Finite Group Databasebeta

← #14651166

Subgroups — #14651166

Order 2816.

514 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 115 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#13077657C211yesmaximal, characteristic
2#13073789C211yesmaximal, characteristic
3#13067298C212yesmaximal, complemented
4#13066517C212yesmaximal, complemented
5C11×#1800C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66922C2211yescharacteristic
8C11×#423C2212yes—
9C2×C11×#100—21no—
10#10622834—21no—
11#10622825—22no—
12#10622820—22no—
13#10622625—24no—
14#10622590—21no—
15#10622560C414yes—
16C4×C4⋊Dic11C2211yescharacteristic
17#10622538C2212yes—
18C11×#343—21no—
19#10622119—24no—
20C22×D4×C11D411yescharacteristic
21C23×C4×C11D412yes—
22C22×Dic22C2×C412yes—
23C2×C11×M16—22no—
24C4×D4×C11—22no—
25C4×D4×C11—22no—
26C2×C11×C4⋊C4D411yescharacteristic
27C2×C11×C22⋊C4C2×C412yes—
28C2×C42×C11C2311yescharacteristic
29C2×C22⋊Dic11—24no—
30C2×C4⋊Dic11—21no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—21no—
33C2×C4×Dic11—21no—
34C2×#4318—24no—
35#66922—22no—
36#66922—22no—
37C11×C4⋊C8—22no—
38C11×C4⋊C8—22no—
39C11×#100—42no—
40C11⋊#95—24no—
41C11⋊#95C2×C412yes—
42C22⋊(C11⋊C8)—24no—
43C22⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)D414yes—
45C4×C11⋊C8—22no—
46#9399—111nomaximal, Sylow
47C24×C11C22⋊C412yes—
48C2×D4×C11—22no—
49C2×D4×C11—21no—
50C2×D4×C11—21no—
51C2×D4×C11—22no—
52C22×C4×C11—22no—
53C22×C4×C11—22no—
54C22×C4×C11—44no—
55C22×C4×C11C22⋊C412yes—
56C22×C4×C11C22×C411yescharacteristic
57C22×C4×C11C2×D411yescharacteristic
58C22×C4×C11C2×D411yescharacteristic
59C22×Dic11—22no—
60C22×Dic11—22no—
61C2×Dic22—24no—
62C2×Dic22—82no—
63C11×M16—42no—
64C11×M16—42no—
65C2×C8×C11—42no—
66C11×C4⋊C4—22no—
67C11×C22⋊C4—24no—
68C42×C11C2×D412yes—
69C42×C11#4112yes—
70C22⋊Dic11—84no—
71C4⋊Dic11—42no—
72C4⋊Dic11—41no—
73C4⋊Dic11—42no—
74C4⋊Dic11—41no—
75C4×Dic11—41no—
76C4×Dic11—41no—
77#4318—84no—
78C2×C11⋊C8—24no—
79#2975—111no—
80#2563—111no—
81#1800D1111yescharacteristic
82#1548—112no—
83#1303—112no—
84C23×C11—22no—
85C23×C11—22no—
86C23×C11—22no—
87C23×C11—42no—
88C23×C11—42no—
89C23×C11C2×C22⋊C411yescharacteristic
90D4×C11—42no—
91D4×C11—42no—
92C2×C4×C11—22no—
93C2×C4×C11—22no—
94C2×C4×C11—41no—
95C2×C4×C11—44no—
96C2×C4×C11—42no—
97C2×C4×C11—82no—
98C2×C4×C11C4×D412yes—
99C2×C4×C11#12011yescharacteristic
100C2×C4×C11#12112yes—
101C2×C4×C11#12311yescharacteristic
102C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C11#13711yescharacteristic
104C2×C4×C11#13712yes—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—44no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110Dic22—84no—
111C8×C11—82no—
112C11⋊C8—44no—
113C2×C4⋊Q8—111no—
114C2×C4×D4C2×D1111yescharacteristic
115#436—224no—
116#431—112no—
117#423C2×D1112yes—
118C2×#100—21no—
119#407—222no—
120#393—114no—
121#390—221no—
122#382—221no—
123#380—222no—
124C4×C4⋊C4—111no—
125#343—21no—
126#333—224no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11—44no—
130C22×C11—42no—
131C22×C11—42no—
132C22×C11—42no—
133C22×C11—82no—
134C22×C11#38611yescharacteristic
135C22×C11#41711yescharacteristic
136C22×C11#41911yescharacteristic
137C4×C11—21no—
138C4×C11—22no—
139C4×C11—42no—
140C4×C11#45512yes—
141C4×C11#46812yes—
142C4×C11#47012yes—
143Dic11—82no—
144Dic11—82no—
145C22×Q8—112no—
146C22×D4C22⋊D1111yescharacteristic
147C23×C4D4412yes—
148C2×M16—22no—
149C2×M16—224no—
150C4⋊Q8—222no—
151C4⋊Q8—222no—
152C4×D4—22no—
153C4×D4—22no—
154C2×C4⋊C4—221no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4—221no—
157C2×C4⋊C4C22⋊D1111yescharacteristic
158C2×C22⋊C4—224no—
159C2×C22⋊C4C4×D1112yes—
160C2×C42—221no—
161C2×C42C22×D1111yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—114no—
165#100—42no—
166C22⋊C8—224no—
167C22⋊C8—222no—
168C4×C8—222no—
169#95—112no—
170#95—224no—
171C2×C11—21no—
172C2×C11—21no—
173C2×C11—82no—
174C2×C11#188511yescharacteristic
175C2×C11#189411yescharacteristic
176C2×C11#191411yescharacteristic
177C24(C2×D11)⋊C412yes—
178C2×Q8—224no—
179C2×Q8—882no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—44no—
187C22×C4—222no—
188C22×C4—222no—
189C22×C4(C2×D11)⋊C412yes—
190C22×C4C2×C4×D1111yescharacteristic
191C22×C4C2×D4411yescharacteristic
192C22×C4C2×C22⋊D1111yescharacteristic
193M16—42no—
194M16—42no—
195M16—884no—
196C2×C8—42no—
197C2×C8—224no—
198C4⋊C4—22no—
199C4⋊C4—442no—
200C4⋊C4—441no—
201C4⋊C4—441no—
202C4⋊C4—442no—
203C22⋊C4—24no—
204C22⋊C4—884no—
205C42—441no—
206C42—441no—
207C42D4×D1112yes—
208C42#434112yes—
209C11#939911yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×(C2×D11)⋊C411yescharacteristic
216Q8—884no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—442no—
226C2×C4—444no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4(C22⋊D11)⋊C412yes—
231C2×C4#6693511yescharacteristic
232C2×C4#6693911yescharacteristic
233C2×C4#6698511yescharacteristic
234C2×C4#6699212yes—
235C2×C4#6699511yescharacteristic
236C2×C4#6700412yes—
237C8—82no—
238C8—444no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#1062257111yescharacteristic
247C22#1062257911yescharacteristic
248C22#1062261711yescharacteristic
249C4—22no—
250C4—21no—
251C4—42no—
252C4—882no—
253C4—882no—
254C4#1062235912yes—
255C4#1062265512yes—
256C4#1062266512yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1306900211yescharacteristic
261C2#1306904711yescharacteristic
262C2#1306916111yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1800C2
socleC22×C11#386
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1800D11
hypocenterC11#9399
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13067298C2semidirect
4. #13066517C2semidirect
209. C11#9399semidirect

Maximal subgroups

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

subgroupindex
#130776572
#130737892
#130672982
#130665172
C11×#18002
#939911