Finite Group Databasebeta

← #21444529

Subgroups — #21444529

Order 7808.

198 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 81 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#16839819C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic
3#16839511C212yesmaximal, complemented
4#16839508C212yesmaximal, complemented
5C61×#533C211yesmaximal, characteristic
6C4⋊#92418C2212yes—
7C4⋊#92418C2212yes—
8C22⋊#92418—21no—
9C22⋊#92418—21no—
10#14519688—21no—
11C4×#92418—21no—
12C4⋊Q8×C61C2211yescharacteristic
13C4⋊Q8×C61C2211yescharacteristic
14#125×C61—21no—
15C22⋊Q8×C61—21no—
16C22⋊Q8×C61C412yes—
17C4×Q8×C61—21no—
18C4×Q8×C61C412yes—
19#117×C61—21no—
20C2×C42×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×Q8×C61C2×C412yes—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C4⋊C4×C61—22no—
27C4⋊C4×C61—22no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—21no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61C2×C412yes—
32C22⋊C4×C61—22no—
33C42×C61—22no—
34C42×C61C2×C411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61C2311yescharacteristic
38C2×#92418—22no—
39C2×#92418—22no—
40C23×C61C22⋊C411yescharacteristic
41Q8×C61—42no—
42Q8×C61—42no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—22no—
46C2×C4×C61—22no—
47C2×C4×C61—41no—
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54#92418—42no—
55#92418—42no—
56C22×C61—21no—
57C22×C61—21no—
58C22×C61—21no—
59C22×C61C2×C22⋊C411yescharacteristic
60C4×C61—21no—
61C4×C61—21no—
62C4×C61—21no—
63C4×C61—21no—
64C4×C61—42no—
65C4×C61—42no—
66C4×C61#13512yes—
67C4×C61#13712yes—
68#1554—611nomaximal, Sylow
69C2×C61—41no—
70C2×C61#41311yescharacteristic
71C2×C61#41611yescharacteristic
72C2×C61#41911yescharacteristic
73#533D6111yescharacteristic
74#432—611no—
75#431—611no—
76#333—612no—
77#332—612no—
78C61#155411yescharacteristic, complemented, Sylow
79C4⋊Q8C2×D6111yescharacteristic
80C4⋊Q8C2×D6111yescharacteristic
81#125—21no—
82C22⋊Q8—21no—
83C22⋊Q8Dic6112yes—
84C4×Q8—21no—
85C4×Q8Dic6112yes—
86#117—21no—
87C2×C42C2×D6111yescharacteristic
88C4⋊C8—612no—
89C4⋊C8—612no—
90C22⋊C8—1221no—
91C22⋊C8—1221no—
92#97—1221no—
93C4×C8—1221no—
94C2×Q8—21no—
95C2×Q8C2×Dic6112yes—
96C22×C4C2×Dic6111yescharacteristic
97C22×C4C22⋊D6111yescharacteristic
98C22×C4C22⋊D6111yescharacteristic
99C2×C8—1222no—
100C2×C8—1222no—
101C4⋊C4—22no—
102C4⋊C4—22no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4C2×Dic6112yes—
107C22⋊C4—22no—
108C42—22no—
109C42C2×Dic6111yescharacteristic
110C42C22⋊D6111yescharacteristic
111C42C22⋊D6111yescharacteristic
112C42C22×D6111yescharacteristic
113C23C22⋊Dic6111yescharacteristic
114Q8—42no—
115Q8—42no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—41no—
121C2×C4C22⋊Dic6111yescharacteristic
122C2×C4C22⋊Dic6111yescharacteristic
123C2×C4C22⋊Dic6111yescharacteristic
124C2×C4C22×Dic6111yescharacteristic
125C2×C4C2×C22⋊D6111yescharacteristic
126C2×C4C2×C22⋊D6111yescharacteristic
127C8—2442no—
128C8—2442no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22C2×C22⋊Dic6111yescharacteristic
133C4—21no—
134C4—21no—
135C4—21no—
136C4—21no—
137C4—42no—
138C4—42no—
139C4#1451979712yes—
140C4#1451980812yes—
141C2—41no—
142C2#1683974611yescharacteristic
143C2#1683975811yescharacteristic
144C2#1683977111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#533C2
socleC22×C61C2×C22⋊C4
hypercenter#533D61
hypocenterC61#1554
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
3. #16839511C2semidirect
4. #16839508C2semidirect
78. C61#1554semidirect