Finite Group Databasebeta

← #21445147

Subgroups — #21445147

Order 7808.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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#16840172C212yesmaximal
2#16840132C211yesmaximal, characteristic
3#16839504C211yesmaximal, characteristic
4#16839504C212yesmaximal
5C61×#564C211yesmaximal, characteristic
6#14519777C2211yescharacteristic
7#14519710—22no—
8#14519708—22no—
9#14519700—22no—
10#14519688C2211yescharacteristic
11#14519688C2212yes—
12#125×C61—22no—
13#125×C61—22no—
14#125×C61—22no—
15#125×C61C2211yescharacteristic
16#125×C61C2212yes—
17C2×Dic122—21no—
18C4⋊C4×C61—22no—
19C4⋊C4×C61—22no—
20C4⋊C4×C61—22no—
21C4⋊C4×C61—22no—
22C4⋊C4×C61—22no—
23C4⋊C4×C61—22no—
24C4⋊C4×C61D412yes—
25C4⋊C4×C61D412yes—
26C4⋊C4×C61D412yes—
27C42×C61—22no—
28C42×C61C2311yescharacteristic
29C4⋊Dic61—22no—
30C2×#92418—22no—
31C2×#92418—21no—
32C2×C4×C61—22no—
33C2×C4×C61—22no—
34C2×C4×C61—22no—
35C2×C4×C61C2×D412yes—
36C2×C4×C61C2×D411yescharacteristic
37C2×Dic61—41no—
38Dic122—42no—
39#92418—24no—
40#92418—41no—
41C22×C61#12011yescharacteristic
42C4×C61—21no—
43C4×C61—22no—
44C4×C61—42no—
45C4×C61—42no—
46C4×C61—42no—
47Dic61—81no—
48#1663—611nomaximal, Sylow
49C2×C61#45411yescharacteristic
50C2×C61#45612yes—
51#564D6111yescharacteristic
52#501—612no—
53#491—611no—
54#330—612no—
55#330—611no—
56C61#166311yescharacteristic, complemented, Sylow
57C4⋊Q8—611no—
58#125—22no—
59#125—22no—
60#125—22no—
61#125C2×D6111yescharacteristic
62#125C2×D6112yes—
63#107—1222no—
64#106—1222no—
65#103—1222no—
66#97—611no—
67#97—612no—
68C2×Q8—1221no—
69C2×C8—1222no—
70C2×C8—1221no—
71C4⋊C4—22no—
72C4⋊C4—22no—
73C4⋊C4—22no—
74C4⋊C4—22no—
75C4⋊C4—22no—
76C4⋊C4—22no—
77C4⋊C4—1222no—
78C4⋊C4C22⋊D6112yes—
79C4⋊C4C22⋊D6112yes—
80C4⋊C4C22⋊D6112yes—
81C42—22no—
82C42C22×D6111yescharacteristic
83Q8—2442no—
84C2×C4—22no—
85C2×C4—22no—
86C2×C4—22no—
87C2×C4—2441no—
88C2×C4C2×C22⋊D6112yes—
89C2×C4C2×C22⋊D6111yescharacteristic
90C8—1224no—
91C8—2441no—
92C22#1451974611yescharacteristic
93C4—22no—
94C4—21no—
95C4—42no—
96C4—42no—
97C4—42no—
98C4—4881no—
99C2#1683993511yescharacteristic
100C2#1683994512yes—
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#564C2
socleC22×C61#120
hypercenter#564D61
hypocenterC61#1663
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #564

Complements

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

NH ≅ G/Ntype
56. C61#1663semidirect