Finite Group Databasebeta

← #13078868

Subgroups — #13078868

Order 1408.

394 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#518C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic, complemented
3#10622831C212yesmaximal
4#10622632C212yesmaximal, complemented
5#10622631C212yesmaximal, complemented
6C4×#4324C212yesmaximal, complemented
7#10622622C212yesmaximal, complemented
8#10622613C211yesmaximal, characteristic, complemented
9#10622609C212yesmaximal, complemented
10C22×D4×C11C2211yescharacteristic
11C4×D4×C11—22no—
12C4×D4×C11C2212yes—
13C4×D4×C11C2212yes—
14C11×#117C2211yescharacteristic
15C11×#117C2211yescharacteristic
16C2×C11×C22⋊C4—22no—
17C2×#4324C2212yes—
18C2×#4324C2212yes—
19#66977C2212yes—
20#66942—22no—
21#66932—22no—
22#66923C2211yescharacteristic, complemented
23#66922C2211yescharacteristic, complemented
24C4×Dic22C2212yescomplemented
25#66896C2212yes—
26#66896C2212yes—
27C22⋊(C11⋊C8)C2212yes—
28#66874C2212yescomplemented
29#66874C2212yescomplemented
30#66872C2212yescomplemented
31#66871C2212yescomplemented
32C4⋊(C11⋊C8)C2212yescomplemented
33#66867C2211yescharacteristic, complemented
34C4×C11⋊C8C2211yescharacteristic, complemented
35C24×C11—21no—
36C2×D4×C11—24no—
37C2×D4×C11—21no—
38C2×D4×C11C2312yes—
39C22×C4×C11—22no—
40C22×C4×C11—22no—
41C22×C4×C11C2311yescharacteristic
42C2×Dic22C2312yes—
43C11×C4⋊C4D412yes—
44C11×C4⋊C4C2312yes—
45C11×C22⋊C4—21no—
46C11×C22⋊C4—22no—
47C11×C22⋊C4—22no—
48C11×C22⋊C4D412yes—
49C42×C11—21no—
50C42×C11C2311yescharacteristic
51C42×C11C2311yescharacteristic
52C22⋊Dic11—22no—
53#4324—24no—
54#4324—24no—
55C4⋊Dic11—22no—
56C4⋊Dic11C2312yes—
57Dic11⋊C4—22no—
58Dic11⋊C4—22no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61C2×C11⋊C8C2312yes—
62C2×C11⋊C8C2312yes—
63#3123—111nomaximal, Sylow
64C23×C11—24no—
65C23×C11—22no—
66C23×C11—82no—
67C23×C11C2×D411yescharacteristic
68D4×C11—24no—
69D4×C11—22no—
70D4×C11#4114yes—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—82no—
74C2×C4×C11—82no—
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2411yescharacteristic
79C2×Dic11—22no—
80C2×Dic11—22no—
81Dic22—22no—
82Dic22—22no—
83C11⋊C8—22no—
84C11⋊C8—22no—
85#541—111no—
86#518D1111yescharacteristic
87#485—112no—
88#478—112no—
89#461—112no—
90#450—112no—
91#440—112no—
92C4×SD16—112no—
93#433—111no—
94C22×C11—21no—
95C22×C11—24no—
96C22×C11—22no—
97C22×C11—42no—
98C22×C11—42no—
99C22×C11—84no—
100C22×C11C22×D411yescharacteristic
101C4×C11—21no—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—42no—
105C4×C11C2×#4112yes—
106Dic11—42no—
107Dic11—42no—
108C22×D4C2×D1111yescharacteristic
109C2×SD16—112no—
110C2×SD16—112no—
111C4⋊Q8—111no—
112#126—222no—
113#125—111no—
114#125—222no—
115C22⋊Q8—112no—
116C4×Q8—112no—
117C4×D4—22no—
118C4×D4C2×D1112yes—
119C4×D4C2×D1112yes—
120#117C2×D1111yescharacteristic
121#117C2×D1111yescharacteristic
122C2×C22⋊C4—22no—
123#107—112no—
124#106—112no—
125C4⋊C8—112no—
126#103—112no—
127#103—112no—
128#102—112no—
129#102—112no—
130C22⋊C8—112no—
131#97—111no—
132C4×C8—111no—
133C2×C11—41no—
134C2×C11—44no—
135C2×C11#52511yescharacteristic
136C2×C11#57712yes—
137C24—21no—
138C2×Q8—112no—
139C2×D4—24no—
140C2×D4—21no—
141C2×D4C22×D1112yes—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4C22×D1111yescharacteristic
145SD16—224no—
146SD16—224no—
147C2×C8—112no—
148C2×C8—112no—
149C4⋊C4—112no—
150C4⋊C4—222no—
151C4⋊C4—222no—
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4C22⋊D1112yes—
155C4⋊C4C22×D1112yes—
156C22⋊C4—21no—
157C22⋊C4—22no—
158C22⋊C4—22no—
159C22⋊C4—222no—
160C22⋊C4C22⋊D1112yes—
161C42—21no—
162C42—222no—
163C42C22×D1111yescharacteristic
164C42C22×D1111yescharacteristic
165C11#312311yescharacteristic, complemented, Sylow
166C23—24no—
167C23—22no—
168C23—82no—
169C23C2×C22⋊D1111yescharacteristic
170Q8—222no—
171Q8—222no—
172D4—24no—
173D4—22no—
174D4#433914yes—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—82no—
178C2×C4—82no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4C2×C22⋊D1111yescharacteristic
182C2×C4C2×C22⋊D1112yes—
183C2×C4C2×C22⋊D1112yes—
184C2×C4C23×D1111yescharacteristic
185C8—222no—
186C8—222no—
187C22—21no—
188C22—24no—
189C22—22no—
190C22—42no—
191C22—42no—
192C22—84no—
193C22C22×C22⋊D1111yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—442no—
199C4—442no—
200C4C2×#433912yes—
201C2—41no—
202C2—44no—
203C2#1062332211yescharacteristic
204C2#1062336712yes—
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#518C2
socleC22×C11C22×D4
prime radicalC22×D4×C11C22
hypercenter#518D11
hypocenterC11#3123
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #10623049C2semidirect
4. #10622632C2semidirect
5. #10622631C2semidirect
6. C4×#4324C2semidirect
7. #10622622C2semidirect
8. #10622613C2semidirect
9. #10622609C2semidirect
22. #66923C22semidirect
23. #66922C22semidirect
24. C4×Dic22C22semidirect
28. #66874C22semidirect
29. #66874C22semidirect
30. #66872C22semidirect
31. #66871C22semidirect
32. C4⋊(C11⋊C8)C22semidirect
33. #66867C22semidirect
34. C4×C11⋊C8C22semidirect
165. C11#3123semidirect

Maximal subgroups

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

subgroupindex
C11×#5182
#106230492
#106228312
#106226322
#106226312
C4×#43242
#106226222
#106226132
#106226092
#312311