Finite Group Databasebeta

← #14670337

Subgroups — #14670337

Order 2816.

414 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 135 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
1C2×#10622719C211yesmaximal, characteristic
2C2×#10622151C212yesmaximal, complemented
3#13068654C211yesmaximal, characteristic
4#13066715C212yesmaximal, complemented
5C11×#2112C211yesmaximal, characteristic
6C23×C8×C11C2211yescharacteristic
7C2×#66979—21no—
8C2×C11×M32C2212yes—
9#10622820—21no—
10C2×#66883C2211yescharacteristic
11C2×#66883C2211yescharacteristic
12#10622719—24no—
13C2×#66882—21no—
14C2×#66881C2212yes—
15C11×C22⋊C16C414yescomplemented
16#10622190—21no—
17#10622151—24no—
18C23×C4×C11D411yescharacteristic
19C22×C8×C11—22no—
20C22×C8×C11—22no—
21C22×C8×C11C2×C412yes—
22C22×C8×C11D411yescharacteristic
23C22×C8×C11Q812yes—
24C22×C8×C11C2311yescharacteristic
25C2×C22⋊Dic11—41no—
26#66979—24no—
27#66979—42no—
28C2×C4⋊Dic11—22no—
29C2×C4×Dic11—41no—
30C2×#4318—21no—
31C2×#4318—21no—
32C11×M32—22no—
33C11×M32—22no—
34C2×C11×C16C2×C414yes—
35C22⋊(C11⋊C8)—42no—
36#66883—22no—
37#66883—22no—
38#66882—24no—
39#66881—22no—
40#66881D414yes—
41#12930—111nomaximal, Sylow
42C24×C11SD1611yescharacteristic
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11C4⋊C412yes—
48C22×C4×C11SD1611yescharacteristic
49C22×C4×C11SD1612yes—
50C22×C4×C11C2×D411yescharacteristic
51C22×Dic11—42no—
52C2×C8×C11—24no—
53C2×C8×C11—24no—
54C2×C8×C11—21no—
55C2×C8×C11—21no—
56C2×C8×C11C4⋊C412yes—
57C2×C8×C11C22×C411yescharacteristic
58C2×C8×C11C2×D412yes—
59C2×C8×C11C2×Q811yescharacteristic
60C2×C8×C11#4112yes—
61C22⋊Dic11—44no—
62C4⋊Dic11—24no—
63C4⋊Dic11—42no—
64C4×Dic11—44no—
65#4318—41no—
66#4318—41no—
67#4318—41no—
68#4318—41no—
69C2×C11⋊C8—41no—
70C2×C11⋊C8—41no—
71C11×C16—24no—
72C2×#427—111no—
73C2×#365—112no—
74#2112D1111yescharacteristic
75#1810—111no—
76#1383—112no—
77C23×C11—21no—
78C23×C11—21no—
79C23×C11—42no—
80C23×C11#10612yes—
81C23×C11C2×SD1611yescharacteristic
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11#10612yes—
89C2×C4×C11C2×C4⋊C411yescharacteristic
90C2×C4×C11#12011yescharacteristic
91C2×C4×C11#12311yescharacteristic
92C2×C4×C11C2×SD1611yescharacteristic
93C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
94C2×C4×C11#13711yescharacteristic
95C2×Dic11—44no—
96C2×Dic11—84no—
97C8×C11—22no—
98C8×C11C4×D412yes—
99C8×C11C22⋊Q812yes—
100C11⋊C8—81no—
101C11⋊C8—81no—
102C23×C8C2×D1111yescharacteristic
103C2×#117—221no—
104C2×M32C2×D1112yes—
105C2×#108—111no—
106C2×#108—111no—
107#427—224no—
108C2×#107—221no—
109C2×#106—112no—
110#407—221no—
111#365—224no—
112C22⋊C16Dic1114yescomplemented
113#341—221no—
114C22×C11—22no—
115C22×C11—22no—
116C22×C11—24no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11C2×#10611yescharacteristic
120C22×C11#45011yescharacteristic
121C22×C11#48311yescharacteristic
122C4×C11—22no—
123C4×C11#38511yescharacteristic
124C4×C11#42811yescharacteristic
125C4×C11#44811yescharacteristic
126C4×C11#48111yescharacteristic
127Dic11—84no—
128C23×C4D4411yescharacteristic
129C2×M16—221no—
130C2×M16—221no—
131C22×C8—22no—
132C22×C8—22no—
133C22×C8Dic2212yes—
134C22×C8D4411yescharacteristic
135C22×C8C2×Dic1112yes—
136C22×C8C22×D1111yescharacteristic
137#117—224no—
138#117—442no—
139C2×C4⋊C4—222no—
140C2×C22⋊C4—441no—
141C2×C42—441no—
142M32—22no—
143M32—22no—
144C2×C16C2×Dic1114yes—
145#108—222no—
146#108—222no—
147#107—224no—
148#106—114no—
149#106—222no—
150C22⋊C8—442no—
151C2×C11—21no—
152C2×C11—21no—
153C2×C11—42no—
154C2×C11#185311yescharacteristic
155C2×C11#215512yes—
156C24#431411yescharacteristic
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—442no—
162C22×C4#431411yescharacteristic
163C22×C4#431412yes—
164C22×C4C4⋊Dic1112yes—
165C22×C4C2×D4411yescharacteristic
166M16—441no—
167M16—441no—
168M16—441no—
169M16—441no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—24no—
173C2×C8—24no—
174C2×C8—441no—
175C2×C8—441no—
176C2×C8C4⋊Dic1112yes—
177C2×C8C2×Dic2211yescharacteristic
178C2×C8D4×D1112yes—
179C2×C8#434112yes—
180C2×C8C22×Dic1111yescharacteristic
181C4⋊C4—224no—
182C4⋊C4—442no—
183C22⋊C4—444no—
184C42—444no—
185C16—24no—
186C11#1293011yescharacteristic, complemented, Sylow
187C23—21no—
188C23—21no—
189C23—42no—
190C23#6688112yes—
191C23C2×#431411yescharacteristic
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—444no—
199C2×C4—884no—
200C2×C4#6688112yes—
201C2×C4#6693511yescharacteristic
202C2×C4#6693911yescharacteristic
203C2×C4C2×#431411yescharacteristic
204C2×C4#6696111yescharacteristic
205C2×C4#6696211yescharacteristic
206C2×C4C2×C4⋊Dic1111yescharacteristic
207C8—22no—
208C8—881no—
209C8—881no—
210C8#6693112yes—
211C8D4×Dic1112yes—
212C22—22no—
213C22—22no—
214C22—24no—
215C22—42no—
216C22—42no—
217C22#1062233411yescharacteristic
218C22#1062234411yescharacteristic
219C22C2×#6688111yescharacteristic
220C4—22no—
221C4—884no—
222C4#1062234811yescharacteristic
223C4#1062235111yescharacteristic
224C4#1062256311yescharacteristic
225C4#1062273411yescharacteristic
226C2—21no—
227C2—21no—
228C2—42no—
229C2#1306881111yescharacteristic
230C2#1307038912yes—
subgroupG/H
centerC22C2×#66881
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#2112C2
socleC22×C11C2×#106
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenter#2112D11
hypocenterC11#12930
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. C2×#10622151C2semidirect
4. #13066715C2semidirect
15. C11×C22⋊C16C4semidirect
112. C22⋊C16Dic11semidirect
186. C11#12930semidirect

Maximal subgroups

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

subgroupindex
C2×#106227192
C2×#106221512
#130686542
#130667152
C11×#21122
#1293011