4×C11#12412yes—
90C2×C4×C11C2×D811yescharacteristic
91C2×C4×C11C2×SD1611yescharacteristic
92C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
93C2×C4×C11#13711yescharacteristic
94C22⋊D11—81no—
95C22⋊D11—81no—
96C2×Dic11—48no—
97C2×Dic11—41no—
98C2×Dic11—44no—
99D44—41no—
100D44—41no—
101D44—82no—
102C4×D11—81no—
103C4×D11—81no—
104Dic22—41no—
105Dic22—41no—
106C8×C11—82no—
107C11⋊C8—81no—
108#532—111no—
109C2×#125—221no—
110#431C2×D1112yes—
111#423—111no—
112C2×#104—221no—
113C2×#104—221no—
114#389—224no—
115#384—221no—
116#382—112no—
117C43C2×D1111yescharacteristic
118#327—224no—
119C22×C11—22no—
120C22×C11#39311yescharacteristic
121C22×C11#44711yescharacteristic
122C22×C11#44811yescharacteristic
123C2×D11—81no—
124C2×D11—82no—
125C4×C11—24no—
126C4×C11—22no—
127C4×C11—22no—
128C4×C11—42no—
129C4×C11#47411yescharacteristic
130C4×C11#47611yescharacteristic
131C4×C11#48611yescharacteristic
132C4×C11#48911yescharacteristic
133Dic11—84no—
134Dic11—81no—
135C2×#41—221no—
136C2×M16—221no—
137C4⋊Q8—111no—
138#127—111no—
139#125—442no—
140#125—442no—
141#124—221no—
142#121—222no—
143C4×D4—222no—
144C2×C4⋊C4—224no—
145C2×C4⋊C4—224no—
146C2×C4⋊C4—222no—
147C2×C42—22no—
148C2×C42D4411yescharacteristic
149C2×C42D4411yescharacteristic
150C2×C42C22×D1111yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—222no—
153#104—442no—
154#104—442no—
155C22⋊C8—22no—
156C4×C8—22no—
157#95—114no—
158#95—222no—
159C2×C11—21no—
160C2×C11—21no—
161C2×C11#202311yescharacteristic
162C2×C11#203112yes—
163D11—161no—
164#41—441no—
165#41—441no—
166#41—441no—
167#41—441no—
168C2×Q8—221no—
169C2×D4—222no—
170C2×D4—221no—
171C2×D4—441no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—224no—
175C22×C4—441no—
176C22×C4C2×D4411yescharacteristic
177C22×C4D4×D1112yes—
178M16—441no—
179M16—441no—
180C2×C8—42no—
181C2×C8—441no—
182C4⋊C4—222no—
183C4⋊C4—448no—
184C4⋊C4—448no—
185C4⋊C4—442no—
186C4⋊C4—442no—
187C22⋊C4—442no—
188C42—21no—
189C42—21no—
190C42—44no—
191C42#431412yes—
192C42D8812yes—
193C42#433912yes—
194C42#434111yescharacteristic
195C42Q8×D1111yescharacteristic
196C11#1036411yescharacteristic, complemented, Sylow
197C23—441no—
198C23#6693511yescharacteristic
199Q8—441no—
200Q8—441no—
201D4—441no—
202D4—441no—
203D4—882no—
204D4—881no—
205D4—881no—
206C2×C4—24no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—448no—
212C2×C4—441no—
213C2×C4—444no—
214C2×C4—881no—
215C2×C4—881no—
216C2×C4#6692811yescharacteristic
217C2×C4#6693812yes—
218C2×C4#6694912yes—
219C2×C4#6695011yescharacteristic
220C2×C4C2×#431411yescharacteristic
221C2×C4C2×D8811yescharacteristic
222C2×C4#6696111yescharacteristic
223C2×C4#6696211yescharacteristic
224C8—82no—
225C8—881no—
226C22—22no—
227C22—881no—
228C22—882no—
229C22#1062228611yescharacteristic
230C22#1062234511yescharacteristic
231C22#1062235111yescharacteristic
232C4—24no—
233C4—22no—
234C4—22no—
235C4—42no—
236C4—884no—
237C4—881no—
238C4#1062230711yescharacteristic
239C4#1062232711yescharacteristic
240C4#1062245511yescharacteristic
241C4#1062245911yescharacteristic
242C2—21no—
243C2—21no—
244C2—1761no—
245C2#1306975311yescharacteristic
246C2#1306978912yes—
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1276D11
hypocenterC11#10364
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #13076979C2semidirect
4. #13066475C2semidirect
5. C11×#1276C2semidirect
78. #1276D11semidirect
196. C11#10364semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130694442
#130671772
#130664752
C11×#12762
#1036411