Finite Group Databasebeta

← #22590555

Subgroups — #22590555

Order 9088.

134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 45 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#17986252C211yesmaximal, characteristic
2#17986048C211yesmaximal, characteristic, complemented
3#17985822C212yesmaximal, complemented
4#17985813C212yesmaximal, complemented
5#349×C71C211yesmaximal, characteristic, complemented
6C2×D568C2211yescharacteristic
7C2×#11765849—21no—
8#14556102—21no—
9#14556064—21no—
10#14556064C2212yes—
11#14556060C2211yescharacteristic
12#14556050—21no—
13C2×M16×C71C2211yescharacteristic
14M32×C71C2212yes—
15C2×D284—21no—
16C2×C22⋊D71—41no—
17D568—22no—
18#11765849—22no—
19#11765849—41no—
20C2×C71⋊C8—41no—
21C4⋊Dic71—21no—
22(C2×D71)⋊C4—41no—
23C22×C4×C71D411yescharacteristic
24M16×C71—22no—
25C2×C8×C71D411yescharacteristic
26C2×C8×C71C2311yescharacteristic
27C16×C71—22no—
28C23×C71SD1611yescharacteristic
29C22×D71—41no—
30C2×C4×C71—21no—
31C2×C4×C71—21no—
32C2×C4×C71SD1611yescharacteristic
33C2×C4×C71C2×D411yescharacteristic
34C22⋊D71—82no—
35C2×Dic71—41no—
36D284—41no—
37D284—41no—
38C8×C71—21no—
39C8×C71#4112yes—
40C71⋊C8—42no—
41C22×C71—21no—
42C22×C71—41no—
43C22×C71C2×SD1611yescharacteristic
44C2×D71—81no—
45C2×D71—81no—
46C2×D71—81no—
47C4×C71—21no—
48C4×C71#12311yescharacteristic
49C4×C71AGL(1,ℤ/8)11yescharacteristic
50Dic71—81no—
51C2×C71—21no—
52C2×C71—41no—
53C2×C71#48111yescharacteristic
54D71—161no—
55#2238—711nomaximal, Sylow
56C71#223811yescharacteristic, complemented, Sylow
57#469—711no—
58#430—711no—
59#365—712no—
60#361—712no—
61#349D7111yescharacteristic, complemented
62C2×D8—711no—
63C2×M16—1421no—
64C2×M16C2×D7111yescharacteristic
65#121—1421no—
66M32C2×D7112yes—
67#108—712no—
68#108—1421no—
69#106—711no—
70#102—1421no—
71C2×D4—2841no—
72C2×D4—1421no—
73C22×C4D28411yescharacteristic
74D8—1422no—
75M16—22no—
76M16—2841no—
77M16—1422no—
78C2×C8—2841no—
79C2×C8D28411yescharacteristic
80C2×C8C22×D7111yescharacteristic
81C4⋊C4—1421no—
82C22⋊C4—2841no—
83C16—22no—
84C23—2841no—
85C23#1176585411yescharacteristic
86D4—2841no—
87D4—2841no—
88D4—5682no—
89C2×C4—21no—
90C2×C4—21no—
91C2×C4—2841no—
92C2×C4#1176585411yescharacteristic
93C2×C4C2×D28411yescharacteristic
94C8—21no—
95C8—2842no—
96C8#1176586412yes—
97C22—21no—
98C22—41no—
99C22—5681no—
100C22—5681no—
101C22—5681no—
102C22C2×#1176585411yescharacteristic
103C4—21no—
104C4—5681no—
105C4#1455611211yescharacteristic
106C4#1455615611yescharacteristic
107C2—21no—
108C2—41no—
109C2—11361no—
110C2#1798631811yescharacteristic
subgroupG/H
centerC2#17986318
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#349×C71C2
socleC2×C71#481
hypercenter#349D71
hypocenterC71#2238
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #17986048C2semidirect
3. #17985822C2semidirect
4. #17985813C2semidirect
5. #349×C71C2semidirect
56. C71#2238semidirect
61. #349D71semidirect