Finite Group Databasebeta

← #22598892

Subgroups — #22598892

Order 9088.

348 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 165 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#17986556C211yesmaximal, characteristic
2C2×#14556120C211yesmaximal, characteristic
3#17986408C214yesmaximal, complemented
4#17986401C214yesmaximal, complemented
5#17986041C214yesmaximal
6C4×M16×C71C211yesmaximal, characteristic
7#14556128C2212yes—
8#14556120—22no—
9#14556120C2212yes—
10#14556120C2212yes—
11#14556120C2212yes—
12#14556107—22no—
13C4×Dic142—22no—
14#14556087C2212yes—
15C2×C4⋊Dic71C2212yes—
16C2×Dic71⋊C4—22no—
17#14556062C2218yes—
18#14556060C2218yes—
19C2×M16×C71C2212yes—
20C2×C42×C71C2211yescharacteristic
21#97×C71C2212yes—
22C4×C8×C71C2212yes—
23C2×Dic142—22no—
24C22×Dic71—22no—
25C4⋊Dic71—22no—
26C4⋊Dic71—22no—
27C4⋊Dic71C2314yes—
28C4⋊Dic71C2314yes—
29Dic71⋊C4—24no—
30Dic71⋊C4—24no—
31Dic71⋊C4—24no—
32C22⋊Dic71—22no—
33C4×Dic71—22no—
34C22×C4×C71D412yes—
35C22×C4×C71C2311yescharacteristic
36M16×C71Q818yescomplemented
37C2×C8×C71C2314yes—
38C42×C71D412yes—
39C42×C71C2311yescharacteristic
40C42×C71C2311yescharacteristic
41C23×C71C2×D411yescharacteristic
42C2×C4×C71—42no—
43C2×C4×C71C2×D412yes—
44C2×C4×C71C2×D412yes—
45C2×C4×C71C2×D411yescharacteristic
46C2×C4×C71C2×Q814yes—
47C2×C4×C71C2411yescharacteristic
48C2×Dic71—24no—
49C2×Dic71—24no—
50C2×Dic71—44no—
51Dic142—44no—
52C8×C71C2×Q818yes—
53C22×C71—22no—
54C22×C71C4⋊Q812yes—
55C22×C71C22×D411yescharacteristic
56C4×C71—22no—
57C4×C71—22no—
58C4×C71C4⋊Q812yes—
59C4×C71C22×Q812yes—
60Dic71—44no—
61Dic71—44no—
62C2×C71—22no—
63C2×C71C2×C4⋊Q811yescharacteristic
64C2×C71#57512yes—
65#3166—711nomaximal, Sylow
66C71#316611yescharacteristic, complemented, Sylow
67#533—711no—
68C2×#125—711no—
69#501—714no—
70#499—714no—
71#428—714no—
72C4×M16D7111yescharacteristic
73C2×M16C2×D7112yes—
74C4⋊Q8—712no—
75#125—712no—
76#125—712no—
77#125—712no—
78#125—1422no—
79C22⋊Q8—1422no—
80C4×Q8—1422no—
81#117—712no—
82C2×C4⋊C4—712no—
83C2×C4⋊C4—1422no—
84C2×C42C2×D7111yescharacteristic
85#107—718no—
86#106—718no—
87#97C2×D7112yes—
88C4×C8C2×D7112yes—
89C2×Q8—1422no—
90C22×C4—1422no—
91C22×C4D28412yes—
92C22×C4C22×D7111yescharacteristic
93M16Dic14218yescomplemented
94C2×C8C22×D7114yes—
95C4⋊C4—714no—
96C4⋊C4—714no—
97C4⋊C4—1424no—
98C4⋊C4—1424no—
99C4⋊C4—1424no—
100C4⋊C4—1422no—
101C4⋊C4—1422no—
102C22⋊C4—1422no—
103C42—1422no—
104C42D28412yes—
105C42C22×D7111yescharacteristic
106C42C22×D7111yescharacteristic
107C23C2×D28411yescharacteristic
108Q8—2844no—
109C2×C4—42no—
110C2×C4—2844no—
111C2×C4—1424no—
112C2×C4—1424no—
113C2×C4C2×D28412yes—
114C2×C4C2×D28412yes—
115C2×C4C2×D28411yescharacteristic
116C2×C4C2×Dic14214yes—
117C2×C4C23×D7111yescharacteristic
118C8C2×Dic14218yes—
119C22—22no—
120C22#1455612812yes—
121C22C22×D28411yescharacteristic
122C4—22no—
123C4—22no—
124C4—2844no—
125C4—2844no—
126C4#1455612812yes—
127C4C22×Dic14212yes—
128C2—22no—
129C2C2×#1455612811yescharacteristic
130C2#1798679912yes—
subgroupG/H
centerC22C22×D284
commutatorC2×C4×C71C24
FrattiniC2×C4C23×D71
FittingC4×M16×C71C2
socleC22×C71C22×D4
hypercenterC4×M16D71
hypocenterC71#3166
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #17986408C2semidirect
4. #17986401C2semidirect
36. M16×C71Q8semidirect
66. C71#3166semidirect
93. M16Dic142semidirect