Finite Group Databasebeta

← #14656862

Subgroups — #14656862

Order 2816.

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

normal subgroups only

This group has 454 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#13076994C211yesmaximal, characteristic, complemented
2#13069444C211yesmaximal, characteristic
3#13067177C212yesmaximal
4#13066475C212yesmaximal, complemented
5C11×#1276C211yesmaximal, characteristic, complemented
6#10623008C2211yescharacteristic
7C2×#66922—21no—
8C11×#431C2212yes—
9C43×C11C2211yescharacteristic
10#10622549—21no—
11#10622549C2212yes—
12#10622542—24no—
13C2×#66869—21no—
14C2×#66869—21no—
15#10622537C2211yescharacteristic
16#10622108—24no—
17C2×#4339—21no—
18C22×Dic22—22no—
19C2×C42×C11—22no—
20C2×C42×C11D411yescharacteristic
21C2×C42×C11D411yescharacteristic
22C2×C42×C11C2311yescharacteristic
23#66983—22no—
24C2×C4⋊Dic11—22no—
25C2×C4⋊Dic11—22no—
26C2×#4318—21no—
27#66928—21no—
28#66927Q811yescharacteristic, complemented
29C4×D44—22no—
30#66922—42no—
31#66922—42no—
32#66922Q811yescharacteristic, complemented
33C11×C4⋊C8—22no—
34C11×C22⋊C8—22no—
35C4×C8×C11—22no—
36C11⋊#95—24no—
37C11⋊#95—22no—
38C11⋊#95D414yes—
39#66869—42no—
40#66869—42no—
41C4⋊(C11⋊C8)—22no—
42#10362—111nomaximal, Sylow
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11C2×D412yes—
46C22×C4×C11C2×D411yescharacteristic
47C2×C22⋊D11—41no—
48C22×Dic11—24no—
49#4339—41no—
50#4339—41no—
51#4339—41no—
52#4339—41no—
53C2×D44—21no—
54C2×D44—22no—
55C2×C4×D11—41no—
56C2×Dic22—21no—
57C2×Dic22—44no—
58C2×Dic22—48no—
59C2×C8×C11—42no—
60C42×C11—21no—
61C42×C11—21no—
62C42×C11—44no—
63C42×C11D812yes—
64C42×C11SD1612yes—
65C42×C11C2×Q811yescharacteristic
66C42×C11#4112yes—
67C42×C11#4111yescharacteristic
68(C2×D11)⋊C4—42no—
69C4⋊Dic11—22no—
70C4⋊Dic11—44no—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73#4318—41no—
74#4318—41no—
75C2×C11⋊C8—41no—
76#2862—111no—
77#1962—111no—
78#1517—112no—
79#1286—112no—
80#1276D1111yescharacteristic, complemented
81C23×C11#12011yescharacteristic
82C22×D11—41no—
83C2×C4×C11—24no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—42no—
87C2×C4×C11—42no—
88C2×C4×C11C22⋊Q812yes—
89C2×C4×C11C22⋊Q811yescharacteristic
90C2×C4×C11#12411yescharacteristic
91C2×C4×C11#12412yes—
92C2×C4×C11C2×D811yescharacteristic
93C2×C4×C11C2×SD1611yescharacteristic
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C11#13711yescharacteristic
96C22⋊D11—81no—
97C22⋊D11—81no—
98C2×Dic11—48no—
99C2×Dic11—41no—
100C2×Dic11—44no—
101D44—41no—
102D44—41no—
103D44—82no—
104C4×D11—81no—
105C4×D11—81no—
106Dic22—41no—
107Dic22—41no—
108Dic22—88no—
109C8×C11—82no—
110C11⋊C8—81no—
111#532—111no—
112C2×C4⋊Q8—221no—
113#431C2×D1112yes—
114#423—111no—
115C2×#104—221no—
116C2×#104—221no—
117#391—224no—
118#382—112no—
119#382—221no—
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#47411yescharacteristic
133C4×C11#47611yescharacteristic
134C4×C11#48611yescharacteristic
135C4×C11#48911yescharacteristic
136Dic11—84no—
137Dic11—81no—
138C2×#41—221no—
139C22×Q8—222no—
140C2×M16—221no—
141C4⋊Q8—111no—
142C4⋊Q8—442no—
143C4⋊Q8—442no—
144#127—111no—
145#124—221no—
146#121—222no—
147C4×D4—222no—
148C2×C4⋊C4—222no—
149C2×C4⋊C4—222no—
150C2×C42—22no—
151C2×C42D4411yescharacteristic
152C2×C42D4411yescharacteristic
153C2×C42C22×D1111yescharacteristic
154C4⋊C8—22no—
155C4⋊C8—222no—
156#104—442no—
157#104—442no—
158C22⋊C8—22no—
159C4×C8—22no—
160#95—114no—
161#95—224no—
162#95—222no—
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—221no—
173C2×Q8—444no—
174C2×Q8—448no—
175C2×D4—222no—
176C2×D4—221no—
177C2×D4—441no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—224no—
181C22×C4—441no—
182C22×C4C2×D4411yescharacteristic
183C22×C4D4×D1112yes—
184M16—441no—
185M16—441no—
186C2×C8—42no—
187C2×C8—441no—
188C4⋊C4—222no—
189C4⋊C4—444no—
190C4⋊C4—442no—
191C4⋊C4—442no—
192C22⋊C4—442no—
193C42—21no—
194C42—21no—
195C42—44no—
196C42#431412yes—
197C42D8812yes—
198C42#433912yes—
199C42#434111yescharacteristic
200C42Q8×D1111yescharacteristic
201C11#1036211yescharacteristic, complemented, Sylow
202C23—441no—
203C23#6693511yescharacteristic
204Q8—441no—
205Q8—441no—
206Q8—888no—
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—448no—
218C2×C4—441no—
219C2×C4—444no—
220C2×C4—881no—
221C2×C4—881no—
222C2×C4#6692811yescharacteristic
223C2×C4#6693812yes—
224C2×C4#6694912yes—
225C2×C4#6695011yescharacteristic
226C2×C4C2×#431411yescharacteristic
227C2×C4C2×D8811yescharacteristic
228C2×C4#6696111yescharacteristic
229C2×C4#6696211yescharacteristic
230C8—82no—
231C8—881no—
232C22—22no—
233C22—881no—
234C22—882no—
235C22#1062228611yescharacteristic
236C22#1062234511yescharacteristic
237C22#1062235111yescharacteristic
238C4—24no—
239C4—22no—
240C4—22no—
241C4—42no—
242C4—884no—
243C4—881no—
244C4#1062230711yescharacteristic
245C4#1062232711yescharacteristic
246C4#1062245511yescharacteristic
247C4#1062245911yescharacteristic
248C2—21no—
249C2—21no—
250C2—1761no—
251C2#1306975311yescharacteristic
252C2#1306978912yes—
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1276C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1276D11
hypocenterC11#10362
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. #13076994C2semidirect
4. #13066475C2semidirect
5. C11×#1276C2semidirect
28. #66927Q8semidirect
32. #66922Q8semidirect
80. #1276D11semidirect
201. C11#10362semidirect

Maximal subgroups

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

subgroupindex
#130769942
#130694442
#130671772
#130664752
C11×#12762
#1036211