Finite Group Databasebeta

← #14652843

Subgroups — #14652843

Order 2816.

478 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 151 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
2C4×C4⋊(C11⋊C8)C211yesmaximal, characteristic
3C2×#10622120C212yesmaximal
4C2×#10622124C212yesmaximal
5C11×#1831C211yesmaximal, characteristic
6C2×#66922C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C2×C11×C4⋊C8C2212yes—
9C43×C11C2211yescharacteristic
10#10622549C414yes—
11#10622542—21no—
12#10622542—21no—
13#10622542—22no—
14C2×C4⋊(C11⋊C8)C2212yes—
15C2×C4×C11⋊C8—21no—
16C11×#336—22no—
17#10622162—21no—
18#10622124—24no—
19#10622120—24no—
20C22×Dic22—21no—
21C22×Dic22—21no—
22C22×C8×C11—22no—
23C2×C42×C11C2×C412yes—
24C2×C42×C11D411yescharacteristic
25C2×C42×C11D411yescharacteristic
26C2×C42×C11D412yes—
27C2×C42×C11C2311yescharacteristic
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4⋊Dic11C2×C412yes—
31C2×C4⋊Dic11C2×C412yes—
32C22×C11⋊C8—22no—
33#66922—22no—
34#66922—22no—
35#66922—22no—
36#66922—22no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39C11⋊#95—24no—
40C11⋊#95—24no—
41C4⋊(C11⋊C8)—22no—
42C4⋊(C11⋊C8)D414yes—
43C4×C11⋊C8—42no—
44#9700—111nomaximal, Sylow
45C22×C4×C11C22⋊C412yes—
46C22×C4×C11C22⋊C412yes—
47C22×C4×C11C22×C411yescharacteristic
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D411yescharacteristic
50C22×Dic11—22no—
51C22×Dic11—22no—
52C2×Dic22—42no—
53C2×Dic22—41no—
54C2×Dic22—41no—
55C2×Dic22—42no—
56C2×Dic22—44no—
57C2×Dic22—41no—
58C2×Dic22—41no—
59C2×C8×C11—42no—
60C2×C8×C11—44no—
61C42×C11—24no—
62C42×C11—24no—
63C42×C11—22no—
64C42×C11—21no—
65C42×C11—21no—
66C42×C11C2×D412yes—
67C42×C11#4112yes—
68C4⋊Dic11—24no—
69C4⋊Dic11—24no—
70C4⋊Dic11—42no—
71C4⋊Dic11—41no—
72C4⋊Dic11—41no—
73C2×C11⋊C8—24no—
74C2×C11⋊C8—42no—
75C2×C11⋊C8—42no—
76#2862—111no—
77#1831D1111yescharacteristic
78C4×C4⋊C8—111no—
79C2×#332—112no—
80C2×#332—112no—
81C23×C11C2×C22⋊C411yescharacteristic
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11#10114yes—
89C2×C4×C11C4×D412yes—
90C2×C4×C11#12112yes—
91C2×C4×C11#12411yescharacteristic
92C2×C4×C11#12711yescharacteristic
93C2×C4×C11#13512yes—
94C2×C4×C11#13514yes—
95C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
96C2×C4×C11#13711yescharacteristic
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—44no—
101C2×Dic11—42no—
102Dic22—82no—
103Dic22—82no—
104Dic22—82no—
105Dic22—82no—
106C8×C11—82no—
107C11⋊C8—44no—
108C2×C4⋊Q8—111no—
109C2×C4⋊Q8—111no—
110C2×C4⋊C8—112no—
111C2×C4⋊C8C2×D1112yes—
112C2×C4×C8—221no—
113#391—221no—
114#391—221no—
115#391—222no—
116#382—114no—
117C43C2×D1111yescharacteristic
118#336—22no—
119#336—221no—
120#332—224no—
121#332—224no—
122C22×C11#39011yescharacteristic
123C22×C11C2×#10112yes—
124C22×C11#41611yescharacteristic
125C22×C11#41612yes—
