Finite Group Databasebeta

← #14656434

Subgroups — #14656434

Order 2816.

542 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 111 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#13079741C212yesmaximal
2#13076994C211yesmaximal, characteristic, complemented
3#13067302C212yesmaximal, complemented
4#13066449C211yesmaximal, characteristic, complemented
5C11×#1962C211yesmaximal, characteristic
6C11×#532C2211yescharacteristic
7C2×#66922C2212yes—
8C11×#423C2211yescharacteristic
9C2×C11×#104—22no—
10C43×C11C2211yescharacteristic
11#10622692—22no—
12#10622683—22no—
13#10622647—24no—
14#10622621—24no—
15#10622549—22no—
16#10622542—24no—
17#10622538C2212yes—
18#10622124—24no—
19C2×C11×#41—21no—
20C22×Dic22—22no—
21C2×C11×M16—21no—
22C11×C4⋊Q8D411yescharacteristic
23C11×#127D411yescharacteristic
24C11×#124—21no—
25C11×#121—22no—
26C4×D4×C11—22no—
27C2×C42×C11—22no—
28C2×C42×C11D412yes—
29C2×C42×C11C2311yescharacteristic
30C2×C4⋊Dic11—22no—
31C2×C4⋊Dic11D414yes—
32#66922—22no—
33#66922—22no—
34#66922—22no—
35#66922—22no—
36C11×C4⋊C8—22no—
37C11×#104—44no—
38#66896—28no—
39C11⋊#95—28no—
40C22⋊(C11⋊C8)—22no—
41#66872—28no—
42C4⋊(C11⋊C8)D414yes—
43C4×C11⋊C8—22no—
44#10285—111nomaximal, Sylow
45C11×#41—42no—
46C11×#41—42no—
47C2×Q8×C11—21no—
48C2×D4×C11—22no—
49C2×D4×C11—21no—
50C2×D4×C11—41no—
51C22×C4×C11—22no—
52C22×C4×C11—41no—
53C22×C4×C11C2×D412yes—
54C22×C4×C11C2×D411yescharacteristic
55C22×Dic11—24no—
56C2×Dic22—48no—
57C2×Dic22—42no—
58C2×Dic22—42no—
59C11×M16—42no—
60C2×C8×C11—41no—
61C11×C4⋊C4—22no—
62C11×C22⋊C4—42no—
63C42×C11—22no—
64C42×C11—44no—
65C42×C11SD1614yes—
66C42×C11C2×D411yescharacteristic
67C42×C11C2×D412yes—
68C42×C11#4111yescharacteristic
69C4⋊Dic11—24no—
70C4⋊Dic11—24no—
71C4⋊Dic11—42no—
72C4⋊Dic11—42no—
73C2×C11⋊C8—24no—
74#3227—112no—
75#2862—111no—
76#1962D1111yescharacteristic
77#1549—112no—
78#1276—111no—
79C23×C11—41no—
80C23×C11#12011yescharacteristic
81Q8×C11—42no—
82D4×C11—44no—
83D4×C11—42no—
84D4×C11—82no—
85C2×C4×C11—24no—
86C2×C4×C11—24no—
87C2×C4×C11—44no—
88C2×C4×C11—41no—
89C2×C4×C11—81no—
90C2×C4×C11—81no—
91C2×C4×C11#12012yes—
92C2×C4×C11#12112yes—
93C2×C4×C11#12111yescharacteristic
94C2×C4×C11#12711yescharacteristic
95C2×C4×C11C2×SD1612yes—
96C2×C4×C11#13712yes—
97C2×Dic11—48no—
98C2×Dic11—44no—
99Dic22—84no—
100Dic22—84no—
101C8×C11—81no—
102C11⋊C8—44no—
103#532C2×D1111yescharacteristic
104C2×C4⋊Q8—112no—
105#498—222no—
106#486—222no—
107#481—224no—
108#476—224no—
109#431—112no—
110#423C2×D1111yescharacteristic
111C2×#104—22no—
112#391—224no—
113#382—222no—
114C43C2×D1111yescharacteristic
115#332—224no—
116C22×C11—22no—
117C22×C11—82no—
118C22×C11—81no—
119C22×C11#39211yescharacteristic
120C22×C11#44812yes—
121C4×C11—22no—
122C4×C11—44no—
123C4×C11—81no—
124C4×C11#45414yes—
125C4×C11#46112yes—
126C4×C11#49211yescharacteristic
127C4×C11#49711yescharacteristic
128Dic11—84no—
129C2×#41—21no—
130C22×Q8—222no—
131C2×M16—21no—
132C4⋊Q8—222no—
133C4⋊Q8—222no—
134C4⋊Q8—222no—
135C4⋊Q8—222no—
136C4⋊Q8D4411yescharacteristic
137#127D4411yescharacteristic
138#124—21no—
139#121—22no—
140C4×D4—22no—
141C2×C4⋊C4—114no—
142C2×C4⋊C4—222no—
143C2×C42—22no—
144C2×C42C22⋊D1112yes—
145C2×C42C22×D1111yescharacteristic
146#106—228no—
147C4⋊C8—22no—
148C4⋊C8—114no—
149#104—44no—
150#102—228no—
151C22⋊C8—222no—
152C4×C8—222no—
153#95—228no—
154C2×C11—22no—
155C2×C11—161no—
156C2×C11#200312yes—
157C2×C11#201311yescharacteristic
158#41—42no—
159#41—42no—
160C2×Q8—21no—
161C2×Q8—448no—
162C2×Q8—442no—
163C2×Q8—442no—
164C2×D4—22no—
165C2×D4—21no—
166C2×D4—41no—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—224no—
170C22×C4D4×D1112yes—
171C22×C4C2×C22⋊D1111yescharacteristic
172M16—42no—
173C2×C8—41no—
174C2×C8—224no—
175C4⋊C4—22no—
176C4⋊C4—224no—
177C4⋊C4—224no—
178C4⋊C4—442no—
179C4⋊C4—442no—
180C22⋊C4—42no—
181C42—22no—
182C42—44no—
183C42#432414yes—
184C42C2×D4411yescharacteristic
185C42#433911yescharacteristic
186C42D4×D1112yes—
187C11#1028511yescharacteristic, complemented, Sylow
188C23—41no—
189C23#6699011yescharacteristic
190Q8—42no—
191Q8—884no—
192Q8—884no—
193D4—42no—
194D4—44no—
195D4—82no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—41no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—448no—
203C2×C4—444no—
204C2×C4#6693512yes—
205C2×C4#6693712yes—
206C2×C4#6698311yescharacteristic
207C2×C4C2×#432412yes—
208C2×C4#6699311yescharacteristic
209C2×C4#6700412yes—
210C8—81no—
211C8—444no—
212C22—22no—
213C22—82no—
214C22—81no—
215C22#1062257311yescharacteristic
216C22#1062265312yes—
217C4—22no—
218C4—44no—
219C4—81no—
220C4—884no—
221C4#1062244014yes—
222C4#1062263212yes—
223C4#1062267311yescharacteristic
224C4#1062268911yescharacteristic
225C2—22no—
226C2—161no—
227C2#1306963712yes—
228C2#1306969811yescharacteristic
subgroupG/H
centerC22#10622573
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1962C2
socleC22×C11#392
prime radicalC11×#532C22
hypercenter#1962D11
hypocenterC11#10285
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #13076994C2semidirect
3. #13067302C2semidirect
4. #13066449C2semidirect
187. C11#10285semidirect

Maximal subgroups

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

subgroupindex
#130797412
#130769942
#130673022
#130664492
C11×#19622
#1028511