Finite Group Databasebeta

← #14643014

Subgroups — #14643014

Order 2816.

434 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 83 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#13075546C211yesmaximal, characteristic
2#13070093C212yesmaximal, complemented
3#13066440C212yesmaximal, complemented
4#13066437C211yesmaximal, characteristic
5C11×#2093C211yesmaximal, characteristic
6C2×#66988—21no—
7C2×C11×#107—21no—
8C2×C11×#102—21no—
9C11×#390C2211yescharacteristic
10C11×#384C2211yescharacteristic
11#10622596—21no—
12C2×#66872—22no—
13#10622566—22no—
14#10622563—22no—
15#10622541C2212yes—
16C11×#336C2211yescharacteristic
17#10622167—22no—
18#10622162C2212yes—
19C22×D4×C11D411yescharacteristic
20C23×Dic11—21no—
21C22×C8×C11—21no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4D411yescharacteristic
25C2×C11×C22⋊C4—22no—
26C2×C42×C11C2311yescharacteristic
27C2×C22⋊Dic11—22no—
28C2×C22⋊Dic11—21no—
29#66988—42no—
30#66988—42no—
31C2×C4⋊Dic11—21no—
32C2×C4⋊Dic11D412yes—
33C2×C4⋊Dic11D412yes—
34C2×Dic11⋊C4—22no—
35C22×C11⋊C8—22no—
36C11×#107—42no—
37C11×#102—42no—
38C11⋊#95—22no—
39C11⋊#95—21no—
40C11⋊#95—22no—
41#66872—44no—
42#7819—111nomaximal, Sylow
43C24×C11—21no—
44C2×D4×C11—21no—
45C2×D4×C11—41no—
46C2×D4×C11—41no—
47C2×D4×C11SD1612yes—
48C22×C4×C11—21no—
49C22×C4×C11—41no—
50C22×C4×C11C2×D411yescharacteristic
51C22×C4×C11C2×D412yes—
52C22×Dic11—22no—
53C22×Dic11—22no—
54C22×Dic11—42no—
55C22×Dic11—81no—
56C22×Dic11—81no—
57C2×C8×C11—22no—
58C2×C8×C11—41no—
59C2×C8×C11—41no—
60C11×C4⋊C4—41no—
61C11×C4⋊C4—41no—
62C11×C4⋊C4—41no—
63C11×C4⋊C4—42no—
64C11×C4⋊C4—42no—
65C11×C22⋊C4—42no—
66C11×C22⋊C4—42no—
67C42×C11—41no—
68C22⋊Dic11—42no—
69C22⋊Dic11—44no—
70C4⋊Dic11—22no—
71C4⋊Dic11—22no—
72C4⋊Dic11—42no—
73C4⋊Dic11—81no—
74Dic11⋊C4—42no—
75Dic11⋊C4—42no—
76C2×C11⋊C8—24no—
77C2×C11⋊C8—42no—
78C2×C11⋊C8—42no—
79#2724—111no—
80#2093D1111yescharacteristic
81#2084—112no—
82#1271—112no—
83#1270—111no—
84C23×C11—22no—
85C23×C11—42no—
86C23×C11—41no—
87C23×C11—42no—
88C23×C11—41no—
89C23×C11#12011yescharacteristic
90D4×C11—42no—
91D4×C11—81no—
92C2×C4×C11—21no—
93C2×C4×C11—22no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—42no—
97C2×C4×C11—41no—
98C2×C4×C11—82no—
99C2×C4×C11—81no—
100C2×C4×C11C2×SD1611yescharacteristic
101C2×C4×C11#13512yes—
102C2×C4×C11AGL(1,ℤ/8)12yes—
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—42no—
105C2×Dic11—42no—
106C2×Dic11—42no—
107C2×Dic11—42no—
108C2×Dic11—42no—
109C2×Dic11—42no—
110C2×Dic11—84no—
111C8×C11—42no—
112C11⋊C8—44no—
113C2×#123—221no—
114C2×#107—21no—
115C2×#106—222no—
116C2×#102—21no—
117#398—221no—
118#397—222no—
119#390C2×D1111yescharacteristic
120#389—112no—
121#385—222no—
122#384C2×D1111yescharacteristic
123#340—222no—
124#336—112no—
125#336C2×D1111yescharacteristic
126C22×C11—42no—
127C22×C11—44no—
128C22×C11—82no—
