Finite Group Databasebeta

← #21461273

Subgroups — #21461273

Order 7808.

270 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 62 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
1C4×#11758217C212yesmaximal, complemented
2#16840618C212yesmaximal, complemented
3#16840617C212yesmaximal, complemented
4#16840308C211yesmaximal, characteristic
5C2×#11758217—22no—
6#14519832C2214yes—
7C4×#92420—22no—
8C2×#11758222C411yescharacteristic
9#14519775C411yescharacteristic
10#14519773C411yescharacteristic
11#14519766C2211yescharacteristic
12#14519764C2211yescharacteristic
13#14519749—22no—
14C4×C22⋊D61—22no—
15C2×C4×Dic61C2211yescharacteristic
16C2×#41×C61C411yescharacteristic
17#41×C61—42no—
18C2×Q8×C61C2×C411yescharacteristic
19C2×D4×C61—21no—
20C2×D4×C61C2×C411yescharacteristic
21C22×C4×C61—21no—
22C22×C4×C61C2×C411yescharacteristic
23C2×C22⋊D61—21no—
24C2×C22⋊D61—22no—
25C22×Dic61D412yes—
26#11758222—42no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122C2×C411yescharacteristic
30#11758217—28no—
31C2×#92420—24no—
32C22⋊Dic61—22no—
33#11758198—22no—
34#11758196—22no—
35C4×Dic61C2×C411yescharacteristic
36C4×Dic61D412yes—
37C4×Dic61C2311yescharacteristic
38C23×C61—21no—
39C23×C61C22⋊C411yescharacteristic
40C22×D61—21no—
41Q8×C61—41no—
42D4×C61—41no—
43D4×C61—42no—
44C2×C4×C61—22no—
45C2×C4×C61—21no—
46C2×C4×C61—42no—
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22×C411yescharacteristic
49C22⋊D61—42no—
50C22⋊D61—44no—
51C2×Dic61—24no—
52C2×Dic61—21no—
53C2×Dic61C22⋊C412yes—
54C2×Dic61C2×D412yes—
55D244—41no—
56C4×D61—42no—
57Dic122—41no—
58#92420—28no—
59C22×C61—21no—
60C22×C61—22no—
61C22×C61—41no—
62C22×C61—42no—
63C22×C61C2×C22⋊C411yescharacteristic
64C2×D61—41no—
65C2×D61—42no—
66C4×C61—21no—
67C4×C61—41no—
68C4×C61#10012yes—
69Dic61—22no—
70Dic61—41no—
71Dic61#10414yes—
72#1525—611nomaximal, Sylow
73C2×C61—41no—
74C2×C61—81no—
75C2×C61C2×#10011yescharacteristic
76C2×C61C2×#10412yes—
77D61—81no—
78#532—611no—
79C4×M16—612no—
80#329—612no—
81#329—612no—
82C61#152511yescharacteristic, complemented, Sylow
83C2×#41—611no—
84C2×#41#692311yescharacteristic
85C2×M16—1222no—
86C4⋊Q8—611no—
87#127—611no—
88#124—611no—
89#124—611no—
90#121—1222no—
91C4×D4—1222no—
92C2×C42—611no—
93#97—614no—
94C4×C8—1222no—
95#41—42no—
96#41—2442no—
97C2×Q8—611no—
98C2×Q8C2×#692311yescharacteristic
99C2×D4—21no—
100C2×D4—611no—
101C2×D4—1222no—
102C2×D4—1221no—
103C2×D4C2×#692311yescharacteristic
104C22×C4—21no—
105C22×C4—612no—
106C22×C4—1221no—
107C22×C4C2×#692311yescharacteristic
108M16—1228no—
109C2×C8—1224no—
110C4⋊C4—1222no—
111C22⋊C4—1222no—
112C22⋊C4—1222no—
113C42—612no—
114C42—611no—
115C42—611no—
116C23—21no—
117C23—1221no—
118C23C22⋊#692311yescharacteristic
119Q8—41no—
120Q8—2441no—
121D4—41no—
122D4—42no—
123D4—2441no—
124D4—2444no—
125D4—2442no—
126C2×C4—22no—
127C2×C4—21no—
128C2×C4—42no—
129C2×C4—612no—
130C2×C4—612no—
131C2×C4—1224no—
132C2×C4—1221no—
133C2×C4—2442no—
134C2×C4C22⋊#692311yescharacteristic
135C2×C4C22×#692311yescharacteristic
136C8—1228no—
137C22—21no—
138C22—22no—
139C22—41no—
140C22—42no—
141C22—2441no—
142C22—2442no—
143C22C2×C22⋊#692311yescharacteristic
144C4—21no—
145C4—41no—
146C4—614no—
147C4—1222no—
148C4—2441no—
149C4#1451983712yes—
150C2—41no—
151C2—81no—
152C2—4881no—
153C2C2×#1451983711yescharacteristic
154C2D61⋊#10412yes—
subgroupG/H
centerC2×C4C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#1525
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C4×#11758217C2semidirect
2. #16840618C2semidirect
3. #16840617C2semidirect
82. C61#1525semidirect