Finite Group Databasebeta

← #22586367

Subgroups — #22586367

Order 9088.

116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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#17985768C211yesmaximal, characteristic
2#17985725C211yesmaximal, characteristic
3#400×C71C211yesmaximal, characteristic
4C2×#11765849—21no—
5C22⋊(C71⋊C8)—21no—
6C2×C4⋊C4×C71C411yescharacteristic
7C2×C4⋊C4×C71C2211yescharacteristic
8#95×C71—21no—
9#95×C71—21no—
10#95×C71C411yescharacteristic
11#11765849—22no—
12#11765849—41no—
13C2×C71⋊C8—41no—
14C2×C71⋊C8—41no—
15C22×C4×C71—21no—
16C22×C4×C71—21no—
17C22×C4×C71C2×C411yescharacteristic
18C22×C4×C71D411yescharacteristic
19C22×C4×C71D411yescharacteristic
20C4⋊C4×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×C71—41no—
30C2×C4×C71—41no—
31C2×C4×C71—42no—
32C2×C4×C71—41no—
33C2×C4×C71—41no—
34C2×C4×C71SD1611yescharacteristic
35C2×C4×C71Q1611yescharacteristic
36C71⋊C8—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—
47C4×C71—81no—
48C4×C71—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#400D7111yescharacteristic
57#343—711no—
58#324—711no—
59C2×M16—1421no—
60C2×C4⋊C4Dic7111yescharacteristic
61C2×C4⋊C4C2×D7111yescharacteristic
62C22⋊C8—1421no—
63#95—21no—
64#95—21no—
65#95Dic7111yescharacteristic
66C22×C4—21no—
67C22×C4—21no—
68C22×C4C2×Dic7111yescharacteristic
69C22×C4C22⋊D7111yescharacteristic
70C22×C4C22⋊D7111yescharacteristic
71M16—2841no—
72M16—1422no—
73C2×C8—2841no—
74C2×C8—2841no—
75C4⋊C4—41no—
76C4⋊C4—41no—
77C23C22⋊Dic7111yescharacteristic
78C2×C4—21no—
79C2×C4—21no—
80C2×C4—21no—
81C2×C4—21no—
82C2×C4—41no—
83C2×C4—41no—
84C2×C4—41no—
85C2×C4—41no—
86C2×C4—42no—
87C2×C4—41no—
88C2×C4—41no—
89C2×C4#1176585211yescharacteristic
90C2×C4#1176585511yescharacteristic
91C8—2842no—
92C8—5681no—
93C22—21no—
94C22—21no—
95C22#1455604311yescharacteristic
96C22#1455605211yescharacteristic
97C22#1455605511yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—81no—
103C4—81no—
104C2—21no—
105C2—21no—
106C2#1798573611yescharacteristic
107C2#1798578911yescharacteristic
108C2#1798579611yescharacteristic
subgroupG/H
centerC22#14556043
commutatorC22×C4×C71C2×C4
FrattiniC2×C4⋊C4C2×D71
Fitting#400×C71C2
socleC22×C71#99
hypercenter#400D71
hypocenterC71#1353
LCSG ▷ C22×C4×C71 ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #400

Complements

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

NH ≅ G/Ntype
55. C71#1353semidirect