Finite Group Databasebeta

← #21445498

Subgroups — #21445498

Order 7808.

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

normal subgroups only

This group has 176 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#16840165C211yesmaximal, characteristic
2#16840165C211yesmaximal, characteristic
3#16840158C211yesmaximal, characteristic
4#16840142C211yesmaximal, characteristic
5#16840112C211yesmaximal, characteristic
6#16839484C211yesmaximal, characteristic
7C61×#487C211yesmaximal, characteristic
8C2×Dic244—22no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519710—22no—
12#14519710—22no—
13#14519708—22no—
14#14519701—22no—
15C4×#92418C2211yescharacteristic
16C4×#92418C2211yescharacteristic
17C4⋊Q8×C61C2211yescharacteristic
18C4⋊Q8×C61C2211yescharacteristic
19#103×C61—22no—
20C4×C8×C61C2211yescharacteristic
21C2×Q8×C61—21no—
22C2×Q8×C61—21no—
23C2×Dic122—21no—
24C2×Dic122—21no—
25C2×C8×C61D412yes—
26C4⋊C4×C61—21no—
27C4⋊C4×C61—21no—
28C4⋊C4×C61—21no—
29C4⋊C4×C61—21no—
30C42×C61C2311yescharacteristic
31C4⋊Dic61—21no—
32C4⋊Dic61—21no—
33C4⋊Dic61—21no—
34C4⋊Dic61—21no—
35C2×#92418D412yes—
36C2×#92418D412yes—
37Dic244—44no—
38Q8×C61—42no—
39Q8×C61—42no—
40C2×C4×C61—41no—
41C2×C4×C61—41no—
42C2×C4×C61C2×D411yescharacteristic
43C2×C4×C61C2×D411yescharacteristic
44C2×C4×C61C2×D411yescharacteristic
45C2×Dic61—41no—
46C2×Dic61—41no—
47Dic122—42no—
48Dic122—42no—
49C8×C61—22no—
50#92418—22no—
51#92418Q1614yescomplemented
52C22×C61#12711yescharacteristic
53C4×C61—81no—
54C4×C61—81no—
55C4×C61C2×Q1612yes—
56C4×C61AGL(1,ℤ/8)12yes—
57C4×C61#13712yes—
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#487D6111yescharacteristic
70#322—611no—
71C61#172311yescharacteristic, complemented, Sylow
72C2×Q16—1222no—
73C4⋊Q8—611no—
74C4⋊Q8—611no—
75C4⋊Q8C2×D6111yescharacteristic
76C4⋊Q8C2×D6111yescharacteristic
77#107—1222no—
78#107—1222no—
79#106—1222no—
80#103—22no—
81#103—1222no—
82C4×C8—611no—
83C4×C8—611no—
84C4×C8C2×D6111yescharacteristic
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—1221no—
88C2×Q8—1221no—
89Q16—2444no—
90C2×C8—612no—
91C2×C8—612no—
92C2×C8C22⋊D6112yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—1221no—
98C4⋊C4—1221no—
99C4⋊C4—1221no—
100C4⋊C4—1221no—
101C42C22×D6111yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—2442no—
105Q8—2442no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—2441no—
109C2×C4—2441no—
110C2×C4D4×D6111yescharacteristic
111C2×C4D4×D6111yescharacteristic
112C2×C4C2×C22⋊D6111yescharacteristic
113C8—22no—
114C8—614no—
115C8—1222no—
116C22#1451977311yescharacteristic
117C4—81no—
118C4—81no—
119C4—4881no—
120C4—4881no—
121C4Q16×D6112yes—
122C4#1451980212yes—
123C4#1451980612yes—
124C2#1684014011yescharacteristic
125C2#1684015211yescharacteristic
126C2#1684015311yescharacteristic
subgroupG/H
centerC22#14519773
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#487C2
socleC22×C61#127
hypercenter#487D61
hypocenterC61#1723
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
51. #92418Q16semidirect
71. C61#1723semidirect