Finite Group Databasebeta

← #14643005

Subgroups — #14643005

Order 2816.

410 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 87 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#13075648C211yesmaximal, characteristic
2#13070159C211yesmaximal, characteristic
3#13070094C212yesmaximal
4#13066438C212yesmaximal
5C11×#1272C211yesmaximal, characteristic
6C2×#66997—21no—
7C11×#391C2211yescharacteristic
8C2×#66899—21no—
9C2×#66881—22no—
10#10622596—21no—
11C2×#66872—21no—
12#10622548C2211yescharacteristic
13#10622541C2212yes—
14#10622269—22no—
15#10622266—22no—
16C11×#336C2212yes—
17#10622189—22no—
18#10622162C2211yescharacteristic
19C22×Q8×C11D411yescharacteristic
20C22×Dic22—21no—
21C22×C8×C11—22no—
22C2×C11×C4⋊C4D411yescharacteristic
23C2×C42×C11C2311yescharacteristic
24#66997—42no—
25#66997—42no—
26C2×C4⋊Dic11—21no—
27C2×C4⋊Dic11—22no—
28C2×C4⋊Dic11—21no—
29C2×C4⋊Dic11D412yes—
30C2×C4⋊Dic11D412yes—
31C2×Dic11⋊C4—22no—
32C2×Dic11⋊C4—22no—
33C2×C4×Dic11—21no—
34C22×C11⋊C8—21no—
35C11×#95—22no—
36#66899—42no—
37C11⋊#95—21no—
38C11⋊#95—22no—
39C11⋊#95—22no—
40#66881—44no—
41#66872—42no—
42#7817—111nomaximal, Sylow
43C2×Q8×C11—21no—
44C2×Q8×C11—41no—
45C2×Q8×C11—41no—
46C2×Q8×C11SD1612yes—
47C22×C4×C11—21no—
48C22×C4×C11—21no—
49C22×C4×C11C2×D411yescharacteristic
50C22×C4×C11C2×D412yes—
51C22×Dic11—22no—
52C22×Dic11—22no—
53C22×Dic11—41no—
54C2×Dic22—42no—
55C2×Dic22—81no—
56C2×Dic22—81no—
57C2×C8×C11—24no—
58C2×C8×C11—42no—
59C2×C8×C11—42no—
60C11×C4⋊C4—41no—
61C42×C11—41no—
62C4⋊Dic11—22no—
63C4⋊Dic11—42no—
64C4⋊Dic11—41no—
65C4⋊Dic11—41no—
66C4⋊Dic11—42no—
67C4⋊Dic11—42no—
68C4⋊Dic11—81no—
69C4⋊Dic11SD1614yes—
70Dic11⋊C4—44no—
71Dic11⋊C4—42no—
72Dic11⋊C4—42no—
73C4×Dic11—42no—
74C2×C11⋊C8—22no—
75C2×C11⋊C8—41no—
76C2×C11⋊C8—41no—
77#2734—111no—
78#2096—111no—
79#2084—112no—
80#1272D1111yescharacteristic
81#1271—112no—
82C23×C11#12011yescharacteristic
83Q8×C11—42no—
84Q8×C11—81no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—22no—
90C2×C4×C11—41no—
91C2×C4×C11—41no—
92C2×C4×C11—41no—
93C2×C4×C11—42no—
94C2×C4×C11C2×SD1611yescharacteristic
95C2×C4×C11C2×SD1612yes—
96C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
97C2×C4×C11#13712yes—
98C2×Dic11—24no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—42no—
103C2×Dic11—42no—
104C2×Dic11—82no—
105C2×Dic11—81no—
106Dic22—84no—
107C8×C11—44no—
108C11⋊C8—42no—
109C2×C4⋊Q8—221no—
110C2×#106—222no—
111C2×#106—221no—
112C2×#103—221no—
113#398—221no—
114#395—222no—
115#391C2×D1111yescharacteristic
116#389—112no—
117#387—222no—
118#384—111no—
119#340—222no—
120#336—111no—
121#336C2×D1112yes—
122C22×C11#44812yes—
123C22×C11#45011yescharacteristic
124C22×C11#45311yescharacteristic
125C22×C11#45612yes—
126C22×C11#45811yescharacteristic
127C4×C11—22no—
128C4×C11—22no—
129C4×C11—21no—
130C4×C11—21no—
131C4×C11—42no—
132C4×C11—81no—
133Dic11—44no—
134Dic11—82no—
135Dic11—161no—
136C22×Q8—221no—
137C22×Q8D4411yescharacteristic
138C22×C8—22no—
139C22×C8—221no—
140C4⋊Q8—442no—
141C4⋊Q8—442no—
142C2×C4⋊C4—112no—
143C2×C4⋊C4—112no—
144C2×C4⋊C4—222no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4—222no—
148C2×C4⋊C4—221no—
149C2×C4⋊C4D4411yescharacteristic
150C2×C42—221no—
151C2×C42C22×D1111yescharacteristic
152#106—442no—
153#106—444no—
154#103—442no—
155#95—22no—
156#95—221no—
157#95—222no—
158#95—222no—
159C2×C11#161112yes—
160C2×C11#161311yescharacteristic
161C2×C11#162311yescharacteristic
162C2×C11#165112yes—
163C2×C11#166011yescharacteristic
164C2×Q8—21no—
165C2×Q8—41no—
166C2×Q8—41no—
167C2×Q8—442no—
168C2×Q8—881no—
169C2×Q8—881no—
170C2×Q8#431412yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—222no—
174C22×C4—222no—
175C22×C4—441no—
176C22×C4C2×D4411yescharacteristic
177C22×C4D4×D1112yes—
178C2×C8—24no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—222no—
182C2×C8—441no—
183C2×C8—441no—
184C4⋊C4—41no—
185C4⋊C4—114no—
186C4⋊C4—222no—
187C4⋊C4—442no—
188C4⋊C4—444no—
189C4⋊C4—441no—
190C4⋊C4—441no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4—881no—
196C42—41no—
197C42—442no—
198C11#781711yescharacteristic, complemented, Sylow
199C23#6693511yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—884no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—224no—
213C2×C4—442no—
214C2×C4—442no—
215C2×C4—442no—
216C2×C4—442no—
217C2×C4—442no—
218C2×C4—881no—
219C2×C4—882no—
220C2×C4C2×#431411yescharacteristic
221C2×C4#6696111yescharacteristic
222C2×C4SD16×D1112yes—
223C2×C4#6697112yes—
224C8—44no—
225C8—442no—
226C22#1062234411yescharacteristic
227C22#1062235511yescharacteristic
228C22#1062236011yescharacteristic
229C22#1062241912yes—
230C22#1062243912yes—
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—42no—
236C4—81no—
237C4—444no—
238C4—882no—
239C4—1761no—
240C2#1306762512yes—
241C2#1306763811yescharacteristic
242C2#1306769511yescharacteristic
243C2#1306788212yes—
244C2#1306792811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11#120
hypercenter#1272D11
hypocenterC11#7817
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
198. C11#7817semidirect

Maximal subgroups

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

subgroupindex
#130756482
#130701592
#130700942
#130664382
C11×#12722
#781711