Finite Group Databasebeta

← #13070110

Subgroups — #13070110

Order 1408.

224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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×#107C211yesmaximal, characteristic
2C2×Dic11⋊C8C211yesmaximal, characteristic
3#10622586C212yesmaximal
4#10622189C211yesmaximal, characteristic
5#10622167C212yesmaximal
6C22×C8×C11C2211yescharacteristic
7C2×C11×C4⋊C4C2212yes—
8C2×C4⋊Dic11C2212yes—
9C2×Dic11⋊C4—22no—
10C2×C4×Dic11C2211yescharacteristic
11C22×C11⋊C8C2211yescharacteristic
12C11×#107—22no—
13C11⋊#95—22no—
14Dic11⋊C8—22no—
15C22×C4×C11—22no—
16C22×C4×C11C2311yescharacteristic
17C22×Dic11—22no—
18C22×Dic11D411yescharacteristic
19C22×Dic11D411yescharacteristic
20C2×C8×C11—22no—
21C2×C8×C11D412yes—
22C11×C4⋊C4—22no—
23C11×C4⋊C4—22no—
24C4⋊Dic11—22no—
25C4⋊Dic11Q814yes—
26Dic11⋊C4—44no—
27C4×Dic11—21no—
28C4×Dic11—21no—
29C2×C11⋊C8—21no—
30C2×C11⋊C8—22no—
31#2087—111nomaximal, Sylow
32C23×C11C2×D411yescharacteristic
33C2×C4×C11—42no—
34C2×C4×C11—42no—
35C2×C4×C11—42no—
36C2×C4×C11C2×D411yescharacteristic
37C2×C4×C11C2×Q812yes—
38C2×C4×C11#4112yes—
39C2×C4×C11#4111yescharacteristic
40C2×Dic11—21no—
41C2×Dic11—21no—
42C2×Dic11—21no—
43C2×Dic11—24no—
44C2×Dic11—22no—
45C2×Dic11—42no—
46C2×Dic11—42no—
47C2×Dic11Q1612yes—
48C8×C11—22no—
49C11⋊C8—41no—
50C2×#107D1111yescharacteristic
51C2×C4⋊C8—111no—
52#389—112no—
53#340—111no—
54#340—112no—
55C22×C11#12111yescharacteristic
56C22×C11C22⋊Q812yes—
57C22×C11C2×Q1611yescharacteristic
58C22×C11#13511yescharacteristic
59C22×C11AGL(1,ℤ/8)12yes—
60C4×C11—82no—
61C4×C11#12311yescharacteristic
62C4×C11#12512yes—
63C4×C11C4⋊Q811yescharacteristic
64Dic11—22no—
65Dic11—41no—
66Dic11—44no—
67C22×C8—111no—
68C22×C8C2×D1111yescharacteristic
69C2×C4⋊C4—112no—
70C2×C4⋊C4—222no—
71C2×C4⋊C4C2×D1112yes—
72C2×C42—111no—
73#107—22no—
74C4⋊C8—222no—
75#95—222no—
76C2×C11#39811yescharacteristic
77C2×C11#46711yescharacteristic
78C2×C11#46911yescharacteristic
79C2×C11#47712yes—
80C2×C11#47812yes—
81C22×C4—22no—
82C22×C4—111no—
83C22×C4—111no—
84C22×C4—222no—
85C22×C4C22×D1111yescharacteristic
86C2×C8—22no—
87C2×C8—222no—
88C2×C8—221no—
89C2×C8C22⋊D1112yes—
90C4⋊C4—22no—
91C4⋊C4—22no—
92C4⋊C4—114no—
93C4⋊C4—222no—
94C4⋊C4—444no—
95C42—221no—
96C42—221no—
97C11#208711yescharacteristic, complemented, Sylow
98C23D4×D1111yescharacteristic
99C2×C4—42no—
100C2×C4—42no—
101C2×C4—42no—
102C2×C4—112no—
103C2×C4—221no—
104C2×C4—221no—
105C2×C4—224no—
106C2×C4—222no—
107C2×C4—221no—
108C2×C4—442no—
109C2×C4—442no—
110C2×C4#433912yes—
111C2×C4#434111yescharacteristic
112C2×C4Q8×D1112yes—
113C2×C4C2×C22⋊D1111yescharacteristic
114C8—22no—
115C8—441no—
116C22#6694912yes—
117C22#6696412yes—
118C22Q16×D1111yescharacteristic
119C22#6697211yescharacteristic
120C22#6699111yescharacteristic
121C4—82no—
122C4—222no—
123C4—444no—
124C4—441no—
125C4#6694212yes—
126C4#6698211yescharacteristic
127C4#6699711yescharacteristic
128C2#1062248812yes—
129C2#1062250412yes—
130C2#1062259311yescharacteristic
131C2#1062277211yescharacteristic
132C2#1062280111yescharacteristic
subgroupG/H
centerC23D4×D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#107C2
socle, prime radicalC23×C11C2×D4
hypercenterC2×#107D11
hypocenterC11#2087
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
97. C11#2087semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1072
C2×Dic11⋊C82
#106225862
#106221892
#106221672
#208711