Finite Group Databasebeta

← #21445465

Subgroups — #21445465

Order 7808.

164 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 61 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#16840167C211yesmaximal, characteristic
2#16840160C211yesmaximal, characteristic
3#16840113C211yesmaximal, characteristic
4#16840113C211yesmaximal, characteristic
5#16840113C211yesmaximal, characteristic
6#16840113C211yesmaximal, characteristic
7C61×#322C211yesmaximal, characteristic
8#14519777C2211yescharacteristic
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519711—22no—
13#14519709—22no—
14#14519702—22no—
15#14519702—22no—
16#14519702—22no—
17#14519702—22no—
18C4×C8×C61C2211yescharacteristic
19C4×C8×C61C2211yescharacteristic
20C4×C8×C61C2211yescharacteristic
21C2×Dic122—21no—
22C2×Dic122—21no—
23C2×Dic122—21no—
24C2×Dic122—21no—
25C2×C8×C61D412yes—
26C2×C8×C61D412yes—
27C2×C8×C61D412yes—
28C42×C61C2311yescharacteristic
29C4⋊Dic61—21no—
30C4⋊Dic61—21no—
31C4⋊Dic61—21no—
32C4⋊Dic61—21no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C4⋊Dic61—21no—
36C4⋊Dic61—21no—
37C2×C4×C61C2×D411yescharacteristic
38C2×C4×C61C2×D411yescharacteristic
39C2×C4×C61C2×D411yescharacteristic
40C2×Dic61—41no—
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44Dic122—42no—
45Dic122—42no—
46Dic122—42no—
47Dic122—42no—
48C8×C61—22no—
49C8×C61—22no—
50C8×C61—22no—
51C22×C61#12711yescharacteristic
52C4×C61#13512yes—
53C4×C61#13712yes—
54C4×C61#13712yes—
55Dic61—81no—
56Dic61—81no—
57Dic61—81no—
58Dic61—81no—
59#1718—611nomaximal, Sylow
60C2×C61#49511yescharacteristic
61C2×C61#49711yescharacteristic
62C2×C61#49711yescharacteristic
63#500—611no—
64#498—611no—
65#487—611no—
66#487—611no—
67#487—611no—
68#487—611no—
69#322D6111yescharacteristic
70C61#171811yescharacteristic, complemented, Sylow
71C4⋊Q8—611no—
72C4⋊Q8—611no—
73C4⋊Q8—611no—
74C4⋊Q8—611no—
75#107—1222no—
76#106—1222no—
77#103—1222no—
78#103—1222no—
79#103—1222no—
80#103—1222no—
81C4×C8C2×D6111yescharacteristic
82C4×C8C2×D6111yescharacteristic
83C4×C8C2×D6111yescharacteristic
84C2×Q8—1221no—
85C2×Q8—1221no—
86C2×Q8—1221no—
87C2×Q8—1221no—
88C2×C8D24412yes—
89C2×C8D24412yes—
90C2×C8D24412yes—
91C4⋊C4—1221no—
92C4⋊C4—1221no—
93C4⋊C4—1221no—
94C4⋊C4—1221no—
95C4⋊C4—1221no—
96C4⋊C4—1221no—
97C4⋊C4—1221no—
98C4⋊C4—1221no—
99C42C22×D6111yescharacteristic
100Q8—2442no—
101Q8—2442no—
102Q8—2442no—
103Q8—2442no—
104C2×C4—2441no—
105C2×C4—2441no—
106C2×C4—2441no—
107C2×C4—2441no—
108C2×C4C2×D24411yescharacteristic
109C2×C4C2×D24411yescharacteristic
110C2×C4C2×D24411yescharacteristic
111C8—22no—
112C8—22no—
113C8—22no—
114C22#1451977411yescharacteristic
115C4—4881no—
116C4—4881no—
117C4—4881no—
118C4—4881no—
119C4#1451979912yes—
120C4#1451981012yes—
121C4#1451981012yes—
122C2#1684014611yescharacteristic
123C2#1684015611yescharacteristic
124C2#1684015611yescharacteristic
subgroupG/H
centerC22#14519774
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#322C2
socleC22×C61#127
hypercenter#322D61
hypocenterC61#1718
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #322

Complements

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

NH ≅ G/Ntype
70. C61#1718semidirect