Finite Group Databasebeta

← #21461299

Subgroups — #21461299

Order 7808.

248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 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#16840784C212yesmaximal, complemented
2#16840618C212yesmaximal, complemented
3#16840617C212yesmaximal, complemented
4#124×D61C211yesmaximal, characteristic
5C4⋊#92420—22no—
6#14519834—22no—
7#14519832C2214yescomplemented
8C2×Q8×D61C411yescharacteristic
9C2×D4×D61C411yescharacteristic
10#14519766C2211yescharacteristic
11#14519765C411yescharacteristic
12#14519764C2211yescharacteristic
13#14519763—22no—
14C22⋊C4×D61—22no—
15C42×D61C2211yescharacteristic
16#124×C61C411yescharacteristic
17C23×D61—21no—
18C2×Q8×C61C2×C411yescharacteristic
19C2×D4×C61C2×C411yescharacteristic
20C2×C22⋊D61—21no—
21Q8×D61—42no—
22D4×D61—42no—
23C2×D244C2×C411yescharacteristic
24C2×C4×D61—21no—
25C2×C4×D61C2×C411yescharacteristic
26C2×C4×D61D412yes—
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29C2×#92420—24no—
30C22⋊C4×C61—22no—
31C42×C61C2×C411yescharacteristic
32C22⋊Dic61—22no—
33#11758198—22no—
34#11758198—22no—
35C4×Dic61D412yes—
36C4×Dic61C2311yescharacteristic
37C23×C61—21no—
38C22×D61—21no—
39C22×D61—44no—
40C22×D61—42no—
41C22×D61C22⋊C411yescharacteristic
42Q8×C61—41no—
43D4×C61—41no—
44C2×C4×C61—21no—
45C2×C4×C61C22⋊C412yes—
46C2×C4×C61C22×C411yescharacteristic
47C22⋊D61—42no—
48C2×Dic61—21no—
49C2×Dic61C22⋊C411yescharacteristic
50C2×Dic61C2×D412yes—
51D244—41no—
52C4×D61—22no—
53C4×D61—42no—
54C4×D61—42no—
55Dic122—42no—
56Dic122—41no—
57#92420—44no—
58C22×C61—41no—
59C22×C61—42no—
60C22×C61C2×C22⋊C411yescharacteristic
61C2×D61—22no—
62C2×D61—41no—
63C2×D61—42no—
64C2×D61—84no—
65C2×D61#10012yes—
66C4×C61—21no—
67C4×C61—22no—
68C4×C61—41no—
69Dic61—21no—
70Dic61—22no—
71Dic61—41no—
72#1533—611nomaximal, Sylow
73C2×C61—81no—
74C2×C61C2×#10011yescharacteristic
75C2×C61#42112yes—
76D61—22no—
77D61—81no—
78C2×#124—611no—
79#432—612no—
80#329—612no—
81#329—612no—
82C61#153311yescharacteristic, complemented, Sylow
83C22×Q8—611no—
84C22×D4—611no—
85#124—611no—
86#124—611no—
87#124—611no—
88#124—1222no—
89#124#692311yescharacteristic
90C2×C22⋊C4—1222no—
91C2×C42—611no—
92C4⋊C8—1222no—
93C22⋊C8—1222no—
94#97—614no—
95C24—1221no—
96C2×Q8—611no—
97C2×Q8—1221no—
98C2×Q8—2442no—
99C2×Q8C2×#692311yescharacteristic
100C2×D4—611no—
101C2×D4—1221no—
102C2×D4—2442no—
103C2×D4C2×#692311yescharacteristic
104C22×C4—611no—
105C22×C4—612no—
106C22×C4—1221no—
107C2×C8—1224no—
108C22⋊C4—22no—
109C22⋊C4—1222no—
110C22⋊C4—1222no—
111C22⋊C4—1222no—
112C42—612no—
113C42—611no—
114C42C2×#692311yescharacteristic
115C23—21no—
116C23—611no—
117C23—1221no—
118C23—2442no—
119C23—2444no—
120Q8—41no—
121Q8—2441no—
122Q8—2442no—
123D4—41no—
124D4—2441no—
125D4—2442no—
126C2×C4—21no—
127C2×C4—611no—
128C2×C4—612no—
129C2×C4—1222no—
130C2×C4—1221no—
131C2×C4—2442no—
132C2×C4—2442no—
133C2×C4C22⋊#692312yes—
134C2×C4C22×#692311yescharacteristic
135C8—2444no—
136C22—41no—
137C22—42no—
138C22—612no—
139C22—1222no—
140C22—4884no—
141C22—2441no—
142C22—2442no—
143C22C2×C22⋊#692311yescharacteristic
144C4—21no—
145C4—22no—
146C4—41no—
147C4—1221no—
148C4—1222no—
149C4—2441no—
150C2—81no—
151C2—1222no—
152C2—4881no—
153C2D61⋊#10011yescharacteristic
154C2#1684075912yes—
subgroupG/H
centerC22C2×C22⋊#6923
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
Fitting#124×C61C4
socleC22×C61C2×C22⋊C4
hypercenter#124#6923
hypocenterC61#1533
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #16840784C2semidirect
2. #16840618C2semidirect
3. #16840617C2semidirect
7. #14519832C22semidirect
82. C61#1533semidirect