Finite Group Databasebeta

← #21445716

Subgroups — #21445716

Order 7808.

272 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#14519711C211yesmaximal, characteristic
2C2×#14519709C211yesmaximal, characteristic
3C4×C4⋊Dic61C212yesmaximal
4#16839525C212yesmaximal
5C2×#97×C61C211yesmaximal, characteristic
6C2×C4⋊Dic61C2212yes—
7C2×C4⋊Dic61C2212yes—
8C2×C4×Dic61—22no—
9#14519711C414yescomplemented
10#14519709C414yescomplemented
11#14519684—22no—
12C22×C8×C61C2211yescharacteristic
13C22×C8×C61C2211yescharacteristic
14C2×C42×C61C2211yescharacteristic
15#97×C61C414yescomplemented
16C22×C4×C61D412yes—
17C22×C4×C61C2311yescharacteristic
18C22×Dic61—22no—
19C22×Dic61—22no—
20C2×C8×C61—21no—
21C2×C8×C61—21no—
22C2×C8×C61C2×C412yes—
23C2×C8×C61C2×C412yes—
24C2×C8×C61C2×C412yes—
25C2×C8×C61C2×C412yes—
26C42×C61C2×C412yes—
27C42×C61Q812yes—
28C4⋊Dic61—22no—
29C4⋊Dic61—22no—
30C4⋊Dic61C2×C414yes—
31C4⋊Dic61C2×C414yes—
32C4×Dic61—44no—
33C23×C61C2×D411yescharacteristic
34C2×C4×C61—22no—
35C2×C4×C61—22no—
36C2×C4×C61C4⋊C414yes—
37C2×C4×C61C22×C411yescharacteristic
38C2×C4×C61C22×C411yescharacteristic
39C2×C4×C61C22×C411yescharacteristic
40C2×C4×C61C2×Q811yescharacteristic
41C2×C4×C61#4111yescharacteristic
42C2×C4×C61#4111yescharacteristic
43C2×Dic61—24no—
44C2×Dic61—24no—
45C2×Dic61—42no—
46C2×Dic61—42no—
47C2×Dic61—42no—
48C2×Dic61—42no—
49C8×C61—22no—
50C8×C61C4214yescomplemented
51C22×C61C2×C4⋊C411yescharacteristic
52C22×C61C4×D411yescharacteristic
53C22×C61C4×D411yescharacteristic
54C22×C61AGL(1,ℤ/8)12yes—
55C22×C61#13712yes—
56C4×C61—24no—
57C4×C61C2×C4211yescharacteristic
58C4×C61#11711yescharacteristic
59C4×C61C4×Q811yescharacteristic
60C4×C61C4×Q811yescharacteristic
61Dic61—44no—
62Dic61—44no—
63#1776—611nomaximal, Sylow
64C2×C61C4×C4⋊C411yescharacteristic
65C2×C61#42812yes—
66C2×C61#44012yes—
67C2×C61#44111yescharacteristic
68C2×C61#44211yescharacteristic
69C2×#107—611no—
70C2×#106—611no—
71C2×#97D6111yescharacteristic
72C4×C4⋊C4—612no—
73#340—612no—
74C61#177611yescharacteristic, complemented, Sylow
75C22×C8C2×D6111yescharacteristic
76C22×C8C2×D6111yescharacteristic
77C2×C4⋊C4—612no—
78C2×C4⋊C4—612no—
79C2×C42—1222no—
80C2×C42C2×D6111yescharacteristic
81#107—614no—
82#106—614no—
83#97Dic6114yescomplemented
84#95—1222no—
85C22×C4—1222no—
86C22×C4—1222no—
87C22×C4D24412yes—
88C22×C4C22×D6111yescharacteristic
89C2×C8—21no—
90C2×C8—21no—
91C2×C8C4×D6112yes—
92C2×C8C4×D6112yes—
93C2×C8C2×Dic6112yes—
94C2×C8C2×Dic6112yes—
95C4⋊C4—614no—
96C4⋊C4—614no—
97C4⋊C4—1222no—
98C4⋊C4—1222no—
99C42—2444no—
100C42Dic12212yes—
101C42C2×Dic6112yes—
102C23C2×D24411yescharacteristic
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—1224no—
106C2×C4—1224no—
107C2×C4—2442no—
108C2×C4—2442no—
109C2×C4—2442no—
110C2×C4—2442no—
111C2×C4C4⋊Dic6114yes—
112C2×C4C2×Dic12211yescharacteristic
113C2×C4C2×C4×D6111yescharacteristic
114C2×C4C2×C4×D6111yescharacteristic
115C2×C4#1175822211yescharacteristic
116C2×C4#1175822211yescharacteristic
117C2×C4C22×Dic6111yescharacteristic
118C8—22no—
119C8C4×Dic6114yescomplemented
120C22C2×C4⋊Dic6111yescharacteristic
121C22C4×D24411yescharacteristic
122C22C4×D24411yescharacteristic
123C22#1451980512yes—
124C22#1451981012yes—
125C4—24no—
126C4—2444no—
127C4—2444no—
128C4C2×C4×Dic6111yescharacteristic
129C4#1451973611yescharacteristic
130C4C4×Dic12211yescharacteristic
131C4C4×Dic12211yescharacteristic
132C2C4×C4⋊Dic6111yescharacteristic
133C2#1683980412yes—
134C2#1683986412yes—
135C2#1683987011yescharacteristic
136C2#1683987511yescharacteristic
subgroupG/H
centerC23C2×D244
commutatorC4×C61C2×C42
FrattiniC22×C4C22×D61
FittingC2×#97×C61C2
socleC23×C61C2×D4
hypercenterC2×#97D61
hypocenterC61#1776
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
9. #14519711C4semidirect
10. #14519709C4semidirect
15. #97×C61C4semidirect
50. C8×C61C42semidirect
74. C61#1776semidirect
83. #97Dic61semidirect
119. C8C4×Dic61semidirect