Finite Group Databasebeta

← #21462102

Subgroups — #21462102

Order 7808.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#16840743C212yesmaximal
2#16840669C212yesmaximal, complemented
3#16840668C212yesmaximal, complemented
4#16840337C211yesmaximal, characteristic
5#14519856—22no—
6#14519836—22no—
7#14519836C2214yes—
8C2×#11758226C2211yescharacteristic
9C2×Q8×D61C411yescharacteristic, complemented
10#14519775C411yescharacteristic, complemented
11#14519766C2211yescharacteristic
12#14519765C2211yescharacteristic
13#14519762—22no—
14#14519755—22no—
15#14519734C411yescharacteristic, complemented
16C4⋊Q8×C61C411yescharacteristic, complemented
17C2×Q8×C61C2×C411yescharacteristic
18C2×Q8×C61C2×C411yescharacteristic
19#11758226—42no—
20Q8×D61—42no—
21C2×D244D412yes—
22C2×D244C2311yescharacteristic
23C2×C4×D61—21no—
24C2×C4×D61C2×C411yescharacteristic
25C2×C4×D61D412yes—
26C2×Dic122—21no—
27C2×Dic122C2×C411yescharacteristic
28C22⋊#6923—24no—
29C4⋊#6923—42no—
30C4×#6923—42no—
31C4⋊C4×C61—22no—
32C42×C61C2×C411yescharacteristic
33#11758198—21no—
34#11758198—22no—
35#11758198—22no—
36#11758196—22no—
37#11758196—21no—
38C4×Dic61C2×C411yescharacteristic
39C22×D61C22⋊C411yescharacteristic
40C22×D61C2×D412yes—
41C2×#6923—44no—
42Q8×C61—41no—
43Q8×C61—41no—
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61C22⋊C412yes—
47C2×C4×C61C22×C411yescharacteristic
48C2×Dic61—21no—
49C2×Dic61—21no—
50C2×Dic61C22⋊C411yescharacteristic
51D244—42no—
52D244—41no—
53C4×D61—22no—
54C4×D61—22no—
55C4×D61—22no—
56C4×D61—42no—
57Dic122—42no—
58Dic122—41no—
59C22×C61C2×C22⋊C411yescharacteristic
60C2×D61—21no—
61C2×D61—22no—
62C2×D61—41no—
63C2×D61—42no—
64#6923—84no—
65C4×C61—21no—
66C4×C61—22no—
67C4×C61—41no—
68C4×C61—41no—
69Dic61—41no—
70Dic61—41no—
71Dic61#9912yes—
72#2129—611nomaximal, Sylow
73C2×C61—21no—
74C2×C61C2×#9911yescharacteristic
75D61—42no—
76D61—41no—
77#536—611no—
78#410—612no—
79#354—612no—
80#354—612no—
81C61#212911yescharacteristic, complemented, Sylow
82C2×#41—611no—
83C22×Q8—611no—
84C4⋊Q8—611no—
85C4⋊Q8#692311yescharacteristic, complemented
86#124—611no—
87#124—611no—
88#123—1222no—
89C22⋊Q8—1222no—
90#117—611no—
91#117—1222no—
92#99—614no—
93#99—1222no—
94#41—2442no—
95C2×Q8—611no—
96C2×Q8—1221no—
97C2×Q8—2442no—
98C2×Q8C2×#692311yescharacteristic
99C2×Q8C2×#692311yescharacteristic
100C2×D4—612no—
101C2×D4—611no—
102C22×C4—612no—
103C22×C4—611no—
104C22×C4—1221no—
105C4⋊C4—22no—
106C4⋊C4—1221no—
107C4⋊C4—1222no—
108C4⋊C4—2442no—
109C22⋊C4—1221no—
110C22⋊C4—1222no—
111C22⋊C4—1222no—
112C22⋊C4—1224no—
113C42—611no—
114C42—2442no—
115C42C2×#692311yescharacteristic
116C23—611no—
117C23—612no—
118Q8—41no—
119Q8—41no—
120Q8—2441no—
121Q8—2442no—
122D4—2442no—
123D4—2441no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—611no—
127C2×C4—1222no—
128C2×C4—1222no—
129C2×C4—1222no—
130C2×C4—1221no—
131C2×C4—1221no—
132C2×C4—2442no—
133C2×C4—2444no—
134C2×C4C22⋊#692312yes—
135C2×C4C22×#692311yescharacteristic
136C22—1222no—
137C22—1221no—
138C22—2442no—
139C22—2441no—
140C22C2×C22⋊#692311yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—41no—
145C4—612no—
146C4—4884no—
147C4—2441no—
148C4—2441no—
149C2—21no—
150C2—2442no—
151C2—2441no—
152C2D61⋊#9911yescharacteristic
subgroupG/H
centerC2D61⋊#99
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC4⋊Q8×C61C4
socleC2×C61C2×#99
hypercenterC4⋊Q8#6923
hypocenterC61#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #16840669C2semidirect
3. #16840668C2semidirect
9. C2×Q8×D61C4semidirect
10. #14519775C4semidirect
15. #14519734C4semidirect
16. C4⋊Q8×C61C4semidirect
81. C61#2129semidirect
85. C4⋊Q8#6923semidirect