Finite Group Databasebeta

← #22590576

Subgroups — #22590576

Order 9088.

142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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#17986404C211yesmaximal, characteristic, complemented
2#17985803C212yesmaximal, complemented
3#17985800C212yesmaximal
4#17985775C211yesmaximal, characteristic, complemented
5#495×C71C211yesmaximal, characteristic
6#14556128—21no—
7C2×C71⋊C16C2212yes—
8#14556062—21no—
9#14556062C2212yes—
10C2×Q16×C71C2211yescharacteristic
11C2×SD16×C71—21no—
12C2×D8×C71C2211yescharacteristic
13#124×C71—21no—
14C4×C8×C71C2211yescharacteristic
15C2×Dic142—41no—
16C4⋊Dic71—22no—
17C4⋊Dic71—41no—
18C71⋊C16—22no—
19C2×Q8×C71—21no—
20C2×D4×C71—21no—
21Q16×C71—22no—
22SD16×C71—42no—
23D8×C71—22no—
24C2×C8×C71D411yescharacteristic
25C2×C8×C71C2311yescharacteristic
26C22⋊C4×C71—41no—
27C22⋊C4×C71—41no—
28C42×C71D411yescharacteristic
29C23×C71—41no—
30Q8×C71—41no—
31Q8×C71—41no—
32D4×C71—41no—
33D4×C71—41no—
34C2×C4×C71—41no—
35C2×C4×C71D811yescharacteristic
36C2×C4×C71D811yescharacteristic
37C2×C4×C71C2×D411yescharacteristic
38C2×Dic71—42no—
39Dic142—82no—
40C8×C71SD1612yes—
41C8×C71#4112yes—
42C22×C71—81no—
43C22×C71—81no—
44C22×C71—81no—
45C22×C71C2×D811yescharacteristic
46C4×C71—21no—
47C4×C71—21no—
48C4×C71—81no—
49C4×C71#12411yescharacteristic
50C4×C71C2×SD1611yescharacteristic
51Dic71—82no—
52C2×C71—161no—
53C2×C71#48611yescharacteristic
54C2×C71#50911yescharacteristic
55C2×C71#51011yescharacteristic
56#2243—711nomaximal, Sylow
57C71#224311yescharacteristic, complemented, Sylow
58#500—711no—
59#495D7111yescharacteristic
60#358—712no—
61#357—712no—
62#346—711no—
63C2×Q16C2×D7111yescharacteristic
64C2×SD16—21no—
65C2×D8C2×D7111yescharacteristic
66C4⋊Q8—1421no—
67#124—21no—
68C2×C16—712no—
69#107—712no—
70#107—1421no—
71C4×C8C2×D7111yescharacteristic
72C2×Q8—21no—
73C2×Q8—2841no—
74C2×D4—21no—
75Q16—22no—
76SD16—42no—
77D8—22no—
78C2×C8C22⋊D7111yescharacteristic
79C2×C8C22×D7111yescharacteristic
80C4⋊C4—2841no—
81C4⋊C4—1422no—
82C22⋊C4—41no—
83C22⋊C4—41no—
84C42C22⋊D7111yescharacteristic
85C16—1422no—
86C23—41no—
87Q8—41no—
88Q8—41no—
89Q8—5682no—
90D4—41no—
91D4—41no—
92C2×C4—41no—
93C2×C4—2842no—
94C2×C4#1176585011yescharacteristic
95C2×C4#1176585011yescharacteristic
96C2×C4C2×C22⋊D7111yescharacteristic
97C8#1176585312yes—
98C8#1176586412yes—
99C22—81no—
100C22—81no—
101C22—81no—
102C22C2×#1176585011yescharacteristic
103C4—21no—
104C4—21no—
105C4—81no—
106C4—5682no—
107C4#1455611511yescharacteristic
108C4C2×#1176585311yescharacteristic
109C2—161no—
110C2#1798634511yescharacteristic
111C2#1798643411yescharacteristic
112C2#1798643911yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC2×C8×C71C23
FrattiniC2×C8C22×D71
Fitting#495×C71C2
socleC22×C71C2×D8
hypercenter#495D71
hypocenterC71#2243
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #17986404C2semidirect
2. #17985803C2semidirect
4. #17985775C2semidirect
57. C71#2243semidirect