Finite Group Databasebeta

← #21461301

Subgroups — #21461301

Order 7808.

196 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 58 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#16840782C211yesmaximal, characteristic
2#16840782C211yesmaximal, characteristic
3#16840619C214yesmaximal, complemented
4C2×#14519768C211yesmaximal, characteristic
5#14519844—21no—
6#14519844—21no—
7C22⋊#92420—21no—
8C22⋊#92420—21no—
9#14519832C2212yes—
10#14519832C2212yes—
11#14519768—21no—
12#14519768—21no—
13#14519768C412yes—
14#14519768C2212yes—
15C2×C4⋊Dic61—21no—
16C2×C4⋊Dic61C411yescharacteristic
17C2×#11758196—21no—
18C2×C4×Dic61C2211yescharacteristic
19C2×C4⋊C4×C61C411yescharacteristic
20C22×C4×C61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×Dic61—21no—
23C22×Dic61D411yescharacteristic
24C22×Dic61D411yescharacteristic
25C2×#92420—22no—
26C2×#92420—22no—
27C4⋊C4×C61—21no—
28C4⋊C4×C61C2×C412yes—
29C4⋊Dic61—21no—
30C4⋊Dic61—22no—
31C4⋊Dic61—22no—
32C4⋊Dic61C2×C412yes—
33#11758196—22no—
34#11758196—22no—
35C4×Dic61C2×C411yescharacteristic
36C4×Dic61D411yescharacteristic
37C4×Dic61D411yescharacteristic
38C4×Dic61C2311yescharacteristic
39C23×C61C22⋊C411yescharacteristic
40C2×C4×C61—22no—
41C2×C4×C61—22no—
42C2×C4×C61—42no—
43C2×C4×C61C22⋊C411yescharacteristic
44C2×C4×C61C22×C411yescharacteristic
45C2×Dic61—22no—
46C2×Dic61—41no—
47C2×Dic61—41no—
48C2×Dic61—42no—
49C2×Dic61C22⋊C411yescharacteristic
50C2×Dic61C22⋊C411yescharacteristic
51C2×Dic61C2×D411yescharacteristic
52C2×Dic61C2×D411yescharacteristic
53#92420—42no—
54#92420—42no—
55C22×C61—21no—
56C22×C61—21no—
57C22×C61#10112yes—
58C22×C61C2×C22⋊C411yescharacteristic
59C4×C61—21no—
60C4×C61—21no—
61C4×C61—42no—
62Dic61—21no—
63Dic61—21no—
64Dic61—21no—
65Dic61—21no—
66Dic61—42no—
67#1534—611nomaximal, Sylow
68C2×C61—22no—
69C2×C61C2×#10111yescharacteristic
70C2×C61#42111yescharacteristic
71C2×C61#42111yescharacteristic
72C2×#125—611no—
73#432—611no—
74#432—611no—
75#330—614no—
76C61#153411yescharacteristic, complemented, Sylow
77#125—612no—
78#125—612no—
79#125—1221no—
80#125—1221no—
81C2×C4⋊C4—611no—
82C2×C4⋊C4—1221no—
83C2×C4⋊C4—1221no—
84C2×C4⋊C4#692311yescharacteristic
85C2×C42—611no—
86C4⋊C8—1221no—
87C4⋊C8—1221no—
88C22⋊C8—1221no—
89C22⋊C8—1221no—
90#97—612no—
91#97—612no—
92C22×C4—21no—
93C22×C4—611no—
94C22×C4—611no—
95C22×C4—1221no—
96C22×C4C2×#692311yescharacteristic
97C2×C8—1222no—
98C2×C8—1222no—
99C4⋊C4—21no—
100C4⋊C4—612no—
101C4⋊C4—1222no—
102C4⋊C4—1222no—
103C4⋊C4—1222no—
104C4⋊C4—1222no—
105C4⋊C4—1221no—
106C4⋊C4C2×#692312yes—
107C42—611no—
108C42—611no—
109C42—611no—
110C42—611no—
111C23C22⋊#692311yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—42no—
115C2×C4—611no—
116C2×C4—611no—
117C2×C4—611no—
118C2×C4—611no—
119C2×C4—1222no—
120C2×C4—2441no—
121C2×C4—2441no—
122C2×C4—2442no—
123C2×C4C22⋊#692311yescharacteristic
124C2×C4C22×#692311yescharacteristic
125C8—2442no—
126C8—2442no—
127C22—21no—
128C22—21no—
129C22#1451983812yes—
130C22C2×C22⋊#692311yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—1221no—
135C4—1221no—
136C4—1221no—
137C4—1221no—
138C4—2442no—
139C2—22no—
140C2C2×#1451983811yescharacteristic
141C2#1684076011yescharacteristic
142C2#1684076111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×C4⋊C4×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×C4⋊C4#6923
hypocenterC61#1534
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #16840619C2semidirect
76. C61#1534semidirect