Finite Group Databasebeta

← #14643074

Subgroups — #14643074

Order 2816.

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

normal subgroups only

This group has 394 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#13070180C212yesmaximal
3#13070154C211yesmaximal, characteristic
4#13066438C212yesmaximal
5C11×#1272C211yesmaximal, characteristic
6C2×#66997—21no—
7C11×#391C2211yescharacteristic
8C2×#66899—21no—
9#10622596—21no—
10C2×#66871—21no—
11#10622548C2211yescharacteristic
12#10622541C2212yes—
13#10622269—22no—
14#10622266—22no—
15C11×#336C2212yes—
16#10622189—22no—
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#66871—42no—
41#7829—111nomaximal, Sylow
42C2×Q8×C11—21no—
43C2×Q8×C11—41no—
44C2×Q8×C11—41no—
45C2×Q8×C11SD1612yes—
46C22×C4×C11—21no—
47C22×C4×C11—21no—
48C22×C4×C11C2×D411yescharacteristic
49C22×C4×C11C2×D412yes—
50C22×Dic11—22no—
51C22×Dic11—22no—
52C22×Dic11—41no—
53C2×Dic22—42no—
54C2×Dic22—81no—
55C2×Dic22—81no—
56C2×C8×C11—42no—
57C2×C8×C11—42no—
58C2×C8×C11—42no—
59C11×C4⋊C4—41no—
60C42×C11—41no—
61C4⋊Dic11—22no—
62C4⋊Dic11—42no—
63C4⋊Dic11—41no—
64C4⋊Dic11—41no—
65C4⋊Dic11—44no—
66C4⋊Dic11—81no—
67C4⋊Dic11Q1614yes—
68Dic11⋊C4—44no—
69Dic11⋊C4—42no—
70Dic11⋊C4—42no—
71C4×Dic11—42no—
72C2×C11⋊C8—22no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—41no—
75#2734—111no—
76#2100—112no—
77#2095—111no—
78#1272D1111yescharacteristic
79#1271—112no—
80C23×C11#12011yescharacteristic
81Q8×C11—42no—
82Q8×C11—81no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—41no—
89C2×C4×C11—41no—
90C2×C4×C11—41no—
91C2×C4×C11—42no—
92C2×C4×C11C2×SD1611yescharacteristic
93C2×C4×C11C2×Q1612yes—
94C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C11#13712yes—
96C2×Dic11—24no—
97C2×Dic11—42no—
98C2×Dic11—42no—
99C2×Dic11—42no—
100C2×Dic11—42no—
101C2×Dic11—42no—
102C2×Dic11—81no—
103C2×Dic11—82no—
104Dic22—84no—
105C8×C11—82no—
106C11⋊C8—42no—
107C2×C4⋊Q8—221no—
108C2×#107—221no—
109C2×#103—221no—
110#398—221no—
111#395—222no—
112#391C2×D1111yescharacteristic
113#389—112no—
114#387—222no—
115#384—111no—
116#340—222no—
117#340—222no—
118#336—111no—
119#336C2×D1112yes—
120C22×C11#45011yescharacteristic
121C22×C11#45112yes—
122C22×C11#45311yescharacteristic
123C22×C11#45412yes—
124C22×C11#45811yescharacteristic
125C4×C11—21no—
126C4×C11—21no—
127C4×C11—22no—
128C4×C11—22no—
129C4×C11—42no—
130C4×C11—81no—
131Dic11—44no—
132Dic11—82no—
133Dic11—161no—
134C22×Q8—221no—
135C22×Q8D4411yescharacteristic
136C22×C8—22no—
137C22×C8—221no—
138C4⋊Q8—442no—
139C4⋊Q8—442no—
140C2×C4⋊C4—112no—
141C2×C4⋊C4—112no—
142C2×C4⋊C4—222no—
143C2×C4⋊C4—222no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4D4411yescharacteristic
148C2×C42—221no—
149C2×C42C22×D1111yescharacteristic
150#107—442no—
151#103—442no—
152#95—22no—
153#95—221no—
154#95—222no—
155#95—222no—
156C2×C11#161311yescharacteristic
157C2×C11#161712yes—
158C2×C11#163311yescharacteristic
159C2×C11#163712yes—
160C2×C11#165711yescharacteristic
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—442no—
165C2×Q8—881no—
166C2×Q8—881no—
167C2×Q8#431412yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—222no—
171C22×C4—222no—
172C22×C4—441no—
173C22×C4C2×D4411yescharacteristic
174C22×C4D4×D1112yes—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—222no—
179C2×C8—441no—
180C2×C8—441no—
181C4⋊C4—41no—
182C4⋊C4—114no—
183C4⋊C4—222no—
184C4⋊C4—442no—
185C4⋊C4—444no—
186C4⋊C4—441no—
187C4⋊C4—441no—
188C4⋊C4—444no—
189C4⋊C4—442no—
190C4⋊C4—442no—
191C4⋊C4—881no—
192C42—41no—
193C42—442no—
194C11#782911yescharacteristic, complemented, Sylow
195C23#6693511yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—884no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—224no—
209C2×C4—442no—
210C2×C4—442no—
211C2×C4—442no—
212C2×C4—442no—
213C2×C4—442no—
214C2×C4—881no—
215C2×C4—882no—
216C2×C4C2×#431411yescharacteristic
217C2×C4#6696111yescharacteristic
218C2×C4#6696812yes—
219C2×C4Q16×D1112yes—
220C8—82no—
221C8—442no—
222C22#1062234411yescharacteristic
223C22#1062235511yescharacteristic
224C22#1062236011yescharacteristic
225C22#1062242112yes—
226C22#1062244012yes—
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—81no—
233C4—444no—
234C4—882no—
235C4—1761no—
236C2#1306763811yescharacteristic
237C2#1306765912yes—
238C2#1306775711yescharacteristic
239C2#1306778312yes—
240C2#1306791511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1272C2
socle, prime radicalC23×C11#120
hypercenter#1272D11
hypocenterC11#7829
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
194. C11#7829semidirect

Maximal subgroups

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

subgroupindex
#130756482
#130701802
#130701542
#130664382
C11×#12722
#782911