Finite Group Databasebeta

← #21444477

Subgroups — #21444477

Order 7808.

212 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 89 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#16839507C212yesmaximal, complemented
5C2×C4⋊C8×C61C211yesmaximal, 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—
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×Dic122C2×C412yes—
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⋊Dic61—21no—
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—41no—
44C2×C4×C61C22⋊C411yescharacteristic
45C2×C4×C61C22⋊C411yescharacteristic
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61SD1612yes—
48C2×C4×C61Q1612yes—
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C2×Dic61—22no—
53C2×Dic61—22no—
54Dic122—42no—
55Dic122—42no—
56C8×C61—42no—
57#92418—42no—
58C22×C61—21no—
59C22×C61—21no—
60C22×C61#10312yes—
61C22×C61C2×C22⋊C411yescharacteristic
62C4×C61—21no—
63C4×C61—21no—
64C4×C61—21no—
65C4×C61#10312yes—
66C4×C61C2×SD1611yescharacteristic
67C4×C61C2×Q1611yescharacteristic
68C4×C61#13512yes—
69Dic61—42no—
70Dic61—42no—
71#1542—611nomaximal, Sylow
72C2×C61—22no—
73C2×C61#41311yescharacteristic
74C2×C61C2×#10311yescharacteristic
75C2×C61#41611yescharacteristic
76#533—611no—
77#431—611no—
78C2×C4⋊C8D6111yescharacteristic
79#333—612no—
80#332—612no—
81C61#154211yescharacteristic, complemented, Sylow
82C22×C8—21no—
83C4⋊Q8—611no—
84C4⋊Q8—611no—
85#125—1221no—
86C22⋊Q8—612no—
87C22⋊Q8—1221no—
88C4×Q8—612no—
89C4×Q8—1221no—
90#117—1221no—
91C2×C42C2×D6111yescharacteristic
92C4⋊C8—21no—
93C4⋊C8—612no—
94C4⋊C8C2×D6112yes—
95C22⋊C8—1221no—
96C4×C8—1221no—
97C2×Q8—612no—
98C2×Q8—1221no—
99C22×C4C4×D6111yescharacteristic
100C22×C4D24411yescharacteristic
101C22×C4C22⋊D6111yescharacteristic
102C2×C8—22no—
103C2×C8—42no—
104C2×C8—1222no—
105C4⋊C4—612no—
106C4⋊C4—1222no—
107C4⋊C4—1222no—
108C4⋊C4—1221no—
109C4⋊C4—1221no—
110C4⋊C4—1221no—
111C22⋊C4—1222no—
112C42—1222no—
113C42C4×D6111yescharacteristic
114C42D24411yescharacteristic
115C42C22⋊D6111yescharacteristic
116C42C22×D6111yescharacteristic
117C23#1175819811yescharacteristic
118Q8—2442no—
119Q8—2442no—
120C2×C4—22no—
121C2×C4—41no—
122C2×C4—1222no—
123C2×C4—1222no—
124C2×C4#1175819811yescharacteristic
125C2×C4#1175819811yescharacteristic
126C2×C4#1175819811yescharacteristic
127C2×C4#1175820012yes—
128C2×C4#1175820212yes—
129C2×C4C2×C4×D6111yescharacteristic
130C2×C4C2×D24411yescharacteristic
131C2×C4C2×C22⋊D6111yescharacteristic
132C8—42no—
133C8—2442no—
134C22—21no—
135C22—21no—
136C22#1451970012yes—
137C22C2×#1175819811yescharacteristic
138C4—21no—
139C4—21no—
140C4—21no—
141C4—2442no—
142C4—2442no—
143C4#1451970012yes—
144C4C2×#1175820011yescharacteristic
145C4C2×#1175820211yescharacteristic
146C4#1451979912yes—
147C2—22no—
148C2#1683974411yescharacteristic
149C2C2×#1451970011yescharacteristic
150C2#1683975911yescharacteristic
subgroupG/H
centerC2×C4#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC2×C4⋊C8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C8D61
hypocenterC61#1542
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #16839510C2semidirect
4. #16839507C2semidirect
81. C61#1542semidirect