Finite Group Databasebeta

← #21445130

Subgroups — #21445130

Order 7808.

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

normal subgroups only

This group has 196 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, complemented
2#16840157C211yesmaximal, characteristic
3#16839504C212yesmaximal, complemented
4#16839502C211yesmaximal, characteristic
5C61×#563C211yesmaximal, characteristic
6C2×#11758202—21no—
7C2×#11758200—21no—
8#14519777C2211yescharacteristic
9#14519710—22no—
10#14519708—22no—
11#14519688C2212yes—
12#14519688C2211yescharacteristic
13C4⋊Q8×C61—21no—
14#126×C61—22no—
15#125×C61C2212yes—
16#124×C61C2211yescharacteristic
17#123×C61—21no—
18C22⋊Q8×C61—22no—
19C2×Q8×C61—21no—
20C2×Q8×C61D411yescharacteristic
21C2×D4×C61D411yescharacteristic
22C22×C4×C61—21no—
23C2×Dic122—21no—
24C4⋊C4×C61—22no—
25C4⋊C4×C61—22no—
26C4⋊C4×C61—22no—
27C4⋊C4×C61D412yes—
28C4⋊C4×C61D412yes—
29C22⋊C4×C61—22no—
30C22⋊C4×C61—21no—
31C22⋊C4×C61—22no—
32C42×C61—21no—
33C42×C61C2311yescharacteristic
34#11758202—42no—
35#11758200—42no—
36C4⋊Dic61—22no—
37C2×#92418—22no—
38C2×#92418—21no—
39C23×C61—21no—
40Q8×C61—41no—
41Q8×C61—81no—
42D4×C61—41no—
43C2×C4×C61—22no—
44C2×C4×C61—21no—
45C2×C4×C61—22no—
46C2×C4×C61—81no—
47C2×C4×C61C2×D412yes—
48C2×C4×C61C2×D411yescharacteristic
49C2×Dic61—41no—
50Dic122—41no—
51Dic122—41no—
52#92418—24no—
53#92418—22no—
54C22×C61—41no—
55C22×C61—42no—
56C22×C61#12011yescharacteristic
57C4×C61—21no—
58C4×C61—22no—
59C4×C61—42no—
60C4×C61—41no—
61C4×C61—42no—
62Dic61—81no—
63#1660—611nomaximal, Sylow
64C2×C61—81no—
65C2×C61#45311yescharacteristic
66C2×C61#45612yes—
67#563D6111yescharacteristic
68#501—612no—
69#497—611no—
70#330—612no—
71#329—611no—
72C61#166011yescharacteristic, complemented, Sylow
73C2×Q16—1221no—
74C2×SD16—1221no—
75C4⋊Q8—21no—
76C4⋊Q8—611no—
77#126—22no—
78#125C2×D6112yes—
79#124C2×D6111yescharacteristic
80#123—21no—
81C22⋊Q8—22no—
82#107—1222no—
83#106—1222no—
84#97—612no—
85#97—611no—
86C2×Q8—21no—
87C2×Q8—1221no—
88C2×Q8C22⋊D6111yescharacteristic
89C2×D4C22⋊D6111yescharacteristic
90C22×C4—21no—
91Q16—2442no—
92SD16—2442no—
93C2×C8—1222no—
94C2×C8—1221no—
95C4⋊C4—22no—
96C4⋊C4—22no—
97C4⋊C4—22no—
98C4⋊C4—1222no—
99C4⋊C4C22⋊D6112yes—
100C4⋊C4C22⋊D6112yes—
101C22⋊C4—22no—
102C22⋊C4—21no—
103C22⋊C4—22no—
104C42—21no—
105C42C22×D6111yescharacteristic
106C23—21no—
107Q8—41no—
108Q8—81no—
109Q8—2441no—
110Q8—2441no—
111D4—41no—
112C2×C4—22no—
113C2×C4—21no—
114C2×C4—22no—
115C2×C4—81no—
116C2×C4—2441no—
117C2×C4C2×C22⋊D6112yes—
118C2×C4C2×C22⋊D6111yescharacteristic
119C8—1224no—
120C8—1222no—
121C22—42no—
122C22—41no—
123C22#1451974611yescharacteristic
124C4—22no—
125C4—21no—
126C4—42no—
127C4—42no—
128C4—41no—
129C4—4881no—
130C2—81no—
131C2#1683993011yescharacteristic
132C2#1683994512yes—
subgroupG/H
centerC22#14519746
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#563C2
socleC22×C61#120
hypercenter#563D61
hypocenterC61#1660
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #16840172C2semidirect
3. #16839504C2semidirect
72. C61#1660semidirect