126C22×C11#41711yescharacteristic
127C4×C11—24no—
128C4×C11—22no—
129C4×C11—42no—
130C4×C11#46312yes—
131C4×C11#46412yes—
132C4×C11#48812yes—
133C4×C11#49512yes—
134Dic11—82no—
135Dic11—82no—
136C22×Q8—221no—
137C22×Q8—221no—
138C22×C8—22no—
139C22×C8—222no—
140C4⋊Q8—222no—
141C4⋊Q8—222no—
142C4⋊Q8—222no—
143C4⋊Q8—222no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4—221no—
148C2×C42C4×D1112yes—
149C2×C42D4411yescharacteristic
150C2×C42D4411yescharacteristic
151C2×C42C22⋊D1112yes—
152C2×C42C22×D1111yescharacteristic
153C4⋊C8—22no—
154C4⋊C8—22no—
155C4⋊C8—114no—
156C4⋊C8—222no—
157C4×C8—442no—
158#95—224no—
159#95—224no—
160C2×C11#154412yes—
161C2×C11#155212yes—
162C2×C11#195811yescharacteristic
163C2×C11#196611yescharacteristic
164C2×C11#198311yescharacteristic
165C2×Q8—442no—
166C2×Q8—442no—
167C2×Q8—441no—
168C2×Q8—441no—
169C2×Q8—441no—
170C2×Q8—441no—
171C2×Q8—444no—
172C22×C4—222no—
173C22×C4—222no—
174C22×C4(C2×D11)⋊C412yes—
175C22×C4(C2×D11)⋊C412yes—
176C22×C4C2×C4×D1111yescharacteristic
177C22×C4C2×D4411yescharacteristic
178C22×C4C2×C22⋊D1111yescharacteristic
179C2×C8—42no—
180C2×C8—44no—
181C2×C8—224no—
182C2×C8—442no—
183C2×C8—442no—
184C4⋊C4—224no—
185C4⋊C4—224no—
186C4⋊C4—442no—
187C4⋊C4—441no—
188C4⋊C4—441no—
189C42—24no—
190C42—22no—
191C42—21no—
192C42—21no—
193C42—24no—
194C42D4×D1112yes—
195C42#434312yes—
196C11#970011yescharacteristic, complemented, Sylow
197C23C2×(C2×D11)⋊C411yescharacteristic
198Q8—882no—
199Q8—882no—
200Q8—882no—
201Q8—882no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—442no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4—444no—
213C2×C4#6688814yes—
214C2×C4#6694612yes—
215C2×C4#6694812yes—
216C2×C4#6695712yes—
217C2×C4#6696111yescharacteristic
218C2×C4#6696211yescharacteristic
219C2×C4#6699311yescharacteristic
220C2×C4#6700011yescharacteristic
221C2×C4#6700314yes—
222C8—82no—
223C8—444no—
224C22#1062260111yescharacteristic
225C22#1062261512yes—
226C22#1062272611yescharacteristic
227C22#1062274611yescharacteristic
228C22C2×#6688812yes—
229C4—24no—
230C4—22no—
231C4—42no—
232C4—882no—
233C4—882no—
234C4#1062245712yes—
235C4#1062245812yes—
236C4#1062267212yes—
237C4#1062268112yes—
238C2#1306728012yes—
239C2#1306731712yes—
240C2#1306942511yescharacteristic
241C2#1306945911yescharacteristic
242C2#1306954611yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1831C2
socle, prime radicalC23×C11C2×C22⋊C4
cosocleC2×C42×C11C23
hypercenter#1831D11
hypocenterC11#9700
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1831

Complements

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

NH ≅ G/Ntype
196. C11#9700semidirect

Maximal subgroups

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

subgroupindex
#130769942
C4×C4⋊(C11⋊C8)2
C2×#106221202
C2×#106221242
C11×#18312
#970011