Finite Group Databasebeta

← #14656858

Subgroups — #14656858

Order 2816.

454 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 101 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#13069444C211yesmaximal, characteristic
2#13067175C212yesmaximal
3#13066474C212yesmaximal, complemented
4#13066449C211yesmaximal, characteristic, complemented
5C11×#2862C211yesmaximal, characteristic, complemented
6C2×C11×C4⋊Q8—21no—
7#10623008C2211yescharacteristic
8C11×#391—24no—
9C11×#382—21no—
10C11×#382C2212yes—
11C43×C11C2211yescharacteristic
12C2×#66869—21no—
13C2×#66869—21no—
14#10622538C2212yes—
15#10622537C2211yescharacteristic
16#10622089—24no—
17C22×Q8×C11—22no—
18C2×#4339—21no—
19C11×C4⋊Q8—42no—
20C11×C4⋊Q8—42no—
21C2×C11×C4⋊C4—22no—
22C2×C11×C4⋊C4—22no—
23C2×C42×C11—22no—
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11C2311yescharacteristic
27#66983—22no—
28C2×#4318—21no—
29#66928—21no—
30#66927Q811yescharacteristic, complemented
31C4×D44—22no—
32#66922Q811yescharacteristic, complemented
33C11×#95—24no—
34C11×#95—22no—
35C11×#95D414yes—
36C22⋊(C11⋊C8)—22no—
37#66869—42no—
38#66869—42no—
39C4⋊(C11⋊C8)—22no—
40C4⋊(C11⋊C8)—22no—
41C4×C11⋊C8—22no—
42#10362—111nomaximal, Sylow
43C2×Q8×C11—44no—
44C2×Q8×C11—48no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—24no—
48C22×C4×C11C2×D412yes—
49C22×C4×C11C2×D411yescharacteristic
50C2×C22⋊D11—41no—
51#4339—41no—
52#4339—41no—
53#4339—41no—
54#4339—41no—
55C2×D44—21no—
56C2×D44—22no—
57C2×C4×D11—41no—
58C2×Dic22—21no—
59C11×C4⋊C4—44no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C42×C11—21no—
63C42×C11—21no—
64C42×C11—44no—
65C42×C11D812yes—
66C42×C11SD1612yes—
67C42×C11C2×Q811yescharacteristic
68C42×C11#4111yescharacteristic
69C42×C11#4112yes—
70(C2×D11)⋊C4—42no—
71C4⋊Dic11—22no—
72#4318—41no—
73#4318—41no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—41no—
76#2862D1111yescharacteristic, complemented
77#1962—111no—
78#1517—112no—
79#1286—112no—
80#1276—111no—
81C23×C11#12011yescharacteristic
82C22×D11—41no—
83Q8×C11—88no—
84C2×C4×C11—24no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11—48no—
90C2×C4×C11—44no—
91C2×C4×C11C22⋊Q812yes—
92C2×C4×C11C22⋊Q811yescharacteristic
93C2×C4×C11#12412yes—
94C2×C4×C11#12411yescharacteristic
95C2×C4×C11C2×D811yescharacteristic
96C2×C4×C11C2×SD1611yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C11#13711yescharacteristic
99C22⋊D11—81no—
100C22⋊D11—81no—
101C2×Dic11—41no—
102D44—41no—
103D44—41no—
104D44—82no—
105C4×D11—81no—
106C4×D11—81no—
107Dic22—41no—
108Dic22—41no—
109C11⋊C8—82no—
110C11⋊C8—81no—
111#532—111no—
112C2×C4⋊Q8—21no—
113#431—112no—
114#423—111no—
115C2×#104—221no—
116C2×#104—221no—
117#391—24no—
118#382—21no—
119#382C2×D1112yes—
120C43C2×D1111yescharacteristic
121#327—224no—
122C22×C11—22no—
123C22×C11#39311yescharacteristic
124C22×C11#44711yescharacteristic
125C22×C11#44811yescharacteristic
126C2×D11—81no—
127C2×D11—82no—
128C4×C11—24no—
129C4×C11—22no—
130C4×C11—22no—
131C4×C11—42no—
132C4×C11—84no—
