Finite Group Databasebeta

← #21444530

Subgroups — #21444530

Order 7808.

198 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839815C211yesmaximal, characteristic
3#16839510C212yesmaximal, complemented
4#16839509C212yesmaximal, complemented
5C61×#432C211yesmaximal, characteristic
6#14519777C2211yescharacteristic
7#14519777C2211yescharacteristic
8#14519769—21no—
9#14519756—21no—
10#14519756C412yes—
11C4×Dic122—21no—
12C4×Dic122C412yes—
13#14519736—21no—
14C4⋊#92418C2212yes—
15C22⋊#92418—21no—
16C4×#92418—21no—
17C2×C42×C61C2211yescharacteristic
18C4⋊C8×C61C2212yes—
19C22⋊C8×C61—21no—
20#97×C61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×Dic122—21no—
25C2×Dic122C2×C412yes—
26C2×C8×C61—22no—
27C42×C61C2×C411yescharacteristic
28C42×C61D411yescharacteristic
29C42×C61D411yescharacteristic
30C42×C61C2311yescharacteristic
31C22⋊Dic61—22no—
32C4⋊Dic61—21no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61C2×C412yes—
36#11758196—22no—
37#11758196—22no—
38C4×Dic61—22no—
39C2×#92418—22no—
40C23×C61C22⋊C411yescharacteristic
41C2×C4×C61—22no—
42C2×C4×C61—22no—
43C2×C4×C61—41no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22×C411yescharacteristic
48C2×C4×C61C2×D411yescharacteristic
49C2×C4×C61C2×D411yescharacteristic
50C2×Dic61—22no—
51C2×Dic61—22no—
52Dic122—42no—
53Dic122—42no—
54C8×C61—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#13512yes—
65C4×C61#13712yes—
66Dic61—42no—
67Dic61—42no—
68#1554—611nomaximal, Sylow
69C2×C61—41no—
70C2×C61#41311yescharacteristic
71C2×C61#41611yescharacteristic
72C2×C61#41911yescharacteristic
73#533—611no—
74#432D6111yescharacteristic
75#431—611no—
76#333—612no—
77#332—612no—
78C61#155411yescharacteristic, complemented, Sylow
79C4⋊Q8—611no—
80C4⋊Q8—611no—
81#125—1221no—
82C22⋊Q8—612no—
83C22⋊Q8—1221no—
84C4×Q8—612no—
85C4×Q8—1221no—
86#117—1221no—
87C2×C42C2×D6111yescharacteristic
88C4⋊C8—612no—
89C4⋊C8C2×D6112yes—
90C22⋊C8—21no—
91C22⋊C8—1221no—
92#97—21no—
93C4×C8—1221no—
94C2×Q8—612no—
95C2×Q8—1221no—
96C22×C4C4×D6111yescharacteristic
97C22×C4D24411yescharacteristic
98C22×C4C22⋊D6111yescharacteristic
99C2×C8—22no—
100C2×C8—1222no—
101C4⋊C4—612no—
102C4⋊C4—1222no—
103C4⋊C4—1222no—
104C4⋊C4—1221no—
105C4⋊C4—1221no—
106C4⋊C4—1221no—
107C22⋊C4—1222no—
108C42—1222no—
109C42C4×D6111yescharacteristic
110C42D24411yescharacteristic
111C42C22⋊D6111yescharacteristic
112C42C22×D6111yescharacteristic
113C23#1175819811yescharacteristic
114Q8—2442no—
115Q8—2442no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—1222no—
120C2×C4—1222no—
121C2×C4#1175819811yescharacteristic
122C2×C4#1175819811yescharacteristic
123C2×C4#1175819811yescharacteristic
124C2×C4C2×C4×D6111yescharacteristic
125C2×C4C2×D24411yescharacteristic
126C2×C4C2×C22⋊D6111yescharacteristic
127C8—42no—
128C8—2442no—
129C22—21no—
130C22—21no—
131C22—21no—
132C22C2×#1175819811yescharacteristic
133C4—21no—
134C4—21no—
135C4—21no—
136C4—21no—
137C4—2442no—
138C4—2442no—
139C4#1451979712yes—
140C4#1451981012yes—
141C2—41no—
142C2#1683974411yescharacteristic
143C2#1683975611yescharacteristic
144C2#1683977211yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1554
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
3. #16839510C2semidirect
4. #16839509C2semidirect
78. C61#1554semidirect