Finite Group Databasebeta

← #13069903

Subgroups — #13069903

Order 1408.

266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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#10623279C211yesmaximal, characteristic
2C11×#423C211yesmaximal, characteristic, complemented
3#10622745C212yesmaximal, complemented
4C2×#66869C212yesmaximal, complemented
5C11⋊#338C211yesmaximal, characteristic, complemented
6C2×#4339C2212yes—
7C2×C11×M16C2211yescharacteristic
8C2×C11×M16C2211yescharacteristic
9C2×C42×C11C2211yescharacteristic
10C2×#4318C2212yes—
11#66962—22no—
12#66961—22no—
13#66957—22no—
14C11×C4⋊C8—22no—
15#66888—22no—
16#66887—22no—
17#66869—22no—
18#66869—22no—
19C22×C4×C11—21no—
20C22×C4×C11C2311yescharacteristic
21C2×C22⋊D11—22no—
22#4339—22no—
23#4339—22no—
24#4339—22no—
25#4339—22no—
26C2×D44D412yes—
27C2×C4×D11—22no—
28C2×Dic22D412yes—
29C11×M16—22no—
30C11×M16—22no—
31C2×C8×C11—21no—
32C2×C8×C11D412yes—
33C42×C11—21no—
34C42×C11D411yescharacteristic
35C42×C11D411yescharacteristic
36#4318—22no—
37#4318—22no—
38C2×C11⋊C8—22no—
39Dic44—22no—
40D88—22no—
41#4314—24no—
42#2050—111nomaximal, Sylow
43C23×C11#4111yescharacteristic
44C22×D11—22no—
45C2×C4×C11—21no—
46C2×C4×C11—21no—
47C2×C4×C11—42no—
48C2×C4×C11C2×D411yescharacteristic
49C2×C4×C11C2×D412yes—
50C2×C4×C11C2×D411yescharacteristic
51C2×C4×C11#4112yes—
52C22⋊D11—42no—
53C22⋊D11—42no—
54C2×Dic11—22no—
55D44—22no—
56D44—22no—
57C4×D11—42no—
58C4×D11—42no—
59Dic22—22no—
60Dic22—22no—
61C8×C11—22no—
62C8×C11—41no—
63C11⋊C8—42no—
64#575—111no—
65#423D1111yescharacteristic, complemented
66C2×#104—112no—
67#413—112no—
68#338—111no—
69C22×C11—41no—
70C22×C11#12111yescharacteristic
71C22×C11#12312yes—
72C2×D11—42no—
73C2×D11—82no—
74C4×C11—22no—
75C4×C11—41no—
76C4×C11#12011yescharacteristic
77C4×C11#12112yes—
78C4×C11#12411yescharacteristic
79Dic11—42no—
80C2×#41—112no—
81#137—222no—
82AGL(1,ℤ/8)—222no—
83#135—222no—
84C2×M16—112no—
85C2×M16C2×D1111yescharacteristic
86C2×M16C2×D1111yescharacteristic
87C2×C42C2×D1111yescharacteristic
88C4⋊C8—22no—
89#104—222no—
90#104—222no—
91#101—222no—
92#100—222no—
93C2×C11—21no—
94C2×C11—22no—
95C2×C11#39411yescharacteristic
96D11—82no—
97#41—222no—
98#41—222no—
99#41—222no—
100#41—222no—
101C2×Q8—112no—
102C2×D4—112no—
103C2×D4—222no—
104C22×C4—21no—
105C22×C4—222no—
106C22×C4C22×D1111yescharacteristic
107Q16—222no—
108SD16—224no—
109D8—222no—
110M16—22no—
111M16—22no—
112M16—222no—
113M16—222no—
114C2×C8—21no—
115C2×C8—222no—
116C2×C8C22⋊D1112yes—
117C42—21no—
118C42D4411yescharacteristic
119C42D4411yescharacteristic
120C11#205011yescharacteristic, complemented, Sylow
121C23—222no—
122C23#433911yescharacteristic
123Q8—222no—
124Q8—222no—
125D4—222no—
126D4—222no—
127D4—442no—
128D4—442no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—42no—
132C2×C4—222no—
133C2×C4—442no—
134C2×C4—442no—
135C2×C4C2×D4411yescharacteristic
136C2×C4D4×D1112yes—
137C2×C4#434312yes—
138C2×C4C2×C22⋊D1111yescharacteristic
139C8—22no—
140C8—41no—
141C8—442no—
142C22—41no—
143C22—442no—
144C22—882no—
145C22#6694712yes—
146C22#6698311yescharacteristic
147C4—22no—
148C4—41no—
149C4—442no—
150C4#6694812yes—
151C4#6699011yescharacteristic
152C4#6700011yescharacteristic
153C2—21no—
154C2—22no—
155C2—882no—
156C2#1062260411yescharacteristic
subgroupG/H
centerC4#67000
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#423C2
socleC2×C11#394
prime radical#10623279C2
hypercenter#423D11
hypocenterC11#2050
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #423

Complements

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

NH ≅ G/Ntype
2. C11×#423C2semidirect
3. #10622745C2semidirect
4. C2×#66869C2semidirect
5. C11⋊#338C2semidirect
65. #423D11semidirect
120. C11#2050semidirect

Maximal subgroups

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

subgroupindex
#106232792
C11×#4232
#106227452
C2×#668692
C11⋊#3382
#205011