Finite Group Databasebeta

← #22586283

Subgroups — #22586283

Order 9088.

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

normal subgroups only

This group has 118 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#17985864C211yesmaximal, characteristic
2#17985725C211yesmaximal, characteristic
3#324×C71C211yesmaximal, characteristic
4C2×C4⋊Dic71C411yescharacteristic
5C2×C4×Dic71C411yescharacteristic
6C22⋊(C71⋊C8)—21no—
7C71⋊#95—21no—
8C71⋊#95—21no—
9C2×C4⋊C4×C71C2211yescharacteristic
10C22⋊C8×C71—21no—
11C22×Dic71—21no—
12C22×Dic71—21no—
13C2×C71⋊C8—41no—
14C4⋊Dic71—41no—
15C4×Dic71—21no—
16C4×Dic71C812yescomplemented
17C22×C4×C71C2×C411yescharacteristic
18C22×C4×C71D411yescharacteristic
19C22×C4×C71D411yescharacteristic
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×C71C2×C811yescharacteristic
30C2×C4×C71M1611yescharacteristic
31C2×Dic71—22no—
32C2×Dic71—41no—
33C2×Dic71—41no—
34C2×Dic71—42no—
35C2×Dic71—41no—
36C8×C71—81no—
37C71⋊C8—81no—
38C22×C71—21no—
39C22×C71—21no—
40C22×C71C22⋊C811yescharacteristic
41C22×C71#9911yescharacteristic
42C22×C71#10111yescharacteristic
43C4×C71—21no—
44C4×C71—21no—
45C4×C71—41no—
46C4×C71—41no—
47Dic71—42no—
48Dic71—81no—
49C2×C71—21no—
50C2×C71—21no—
51C2×C71#32411yescharacteristic
52C2×C71#35411yescharacteristic
53C2×C71#35511yescharacteristic
54#1324—711nomaximal, Sylow
55C71#132411yescharacteristic, complemented, Sylow
56#382—711no—
57#324—711no—
58#324D7111yescharacteristic
59C2×C4⋊C4—711no—
60C2×C4⋊C4C2×D7111yescharacteristic
61C2×C42—711no—
62C22⋊C8—21no—
63C22⋊C8—1421no—
64#95—1421no—
65#95—1421no—
66C22×C4—1421no—
67C22×C4—1421no—
68C22×C4C4×D7111yescharacteristic
69C22×C4D28411yescharacteristic
70C22×C4C22⋊D7111yescharacteristic
71C2×C8—41no—
72C2×C8—2841no—
73C4⋊C4—41no—
74C4⋊C4—2841no—
75C42—712no—
76C42—1421no—
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—1422no—
89C2×C4C8×D7111yescharacteristic
90C2×C4#1176584811yescharacteristic
91C8—81no—
92C8—5681no—
93C22—21no—
94C22—21no—
95C22(C2×D71)⋊C811yescharacteristic
96C22#1455604211yescharacteristic
97C22#1455604611yescharacteristic
98C4—21no—
99C4—21no—
100C4—41no—
101C4—41no—
102C4—2842no—
103C4—5681no—
104C2—21no—
105C2—21no—
106C2#1798572411yescharacteristic
107C2#1798579311yescharacteristic
108C2#1798579511yescharacteristic
subgroupG/H
centerC22#14556042
commutatorC2×C4×C71C2×C8
FrattiniC2×C4⋊C4C2×D71
Fitting#324×C71C2
socleC22×C71#99
hypercenter#324D71
hypocenterC71#1324
LCSG ▷ C2×C4×C71 ▷ C22×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
16. C4×Dic71C8semidirect
55. C71#1324semidirect