133C4×C11#47411yescharacteristic
134C4×C11#47611yescharacteristic
135C4×C11#48611yescharacteristic
136C4×C11#48911yescharacteristic
137Dic11—81no—
138C2×#41—221no—
139C22×Q8—22no—
140C2×M16—221no—
141C4⋊Q8—42no—
142C4⋊Q8—42no—
143C4⋊Q8—111no—
144#127—111no—
145#124—221no—
146#121—222no—
147C4×D4—222no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C42—22no—
151C2×C42C22⋊D1111yescharacteristic
152C2×C42C22⋊D1111yescharacteristic
153C2×C42C22×D1111yescharacteristic
154C4⋊C8—222no—
155C4⋊C8—222no—
156#104—442no—
157#104—442no—
158C22⋊C8—222no—
159C4×C8—222no—
160#95—24no—
161#95—22no—
162#95C22⋊D1114yes—
163C2×C11—21no—
164C2×C11—21no—
165C2×C11#202311yescharacteristic
166C2×C11#203112yes—
167D11—161no—
168#41—441no—
169#41—441no—
170#41—441no—
171#41—441no—
172C2×Q8—44no—
173C2×Q8—48no—
174C2×Q8—221no—
175C2×D4—221no—
176C2×D4—222no—
177C2×D4—441no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—24no—
181C22×C4—441no—
182C22×C4C2×C22⋊D1112yes—
183C22×C4C2×C22⋊D1111yescharacteristic
184M16—441no—
185M16—441no—
186C2×C8—442no—
187C2×C8—441no—
188C4⋊C4—44no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—222no—
192C22⋊C4—442no—
193C42—21no—
194C42—21no—
195C42—44no—
196C42#432312yes—
197C42#432512yes—
198C42Q8×D1111yescharacteristic
199C42#434311yescharacteristic
200C42#434312yes—
201C11#1036211yescharacteristic, complemented, Sylow
202C23—441no—
203C23#6700611yescharacteristic
204Q8—88no—
205Q8—441no—
206Q8—441no—
207D4—441no—
208D4—441no—
209D4—882no—
210D4—881no—
211D4—881no—
212C2×C4—24no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—48no—
218C2×C4—44no—
219C2×C4—441no—
220C2×C4—881no—
221C2×C4—881no—
222C2×C4C2×#432311yescharacteristic
223C2×C4#6698511yescharacteristic
224C2×C4C2×#432511yescharacteristic
225C2×C4#6699511yescharacteristic
226C2×C4#6699912yes—
227C2×C4#6699911yescharacteristic
228C2×C4#6700012yes—
229C2×C4#6700011yescharacteristic
230C8—882no—
231C8—881no—
232C22—22no—
233C22—881no—
234C22—882no—
235C22#1062283011yescharacteristic
236C22#1062284011yescharacteristic
237C22#1062284411yescharacteristic
238C4—24no—
239C4—22no—
240C4—22no—
241C4—42no—
242C4—84no—
243C4—881no—
244C4#1062269711yescharacteristic
245C4#1062270011yescharacteristic
246C4#1062270111yescharacteristic
247C4#1062270211yescharacteristic
248C2—21no—
249C2—21no—
250C2—1761no—
251C2#1306974911yescharacteristic
252C2#1306978512yes—
subgroupG/H
centerC22#10622844
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2862C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#2862D11
hypocenterC11#10362
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2862

Complements

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

NH ≅ G/Ntype
3. #13066474C2semidirect
4. #13066449C2semidirect
5. C11×#2862C2semidirect
30. #66927Q8semidirect
32. #66922Q8semidirect
76. #2862D11semidirect
201. C11#10362semidirect

Maximal subgroups

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

subgroupindex
#130694442
#130671752
#130664742
#130664492
C11×#28622
#1036211