Finite Group Databasebeta

← #14647370

Subgroups — #14647370

Order 2816.

426 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 107 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#13071589C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic
3#13066518C212yesmaximal, complemented
4#13066475C212yesmaximal, complemented
5C11×#1460C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C11×#431C2212yes—
8#10622834—21no—
9C2×#66897—21no—
10#10622824C412yes—
11C4×C22⋊Dic11C412yes—
12C4⋊C4×Dic11—21no—
13#10622564—22no—
14#10622549C2211yescharacteristic
15C4×C4⋊Dic11C2211yescharacteristic
16#10622537C2212yes—
17C11×#323—22no—
18#10622168—21no—
19C22×D4×C11D411yescharacteristic
20C23×C4×C11C2×C412yes—
21C4×D4×C11—22no—
22C4×D4×C11—22no—
23C2×C11×C4⋊C4D411yescharacteristic
24C2×C11×C22⋊C4D412yes—
25C2×C42×C11C2311yescharacteristic
26C2×C22⋊Dic11—22no—
27C2×C22⋊Dic11—22no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11—21no—
30C2×C4×Dic11—21no—
31C2×C4×Dic11—22no—
32C2×#4318—22no—
33C11×C4⋊C8—22no—
34C11×C22⋊C8—22no—
35C4×C8×C11—22no—
36#66897—42no—
37C11⋊#95—22no—
38C11⋊#95—21no—
39C11⋊#95C2×C411yescharacteristic
40C11⋊#95C2×C411yescharacteristic
41C11⋊#95C2×C412yes—
42C4⋊(C11⋊C8)—22no—
43C4⋊(C11⋊C8)—22no—
44#8770—111nomaximal, Sylow
45C24×C11C22⋊C412yes—
46C2×D4×C11—22no—
47C2×D4×C11—22no—
48C2×D4×C11—21no—
49C2×D4×C11—21no—
50C22×C4×C11—22no—
51C22×C4×C11—22no—
52C22×C4×C11—82no—
53C22×C4×C11C22⋊C412yes—
54C22×C4×C11C22×C411yescharacteristic
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×Dic11—21no—
58C22×Dic11—22no—
59C22×Dic11—21no—
60C2×C8×C11—42no—
61C11×C4⋊C4—22no—
62C11×C22⋊C4—24no—
63C42×C11#4112yes—
64C42×C11#4112yes—
65C22⋊Dic11—44no—
66C22⋊Dic11—82no—
67C4⋊Dic11—42no—
68C4⋊Dic11—42no—
69C4×Dic11—41no—
70C4×Dic11—41no—
71C4×Dic11—82no—
72#4318—42no—
73#4318—42no—
74C2×C11⋊C8—42no—
75#2357—111no—
76#1800—111no—
77#1460D1111yescharacteristic
78#1303—112no—
79#1286—112no—
80C23×C11—22no—
81C23×C11—22no—
82C23×C11—22no—
83C23×C11—42no—
84C23×C11—42no—
85C23×C11C2×C22⋊C411yescharacteristic
86D4×C11—42no—
87D4×C11—42no—
88C2×C4×C11—22no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11—82no—
93C2×C4×C11—82no—
94C2×C4×C11#11711yescharacteristic
95C2×C4×C11#11711yescharacteristic
96C2×C4×C11#12312yes—
97C2×C4×C11#12312yes—
98C2×C4×C11#13512yes—
99C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C11#13711yescharacteristic
101C2×Dic11—22no—
102C2×Dic11—41no—
103C2×Dic11—41no—
104C2×Dic11—42no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—41no—
108C2×Dic11—42no—
109C2×Dic11—41no—
110C8×C11—82no—
111C11⋊C8—82no—
112C2×C4×D4C2×D1111yescharacteristic
113#431C2×D1112yes—
114#423—112no—
115C2×#100—221no—
116#390—221no—
117#388—222no—
118#382—111no—
119#381—112no—
120C4×C4⋊C4—111no—
121C4×C4⋊C4—221no—
122C4×C22⋊C4—112no—
123#343—221no—
124#323—22no—
125C22×C11—21no—
126C22×C11—21no—
127C22×C11—42no—
128C22×C11—42no—
129C22×C11—42no—
130C22×C11—82no—
131C22×C11—82no—
132C22×C11#38111yescharacteristic
