Finite Group Databasebeta

← #14670330

Subgroups — #14670330

Order 2816.

458 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 139 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×#10622125C212yesmaximal, complemented
2#13070227C211yesmaximal, characteristic
3#13068654C211yesmaximal, characteristic
4#13066714C212yesmaximal, complemented
5C22×C11×#106C211yesmaximal, characteristic
6C23×C8×C11C2211yescharacteristic
7C22×C11×C4⋊C4—21no—
8C2×C11×#106—21no—
9C2×C11×#106—24no—
10C2×C11×#106C2212yes—
11#10622820—21no—
12C2×#66883C2211yescharacteristic
13C2×#66883C2211yescharacteristic
14C2×#66876C2212yes—
15#10622190—21no—
16C22⋊(C11⋊C16)C414yescomplemented
17#10622125—24no—
18C23×C4×C11—41no—
19C23×C4×C11D411yescharacteristic
20C22×C8×C11—22no—
21C22×C8×C11—22no—
22C22×C8×C11C2×C412yes—
23C22×C8×C11D411yescharacteristic
24C22×C8×C11Q812yes—
25C22×C8×C11C2311yescharacteristic
26C2×C11×C4⋊C4—24no—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—42no—
29C2×C11×C4⋊C4—41no—
30C2×#4318—21no—
31C2×#4318—21no—
32C11×#106—24no—
33C11×#106—22no—
34C11×#106D414yes—
35C22⋊(C11⋊C8)—42no—
36#66883—22no—
37#66883—22no—
38#66876—22no—
39#66876—22no—
40C2×C11⋊C16C2×C414yescomplemented
41#12929—111nomaximal, Sylow
42C24×C11SD1611yescharacteristic
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C22×C4×C11—21no—
46C22×C4×C11—21no—
47C22×C4×C11—44no—
48C22×C4×C11—42no—
49C22×C4×C11—84no—
50C22×C4×C11C4⋊C412yes—
51C22×C4×C11SD1611yescharacteristic
52C22×C4×C11SD1612yes—
53C22×C4×C11C2×D411yescharacteristic
54C2×C8×C11—24no—
55C2×C8×C11—24no—
56C2×C8×C11—21no—
57C2×C8×C11—21no—
58C2×C8×C11C4⋊C412yes—
59C2×C8×C11C22×C411yescharacteristic
60C2×C8×C11C2×D412yes—
61C2×C8×C11C2×Q811yescharacteristic
62C2×C8×C11#4112yes—
63C11×C4⋊C4—24no—
64C11×C4⋊C4—44no—
65C11×C4⋊C4—42no—
66#4318—41no—
67#4318—41no—
68#4318—41no—
69#4318—41no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—41no—
72C11⋊C16—24no—
73C22×#106D1111yescharacteristic
74C2×#365—112no—
75#2112—111no—
76#1810—111no—
77#1383—112no—
78C23×C11—24no—
79C23×C11—21no—
80C23×C11—21no—
81C23×C11#10612yes—
82C23×C11C2×SD1611yescharacteristic
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—44no—
90C2×C4×C11—88no—
91C2×C4×C11—84no—
92C2×C4×C11#10612yes—
93C2×C4×C11C2×C4⋊C411yescharacteristic
94C2×C4×C11#12011yescharacteristic
95C2×C4×C11#12311yescharacteristic
96C2×C4×C11C2×SD1611yescharacteristic
97C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
98C2×C4×C11#13711yescharacteristic
99C8×C11—22no—
100C8×C11C4×D412yes—
101C8×C11C22⋊Q812yes—
102C11⋊C8—81no—
103C11⋊C8—81no—
104C23×C8C2×D1111yescharacteristic
105C22×C4⋊C4—21no—
106C2×M32—112no—
107C2×#108—111no—
108C2×#108—111no—
109C2×#106—21no—
110C2×#106—24no—
111C2×#106C2×D1112yes—
112#407—221no—
113#365—224no—
114C22⋊C16—114no—
115#341—221no—
116C22×C11—24no—
117C22×C11—24no—
118C22×C11—22no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11#36514yescomplemented
122C22×C11C2×#10611yescharacteristic
123C22×C11#45011yescharacteristic
124C22×C11#48311yescharacteristic
125C4×C11—22no—
