Finite Group Databasebeta

← #21456371

Subgroups — #21456371

Order 7808.

348 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 165 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#16840319C211yesmaximal, characteristic
2C2×#14519769C211yesmaximal, characteristic
3#16840171C214yesmaximal, complemented
4#16840164C214yesmaximal, complemented
5#16839804C214yesmaximal
6C4×M16×C61C211yesmaximal, characteristic
7#14519777C2212yes—
8#14519769—22no—
9#14519769C2212yes—
10#14519769C2212yes—
11#14519769C2212yes—
12#14519756—22no—
13C4×Dic122—22no—
14#14519736C2212yes—
15C2×C4⋊Dic61C2212yes—
16C2×#11758196—22no—
17#14519711C2218yes—
18#14519709C2218yes—
19C2×M16×C61C2212yes—
20C2×C42×C61C2211yescharacteristic
21#97×C61C2212yes—
22C4×C8×C61C2212yes—
23C22×C4×C61D412yes—
24C22×C4×C61C2311yescharacteristic
25C22×Dic61—22no—
26C2×Dic122—22no—
27M16×C61Q818yescomplemented
28C2×C8×C61C2314yes—
29C42×C61D412yes—
30C42×C61C2311yescharacteristic
31C42×C61C2311yescharacteristic
32C22⋊Dic61—22no—
33C4⋊Dic61—22no—
34C4⋊Dic61—22no—
35C4⋊Dic61C2314yes—
36C4⋊Dic61C2314yes—
37#11758196—24no—
38#11758196—24no—
39#11758196—24no—
40C4×Dic61—22no—
41C23×C61C2×D411yescharacteristic
42C2×C4×C61—42no—
43C2×C4×C61C2×D412yes—
44C2×C4×C61C2×D412yes—
45C2×C4×C61C2×D411yescharacteristic
46C2×C4×C61C2×Q814yes—
47C2×C4×C61C2411yescharacteristic
48C2×Dic61—24no—
49C2×Dic61—24no—
50C2×Dic61—44no—
51Dic122—44no—
52C8×C61C2×Q818yes—
53C22×C61—22no—
54C22×C61C4⋊Q812yes—
55C22×C61C22×D411yescharacteristic
56C4×C61—22no—
57C4×C61—22no—
58C4×C61C4⋊Q812yes—
59C4×C61C22×Q812yes—
60Dic61—44no—
61Dic61—44no—
62#3166—611nomaximal, Sylow
63C2×C61—22no—
64C2×C61C2×C4⋊Q811yescharacteristic
65C2×C61#57512yes—
66#533—611no—
67C2×#125—611no—
68#501—614no—
69#499—614no—
70#428—614no—
71C4×M16D6111yescharacteristic
72C61#316611yescharacteristic, complemented, Sylow
73C2×M16C2×D6112yes—
74C4⋊Q8—612no—
75#125—612no—
76#125—612no—
77#125—612no—
78#125—1222no—
79C22⋊Q8—1222no—
80C4×Q8—1222no—
81#117—612no—
82C2×C4⋊C4—612no—
83C2×C4⋊C4—1222no—
84C2×C42C2×D6111yescharacteristic
85#107—618no—
86#106—618no—
87#97C2×D6112yes—
88C4×C8C2×D6112yes—
89C2×Q8—1222no—
90C22×C4—1222no—
91C22×C4D24412yes—
92C22×C4C22×D6111yescharacteristic
93M16Dic12218yescomplemented
94C2×C8C22×D6114yes—
95C4⋊C4—614no—
96C4⋊C4—614no—
97C4⋊C4—1222no—
98C4⋊C4—1224no—
99C4⋊C4—1224no—
100C4⋊C4—1224no—
101C4⋊C4—1222no—
102C22⋊C4—1222no—
103C42—1222no—
104C42D24412yes—
105C42C22×D6111yescharacteristic
106C42C22×D6111yescharacteristic
107C23C2×D24411yescharacteristic
108Q8—2444no—
109C2×C4—42no—
110C2×C4—1224no—
111C2×C4—1224no—
112C2×C4—2444no—
113C2×C4C2×Dic12214yes—
114C2×C4C2×D24412yes—
115C2×C4C2×D24412yes—
116C2×C4C2×D24411yescharacteristic
117C2×C4C23×D6111yescharacteristic
118C8C2×Dic12218yes—
119C22—22no—
120C22#1451977712yes—
121C22C22×D24411yescharacteristic
122C4—22no—
123C4—22no—
124C4—2444no—
125C4—2444no—
126C4#1451977712yes—
127C4C22×Dic12212yes—
128C2—22no—
129C2C2×#1451977711yescharacteristic
130C2#1684056212yes—
subgroupG/H
centerC22C22×D244
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×M16×C61C2
socleC22×C61C22×D4
hypercenterC4×M16D61
hypocenterC61#3166
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
3. #16840171C2semidirect
4. #16840164C2semidirect
27. M16×C61Q8semidirect
72. C61#3166semidirect
93. M16Dic122semidirect