Finite Group Databasebeta

← #22586370

Subgroups — #22586370

Order 9088.

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

normal subgroups only

This group has 140 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#395×C71C211yesmaximal, characteristic
4C2×#11765849—21no—
5C22⋊(C71⋊C8)—21no—
6C22×Q8×C71C411yescharacteristic
7C2×C4⋊C4×C71—21no—
8C2×C4⋊C4×C71C2211yescharacteristic
9#95×C71—21no—
10#95×C71C411yescharacteristic
11#11765849—22no—
12#11765849—41no—
13C2×C71⋊C8—41no—
14C2×C71⋊C8—41no—
15C2×Q8×C71—42no—
16C2×Q8×C71—41no—
17C22×C4×C71—21no—
18C22×C4×C71—21no—
19C22×C4×C71C2×C411yescharacteristic
20C22×C4×C71D411yescharacteristic
21C22×C4×C71D411yescharacteristic
22C4⋊C4×C71—41no—
23C4⋊C4×C71—42no—
24C23×C71C22⋊C411yescharacteristic
25Q8×C71—42no—
26Q8×C71—42no—
27C2×C4×C71—21no—
28C2×C4×C71—21no—
29C2×C4×C71—22no—
30C2×C4×C71—22no—
31C2×C4×C71—21no—
32C2×C4×C71—21no—
33C2×C4×C71—41no—
34C2×C4×C71—41no—
35C2×C4×C71—41no—
36C2×C4×C71—41no—
37C2×C4×C71—41no—
38C2×C4×C71—41no—
39C2×C4×C71SD1611yescharacteristic
40C2×C4×C71Q1611yescharacteristic
41C71⋊C8—42no—
42C71⋊C8—81no—
43C22×C71—21no—
44C22×C71—21no—
45C22×C71#9911yescharacteristic
46C22×C71#10311yescharacteristic
47C22×C71#10411yescharacteristic
48C4×C71—21no—
49C4×C71—21no—
50C4×C71—42no—
51C4×C71—41no—
52C4×C71—42no—
53C4×C71—41no—
54C2×C71—21no—
55C2×C71—21no—
56C2×C71#32811yescharacteristic
57C2×C71AΣL(1,𝔽16)11yescharacteristic
58C2×C71#35611yescharacteristic
59#1354—711nomaximal, Sylow
60C71#135411yescharacteristic, complemented, Sylow
61#395D7111yescharacteristic
62#343—711no—
63#324—711no—
64C22×Q8Dic7111yescharacteristic
65C2×M16—1421no—
66C2×C4⋊C4—21no—
67C2×C4⋊C4C2×D7111yescharacteristic
68C22⋊C8—1421no—
69#95—21no—
70#95Dic7111yescharacteristic
71C2×Q8—42no—
72C2×Q8—41no—
73C22×C4—21no—
74C22×C4—21no—
75C22×C4C2×Dic7111yescharacteristic
76C22×C4C22⋊D7111yescharacteristic
77C22×C4C22⋊D7111yescharacteristic
78M16—2841no—
79M16—1422no—
80C2×C8—2841no—
81C2×C8—2841no—
82C4⋊C4—41no—
83C4⋊C4—42no—
84C23C22⋊Dic7111yescharacteristic
85Q8—42no—
86Q8—42no—
87C2×C4—21no—
88C2×C4—21no—
89C2×C4—22no—
90C2×C4—22no—
91C2×C4—21no—
92C2×C4—21no—
93C2×C4—41no—
94C2×C4—41no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—41no—
98C2×C4—41no—
99C2×C4#1176585211yescharacteristic
100C2×C4#1176585511yescharacteristic
101C8—2842no—
102C8—5681no—
103C22—21no—
104C22—21no—
105C22#1455604311yescharacteristic
106C22#1455605211yescharacteristic
107C22#1455605511yescharacteristic
108C4—21no—
109C4—21no—
110C4—42no—
111C4—41no—
112C4—42no—
113C4—41no—
114C2—21no—
115C2—21no—
116C2#1798573611yescharacteristic
117C2#1798578611yescharacteristic
118C2#1798579811yescharacteristic
subgroupG/H
centerC22#14556043
commutatorC22×C4×C71C2×C4
FrattiniC2×C4⋊C4C2×D71
Fitting#395×C71C2
socleC22×C71#99
hypercenter#395D71
hypocenterC71#1354
LCSG ▷ C22×C4×C71 ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #395

Complements

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

NH ≅ G/Ntype
60. C71#1354semidirect