126C4×C11—84no—
127C4×C11#38511yescharacteristic
128C4×C11#42811yescharacteristic
129C4×C11#44811yescharacteristic
130C4×C11#48111yescharacteristic
131C23×C4—41no—
132C23×C4C22⋊D1111yescharacteristic
133C2×M16—221no—
134C2×M16—221no—
135C22×C8—22no—
136C22×C8—22no—
137C22×C8Dic2212yes—
138C22×C8C4×D1112yes—
139C22×C8C22⋊D1111yescharacteristic
140C22×C8C22×D1111yescharacteristic
141C2×C4⋊C4—24no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—42no—
144C2×C4⋊C4—41no—
145M32—222no—
146M32—222no—
147C2×C16—114no—
148#108—222no—
149#108—222no—
150#106—24no—
151#106—22no—
152#106C22⋊D1114yes—
153C22⋊C8—442no—
154C2×C11—21no—
155C2×C11—24no—
156C2×C11—21no—
157C2×C11#185311yescharacteristic
158C2×C11C2×#36512yes—
159C24#432411yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4—44no—
165C22×C4—42no—
166C22×C4—84no—
167C22×C4Dic11⋊C412yes—
168C22×C4#432411yescharacteristic
169C22×C4#432512yes—
170C22×C4C2×C22⋊D1111yescharacteristic
171M16—441no—
172M16—441no—
173M16—441no—
174M16—441no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—24no—
178C2×C8—24no—
179C2×C8—441no—
180C2×C8—441no—
181C2×C8Dic11⋊C412yes—
182C2×C8C2×Dic2211yescharacteristic
183C2×C8C2×C4×D1111yescharacteristic
184C2×C8#433912yes—
185C2×C8C2×C22⋊D1112yes—
186C4⋊C4—24no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C16—224no—
190C11#1292911yescharacteristic, complemented, Sylow
191C23—21no—
192C23—21no—
193C23—24no—
194C23#6687212yes—
195C23C2×#432411yescharacteristic
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—44no—
203C2×C4—88no—
204C2×C4—84no—
205C2×C4#6687212yes—
206C2×C4C2×Dic11⋊C411yescharacteristic
207C2×C4#6698211yescharacteristic
208C2×C4#6698511yescharacteristic
209C2×C4C2×#432511yescharacteristic
210C2×C4#6699511yescharacteristic
211C2×C4#6700611yescharacteristic
212C8—22no—
213C8—881no—
214C8—881no—
215C8#6697712yes—
216C8C4×C22⋊D1112yes—
217C22—24no—
218C22—24no—
219C22—22no—
220C22—22no—
221C22—22no—
222C22#1062212514yescomplemented
223C22C2×#6687211yescharacteristic
224C22#1062258411yescharacteristic
225C22#1062283111yescharacteristic
226C4—22no—
227C4—84no—
228C4#1062257711yescharacteristic
229C4#1062258111yescharacteristic
230C4#1062282311yescharacteristic
231C4#1062284011yescharacteristic
232C2—21no—
233C2—21no—
234C2—24no—
235C2#1306880911yescharacteristic
236C2C2×#1062212512yes—
subgroupG/H
centerC22C2×#66872
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC22×C11×#106C2
socleC22×C11C2×#106
prime radicalC24×C11SD16
cosocleC22×C8×C11C23
hypercenterC22×#106D11
hypocenterC11#12929
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ C22×#106

Complements

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

NH ≅ G/Ntype
1. C2×#10622125C2semidirect
4. #13066714C2semidirect
16. C22⋊(C11⋊C16)C4semidirect
40. C2×C11⋊C16C2×C4semidirect
121. C22×C11#365semidirect
190. C11#12929semidirect
222. C22#10622125semidirect

Maximal subgroups

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

subgroupindex
C2×#106221252
#130702272
#130686542
#130667142
C22×C11×#1062
#1292911