Finite Group Databasebeta

← #13070057

Subgroups — #13070057

Order 1408.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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, complemented
2#10622723C211yesmaximal, characteristic
3#10622579C212yesmaximal
4#10622190C211yesmaximal, characteristic, complemented
5#10622168C212yesmaximal, complemented
6C2×#4339C2211yescharacteristic
7C22×C8×C11C2211yescharacteristic
8C2×C11×C4⋊C4C2212yes—
9C2×#4318C2211yescharacteristic
10C2×#4318C2212yes—
11C11×#107—22no—
12(C2×D11)⋊C8—22no—
13#66874—22no—
14#66873—22no—
15C22×C4×C11—22no—
16C22×C4×C11C2311yescharacteristic
17C2×C22⋊D11—21no—
18#4339—22no—
19#4339—22no—
20C2×D44D411yescharacteristic
21C2×C4×D11—21no—
22C2×Dic22D411yescharacteristic
23C2×C8×C11—22no—
24C2×C8×C11D412yes—
25C11×C4⋊C4—22no—
26C11×C4⋊C4—22no—
27#4318—22no—
28#4318—22no—
29#4318—22no—
30C2×C11⋊C8—22no—
31C2×C11⋊C8—21no—
32#2078—111nomaximal, Sylow
33C23×C11#4111yescharacteristic
34C22×D11—21no—
35C2×C4×C11—42no—
36C2×C4×C11—82no—
37C2×C4×C11C2×D411yescharacteristic
38C2×C4×C11C2×D411yescharacteristic
39C2×C4×C11#4112yes—
40C2×C4×C11#4112yes—
41C22⋊D11—42no—
42C2×Dic11—21no—
43D44—22no—
44C4×D11—41no—
45C4×D11—41no—
46Dic22—22no—
47C8×C11—22no—
48C11⋊C8—42no—
49C11⋊C8—41no—
50C2×#107D1111yescharacteristic, complemented
51#417—112no—
52#408—111no—
53#343—112no—
54#341—111no—
55C22×C11—21no—
56C22×C11—21no—
57C22×C11#12111yescharacteristic
58C22×C11#12612yes—
59C2×D11—41no—
60C2×D11—41no—
61C2×D11—41no—
62C4×C11—82no—
63C4×C11#12312yes—
64C4×C11#12311yescharacteristic
65C4×C11#12411yescharacteristic
66Dic11—41no—
67C2×#41—111no—
68C2×M16—112no—
69C2×M16—111no—
70C22×C8C2×D1111yescharacteristic
71C2×C4⋊C4C2×D1112yes—
72#107—22no—
73#103—222no—
74#102—222no—
75C22⋊C8—222no—
76C2×C11—22no—
77C2×C11#39711yescharacteristic
78C2×C11#47211yescharacteristic
79C2×C11#47311yescharacteristic
80D11—81no—
81#41—222no—
82#41—222no—
83C2×Q8—111no—
84C2×D4—111no—
85C2×D4—221no—
86C22×C4—22no—
87C22×C4—221no—
88C22×C4C22×D1111yescharacteristic
89M16—222no—
90M16—222no—
91M16—222no—
92C2×C8—22no—
93C2×C8—222no—
94C2×C8—221no—
95C2×C8C22⋊D1112yes—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C11#207811yescharacteristic, complemented, Sylow
99C23—221no—
100C23#434111yescharacteristic
101Q8—222no—
102D4—222no—
103D4—442no—
104C2×C4—42no—
105C2×C4—82no—
106C2×C4—221no—
107C2×C4—441no—
108C2×C4—441no—
109C2×C4#433912yes—
110C2×C4D4×D1111yescharacteristic
111C2×C4#434312yes—
112C2×C4C2×C22⋊D1111yescharacteristic
113C8—22no—
114C8—442no—
115C8—441no—
116C22—21no—
117C22—21no—
118C22—441no—
119C22—441no—
120C22—441no—
121C22#6695112yes—
122C22#6699111yescharacteristic
123C4—82no—
124C4—441no—
125C4#6694712yes—
126C4#6698211yescharacteristic
127C4#6700011yescharacteristic
128C2—22no—
129C2—881no—
130C2#1062260611yescharacteristic
131C2#1062277311yescharacteristic
132C2#1062280511yescharacteristic
subgroupG/H
centerC22#66991
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC2×C11×#107C2
socleC22×C11#121
prime radicalC2×#4339C22
hypercenterC2×#107D11
hypocenterC11#2078
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
1. C2×C11×#107C2semidirect
4. #10622190C2semidirect
5. #10622168C2semidirect
50. C2×#107D11semidirect
98. C11#2078semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1072
#106227232
#106225792
#106221902
#106221682
#207811