Finite Group Databasebeta

← #13069153

Subgroups — #13069153

Order 1408.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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×#519C211yesmaximal, characteristic, complemented
2#10623347C211yesmaximal, characteristic
3C2×#66900C211yesmaximal, characteristic, complemented
4#10622618C212yesmaximal
5#10622169C212yesmaximal, complemented
6C22×Q8×C11C2211yescharacteristic
7C2×#4339C2211yescharacteristic
8C4×Q8×C11—24no—
9C11×#117—22no—
10C11×#117C2212yes—
11#67000C412yescomplemented
12#66999—22no—
13#66997C412yescomplemented
14#66982—22no—
15#66979C2211yescharacteristic
16C2×#4318C2212yes—
17#66900—22no—
18#66869—24no—
19C2×Q8×C11—22no—
20C2×Q8×C11—22no—
21C2×Q8×C11C2×C412yes—
22C2×Q8×C11D412yes—
23C22×C4×C11D412yes—
24C22×C4×C11C2311yescharacteristic
25C2×C22⋊D11—21no—
26#4339—22no—
27#4339—22no—
28C2×D44C2×C411yescharacteristic
29C2×C4×D11—21no—
30C2×Dic22C2×C411yescharacteristic
31C11×C4⋊C4—24no—
32C11×C4⋊C4—22no—
33C11×C22⋊C4—22no—
34C42×C11—24no—
35C42×C11D414yes—
36C22⋊Dic11—21no—
37(C2×D11)⋊C4—24no—
38C4⋊Dic11—21no—
39Dic11⋊C4—24no—
40C4×Dic11C2×C412yes—
41#4318—22no—
42#4318—22no—
43C2×C11⋊C8—22no—
44#1912—111nomaximal, Sylow
45C23×C11C2×D411yescharacteristic
46C22×D11—21no—
47Q8×C11—24no—
48Q8×C11—24no—
49C2×C4×C11—22no—
50C2×C4×C11—22no—
51C2×C4×C11—24no—
52C2×C4×C11C22⋊C414yes—
53C2×C4×C11C22×C411yescharacteristic
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D412yes—
56C2×C4×C11#4112yes—
57C22⋊D11—41no—
58C22⋊D11—41no—
59C2×Dic11—22no—
60C2×Dic11—21no—
61D44—22no—
62C4×D11—42no—
63Dic22—22no—
64C11⋊C8—42no—
65#536—111no—
66#519D1111yescharacteristic, complemented
67#421—112no—
68C2×#101—111no—
69H(3,ℤ/4)—112no—
70C22×C11—41no—
71C22×C11C2×C22⋊C411yescharacteristic
72C22×C11#12011yescharacteristic
73C22×C11#12311yescharacteristic
74C2×D11—42no—
75C2×D11—41no—
76C4×C11—24no—
77C4×C11—44no—
78C4×C11C4×D412yes—
79C4×C11#12112yes—
80Dic11—42no—
81Dic11—41no—
82C2×#41—111no—
83C22×Q8C2×D1111yescharacteristic
84C2×M16—112no—
85C4⋊Q8—112no—
86#124—112no—
87#123—222no—
88C22⋊Q8—222no—
89C4×Q8—24no—
90#117—22no—
91#117—111no—
92#117C2×D1112yes—
93#104—224no—
94#101—222no—
95C2×C11—21no—
96C2×C11—21no—
97C2×C11—21no—
98C2×C11#38611yescharacteristic
99D11—81no—
100#41—222no—
101#41—222no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—111no—
105C2×Q8C4×D1112yes—
106C2×Q8D4412yes—
107C2×D4—111no—
108C2×D4—221no—
109C22×C4—221no—
110C22×C4C22⋊D1112yes—
111C22×C4C22×D1111yescharacteristic
112M16—222no—
113M16—222no—
114C2×C8—222no—
115C4⋊C4—24no—
116C4⋊C4—22no—
117C4⋊C4—224no—
118C4⋊C4—221no—
119C22⋊C4—22no—
120C22⋊C4—221no—
121C22⋊C4—224no—
122C42—24no—
123C42—112no—
124C42C22⋊D1114yes—
125C11#191211yescharacteristic, complemented, Sylow
126C23—221no—
127C23C2×C22⋊D1111yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—222no—
131D4—222no—
132D4—441no—
133D4—441no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—222no—
138C2×C4—221no—
139C2×C4—442no—
140C2×C4(C2×D11)⋊C414yes—
141C2×C4C2×C4×D1111yescharacteristic
142C2×C4C2×D4411yescharacteristic
143C2×C4#433912yes—
144C2×C4C2×C22⋊D1112yes—
145C8—442no—
146C22—41no—
147C22—442no—
148C22—441no—
149C22C2×(C2×D11)⋊C411yescharacteristic
150C22#6698211yescharacteristic
151C22#6700611yescharacteristic
152C4—24no—
153C4—44no—
154C4—442no—
155C4—441no—
156C4C4×C22⋊D1112yes—
157C4#6698312yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—881no—
162C2#1062282611yescharacteristic
subgroupG/H
centerC2#10622826
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC11×#519C2
socleC2×C11#386
prime radicalC2×#4339C22
cosocleC22×C4×C11C23
hypercenter#519D11
hypocenterC11#1912
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
1. C11×#519C2semidirect
3. C2×#66900C2semidirect
5. #10622169C2semidirect
11. #67000C4semidirect
13. #66997C4semidirect
66. #519D11semidirect
125. C11#1912semidirect

Maximal subgroups

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

subgroupindex
C11×#5192
#106233472
C2×#669002
#106226182
#106221692
#191211