Finite Group Databasebeta

← #22590542

Subgroups — #22590542

Order 9088.

140 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#17986240C211yesmaximal, characteristic
2#17985824C212yesmaximal, complemented
3#17985802C212yesmaximal, complemented
4C22⋊(C71⋊C16)C211yesmaximal, characteristic
5C2×#107×C71C211yesmaximal, characteristic
6C2×Dic284C2211yescharacteristic
7#14556107—21no—
8C2×C71⋊C16C2212yes—
9#14556062C2211yescharacteristic
10#14556053—21no—
11C22×C8×C71C2211yescharacteristic
12C2×C4⋊C4×C71—21no—
13#107×C71—21no—
14#107×C71C2212yes—
15C2×Dic142—21no—
16Dic284—22no—
17C4⋊Dic71—21no—
18Dic71⋊C4—41no—
19C22⋊Dic71—41no—
20C71⋊C16—22no—
21C22×C4×C71—41no—
22C22×C4×C71D411yescharacteristic
23C2×C8×C71—22no—
24C2×C8×C71D411yescharacteristic
25C2×C8×C71C2311yescharacteristic
26C4⋊C4×C71—22no—
27C4⋊C4×C71—41no—
28C23×C71D811yescharacteristic
29C2×C4×C71—21no—
30C2×C4×C71—21no—
31C2×C4×C71—42no—
32C2×C4×C71—82no—
33C2×C4×C71D811yescharacteristic
34C2×C4×C71C2×D411yescharacteristic
35C2×Dic71—41no—
36C2×Dic71—41no—
37Dic142—41no—
38Dic142—41no—
39C8×C71—21no—
40C8×C71#4112yes—
41C22×C71—21no—
42C22×C71—21no—
43C22×C71Q3212yes—
44C22×C71C2×D811yescharacteristic
45C4×C71—21no—
46C4×C71—82no—
47C4×C71#12311yescharacteristic
48C4×C71#13711yescharacteristic
49Dic71—81no—
50Dic71—81no—
51C2×C71—22no—
52C2×C71#48011yescharacteristic
53C2×C71C2×Q3211yescharacteristic
54C2×C71#50911yescharacteristic
55#2236—711nomaximal, Sylow
56C71#223611yescharacteristic, complemented, Sylow
57#467—711no—
58C2×#107D7111yescharacteristic
59#366—712no—
60#358—712no—
61C22⋊C16—711no—
62C2×Q16—711no—
63C22×C8C2×D7111yescharacteristic
64C22⋊Q8—1421no—
65C2×C4⋊C4—21no—
66C2×C16—712no—
67#107—21no—
68#107—711no—
69#107C2×D7112yes—
70#103—1421no—
71C2×Q8—1421no—
72C22×C4—41no—
73C22×C4C22⋊D7111yescharacteristic
74Q16—1422no—
75C2×C8—22no—
76C2×C8C22⋊D7111yescharacteristic
77C2×C8C22×D7111yescharacteristic
78C4⋊C4—22no—
79C4⋊C4—41no—
80C4⋊C4—2841no—
81C4⋊C4—1421no—
82C22⋊C4—2841no—
83C16—1422no—
84C23#1176585011yescharacteristic
85Q8—2841no—
86Q8—2841no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—42no—
90C2×C4—82no—
91C2×C4—2841no—
92C2×C4—2841no—
93C2×C4#1176585011yescharacteristic
94C2×C4C2×C22⋊D7111yescharacteristic
95C8—21no—
96C8#1176586512yes—
97C22—21no—
98C22—21no—
99C22#1455607412yes—
100C22C2×#1176585011yescharacteristic
101C4—21no—
102C4—82no—
103C4—5681no—
104C4—5681no—
105C4#1455611111yescharacteristic
106C4#1455615911yescharacteristic
107C2—22no—
108C2#1798631211yescharacteristic
109C2C2×#1455607411yescharacteristic
110C2#1798643511yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
FittingC2×#107×C71C2
socleC22×C71C2×D8
hypercenterC2×#107D71
hypocenterC71#2236
LCSG ▷ C2×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
2. #17985824C2semidirect
3. #17985802C2semidirect
56. C71#2236semidirect