129C22×C11—81no—
130C22×C11—81no—
131C22×C11#44912yes—
132C22×C11#45011yescharacteristic
133C22×C11#45311yescharacteristic
134C22×C11#45612yes—
135C22×C11#45811yescharacteristic
136C4×C11—22no—
137C4×C11—22no—
138C4×C11—21no—
139C4×C11—21no—
140C4×C11—81no—
141C4×C11—161no—
142Dic11—82no—
143Dic11—82no—
144C22×D4C22⋊D1111yescharacteristic
145C23×C4—221no—
146C22×C8—21no—
147C22×C8—222no—
148#123—442no—
149#123—442no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—112no—
153C2×C4⋊C4—112no—
154C2×C4⋊C4—222no—
155C2×C4⋊C4—221no—
156C2×C4⋊C4C22⋊D1111yescharacteristic
157C2×C22⋊C4—22no—
158C2×C22⋊C4—222no—
159C2×C22⋊C4—221no—
160C2×C42C22×D1111yescharacteristic
161#107—42no—
162#106—444no—
163#102—42no—
164#95—222no—
165#95—221no—
166#95—222no—
167C2×C11—82no—
168C2×C11#160912yes—
169C2×C11#161311yescharacteristic
170C2×C11#162011yescharacteristic
171C2×C11#165412yes—
172C2×C11#166011yescharacteristic
173C24—21no—
174C2×D4—21no—
175C2×D4—41no—
176C2×D4—41no—
177C2×D4#432512yes—
178C22×C4—21no—
179C22×C4—41no—
180C22×C4—222no—
181C22×C4—222no—
182C22×C4—442no—
183C22×C4—881no—
184C22×C4—881no—
185C22×C4D4×D1112yes—
186C22×C4C2×C22⋊D1111yescharacteristic
187C2×C8—22no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—224no—
191C2×C8—442no—
192C2×C8—442no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—42no—
198C4⋊C4—222no—
199C4⋊C4—222no—
200C4⋊C4—442no—
201C4⋊C4—442no—
202C4⋊C4—442no—
203C4⋊C4—881no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—442no—
207C22⋊C4—444no—
208C42—41no—
209C11#781911yescharacteristic, complemented, Sylow
210C23—22no—
211C23—42no—
212C23—42no—
213C23—41no—
214C23—41no—
215C23#6699011yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—82no—
225C2×C4—81no—
226C2×C4—442no—
227C2×C4—442no—
228C2×C4—442no—
229C2×C4—442no—
230C2×C4—442no—
231C2×C4—442no—
232C2×C4—884no—
233C2×C4#6696412yes—
234C2×C4#6696512yes—
235C2×C4C2×#432511yescharacteristic
236C2×C4#6700211yescharacteristic
237C8—42no—
238C8—444no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#1062265911yescharacteristic
245C22#1062266611yescharacteristic
246C22#1062269011yescharacteristic
247C22#1062277112yes—
248C22#1062281812yes—
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—81no—
254C4—161no—
255C4—882no—
256C4—882no—
257C2—82no—
258C2#1306761012yes—
259C2#1306763511yescharacteristic
260C2#1306767311yescharacteristic
261C2#1306789912yes—
262C2#1306792511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2093C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenter#2093D11
hypocenterC11#7819
LCSG ▷ C2×C42×C11 ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #13070093C2semidirect
3. #13066440C2semidirect
209. C11#7819semidirect

Maximal subgroups

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

subgroupindex
#130755462
#130700932
#130664402
#130664372
C11×#20932
#781911