Finite Group Databasebeta

← #14670347

Subgroups — #14670347

Order 2816.

402 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 131 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#13077206C211yesmaximal, characteristic
2#13070389C212yesmaximal, complemented
3#13068658C211yesmaximal, characteristic
4#13066731C212yesmaximal, complemented
5C2×C11×#349C211yesmaximal, characteristic
6C22×C11×M16C2211yescharacteristic
7C2×#66979—21no—
8C2×C11×M32C2212yes—
9#10622820—21no—
10#10622734—24no—
11C2×#66883C2211yescharacteristic
12C2×#66883C2211yescharacteristic
13#10622719—21no—
14#10622719C2212yes—
15C11×#349C414yescomplemented
16#10622190—21no—
17#10622151—24no—
18C23×C4×C11D411yescharacteristic
19C2×C11×M16—22no—
20C2×C11×M16—22no—
21C2×C11×M16C2×C412yes—
22C2×C11×M16Q812yes—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11C2311yescharacteristic
25C2×C22⋊Dic11—41no—
26#66979—22no—
27#66979—22no—
28#66979—41no—
29#66979—41no—
30C2×C4⋊Dic11—22no—
31C2×C4×Dic11—41no—
32C2×#4318—21no—
33C2×#4318—21no—
34C11×M32—22no—
35C11×M32C2×C414yescomplemented
36C2×C11×C16—22no—
37C22⋊(C11⋊C8)—42no—
38#66883—22no—
39#66883—22no—
40#66882—22no—
41#66882—22no—
42#66881—22no—
43#66881D414yes—
44#12932—111nomaximal, Sylow
45C24×C11SD1611yescharacteristic
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11—21no—
50C22×C4×C11C4⋊C412yes—
51C22×C4×C11SD1611yescharacteristic
52C22×C4×C11SD1612yes—
53C22×C4×C11C2×D411yescharacteristic
54C22×Dic11—42no—
55C11×M16—24no—
56C11×M16—24no—
57C2×C8×C11—21no—
58C2×C8×C11—21no—
59C2×C8×C11C4⋊C412yes—
60C2×C8×C11C22×C411yescharacteristic
61C2×C8×C11C2×D412yes—
62C2×C8×C11C2×Q811yescharacteristic
63C2×C8×C11#4112yes—
64C22⋊Dic11—42no—
65C22⋊Dic11—42no—
66C4⋊Dic11—24no—
67C4⋊Dic11—42no—
68C4×Dic11—42no—
69C4×Dic11—42no—
70#4318—41no—
71#4318—41no—
72#4318—41no—
73#4318—41no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—41no—
76C11×C16—24no—
77#2911—111no—
78#2155—112no—
79C2×#349D1111yescharacteristic
80#1811—111no—
81#1389—112no—
82C23×C11—21no—
83C23×C11—21no—
84C23×C11—81no—
85C23×C11#10612yes—
86C23×C11C2×SD1611yescharacteristic
87C2×C4×C11—21no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—22no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11#10612yes—
94C2×C4×C11C2×C4⋊C411yescharacteristic
95C2×C4×C11#12011yescharacteristic
96C2×C4×C11#12311yescharacteristic
97C2×C4×C11C2×SD1611yescharacteristic
98C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
99C2×C4×C11#13711yescharacteristic
100C2×Dic11—44no—
101C2×Dic11—84no—
102C8×C11—22no—
103C8×C11C4×D412yes—
104C8×C11C22⋊Q812yes—
105C11⋊C8—81no—
106C11⋊C8—81no—
107C22×M16C2×D1111yescharacteristic
108C2×#117—221no—
109C2×M32C2×D1112yes—
110C2×#108—111no—
111C2×#108—111no—
112#428—224no—
113#427—112no—
114#427—221no—
115#407—221no—
116#365—224no—
117#349Dic1114yescomplemented
118#341—221no—
119C22×C11—22no—
120C22×C11—41no—
121C22×C11—42no—
122C22×C11—42no—
123C22×C11—81no—
124C22×C11C2×#10611yescharacteristic
125C22×C11#45011yescharacteristic
