Finite Group Databasebeta

← #13069005

Subgroups — #13069005

Order 1408.

360 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C11×#124C211yesmaximal, characteristic
2#10623329C211yesmaximal, characteristic
3#10622838C212yesmaximal, complemented
4C2×#66897C211yesmaximal, characteristic
5#10622161C212yesmaximal, complemented
6C22×Q8×C11C2211yescharacteristic
7C22×D4×C11C2211yescharacteristic
8C11×#124—22no—
9C11×#124C414yescomplemented
10C2×C11×C22⋊C4—22no—
11C2×C42×C11C2211yescharacteristic
12C2×C22⋊Dic11—22no—
13D4×Dic11—24no—
14#66979C2212yes—
15C2×#4318C2212yes—
16#66899—24no—
17#66897—22no—
18C24×C11D412yes—
19C2×Q8×C11—21no—
20C2×Q8×C11—22no—
21C2×Q8×C11—22no—
22C2×Q8×C11C2×C412yescomplemented
23C2×D4×C11—22no—
24C2×D4×C11—22no—
25C2×D4×C11C2×C412yes—
26C2×D4×C11D412yes—
27C22×C4×C11—21no—
28C22×C4×C11—21no—
29C22×C4×C11C2311yescharacteristic
30C22×Dic11—24no—
31C11×C22⋊C4—28no—
32C42×C11—21no—
33C42×C11C2×C412yescomplemented
34C22⋊Dic11—24no—
35C22⋊Dic11—22no—
36C4⋊Dic11D414yes—
37C4×Dic11—22no—
38#4318—22no—
39#4318—22no—
40C2×C11⋊C8—22no—
41#1885—111nomaximal, Sylow
42C23×C11—22no—
43C23×C11—22no—
44C23×C11—44no—
45C23×C11C22⋊C414yes—
46C23×C11C2×D411yescharacteristic
47Q8×C11—24no—
48Q8×C11—42no—
49D4×C11—24no—
50D4×C11—24no—
51C2×C4×C11—22no—
52C2×C4×C11—22no—
53C2×C4×C11—42no—
54C2×C4×C11—41no—
55C2×C4×C11—41no—
56C2×C4×C11C22×C411yescharacteristic
57C2×C4×C11C2×D412yes—
58C2×C4×C11C2×D411yescharacteristic
59C2×C4×C11#4112yes—
60C2×Dic11—24no—
61C2×Dic11—84no—
62C11⋊C8—42no—
63C2×#124D1111yescharacteristic
64#518—111no—
65#419—112no—
66C2×#100—111no—
67#339—112no—
68C22×C11—22no—
69C22×C11—24no—
70C22×C11—44no—
71C22×C11—44no—
72C22×C11—82no—
73C22×C11C2×C22⋊C411yescharacteristic
74C22×C11#12011yescharacteristic
75C22×C11#12311yescharacteristic
76C4×C11—42no—
77C4×C11—42no—
78C4×C11C4×D412yes—
79C4×C11#12112yes—
80Dic11—44no—
81C22×Q8C2×D1111yescharacteristic
82C22×D4C2×D1111yescharacteristic
83C2×M16—112no—
84#124—22no—
85#124Dic1114yescomplemented
86C4×D4—224no—
87#117—112no—
88C2×C22⋊C4—22no—
89C2×C22⋊C4—222no—
90C2×C42C2×D1111yescharacteristic
91#103—224no—
92#100—222no—
93C2×C11—21no—
94C2×C11—21no—
95C2×C11—44no—
96C2×C11#38611yescharacteristic
97C2×C11#45512yes—
98C24C22⋊D1112yes—
99C2×Q8—21no—
100C2×Q8—22no—
101C2×Q8—22no—
102C2×Q8C2×Dic1112yescomplemented
103C2×D4—22no—
104C2×D4—22no—
105C2×D4C2×Dic1112yes—
106C2×D4C22⋊D1112yes—
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—224no—
110C22×C4C22×D1111yescharacteristic
111M16—222no—
112M16—222no—
113C2×C8—222no—
114C4⋊C4—114no—
115C22⋊C4—28no—
116C22⋊C4—224no—
117C22⋊C4—222no—
118C42—21no—
119C42—222no—
120C42C2×Dic1112yescomplemented
121C11#188511yescharacteristic, complemented, Sylow
122C23—22no—
123C23—22no—
124C23—44no—
125C23C22⋊Dic1114yes—
126C23C2×C22⋊D1111yescharacteristic
127Q8—24no—
128Q8—42no—
129D4—24no—
130D4—24no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—42no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—224no—
137C2×C4—884no—
138C2×C4D4×D1112yes—
139C2×C4#434112yes—
140C2×C4C22×Dic1111yescharacteristic
141C2×C4C2×C22⋊D1111yescharacteristic
142C8—442no—
143C22—22no—
144C22—24no—
145C22—44no—
146C22—44no—
147C22—82no—
148C22#6698811yescharacteristic
149C22#6699011yescharacteristic
150C22C2×C22⋊Dic1111yescharacteristic
151C4—42no—
152C4—42no—
153C4—444no—
154C4D4×Dic1112yes—
155C4#6699212yes—
156C2—21no—
157C2—21no—
158C2—44no—
159C2#1062267412yes—
160C2#1062283311yescharacteristic
subgroupG/H
centerC22#66990
commutatorC2×C4×C11C22×C4
FrattiniC22×C4C22×D11
FittingC2×C11×#124C2
socleC22×C11#120
prime radicalC22×D4×C11C22
cosocleC22×C4×C11C23
hypercenterC2×#124D11
hypocenterC11#1885
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
3. #10622838C2semidirect
5. #10622161C2semidirect
9. C11×#124C4semidirect
22. C2×Q8×C11C2×C4semidirect
33. C42×C11C2×C4semidirect
85. #124Dic11semidirect
102. C2×Q8C2×Dic11semidirect
120. C42C2×Dic11semidirect
121. C11#1885semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1242
#106233292
#106228382
C2×#668972
#106221612
#188511