133C22×C11#41611yescharacteristic
134C22×C11#41711yescharacteristic
135C4×C11—22no—
136C4×C11—21no—
137C4×C11—21no—
138C4×C11—42no—
139C4×C11#48212yes—
140C4×C11#48512yes—
141Dic11—42no—
142Dic11—81no—
143Dic11—82no—
144C22×D4D4411yescharacteristic
145C23×C4C4×D1112yes—
146C2×M16—222no—
147C4×D4—22no—
148C4×D4—22no—
149C2×C4⋊C4—221no—
150C2×C4⋊C4—221no—
151C2×C4⋊C4D4411yescharacteristic
152C2×C22⋊C4—222no—
153C2×C22⋊C4—222no—
154C2×C22⋊C4C22⋊D1112yes—
155C2×C42—221no—
156C2×C42—222no—
157C2×C42C22×D1111yescharacteristic
158C4⋊C8—22no—
159C4⋊C8—222no—
160C4⋊C8—222no—
161#100—442no—
162C22⋊C8—22no—
163C4×C8—22no—
164#95—111no—
165#95—112no—
166#95—111no—
167#95—222no—
168#95—221no—
169C2×C11—21no—
170C2×C11—21no—
171C2×C11—82no—
172C2×C11#182511yescharacteristic
173C2×C11#182711yescharacteristic
174C2×C11#182911yescharacteristic
175C24(C2×D11)⋊C412yes—
176C2×D4—22no—
177C2×D4—22no—
178C2×D4—21no—
179C2×D4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—82no—
183C22×C4—221no—
184C22×C4—222no—
185C22×C4—221no—
186C22×C4(C2×D11)⋊C412yes—
187C22×C4C2×C4×D1111yescharacteristic
188C22×C4C2×D4411yescharacteristic
189C22×C4C2×C22⋊D1111yescharacteristic
190M16—442no—
191M16—442no—
192C2×C8—42no—
193C2×C8—442no—
194C4⋊C4—22no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C22⋊C4—24no—
198C22⋊C4—444no—
199C22⋊C4—882no—
200C42—441no—
201C42—441no—
202C42—882no—
203C42#434112yes—
204C42#434112yes—
205C11#877011yescharacteristic, complemented, Sylow
206C23—22no—
207C23—22no—
208C23—22no—
209C23—42no—
210C23—42no—
211C23C2×(C2×D11)⋊C411yescharacteristic
212D4—42no—
213D4—42no—
214C2×C4—22no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4—222no—
221C2×C4—441no—
222C2×C4—441no—
223C2×C4—442no—
224C2×C4—442no—
225C2×C4—441no—
226C2×C4—441no—
227C2×C4—442no—
228C2×C4—441no—
229C2×C4#6693011yescharacteristic
230C2×C4#6693011yescharacteristic
231C2×C4#6693912yes—
232C2×C4#6695712yes—
233C2×C4#6696111yescharacteristic
234C2×C4#6696211yescharacteristic
235C2×C4#6698812yes—
236C8—82no—
237C8—882no—
238C22—21no—
239C22—21no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—82no—
244C22—82no—
245C22#1062255611yescharacteristic
246C22#1062272611yescharacteristic
247C22#1062274611yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—442no—
253C4—881no—
254C4—882no—
255C4#1062233612yes—
256C4#1062235012yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1306871211yescharacteristic
261C2#1306871711yescharacteristic
262C2#1306872511yescharacteristic
subgroupG/H
centerC22#10622556
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1460C2
socleC22×C11#381
prime radicalC22×D4×C11D4
cosocleC2×C42×C11C23
hypercenter#1460D11
hypocenterC11#8770
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
3. #13066518C2semidirect
4. #13066475C2semidirect
205. C11#8770semidirect

Maximal subgroups

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

subgroupindex
#130715892
#130686082
#130665182
#130664752
C11×#14602
#877011