Finite Group Databasebeta

← #22559082

Subgroups — #22559082

Order 8576.

152 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 63 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#16863526C211yesmaximal, characteristic
2C8×Dic134C211yesmaximal, characteristic
3C4×Dic268C211yesmaximal, characteristic
4#16863147C211yesmaximal, characteristic
5#16863128C211yesmaximal, characteristic
6#16863128C211yesmaximal, characteristic
7#322×C67C211yesmaximal, characteristic
8C2×Dic268C411yescharacteristic
9C4×Dic134C2211yescharacteristic
10C4×Dic134C2211yescharacteristic
11#14523977C411yescharacteristic
12C4⋊(C67⋊C8)C2211yescharacteristic
13C4⋊(C67⋊C8)C2211yescharacteristic
14Dic67⋊C8—21no—
15Dic67⋊C8—21no—
16#14523968C411yescharacteristic
17#14523968C411yescharacteristic
18#14523953—21no—
19C8×Dic67—21no—
20C4×C8×C67C2211yescharacteristic
21C4×C8×C67C2211yescharacteristic
22C4×C8×C67C2211yescharacteristic
23C2×Dic134C2×C411yescharacteristic
24C2×Dic134C2×C411yescharacteristic
25Dic268—22no—
26C2×C67⋊C8—21no—
27C2×C67⋊C8—21no—
28C4⋊Dic67C2×C411yescharacteristic
29C4⋊Dic67C2×C411yescharacteristic
30Dic67⋊C4—21no—
31Dic67⋊C4—21no—
32C4×Dic67—21no—
33C4×Dic67—21no—
34C2×C8×C67—21no—
35C2×C8×C67C2×C411yescharacteristic
36C2×C8×C67C2×C411yescharacteristic
37C2×C8×C67D411yescharacteristic
38C2×C8×C67D411yescharacteristic
39C42×C67C2311yescharacteristic
40C2×C4×C67C22×C411yescharacteristic
41C2×C4×C67C2×D411yescharacteristic
42C2×C4×C67#4111yescharacteristic
43C2×Dic67—21no—
44C2×Dic67—21no—
45C2×Dic67—21no—
46C2×Dic67—21no—
47Dic134—21no—
48Dic134—21no—
49Dic134—21no—
50Dic134M1612yes—
51C8×C67—22no—
52C8×C67—21no—
53C8×C67—21no—
54C8×C67—21no—
55C8×C67—21no—
56C67⋊C8—41no—
57C67⋊C8—41no—
58C22×C67C4×D411yescharacteristic
59C4×C67—21no—
60C4×C67C2×M1611yescharacteristic
61C4×C67#13111yescharacteristic
62C4×C67#13711yescharacteristic
63C4×C67#13711yescharacteristic
64Dic67—22no—
65Dic67—41no—
66Dic67—41no—
67Dic67—41no—
68C2×C67#43511yescharacteristic
69C2×C67#44111yescharacteristic
70C2×C67#44311yescharacteristic
71#1587—671nomaximal, Sylow
72C67#158711yescharacteristic, complemented, Sylow
73#446—671no—
74C8×Q8—671no—
75C4×Q16—671no—
76#334—671no—
77Q8⋊C8—671no—
78Q8⋊C8—671no—
79#322D6711yescharacteristic
80C2×Q16—671no—
81C4×Q8—671no—
82C4×Q8—671no—
83#107—671no—
84C4⋊C8—671no—
85C4⋊C8—671no—
86C4⋊C8—1341no—
87C4⋊C8—1341no—
88#103—671no—
89#103—671no—
90#97—1341no—
91C4×C8—1341no—
92C4×C8C2×D6711yescharacteristic
93C4×C8C2×D6711yescharacteristic
94C4×C8C2×D6711yescharacteristic
95C2×Q8—671no—
96C2×Q8—671no—
97Q16—1342no—
98C2×C8—21no—
99C2×C8—1341no—
100C2×C8—1341no—
101C2×C8C4×D6711yescharacteristic
102C2×C8C4×D6711yescharacteristic
103C2×C8D26811yescharacteristic
104C2×C8D26811yescharacteristic
105C4⋊C4—671no—
106C4⋊C4—671no—
107C4⋊C4—1341no—
108C4⋊C4—1341no—
109C42—1341no—
110C42—1341no—
111C42C22×D6711yescharacteristic
112Q8—672no—
113Q8—1341no—
114Q8—1341no—
115Q8—1341no—
116C2×C4—1341no—
117C2×C4—1341no—
118C2×C4—1341no—
119C2×C4—1341no—
120C2×C4C2×C4×D6711yescharacteristic
121C2×C4C2×D26811yescharacteristic
122C2×C4#1176162811yescharacteristic
123C8—22no—
124C8—21no—
125C8—21no—
126C8—21no—
127C8—21no—
128C8—2681no—
129C8—2681no—
130C22C4×D26811yescharacteristic
131C4—21no—
132C4—2681no—
133C4—2681no—
134C4—2681no—
135C4—1342no—
136C4M16×D6711yescharacteristic
137C4#1452405111yescharacteristic
138C4#1452407611yescharacteristic
139C4#1452407611yescharacteristic
140C2#1686346911yescharacteristic
141C2#1686350411yescharacteristic
142C2#1686351411yescharacteristic
subgroupG/H
centerC2×C4C2×D268
commutatorC2×C4×C67C22×C4
FrattiniC42C22×D67
Fitting#322×C67C2
socleC22×C67C4×D4
hypercenter#322D67
hypocenterC67#1587
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
72. C67#1587semidirect