Finite Group Databasebeta

← #22587130

Subgroups — #22587130

Order 9088.

158 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 67 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#17986051C211yesmaximal, characteristic
2#17986050C211yesmaximal, characteristic
3#17986021C211yesmaximal, characteristic
4#17985751C211yesmaximal, characteristic, complemented
5#17985750C211yesmaximal, characteristic, complemented
6#17985749C211yesmaximal, characteristic, complemented
7#335×C71C211yesmaximal, characteristic, complemented
8C2×#11765848—21no—
9C42×D71C2211yescharacteristic
10C4⋊(C71⋊C8)C2211yescharacteristic
11C4⋊(C71⋊C8)C2211yescharacteristic
12Dic71⋊C8—21no—
13Dic71⋊C8C411yescharacteristic
14Dic71⋊C8C411yescharacteristic
15(C2×D71)⋊C8—21no—
16(C2×D71)⋊C8C411yescharacteristic
17(C2×D71)⋊C8C411yescharacteristic
18C4×C71⋊C8C2211yescharacteristic
19C8×Dic71—21no—
20C4⋊C8×C71C2211yescharacteristic
21C4⋊C8×C71C2211yescharacteristic
22C4×C8×C71C2211yescharacteristic
23C2×C4×D71C2×C411yescharacteristic
24C2×C4×D71D411yescharacteristic
25C2×C4×D71Q811yescharacteristic
26#11765848—42no—
27C2×C71⋊C8—21no—
28C2×C71⋊C8—21no—
29C2×C71⋊C8C2×C411yescharacteristic
30C2×C71⋊C8C2×C411yescharacteristic
31C4×Dic71C2×C411yescharacteristic
32C4×Dic71D411yescharacteristic
33C4×Dic71Q811yescharacteristic
34C2×C8×C71—21no—
35C2×C8×C71—21no—
36C2×C8×C71C2×C411yescharacteristic
37C2×C8×C71C2×C411yescharacteristic
38C42×C71C2311yescharacteristic
39C22×D71C4⋊C411yescharacteristic
40C2×C4×C71C22×C411yescharacteristic
41C2×C4×C71C2×D411yescharacteristic
42C2×C4×C71C2×Q811yescharacteristic
43C2×Dic71C4⋊C411yescharacteristic
44C2×Dic71C4⋊C411yescharacteristic
45C2×Dic71C4⋊C411yescharacteristic
46C4×D71—21no—
47C4×D71—21no—
48C4×D71—21no—
49C4×D71—21no—
50C4×D71—22no—
51C8×C71—21no—
52C8×C71—21no—
53C8×C71—41no—
54C8×C71—41no—
55C71⋊C8—21no—
56C71⋊C8—21no—
57C71⋊C8—41no—
58C71⋊C8—41no—
59C22×C71C2×C4⋊C411yescharacteristic
60C2×D71—21no—
61C2×D71—21no—
62C2×D71—21no—
63C4×C71—21no—
64C4×C71#13111yescharacteristic
65C4×C71#13111yescharacteristic
66C4×C71AGL(1,ℤ/8)11yescharacteristic
67C4×C71#13711yescharacteristic
68Dic71—21no—
69Dic71—21no—
70Dic71#10812yes—
71C2×C71#42411yescharacteristic
72C2×C71#42811yescharacteristic
73C2×C71C2×#10811yescharacteristic
74D71—41no—
75#1574—711nomaximal, Sylow
76C71#157411yescharacteristic, complemented, Sylow
77#431—711no—
78#431—711no—
79#423—711no—
80#335—711no—
81#335D7111yescharacteristic, complemented
82#334—711no—
83#334—711no—
84C2×M16—1421no—
85C2×C42—711no—
86C4⋊C8—711no—
87C4⋊C8—711no—
88C4⋊C8—711no—
89C4⋊C8—711no—
90C4⋊C8—1421no—
91C4⋊C8C2×D7111yescharacteristic
92C4⋊C8C2×D7111yescharacteristic
93C22⋊C8—711no—
94C22⋊C8—711no—
95C22⋊C8—1421no—
96C4×C8—711no—
97C4×C8—1421no—
98C4×C8C2×D7111yescharacteristic
99C22×C4—711no—
100C22×C4—711no—
101C22×C4—711no—
102M16—2842no—
103C2×C8—21no—
104C2×C8—21no—
105C2×C8—711no—
106C2×C8—711no—
107C2×C8—1421no—
108C2×C8—1421no—
109C2×C8C4×D7111yescharacteristic
110C2×C8C4×D7111yescharacteristic
111C42—711no—
112C42—711no—
113C42—711no—
114C42C22×D7111yescharacteristic
115C23—711no—
116C2×C4—711no—
117C2×C4—711no—
118C2×C4—711no—
119C2×C4—1422no—
120C2×C4—1421no—
121C2×C4—1421no—
122C2×C4—1421no—
123C2×C4—1421no—
124C2×C4C2×C4×D7111yescharacteristic
125C2×C4D4×D7111yescharacteristic
126C2×C4Q8×D7111yescharacteristic
127C8—21no—
128C8—21no—
129C8—41no—
130C8—41no—
131C8—2841no—
132C8—2841no—
133C8—1421no—
134C8—1421no—
135C22—1421no—
136C22—1421no—
137C22—1421no—
138C22C4⋊C4×D7111yescharacteristic
139C4—21no—
140C4—712no—
141C4—1421no—
142C4—1421no—
143C4#1455613411yescharacteristic
144C4#1455613611yescharacteristic
145C4#1455615211yescharacteristic
146C4#1455616011yescharacteristic
147C2—2841no—
148C2#1798602411yescharacteristic
149C2#1798604011yescharacteristic
150C2#108×D7111yescharacteristic
subgroupG/H
centerC2×C4D4×D71
commutatorC2×C4×C71C22×C4
FrattiniC42C22×D71
Fitting#335×C71C2
socleC22×C71C2×C4⋊C4
hypercenter#335D71
hypocenterC71#1574
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C42 ◁ #335

Complements

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

NH ≅ G/Ntype
4. #17985751C2semidirect
5. #17985750C2semidirect
6. #17985749C2semidirect
7. #335×C71C2semidirect
76. C71#1574semidirect
81. #335D71semidirect