Finite Group Databasebeta

← #21445496

Subgroups — #21445496

Order 7808.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840167C211yesmaximal, characteristic
3#16840160C211yesmaximal, characteristic
4#16840142C211yesmaximal, characteristic
5#16840113C211yesmaximal, characteristic
6#16840113C211yesmaximal, characteristic
7C61×#322C211yesmaximal, characteristic
8C2×Dic244—22no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519711—22no—
14#14519711—22no—
15#14519709—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—
37Dic244—44no—
38C2×C4×C61C2×D411yescharacteristic
39C2×C4×C61C2×D411yescharacteristic
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—41no—
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61—41no—
45Dic122—42no—
46Dic122—42no—
47Dic122—42no—
48Dic122—42no—
49C8×C61—22no—
50C8×C61—22no—
51C8×C61Q1614yescomplemented
52C22×C61#12711yescharacteristic
53C4×C61C2×Q1612yes—
54C4×C61AGL(1,ℤ/8)12yes—
55C4×C61#13712yes—
56Dic61—81no—
57Dic61—81no—
58Dic61—81no—
59Dic61—81no—
60#1723—611nomaximal, Sylow
61C2×C61#49411yescharacteristic
62C2×C61#49611yescharacteristic
63C2×C61#49711yescharacteristic
64#500—611no—
65#500—611no—
66#498—611no—
67#494—611no—
68#487—611no—
69#487—611no—
70#322D6111yescharacteristic
71C61#172311yescharacteristic, complemented, Sylow
72C2×Q16—1222no—
73C4⋊Q8—611no—
74C4⋊Q8—611no—
75C4⋊Q8—611no—
76C4⋊Q8—611no—
77#107—1222no—
78#107—1222no—
79#106—1222no—
80#103—1222no—
81#103—1222no—
82C4×C8C2×D6111yescharacteristic
83C4×C8C2×D6111yescharacteristic
84C4×C8C2×D6111yescharacteristic
85C2×Q8—1221no—
86C2×Q8—1221no—
87C2×Q8—1221no—
88C2×Q8—1221no—
89Q16—2444no—
90C2×C8D24412yes—
91C2×C8D24412yes—
92C2×C8D24412yes—
93C4⋊C4—1221no—
94C4⋊C4—1221no—
95C4⋊C4—1221no—
96C4⋊C4—1221no—
97C4⋊C4—1221no—
98C4⋊C4—1221no—
99C4⋊C4—1221no—
100C4⋊C4—1221no—
101C42C22×D6111yescharacteristic
102Q8—2442no—
103Q8—2442no—
104Q8—2442no—
105Q8—2442no—
106C2×C4—2441no—
107C2×C4—2441no—
108C2×C4—2441no—
109C2×C4—2441no—
110C2×C4C2×D24411yescharacteristic
111C2×C4C2×D24411yescharacteristic
112C2×C4C2×D24411yescharacteristic
113C8—22no—
114C8—22no—
115C8Dic24414yescomplemented
116C22#1451977411yescharacteristic
117C4—4881no—
118C4—4881no—
119C4—4881no—
120C4—4881no—
121C4C2×Dic24412yes—
122C4#1451980512yes—
123C4#1451981012yes—
124C2#1684014211yescharacteristic
125C2#1684015111yescharacteristic
126C2#1684015611yescharacteristic
subgroupG/H
centerC22#14519774
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#322C2
socleC22×C61#127
hypercenter#322D61
hypocenterC61#1723
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #322

Complements

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

NH ≅ G/Ntype
51. C8×C61Q16semidirect
71. C61#1723semidirect
115. C8Dic244semidirect