Finite Group Databasebeta

← #21444517

Subgroups — #21444517

Order 7808.

208 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 77 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#16840319C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic
3#16839509C212yesmaximal, complemented
4#16839507C212yesmaximal, complemented
5C2×C4⋊C8×C61C211yesmaximal, characteristic
6#14519777C2211yescharacteristic
7#14519777C2211yescharacteristic
8#14519769C412yes—
9#14519756—21no—
10#14519756—21no—
11C4×Dic122—21no—
12C4×Dic122—21no—
13#14519736C412yes—
14C4⋊#92418C2212yes—
15C22⋊#92418—21no—
16#14519688—21no—
17C22×C8×C61—21no—
18C2×C42×C61C2211yescharacteristic
19C4⋊C8×C61—21no—
20C4⋊C8×C61C2212yes—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×Dic122—21no—
25C2×Dic122—21no—
26C2×C8×C61—22no—
27C2×C8×C61—42no—
28C42×C61C2×C411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61D411yescharacteristic
31C42×C61C2311yescharacteristic
32C22⋊Dic61—22no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61C2×C412yes—
36C4⋊Dic61C2×C412yes—
37#11758196—22no—
38#11758196—22no—
39C4×Dic61—22no—
40C2×#92418—22no—
41C23×C61C22⋊C411yescharacteristic
42C2×C4×C61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×Dic61—22no—
53C2×Dic61—22no—
54Dic122—42no—
55Dic122—41no—
56Dic122—41no—
57C8×C61—42no—
58#92418—42no—
59C22×C61—21no—
60C22×C61—21no—
61C22×C61#10112yes—
62C22×C61C2×C22⋊C411yescharacteristic
63C4×C61—21no—
64C4×C61—21no—
65C4×C61—21no—
66C4×C61—21no—
67C4×C61#13512yes—
68C4×C61AGL(1,ℤ/8)11yescharacteristic
69C4×C61#13711yescharacteristic
70Dic61—42no—
71Dic61—42no—
72#1552—611nomaximal, Sylow
73C2×C61—22no—
74C2×C61C2×#10111yescharacteristic
75C2×C61#41611yescharacteristic
76C2×C61#41711yescharacteristic
77#533—611no—
78#432—611no—
79C2×C4⋊C8D6111yescharacteristic
80#332—612no—
81#332—612no—
82C61#155211yescharacteristic, complemented, Sylow
83C22×C8—21no—
84C4⋊Q8—611no—
85C4⋊Q8—611no—
86#125—612no—
87C22⋊Q8—1221no—
88C22⋊Q8—1221no—
89C4×Q8—1221no—
90C4×Q8—1221no—
91#117—612no—
92C2×C42C2×D6111yescharacteristic
93C4⋊C8—21no—
94C4⋊C8—612no—
95C4⋊C8C2×D6112yes—
96C22⋊C8—1221no—
97#97—1221no—
98C2×Q8—1221no—
99C2×Q8—1221no—
100C22×C4C4×D6111yescharacteristic
101C22×C4D24411yescharacteristic
102C22×C4C22⋊D6111yescharacteristic
103C2×C8—22no—
104C2×C8—42no—
105C2×C8—1222no—
106C4⋊C4—612no—
107C4⋊C4—612no—
108C4⋊C4—1222no—
109C4⋊C4—1222no—
110C4⋊C4—1221no—
111C4⋊C4—1221no—
112C22⋊C4—1222no—
113C42—1222no—
114C42C4×D6111yescharacteristic
115C42D24411yescharacteristic
116C42C22⋊D6111yescharacteristic
117C42C22×D6111yescharacteristic
118C23#1175819811yescharacteristic
119Q8—2441no—
120Q8—2442no—
121Q8—2441no—
122C2×C4—22no—
123C2×C4—21no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—1222no—
127C2×C4—1222no—
128C2×C4#1175819811yescharacteristic
129C2×C4#1175819811yescharacteristic
130C2×C4#1175819811yescharacteristic
131C2×C4C2×C4×D6111yescharacteristic
132C2×C4C2×D24411yescharacteristic
133C2×C4C2×C22⋊D6111yescharacteristic
134C8—42no—
135C8—2442no—
136C22—21no—
137C22—21no—
138C22#1451969512yes—
139C22C2×#1175819811yescharacteristic
140C4—21no—
141C4—21no—
142C4—21no—
143C4—21no—
144C4—2442no—
145C4—2442no—
146C4#1451979912yes—
147C4#1451980311yescharacteristic
148C4#1451980811yescharacteristic
149C2—22no—
150C2C2×#1451969511yescharacteristic
151C2#1683975911yescharacteristic
152C2#1683976111yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4⋊C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C8D61
hypocenterC61#1552
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #16839509C2semidirect
4. #16839507C2semidirect
82. C61#1552semidirect