Finite Group Databasebeta

← #13070061

Subgroups — #13070061

Order 1408.

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

normal subgroups only

This group has 198 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
1C11×#408C211yesmaximal, characteristic
2#10622845C212yesmaximal
3C2×#66881C211yesmaximal, characteristic, complemented
4#10622192C212yesmaximal, complemented
5#10622190C211yesmaximal, characteristic, complemented
6C2×C11×#41C2211yescharacteristic
7C2×C11×M16C2211yescharacteristic
8C22×C8×C11C2211yescharacteristic
9C2×C4⋊Dic11C2212yes—
10C2×#4318C2212yes—
11C11×C22⋊C8—22no—
12#66899—22no—
13#66896—22no—
14#66881—22no—
15C11×#41—22no—
16C11×#41—22no—
17C2×Q8×C11D411yescharacteristic
18C2×D4×C11—21no—
19C2×D4×C11D411yescharacteristic
20C22×C4×C11—21no—
21C22×C4×C11C2311yescharacteristic
22C22×Dic11—22no—
23C11×M16—22no—
24C2×C8×C11—21no—
25C2×C8×C11—22no—
26C2×C8×C11D412yes—
27C4⋊Dic11—22no—
28C4⋊Dic11—22no—
29#4318—22no—
30#4318—22no—
31C2×C11⋊C8—22no—
32#2079—111nomaximal, Sylow
33C23×C11—21no—
34C23×C11#4111yescharacteristic
35Q8×C11—22no—
36D4×C11—22no—
37D4×C11—42no—
38C2×C4×C11—21no—
39C2×C4×C11—41no—
40C2×C4×C11—41no—
41C2×C4×C11C2×D411yescharacteristic
42C2×C4×C11C2×D411yescharacteristic
43C2×C4×C11#4112yes—
44C2×C4×C11#4112yes—
45C2×Dic11—42no—
46C2×Dic11—82no—
47C8×C11—22no—
48C8×C11—41no—
49C11⋊C8—42no—
50C2×#106—111no—
51#417—112no—
52#408D1111yescharacteristic
53#343—112no—
54#341—111no—
55C22×C11—22no—
56C22×C11—41no—
57C22×C11—42no—
58C22×C11#12111yescharacteristic
59C22×C11#12612yes—
60C4×C11—41no—
61C4×C11#12312yes—
62C4×C11#12311yescharacteristic
63C4×C11#12411yescharacteristic
64Dic11—82no—
65C2×#41C2×D1111yescharacteristic
66C2×M16—112no—
67C2×M16C2×D1111yescharacteristic
68C22×C8C2×D1111yescharacteristic
69C2×C4⋊C4—112no—
70#106—222no—
71#103—222no—
72#102—222no—
73C22⋊C8—22no—
74C2×C11—22no—
75C2×C11—81no—
76C2×C11#39711yescharacteristic
77C2×C11#47112yes—
78#41—22no—
79#41—22no—
80C2×Q8D4411yescharacteristic
81C2×D4—21no—
82C2×D4D4411yescharacteristic
83C22×C4—21no—
84C22×C4—222no—
85C22×C4C22×D1111yescharacteristic
86M16—22no—
87M16—222no—
88M16—222no—
89C2×C8—22no—
90C2×C8—21no—
91C2×C8—222no—
92C2×C8C22⋊D1112yes—
93C4⋊C4—222no—
94C4⋊C4—222no—
95C11#207911yescharacteristic, complemented, Sylow
96C23—21no—
97C23#433911yescharacteristic
98Q8—22no—
99D4—22no—
100D4—42no—
101C2×C4—21no—
102C2×C4—41no—
103C2×C4—41no—
104C2×C4—442no—
105C2×C4—882no—
106C2×C4C2×D4411yescharacteristic
107C2×C4#434112yes—
108C2×C4#434112yes—
109C2×C4C2×C22⋊D1111yescharacteristic
110C8—22no—
111C8—41no—
112C8—442no—
113C22—22no—
114C22—42no—
115C22—41no—
116C22#6693212yes—
117C22#6698311yescharacteristic
118C4—41no—
119C4—882no—
120C4#6693912yes—
121C4#6698811yescharacteristic
122C4#6698911yescharacteristic
123C2—22no—
124C2—81no—
125C2#1062256611yescharacteristic
126C2#1062275412yes—
subgroupG/H
centerC22#66983
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#408C2
socleC22×C11#121
prime radicalC2×C11×#41C22
hypercenter#408D11
hypocenterC11#2079
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
3. C2×#66881C2semidirect
4. #10622192C2semidirect
5. #10622190C2semidirect
95. C11#2079semidirect

Maximal subgroups

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

subgroupindex
C11×#4082
#106228452
C2×#668812
#106221922
#106221902
#207911