Finite Group Databasebeta

← #22590126

Subgroups — #22590126

Order 9088.

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

normal subgroups only

This group has 156 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×#14556068C211yesmaximal, characteristic
2#17986037C211yesmaximal, characteristic
3#17985826C212yesmaximal, complemented
4#17985824C212yesmaximal, complemented
5C2×#107×C71C211yesmaximal, characteristic
6#14556087—21no—
7#14556068C414yescomplemented
8C2×C71⋊C16C2212yes—
9#14556062C2211yescharacteristic
10#14556062C2211yescharacteristic
11#14556060—21no—
12C22×C8×C71C2211yescharacteristic
13C2×C4⋊C4×C71—21no—
14#107×C71—21no—
15#107×C71C2212yes—
16C4⋊Dic71—21no—
17C4⋊Dic71—21no—
18C22⋊Dic71—41no—
19C4×Dic71—41no—
20C71⋊C16C2×C414yescomplemented
21C22×C4×C71—41no—
22C22×C4×C71D411yescharacteristic
23C2×C8×C71C2×C412yes—
24C2×C8×C71D411yescharacteristic
25C2×C8×C71Q812yes—
26C2×C8×C71C2311yescharacteristic
27C4⋊C4×C71—22no—
28C4⋊C4×C71—41no—
29C23×C71D811yescharacteristic
30C2×C4×C71—42no—
31C2×C4×C71—82no—
32C2×C4×C71C4⋊C412yes—
33C2×C4×C71D811yescharacteristic
34C2×C4×C71Q1612yes—
35C2×C4×C71C2×D411yescharacteristic
36C2×Dic71—41no—
37C2×Dic71—41no—
38C8×C71C4⋊C412yes—
39C8×C71C22×C411yescharacteristic
40C8×C71C2×Q811yescharacteristic
41C22×C71—21no—
42C22×C71—21no—
43C22×C71#10712yes—
44C22×C71C2×D811yescharacteristic
45C4×C71—82no—
46C4×C71#10712yes—
47C4×C71C2×C4⋊C411yescharacteristic
48C4×C71C2×Q1611yescharacteristic
49Dic71—81no—
50Dic71—81no—
51C2×C71—22no—
52C2×C71C2×#10711yescharacteristic
53C2×C71#50911yescharacteristic
54C2×C71#51011yescharacteristic
55#2159—711nomaximal, Sylow
56C71#215911yescharacteristic, complemented, Sylow
57C2×M32—711no—
58#427—711no—
59C2×#107D7111yescharacteristic
60#367—712no—
61#366—712no—
62C22×C8C2×D7111yescharacteristic
63#117—1421no—
64C2×C4⋊C4—21no—
65M32—714no—
66C2×C16—712no—
67#107—21no—
68#107—711no—
69#107—711no—
70#107C2×D7112yes—
71#106—1421no—
72C22×C4—41no—
73C22×C4C22⋊D7111yescharacteristic
74C2×C8Dic14212yes—
75C2×C8C4×D7112yes—
76C2×C8C22⋊D7111yescharacteristic
77C2×C8C22×D7111yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C4⋊C4—1421no—
81C4⋊C4—1421no—
82C22⋊C4—2841no—
83C42—2841no—
84C16—714no—
85C23#1176585011yescharacteristic
86C2×C4—42no—
87C2×C4—82no—
88C2×C4—2841no—
89C2×C4—2841no—
90C2×C4Dic71⋊C412yes—
91C2×C4#1176585011yescharacteristic
92C2×C4#1176585512yes—
93C2×C4C2×C22⋊D7111yescharacteristic
94C8Dic71⋊C412yes—
95C8C2×C4×D7111yescharacteristic
96C8C2×Dic14211yescharacteristic
97C22—21no—
98C22—21no—
99C22#1455606112yes—
100C22C2×#1176585011yescharacteristic
101C4—82no—
102C4—5681no—
103C4—5681no—
104C4#1455606112yes—
105C4C2×Dic71⋊C411yescharacteristic
106C4C2×#1176585511yescharacteristic
107C2—22no—
108C2C2×#1455606111yescharacteristic
109C2#1798643511yescharacteristic
110C2#1798644011yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC8×C71C22×C4
FrattiniC2×C8C22×D71
FittingC2×#107×C71C2
socleC22×C71C2×D8
hypercenterC2×#107D71
hypocenterC71#2159
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
3. #17985826C2semidirect
4. #17985824C2semidirect
7. #14556068C4semidirect
20. C71⋊C16C2×C4semidirect
56. C71#2159semidirect