Finite Group Databasebeta

← #22590129

Subgroups — #22590129

Order 9088.

156 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 85 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
1C2×#14556068C211yesmaximal, characteristic
2C2×#14556062C211yesmaximal, characteristic
3#17985826C212yesmaximal, complemented
4#17985824C212yesmaximal, complemented
5#427×C71C211yesmaximal, characteristic
6C2×C4⋊Dic71—21no—
7#14556068C414yescomplemented
8C2×C71⋊C16C2212yes—
9#14556062—21no—
10#14556062C2212yes—
11C22×C8×C71C2211yescharacteristic
12#117×C71—21no—
13#107×C71C2211yescharacteristic
14#107×C71C2211yescharacteristic
15#106×C71—21no—
16C22×Dic71—41no—
17C4⋊Dic71—22no—
18C4⋊Dic71—41no—
19C71⋊C16C2×C414yescomplemented
20C22×C4×C71D411yescharacteristic
21C2×C8×C71C2×C412yes—
22C2×C8×C71D411yescharacteristic
23C2×C8×C71Q812yes—
24C2×C8×C71C2311yescharacteristic
25C4⋊C4×C71—21no—
26C4⋊C4×C71—21no—
27C22⋊C4×C71—41no—
28C42×C71—41no—
29C23×C71D811yescharacteristic
30C2×C4×C71—41no—
31C2×C4×C71—41no—
32C2×C4×C71C4⋊C412yes—
33C2×C4×C71D811yescharacteristic
34C2×C4×C71Q1612yes—
35C2×C4×C71C2×D411yescharacteristic
36C2×Dic71—42no—
37C2×Dic71—82no—
38C8×C71C4⋊C412yes—
39C8×C71C22×C411yescharacteristic
40C8×C71C2×Q811yescharacteristic
41C22×C71—21no—
42C22×C71—21no—
43C22×C71#10712yes—
44C22×C71C2×D811yescharacteristic
45C4×C71—81no—
46C4×C71—81no—
47C4×C71#10712yes—
48C4×C71C2×C4⋊C411yescharacteristic
49C4×C71C2×Q1611yescharacteristic
50Dic71—82no—
51C2×C71—22no—
52C2×C71C2×#10711yescharacteristic
53C2×C71#50911yescharacteristic
54C2×C71#51011yescharacteristic
55#2159—711nomaximal, Sylow
56C71#215911yescharacteristic, complemented, Sylow
57C2×M32—711no—
58#427D7111yescharacteristic
59C2×#107—711no—
60#367—712no—
61#366—712no—
62C22×C8C2×D7111yescharacteristic
63#117—21no—
64C2×C4⋊C4—1421no—
65M32—714no—
66C2×C16—712no—
67#107—712no—
68#107—1421no—
69#107C2×D7111yescharacteristic
70#107C2×D7111yescharacteristic
71#106—21no—
72C22×C4—2841no—
73C22×C4C22⋊D7111yescharacteristic
74C2×C8Dic14212yes—
75C2×C8C4×D7112yes—
76C2×C8C22⋊D7111yescharacteristic
77C2×C8C22×D7111yescharacteristic
78C4⋊C4—21no—
79C4⋊C4—21no—
80C4⋊C4—2841no—
81C4⋊C4—1422no—
82C22⋊C4—41no—
83C42—41no—
84C16—714no—
85C23#1176585011yescharacteristic
86C2×C4—41no—
87C2×C4—41no—
88C2×C4—2842no—
89C2×C4—5682no—
90C2×C4Dic71⋊C412yes—
91C2×C4#1176585011yescharacteristic
92C2×C4#1176585512yes—
93C2×C4C2×C22⋊D7111yescharacteristic
94C8Dic71⋊C412yes—
95C8C2×C4×D7111yescharacteristic
96C8C2×Dic14211yescharacteristic
97C22—21no—
98C22—21no—
99C22#1455606112yes—
100C22C2×#1176585011yescharacteristic
101C4—81no—
102C4—81no—
103C4—5682no—
104C4#1455606112yes—
105C4C2×Dic71⋊C411yescharacteristic
106C4C2×#1176585511yescharacteristic
107C2—22no—
108C2C2×#1455606111yescharacteristic
109C2#1798643411yescharacteristic
110C2#1798643911yescharacteristic
subgroupG/H
centerC22C2×#11765850
commutatorC8×C71C22×C4
FrattiniC2×C8C22×D71
Fitting#427×C71C2
socleC22×C71C2×D8
hypercenter#427D71
hypocenterC71#2159
LCSG ▷ C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #427

Complements

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

NH ≅ G/Ntype
3. #17985826C2semidirect
4. #17985824C2semidirect
7. #14556068C4semidirect
19. C71⋊C16C2×C4semidirect
56. C71#2159semidirect