Finite Group Databasebeta

← #13069723

Subgroups — #13069723

Order 1408.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C22×C11×D8C211yesmaximal, characteristic, complemented
2C2×#66985C212yesmaximal, complemented
3C2×#66897C212yesmaximal, complemented
4#10622723C211yesmaximal, characteristic, complemented
5#10622190C211yesmaximal, characteristic, complemented
6C22×D4×C11C2212yes—
7C2×#4339C2211yescharacteristic
8C2×C11×D8—24no—
9C2×C11×D8—22no—
10C22×C8×C11C2211yescharacteristic
11C2×#4324—22no—
12#66985—24no—
13#66985—24no—
14C2×#4323—22no—
15C2×#4318C2211yescharacteristic
16C2×#4318C2212yes—
17#66897—24no—
18(C2×D11)⋊C8—22no—
19C24×C11—22no—
20C2×D4×C11—22no—
21C2×D4×C11—22no—
22C2×D4×C11—22no—
23C2×D4×C11—22no—
24C2×D4×C11—22no—
25C2×D4×C11D414yes—
26C22×C4×C11C2311yescharacteristic
27C2×C22⋊D11—21no—
28#4339—22no—
29#4339—22no—
30C2×D44D411yescharacteristic
31C2×C4×D11—21no—
32C2×Dic22D411yescharacteristic
33C11×D8—28no—
34C2×C8×C11—22no—
35C2×C8×C11D412yes—
36#4324—28no—
37#4323—28no—
38#4318—22no—
39#4318—22no—
40#4318D414yes—
41C2×C11⋊C8—22no—
42C2×C11⋊C8—21no—
43#2018—111nomaximal, Sylow
44C23×C11—24no—
45C23×C11—42no—
46C23×C11—42no—
47C23×C11—84no—
48C23×C11#4111yescharacteristic
49C22×D11—21no—
50D4×C11—24no—
51D4×C11—24no—
52D4×C11—42no—
53D4×C11—42no—
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D412yes—
56C2×C4×C11C2×D412yes—
57C2×C4×C11C2×D411yescharacteristic
58C22⋊D11—42no—
59C2×Dic11—21no—
60D44—22no—
61C4×D11—41no—
62C4×D11—41no—
63Dic22—22no—
64C8×C11—22no—
65C11⋊C8—24no—
66C11⋊C8—41no—
67C2×AGL(1,ℤ/8)—112no—
68C22×D8D1111yescharacteristic, complemented
69C2×#100—112no—
70#408—111no—
71#341—111no—
72C22×C11—22no—
73C22×C11—44no—
74C22×C11—84no—
75C22×C11—84no—
76C22×C11—84no—
77C22×C11#12111yescharacteristic
78C22×C11#12112yes—
79C2×D11—41no—
80C2×D11—42no—
81C4×C11#12012yes—
82C4×C11#12011yescharacteristic
83C4×C11#12711yescharacteristic
84Dic11—41no—
85C2×#41—111no—
86C22×D4C2×D1112yes—
87AGL(1,ℤ/8)—224no—
88AGL(1,ℤ/8)—224no—
89C2×SD16—222no—
90C2×D8—24no—
91C2×D8—22no—
92C2×D8—222no—
93C2×M16—112no—
94C2×M16—111no—
95C22×C8C2×D1111yescharacteristic
96#100—224no—
97C22⋊C8—222no—
98C2×C11—22no—
99C2×C11—84no—
100C2×C11#39211yescharacteristic
101C2×C11#47212yes—
102D11—81no—
103C24—22no—
104#41—222no—
105#41—222no—
106C2×Q8—111no—
107C2×D4—22no—
108C2×D4—22no—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4—22no—
112C2×D4—111no—
113C2×D4—221no—
114C2×D4C22⋊D1114yes—
115C22×C4—221no—
116C22×C4C22×D1111yescharacteristic
117SD16—228no—
118D8—28no—
119D8—228no—
120M16—114no—
121M16—222no—
122M16—222no—
123C2×C8—22no—
124C2×C8—222no—
125C2×C8—221no—
126C2×C8C22⋊D1112yes—
127C11#201811yescharacteristic, complemented, Sylow
128C23—24no—
129C23—42no—
130C23—42no—
131C23—84no—
132C23—221no—
133C23#434111yescharacteristic
134Q8—222no—
135D4—24no—
136D4—24no—
137D4—42no—
138D4—42no—
139D4—222no—
140D4—442no—
141C2×C4—221no—
142C2×C4—441no—
143C2×C4—441no—
144C2×C4D4×D1111yescharacteristic
145C2×C4D4×D1112yes—
146C2×C4C2×C22⋊D1112yes—
147C2×C4C2×C22⋊D1111yescharacteristic
148C8—22no—
149C8—224no—
150C8—441no—
151C22—22no—
152C22—44no—
153C22—84no—
154C22—84no—
155C22—84no—
156C22—442no—
157C22—441no—
158C22#6699111yescharacteristic
159C22#6699212yes—
160C4—441no—
161C4#6699012yes—
162C4#6699311yescharacteristic
163C4#6700611yescharacteristic
164C2—22no—
165C2—84no—
166C2—881no—
167C2#1062277312yes—
168C2#1062283611yescharacteristic
subgroupG/H
centerC22#66991
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC22×C11×D8C2
socleC22×C11#121
hypercenterC22×D8D11
hypocenterC11#2018
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×C11×D8C2semidirect
2. C2×#66985C2semidirect
3. C2×#66897C2semidirect
4. #10622723C2semidirect
5. #10622190C2semidirect
68. C22×D8D11semidirect
127. C11#2018semidirect

Maximal subgroups

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

subgroupindex
C22×C11×D82
C2×#669852
C2×#668972
#106227232
#106221902
#201811