Finite Group Databasebeta

← #21461307

Subgroups — #21461307

Order 7808.

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

normal subgroups only

This group has 238 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#16840783C212yesmaximal, complemented
2#16840618C212yesmaximal, complemented
3#16840617C212yesmaximal, complemented
4#16840308C211yesmaximal, characteristic
5C4⋊#92420—22no—
6C22⋊#92420—22no—
7#14519832C2214yes—
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
30C2×#92420—24no—
31C22⋊Dic61—22no—
32#11758198—22no—
33#11758196—22no—
34C4×Dic61C2×C411yescharacteristic
35C4×Dic61D412yes—
36C4×Dic61C2311yescharacteristic
37C23×C61—21no—
38C23×C61C22⋊C411yescharacteristic
39C22×D61—21no—
40Q8×C61—41no—
41D4×C61—41no—
42D4×C61—42no—
43C2×C4×C61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—42no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22×C411yescharacteristic
48C22⋊D61—44no—
49C22⋊D61—42no—
50C2×Dic61—21no—
51C2×Dic61—42no—
52C2×Dic61C22⋊C412yes—
53C2×Dic61C2×D412yes—
54D244—41no—
55C4×D61—42no—
56Dic122—41no—
57#92420—44no—
58C22×C61—21no—
59C22×C61—22no—
60C22×C61—41no—
61C22×C61—42no—
62C22×C61C2×C22⋊C411yescharacteristic
63C2×D61—41no—
64C2×D61—42no—
65C4×C61—21no—
66C4×C61—41no—
67C4×C61#10012yes—
68Dic61—22no—
69Dic61—22no—
70Dic61—41no—
71#1536—611nomaximal, Sylow
72C2×C61—41no—
73C2×C61—81no—
74C2×C61C2×#10011yescharacteristic
75C2×C61#42112yes—
76D61—81no—
77#532—611no—
78#432—612no—
79#329—612no—
80#329—612no—
81C61#153611yescharacteristic, complemented, Sylow
82C2×#41—611no—
83C2×#41#692311yescharacteristic
84C4⋊Q8—611no—
85#127—611no—
86#124—611no—
87#124—611no—
88#121—1222no—
89C4×D4—1222no—
90C2×C42—611no—
91C4⋊C8—1222no—
92C22⋊C8—1222no—
93#97—614no—
94#41—42no—
95#41—2442no—
96C2×Q8—611no—
97C2×Q8C2×#692311yescharacteristic
98C2×D4—21no—
99C2×D4—611no—
100C2×D4—1222no—
101C2×D4—1221no—
102C2×D4C2×#692311yescharacteristic
103C22×C4—21no—
104C22×C4—612no—
105C22×C4—1221no—
106C22×C4C2×#692311yescharacteristic
107C2×C8—1224no—
108C4⋊C4—1222no—
109C22⋊C4—1222no—
110C22⋊C4—1222no—
111C42—612no—
112C42—611no—
113C42—611no—
114C23—21no—
115C23—1221no—
116C23C22⋊#692311yescharacteristic
117Q8—41no—
118Q8—2441no—
119D4—41no—
120D4—42no—
121D4—2441no—
122D4—2444no—
123D4—2442no—
124C2×C4—22no—
125C2×C4—21no—
126C2×C4—42no—
127C2×C4—612no—
128C2×C4—612no—
129C2×C4—1221no—
130C2×C4—2442no—
131C2×C4—2442no—
132C2×C4C22⋊#692311yescharacteristic
133C2×C4C22×#692311yescharacteristic
134C8—2444no—
135C22—21no—
136C22—22no—
137C22—41no—
138C22—42no—
139C22—2441no—
140C22—2442no—
141C22C2×C22⋊#692311yescharacteristic
142C4—21no—
143C4—41no—
144C4—1222no—
145C4—1222no—
146C4—2441no—
147C4#1451983712yes—
148C2—41no—
149C2—81no—
150C2—4881no—
151C2C2×#1451983711yescharacteristic
152C2#1684075912yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×#41×C61C4
socleC22×C61C2×C22⋊C4
hypercenterC2×#41#6923
hypocenterC61#1536
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #16840783C2semidirect
2. #16840618C2semidirect
3. #16840617C2semidirect
81. C61#1536semidirect