Finite Group Databasebeta

← #13069900

Subgroups — #13069900

Order 1408.

266 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 67 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×#575C211yesmaximal, characteristic
2#10622850C212yesmaximal, complemented
3C2×#66901C212yesmaximal, complemented
4#10622731C211yesmaximal, characteristic, complemented
5C11⋊#338C211yesmaximal, characteristic, complemented
6C2×C11×#41C2212yes—
7C11×#137—22no—
8C11×AGL(1,ℤ/8)—22no—
9C11×#135—22no—
10C2×C11×M16C2211yescharacteristic
11C2×C4×Dic11C2211yescharacteristic
12C2×#4318C2211yescharacteristic
13C2×#4318C2212yes—
14#66901—22no—
15#66901—22no—
16#66900—22no—
17#66897—22no—
18Dic11⋊C8—22no—
19C11×#41—22no—
20C11×#41—22no—
21C11×#41—22no—
22C11×#41—22no—
23C2×Q8×C11D412yes—
24C2×D4×C11—22no—
25C2×D4×C11D412yes—
26C22×C4×C11—22no—
27C22×C4×C11C2311yescharacteristic
28C22×Dic11—21no—
29C11×Q16—22no—
30C11×SD16—24no—
31C11×D8—22no—
32C11×M16—22no—
33C2×C8×C11D412yes—
34C4×Dic11—21no—
35C4×Dic11D411yescharacteristic
36C4×Dic11D411yescharacteristic
37#4318—22no—
38#4318—22no—
39#4318—22no—
40C2×C11⋊C8—21no—
41C2×C11⋊C8—22no—
42#2050—111nomaximal, Sylow
43C23×C11—22no—
44C23×C11#4111yescharacteristic
45Q8×C11—22no—
46Q8×C11—22no—
47D4×C11—22no—
48D4×C11—22no—
49D4×C11—42no—
50D4×C11—42no—
51C2×C4×C11—22no—
52C2×C4×C11—42no—
53C2×C4×C11—42no—
54C2×C4×C11C2×D411yescharacteristic
55C2×C4×C11C2×D412yes—
56C2×C4×C11C2×D411yescharacteristic
57C2×C4×C11#4112yes—
58C2×Dic11—21no—
59C2×Dic11—21no—
60C2×Dic11—42no—
61C8×C11—22no—
62C11⋊C8—41no—
63C11⋊C8—42no—
64#575D1111yescharacteristic
65#423—111no—
66C2×#104—112no—
67#413—112no—
68#338—111no—
69C22×C11—41no—
70C22×C11—42no—
71C22×C11—82no—
72C22×C11#12111yescharacteristic
73C22×C11#12312yes—
74C4×C11—42no—
75C4×C11#12011yescharacteristic
76C4×C11#12112yes—
77C4×C11#12411yescharacteristic
78Dic11—22no—
79Dic11—41no—
80C2×#41C2×D1112yes—
81#137—22no—
82AGL(1,ℤ/8)—22no—
83#135—22no—
84C2×M16—112no—
85C2×M16—111no—
86C2×M16C2×D1111yescharacteristic
87C2×C42—111no—
88C4⋊C8—222no—
89#104—222no—
90#104—222no—
91#101—222no—
92#100—222no—
93C2×C11—21no—
94C2×C11—22no—
95C2×C11—82no—
96C2×C11#39411yescharacteristic
97#41—22no—
98#41—22no—
99#41—22no—
100#41—22no—
101C2×Q8C22⋊D1112yes—
102C2×D4—22no—
103C2×D4C22⋊D1112yes—
104C22×C4—22no—
105C22×C4—221no—
106C22×C4C22×D1111yescharacteristic
107Q16—22no—
108SD16—24no—
109D8—22no—
110M16—22no—
111M16—222no—
112M16—222no—
113M16—222no—
114C2×C8—222no—
115C2×C8—221no—
116C2×C8C22⋊D1112yes—
117C42—111no—
118C42—111no—
119C42—221no—
120C11#205011yescharacteristic, complemented, Sylow
121C23—22no—
122C23#434111yescharacteristic
123Q8—22no—
124Q8—22no—
125D4—22no—
126D4—22no—
127D4—42no—
128D4—42no—
129C2×C4—22no—
130C2×C4—42no—
131C2×C4—42no—
132C2×C4—221no—
133C2×C4—221no—
134C2×C4—442no—
135C2×C4D4×D1111yescharacteristic
136C2×C4#434112yes—
137C2×C4C2×C22⋊D1111yescharacteristic
138C2×C4C2×C22⋊D1112yes—
139C8—22no—
140C8—442no—
141C8—441no—
142C22—41no—
143C22—42no—
144C22—82no—
145C22#6698812yes—
146C22#6699111yescharacteristic
147C4—42no—
148C4—222no—
149C4—441no—
150C4#6698911yescharacteristic
151C4#6699212yes—
152C4#6700611yescharacteristic
153C2—21no—
154C2—22no—
155C2—82no—
156C2#1062283511yescharacteristic
subgroupG/H
centerC4#66989
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC11×#575C2
socleC2×C11#394
hypercenter#575D11
hypocenterC11#2050
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
2. #10622850C2semidirect
3. C2×#66901C2semidirect
4. #10622731C2semidirect
5. C11⋊#338C2semidirect
120. C11#2050semidirect

Maximal subgroups

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

subgroupindex
C11×#5752
#106228502
C2×#669012
#106227312
C11⋊#3382
#205011