Finite Group Databasebeta

← #22590538

Subgroups — #22590538

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
2C2×#14556062C211yesmaximal, characteristic
3#17985827C212yesmaximal, complemented
4#17985804C212yesmaximal, complemented
5C22⋊C16×C71C211yesmaximal, characteristic
6C2×Dic284C2211yescharacteristic
7#14556107—21no—
8C2×C4⋊Dic71—21no—
9#14556062—21no—
10#14556062C2212yes—
11#14556062C2211yescharacteristic
12#14556053—21no—
13C22×C8×C71C2211yescharacteristic
14C2×C16×C71C2212yes—
15C2×Dic142—21no—
16C22×Dic71—41no—
17Dic284—22no—
18C4⋊Dic71—21no—
19C4⋊Dic71—22no—
20C4⋊Dic71—41no—
21Dic71⋊C4—41no—
22C22⋊Dic71—41no—
23C22×C4×C71D411yescharacteristic
24C2×C8×C71—22no—
25C2×C8×C71D411yescharacteristic
26C2×C8×C71C2311yescharacteristic
27C16×C71—22no—
28C23×C71D811yescharacteristic
29C2×C4×C71—21no—
30C2×C4×C71—21no—
31C2×C4×C71D811yescharacteristic
32C2×C4×C71C2×D411yescharacteristic
33C2×Dic71—41no—
34C2×Dic71—41no—
35C2×Dic71—42no—
36C2×Dic71—82no—
37Dic142—41no—
38Dic142—41no—
39C8×C71—21no—
40C8×C71#4112yes—
41C22×C71—21no—
42C22×C71—21no—
43C22×C71SD3212yes—
44C22×C71C2×D811yescharacteristic
45C4×C71—21no—
46C4×C71#12311yescharacteristic
47C4×C71#13711yescharacteristic
48Dic71—81no—
49Dic71—82no—
50Dic71—81no—
51C2×C71—22no—
52C2×C71#48011yescharacteristic
53C2×C71C2×SD3211yescharacteristic
54C2×C71#51011yescharacteristic
55#2235—711nomaximal, Sylow
56C71#223511yescharacteristic, complemented, Sylow
57#467—711no—
58C2×#107—711no—
59#367—712no—
60#358—712no—
61C22⋊C16D7111yescharacteristic
62C2×Q16—711no—
63C22×C8C2×D7111yescharacteristic
64C22⋊Q8—1421no—
65C2×C4⋊C4—1421no—
66C2×C16C2×D7112yes—
67#107—712no—
68#107—711no—
69#107—1421no—
70#103—1421no—
71C2×Q8—1421no—
72C22×C4—2841no—
73C22×C4D28411yescharacteristic
74Q16—1422no—
75C2×C8—22no—
76C2×C8D28411yescharacteristic
77C2×C8C22×D7111yescharacteristic
78C4⋊C4—2841no—
79C4⋊C4—2841no—
80C4⋊C4—1421no—
81C4⋊C4—1422no—
82C22⋊C4—2841no—
83C16—22no—
84C23D56811yescharacteristic
85Q8—2841no—
86Q8—2841no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—2841no—
90C2×C4—2841no—
91C2×C4—2842no—
92C2×C4—5682no—
93C2×C4D56811yescharacteristic
94C2×C4C2×D28411yescharacteristic
95C8—21no—
96C8#1176586412yes—
97C22—21no—
98C22—21no—
99C22#1455607312yes—
100C22C2×D56811yescharacteristic
101C4—21no—
102C4—5681no—
103C4—5682no—
104C4—5681no—
105C4#1455611211yescharacteristic
106C4#1455616111yescharacteristic
107C2—22no—
108C2#1798631311yescharacteristic
109C2C2×#1455607311yescharacteristic
110C2#1798644211yescharacteristic
subgroupG/H
centerC22C2×D568
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
FittingC22⋊C16×C71C2
socleC22×C71C2×D8
hypercenterC22⋊C16D71
hypocenterC71#2235
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
3. #17985827C2semidirect
4. #17985804C2semidirect
56. C71#2235semidirect