Finite Group Databasebeta

← #14643073

Subgroups — #14643073

Order 2816.

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

normal subgroups only

This group has 394 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#13070179C212yesmaximal
2#13070154C211yesmaximal, characteristic
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×#66871—21no—
14#10622548C2211yescharacteristic
15#10622167—22no—
16#10622167—22no—
17#10622162C2211yescharacteristic
18#10622162C2212yes—
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#66871—42no—
41#7829—111nomaximal, Sylow
42C2×Q8×C11—21no—
43C2×Q8×C11—42no—
44C2×Q8×C11—41no—
45C2×Q8×C11—41no—
46C2×Q8×C11—81no—
47C2×Q8×C11—81no—
48C2×Q8×C11SD1612yes—
49C22×C4×C11—22no—
50C22×C4×C11—21no—
51C22×C4×C11—21no—
52C22×C4×C11—22no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D412yes—
55C22×Dic11—41no—
56C11×C4⋊C4—22no—
57C11×C4⋊C4—44no—
58C11×C4⋊C4—41no—
59C11×C4⋊C4—42no—
60C11×C4⋊C4—42no—
61C11×C4⋊C4—42no—
62C11×C4⋊C4—81no—
63C11×C4⋊C4Q1614yes—
64C42×C11—41no—
65C42×C11—42no—
66C4⋊Dic11—41no—
67C4⋊Dic11—41no—
68C4⋊Dic11—44no—
69C2×C11⋊C8—22no—
70C2×C11⋊C8—41no—
71C2×C11⋊C8—42no—
72C2×C11⋊C8—42no—
73C2×C11⋊C8—41no—
74C2×C11⋊C8—42no—
75#2734D1111yescharacteristic
76#2100—112no—
77#2095—111no—
78#1272—111no—
79#1271—112no—
80C23×C11#12011yescharacteristic
81Q8×C11—42no—
82Q8×C11—81no—
83Q8×C11—84no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—21no—
88C2×C4×C11—22no—
89C2×C4×C11—24no—
90C2×C4×C11—42no—
91C2×C4×C11—41no—
92C2×C4×C11—42no—
93C2×C4×C11—41no—
94C2×C4×C11—42no—
95C2×C4×C11—41no—
96C2×C4×C11—42no—
97C2×C4×C11—42no—
98C2×C4×C11—42no—
99C2×C4×C11C2×SD1611yescharacteristic
100C2×C4×C11C2×Q1612yes—
101C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C11#13712yes—
103C2×Dic11—81no—
104C2×Dic11—82no—
105C11⋊C8—42no—
106C11⋊C8—82no—
107C2×C4⋊Q8—21no—
108C2×#107—221no—
109C2×#103—221no—
110#398—21no—
111#395—22no—
112#391C2×D1111yescharacteristic
113#389C2×D1112yes—
114#387—22no—
115#384—111no—
116#340—222no—
117#340—222no—
118#336—111no—
119#336—112no—
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—44no—
131C4×C11—82no—
132C4×C11—81no—
133Dic11—161no—
134C22×Q8—21no—
135C22×Q8C22⋊D1111yescharacteristic
136C22×C8—221no—
137C22×C8—222no—
138C4⋊Q8—42no—
139C4⋊Q8—42no—
140C2×C4⋊C4—22no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C4⋊C4—222no—
144C2×C4⋊C4—221no—
145C2×C4⋊C4C22⋊D1112yes—
146C2×C4⋊C4C22⋊D1112yes—
147C2×C4⋊C4C22⋊D1111yescharacteristic
148C2×C42—21no—
149C2×C42C22×D1111yescharacteristic
150#107—442no—
151#103—442no—
152#95—21no—
153#95—22no—
154#95—22no—
155#95—22no—
156C2×C11#161311yescharacteristic
157C2×C11#161712yes—
158C2×C11#163311yescharacteristic
159C2×C11#163712yes—
160C2×C11#165711yescharacteristic
161C2×Q8—21no—
162C2×Q8—42no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—81no—
166C2×Q8—81no—
167C2×Q8#432412yes—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—22no—
172C22×C4—441no—
173C22×C4C2×C22⋊D1111yescharacteristic
174C22×C4C2×C22⋊D1112yes—
175C2×C8—222no—
176C2×C8—441no—
177C2×C8—441no—
178C2×C8—442no—
179C2×C8—442no—
180C2×C8—442no—
181C4⋊C4—22no—
182C4⋊C4—41no—
183C4⋊C4—42no—
184C4⋊C4—44no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—81no—
188C4⋊C4—441no—
189C4⋊C4—441no—
190C4⋊C4—444no—
191C4⋊C4#432614yes—
192C42—41no—
193C42—42no—
194C11#782911yescharacteristic, complemented, Sylow
195C23#6700611yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—84no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—24no—
205C2×C4—42no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—881no—
215C2×C4—882no—
216C2×C4#6698511yescharacteristic
217C2×C4C2×#432411yescharacteristic
218C2×C4#6699512yes—
219C2×C4C2×#432612yes—
220C8—442no—
221C8—882no—
222C22#1062283111yescharacteristic
223C22#1062284112yes—
224C22#1062285411yescharacteristic
225C22#1062285611yescharacteristic
226C22#1062285812yes—
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—44no—
232C4—42no—
233C4—82no—
234C4—81no—
235C4—1761no—
236C2#1306763611yescharacteristic
237C2#1306765812yes—
238C2#1306775611yescharacteristic
239C2#1306778112yes—
240C2#1306791411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2734C2
socle, prime radicalC23×C11#120
hypercenter#2734D11
hypocenterC11#7829
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
194. C11#7829semidirect

Maximal subgroups

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

subgroupindex
#130701792
#130701542
#130664422
#130664392
C11×#27342
#782911