Finite Group Databasebeta

← #14643003

Subgroups — #14643003

Order 2816.

410 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 95 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#13070159C211yesmaximal, characteristic
2#13070092C212yesmaximal
3#13066442C211yesmaximal, characteristic
4#13066439C212yesmaximal
5C11×#2734C211yesmaximal, characteristic
6C2×C11×C4⋊Q8—21no—
7C11×#398—21no—
8C11×#395—22no—
9C11×#391C2211yescharacteristic
10C11×#389C2212yes—
11C11×#387—22no—
12C2×#66899—21no—
13C2×#66872—22no—
14C2×#66872—21no—
15#10622548C2211yescharacteristic
16#10622167—22no—
17#10622162C2212yes—
18#10622162C2211yescharacteristic
19C22×Q8×C11—21no—
20C22×Q8×C11D411yescharacteristic
21C11×C4⋊Q8—42no—
22C11×C4⋊Q8—42no—
23C2×C11×C4⋊C4—22no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4D412yes—
27C2×C11×C4⋊C4D411yescharacteristic
28C2×C11×C4⋊C4D412yes—
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11—22no—
33C22×C11⋊C8—21no—
34C22×C11⋊C8—22no—
35C11×#95—21no—
36C11×#95—22no—
37C11×#95—22no—
38C11×#95—22no—
39#66899—42no—
40#66872—42no—
41#66872—44no—
42#7817—111nomaximal, Sylow
43C2×Q8×C11—21no—
44C2×Q8×C11—42no—
45C2×Q8×C11—41no—
46C2×Q8×C11—41no—
47C2×Q8×C11—81no—
48C2×Q8×C11—81no—
49C2×Q8×C11SD1612yes—
50C22×C4×C11—22no—
51C22×C4×C11—21no—
52C22×C4×C11—21no—
53C22×C4×C11—22no—
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11C2×D412yes—
56C22×Dic11—41no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—44no—
59C11×C4⋊C4—41no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—42no—
63C11×C4⋊C4—81no—
64C11×C4⋊C4SD1614yes—
65C42×C11—41no—
66C42×C11—42no—
67C4⋊Dic11—41no—
68C4⋊Dic11—41no—
69C4⋊Dic11—42no—
70C4⋊Dic11—42no—
71C2×C11⋊C8—22no—
72C2×C11⋊C8—24no—
73C2×C11⋊C8—42no—
74C2×C11⋊C8—41no—
75C2×C11⋊C8—42no—
76C2×C11⋊C8—41no—
77#2734D1111yescharacteristic
78#2096—111no—
79#2084—112no—
80#1272—111no—
81#1271—112no—
82C23×C11#12011yescharacteristic
83Q8×C11—42no—
84Q8×C11—81no—
85Q8×C11—84no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—24no—
91C2×C4×C11—22no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—41no—
98C2×C4×C11—42no—
99C2×C4×C11—42no—
100C2×C4×C11—42no—
101C2×C4×C11C2×SD1611yescharacteristic
102C2×C4×C11C2×SD1612yes—
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×C4×C11#13712yes—
105C2×Dic11—82no—
106C2×Dic11—81no—
107C11⋊C8—44no—
108C11⋊C8—42no—
109C2×C4⋊Q8—21no—
110C2×#106—222no—
111C2×#106—221no—
112C2×#103—221no—
113#398—21no—
114#395—22no—
115#391C2×D1111yescharacteristic
116#389C2×D1112yes—
117#387—22no—
118#384—111no—
119#340—222no—
120#336—112no—
121#336—111no—
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—44no—
133C4×C11—82no—
134C4×C11—81no—
135Dic11—161no—
136C22×Q8—21no—
137C22×Q8C22⋊D1111yescharacteristic
138C22×C8—222no—
139C22×C8—221no—
140C4⋊Q8—42no—
141C4⋊Q8—42no—
142C2×C4⋊C4—22no—
143C2×C4⋊C4—22no—
144C2×C4⋊C4—21no—
145C2×C4⋊C4—222no—
146C2×C4⋊C4—221no—
147C2×C4⋊C4C22⋊D1112yes—
148C2×C4⋊C4C22⋊D1112yes—
149C2×C4⋊C4C22⋊D1111yescharacteristic
150C2×C42—21no—
151C2×C42C22×D1111yescharacteristic
152#106—442no—
153#106—444no—
154#103—442no—
155#95—21no—
156#95—22no—
157#95—22no—
158#95—22no—
159C2×C11#161112yes—
160C2×C11#161311yescharacteristic
161C2×C11#162311yescharacteristic
162C2×C11#165112yes—
163C2×C11#166011yescharacteristic
164C2×Q8—21no—
165C2×Q8—42no—
166C2×Q8—41no—
167C2×Q8—41no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8#432412yes—
171C22×C4—22no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—441no—
176C22×C4C2×C22⋊D1111yescharacteristic
177C22×C4C2×C22⋊D1112yes—
178C2×C8—222no—
179C2×C8—224no—
180C2×C8—442no—
181C2×C8—441no—
182C2×C8—441no—
183C2×C8—442no—
184C4⋊C4—22no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—44no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—81no—
191C4⋊C4—441no—
192C4⋊C4—441no—
193C4⋊C4—442no—
194C4⋊C4—442no—
195C4⋊C4#432514yes—
196C42—41no—
197C42—42no—
198C11#781711yescharacteristic, complemented, Sylow
199C23#6700611yescharacteristic
200Q8—42no—
201Q8—81no—
202Q8—84no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—24no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—882no—
219C2×C4—881no—
220C2×C4#6698511yescharacteristic
221C2×C4C2×#432411yescharacteristic
222C2×C4C2×#432512yes—
223C2×C4#6699512yes—
224C8—444no—
225C8—442no—
226C22#1062283111yescharacteristic
227C22#1062284012yes—
228C22#1062285411yescharacteristic
229C22#1062285611yescharacteristic
230C22#1062285912yes—
231C4—22no—
232C4—22no—
233C4—21no—
234C4—21no—
235C4—44no—
236C4—42no—
237C4—82no—
238C4—81no—
239C4—1761no—
240C2#1306762412yes—
241C2#1306763611yescharacteristic
242C2#1306769411yescharacteristic
243C2#1306787912yes—
244C2#1306792711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2734C2
socle, prime radicalC23×C11#120
hypercenter#2734D11
hypocenterC11#7817
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2734

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
#130701592
#130700922
#130664422
#130664392
C11×#27342
#781711