Finite Group Databasebeta

← #22586366

Subgroups — #22586366

Order 9088.

116 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 35 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#17985938C211yesmaximal, characteristic
2#17985725C211yesmaximal, characteristic
3#343×C71C211yesmaximal, characteristic
4C2×C4⋊Dic71C411yescharacteristic
5C22⋊(C71⋊C8)—21no—
6C71⋊#95—21no—
7C71⋊#95—21no—
8C71⋊#95C411yescharacteristic
9C2×M16×C71—21no—
10C2×C4⋊C4×C71C2211yescharacteristic
11C22×Dic71—21no—
12C22×Dic71—21no—
13C2×C71⋊C8—41no—
14C4⋊Dic71—41no—
15C22×C4×C71C2×C411yescharacteristic
16C22×C4×C71D411yescharacteristic
17C22×C4×C71D411yescharacteristic
18M16×C71—22no—
19M16×C71—41no—
20C2×C8×C71—41no—
21C4⋊C4×C71—41no—
22C23×C71C22⋊C411yescharacteristic
23C2×C4×C71—21no—
24C2×C4×C71—21no—
25C2×C4×C71—21no—
26C2×C4×C71—21no—
27C2×C4×C71—41no—
28C2×C4×C71—41no—
29C2×C4×C71SD1611yescharacteristic
30C2×C4×C71Q1611yescharacteristic
31C2×Dic71—41no—
32C2×Dic71—41no—
33C2×Dic71—42no—
34C2×Dic71—41no—
35C2×Dic71—41no—
36C8×C71—42no—
37C71⋊C8—81no—
38C22×C71—21no—
39C22×C71—21no—
40C22×C71#9911yescharacteristic
41C22×C71#10311yescharacteristic
42C22×C71#10411yescharacteristic
43C4×C71—21no—
44C4×C71—21no—
45C4×C71—41no—
46C4×C71—41no—
47Dic71—81no—
48Dic71—81no—
49C2×C71—21no—
50C2×C71—21no—
51C2×C71#32811yescharacteristic
52C2×C71#35211yescharacteristic
53C2×C71#35511yescharacteristic
54#1353—711nomaximal, Sylow
55C71#135311yescharacteristic, complemented, Sylow
56#400—711no—
57#343D7111yescharacteristic
58#324—711no—
59C2×M16—21no—
60C2×C4⋊C4—711no—
61C2×C4⋊C4C2×D7111yescharacteristic
62C22⋊C8—1421no—
63#95—711no—
64#95—1421no—
65#95—1421no—
66C22×C4—1421no—
67C22×C4—1421no—
68C22×C4C4×D7111yescharacteristic
69C22×C4D28411yescharacteristic
70C22×C4C22⋊D7111yescharacteristic
71M16—22no—
72M16—41no—
73C2×C8—41no—
74C2×C8—2841no—
75C4⋊C4—41no—
76C4⋊C4—2841no—
77C23(C2×D71)⋊C411yescharacteristic
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—2841no—
85C2×C4—2841no—
86C2×C4—2842no—
87C2×C4—2841no—
88C2×C4—2841no—
89C2×C4#1176585311yescharacteristic
90C2×C4#1176585511yescharacteristic
91C8—42no—
92C8—5681no—
93C22—21no—
94C22—21no—
95C22#1455604211yescharacteristic
96C22#1455605111yescharacteristic
97C22#1455605611yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—5681no—
103C4—5681no—
104C2—21no—
105C2—21no—
106C2#1798573511yescharacteristic
107C2#1798579011yescharacteristic
108C2#1798579511yescharacteristic
subgroupG/H
centerC22#14556042
commutatorC22×C4×C71C2×C4
FrattiniC2×C4⋊C4C2×D71
Fitting#343×C71C2
socleC22×C71#99
hypercenter#343D71
hypocenterC71#1353
LCSG ▷ C22×C4×C71 ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
55. C71#1353semidirect