Finite Group Databasebeta

← #22562374

Subgroups — #22562374

Order 8576.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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#16863798C211yesmaximal, characteristic
2C4×Dic268C211yesmaximal, characteristic
3#16863224C211yesmaximal, characteristic
4#16863222C211yesmaximal, characteristic
5#16863201C211yesmaximal, characteristic
6#16863201C211yesmaximal, characteristic
7C4⋊C16×C67C211yesmaximal, characteristic
8C2×Dic268C2211yescharacteristic
9#14524035—21no—
10C4×Dic134—21no—
11#14523977C2211yescharacteristic
12#14523977C2211yescharacteristic
13#14523977C2211yescharacteristic
14#14523975—21no—
15#14523968—21no—
16C2×C16×C67C2211yescharacteristic
17C2×C16×C67C2211yescharacteristic
18C4×C8×C67C2211yescharacteristic
19C2×Dic134—21no—
20Dic268—21no—
21Dic268Q812yes—
22C4⋊Dic67—21no—
23C4⋊Dic67—21no—
24C4⋊Dic67—21no—
25Dic67⋊C4—41no—
26Dic67⋊C4—41no—
27Dic67⋊C4—41no—
28C4×Dic67—41no—
29C2×C8×C67D411yescharacteristic
30C2×C8×C67C2311yescharacteristic
31C42×C67D411yescharacteristic
32C16×C67—21no—
33C16×C67—21no—
34C2×C4×C67D811yescharacteristic
35C2×C4×C67D811yescharacteristic
36C2×C4×C67C2×D411yescharacteristic
37C2×Dic67—41no—
38C2×Dic67—41no—
39C2×Dic67—41no—
40C2×Dic67—41no—
41Dic134—22no—
42Dic134—41no—
43C8×C67—21no—
44C8×C67C2×Q811yescharacteristic
45C8×C67#4111yescharacteristic
46C22×C67C2×D811yescharacteristic
47C4×C67—21no—
48C4×C67—21no—
49C4×C67C22⋊Q811yescharacteristic
50C4×C67#13711yescharacteristic
51Dic67—42no—
52Dic67—81no—
53Dic67—81no—
54Dic67—81no—
55C2×C67#47411yescharacteristic
56C2×C67#50811yescharacteristic
57C2×C67#51011yescharacteristic
58#2229—671nomaximal, Sylow
59C67#222911yescharacteristic, complemented, Sylow
60#499—671no—
61C4×Q16—671no—
62#367—671no—
63#366—671no—
64C4⋊C16D6711yescharacteristic
65#358—671no—
66#358—671no—
67C2×Q16—671no—
68#125—1341no—
69C4×Q8—1341no—
70C2×C16C2×D6711yescharacteristic
71C2×C16C2×D6711yescharacteristic
72#107—671no—
73#107—671no—
74#107—671no—
75#106—1341no—
76#103—1341no—
77C4×C8C2×D6711yescharacteristic
78C2×Q8—1341no—
79Q16—672no—
80Q16—1341no—
81C2×C8D26811yescharacteristic
82C2×C8C22×D6711yescharacteristic
83C4⋊C4—2681no—
84C4⋊C4—2681no—
85C4⋊C4—2681no—
86C4⋊C4—1341no—
87C4⋊C4—1341no—
88C4⋊C4—1341no—
89C42—2681no—
90C42D26811yescharacteristic
91C16—21no—
92C16—21no—
93Q8—2681no—
94Q8—1342no—
95C2×C4—2681no—
96C2×C4—2681no—
97C2×C4—2681no—
98C2×C4—2681no—
99C2×C4D53611yescharacteristic
100C2×C4D53611yescharacteristic
101C2×C4C2×D26811yescharacteristic
102C8—21no—
103C8Q8×D6711yescharacteristic
104C8#1176162711yescharacteristic
105C22C2×D53611yescharacteristic
106C4—21no—
107C4—21no—
108C4—2682no—
109C4—5361no—
110C4—5361no—
111C4—5361no—
112C4#1452402311yescharacteristic
113C4#1452407611yescharacteristic
114C2#1686367711yescharacteristic
115C2#1686382811yescharacteristic
116C2#1686383911yescharacteristic
subgroupG/H
centerC22C2×D536
commutatorC2×C8×C67C23
FrattiniC2×C8C22×D67
FittingC4⋊C16×C67C2
socleC22×C67C2×D8
hypercenterC4⋊C16D67
hypocenterC67#2229
LCSG ▷ C2×C8×C67 ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4⋊C16

Complements

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

NH ≅ G/Ntype
59. C67#2229semidirect