126C22×C11#48311yescharacteristic
127C4×C11—22no—
128C4×C11#38511yescharacteristic
129C4×C11#42811yescharacteristic
130C4×C11#44811yescharacteristic
131C4×C11#48111yescharacteristic
132Dic11—84no—
133C23×C4D4411yescharacteristic
134C2×M16—22no—
135C2×M16—22no—
136C2×M16—221no—
137C2×M16—221no—
138C2×M16Dic2212yes—
139C2×M16C2×Dic1112yes—
140C22×C8D4411yescharacteristic
141C22×C8C22×D1111yescharacteristic
142#117—222no—
143#117—222no—
144#117—441no—
145#117—441no—
146C2×C4⋊C4—222no—
147C2×C22⋊C4—441no—
148C2×C42—441no—
149M32—22no—
150M32C2×Dic1114yescomplemented
151C2×C16—22no—
152#108—222no—
153#108—222no—
154#107—222no—
155#107—222no—
156#106—114no—
157#106—222no—
158C22⋊C8—442no—
159C2×C11—21no—
160C2×C11—21no—
161C2×C11—21no—
162C2×C11—42no—
163C2×C11#185311yescharacteristic
164C24#431411yescharacteristic
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—442no—
170C22×C4#431411yescharacteristic
171C22×C4#431412yes—
172C22×C4C4⋊Dic1112yes—
173C22×C4C2×D4411yescharacteristic
174M16—24no—
175M16—24no—
176M16—441no—
177M16—441no—
178M16—441no—
179M16—441no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—441no—
183C2×C8—441no—
184C2×C8C4⋊Dic1112yes—
185C2×C8C2×Dic2211yescharacteristic
186C2×C8D4×D1112yes—
187C2×C8#434112yes—
188C2×C8C22×Dic1111yescharacteristic
189C4⋊C4—224no—
190C4⋊C4—442no—
191C22⋊C4—442no—
192C22⋊C4—442no—
193C42—442no—
194C42—442no—
195C16—24no—
196C11#1293211yescharacteristic, complemented, Sylow
197C23—21no—
198C23—21no—
199C23—81no—
200C23#6688112yes—
201C23C2×#431411yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—444no—
209C2×C4—884no—
210C2×C4#6688112yes—
211C2×C4#6693511yescharacteristic
212C2×C4#6693911yescharacteristic
213C2×C4C2×#431411yescharacteristic
214C2×C4#6696111yescharacteristic
215C2×C4#6696211yescharacteristic
216C2×C4C2×C4⋊Dic1111yescharacteristic
217C8—22no—
218C8—881no—
219C8—881no—
220C8#6693112yes—
221C8D4×Dic1112yes—
222C22—22no—
223C22—41no—
224C22—42no—
225C22—42no—
226C22—81no—
227C22#1062233411yescharacteristic
228C22#1062234411yescharacteristic
229C22C2×#6688111yescharacteristic
230C4—22no—
231C4—884no—
232C4#1062234811yescharacteristic
233C4#1062235111yescharacteristic
234C4#1062256311yescharacteristic
235C4#1062273411yescharacteristic
236C2—21no—
237C2—21no—
238C2—21no—
239C2—42no—
240C2#1306881111yescharacteristic
subgroupG/H
centerC4#10622348
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC2×C11×#349C2
socleC2×C11#1853
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC2×#349D11
hypocenterC11#12932
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×M16 ◁ C2×#349

Complements

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

NH ≅ G/Ntype
2. #13070389C2semidirect
4. #13066731C2semidirect
15. C11×#349C4semidirect
35. C11×M32C2×C4semidirect
117. #349Dic11semidirect
150. M32C2×Dic11semidirect
196. C11#12932semidirect

Maximal subgroups

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

subgroupindex
#130772062
#130703892
#130686582
#130667312
C2×C11×#3492
#1293211