Finite Group Databasebeta

← #21448025

Subgroups — #21448025

Order 7808.

132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 45 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#16840000C211yesmaximal, characteristic
2#16839799C211yesmaximal, characteristic
3#16839590C211yesmaximal, characteristic, complemented
4#16839587C211yesmaximal, characteristic, complemented
5#16839566C211yesmaximal, characteristic, complemented
6#16839541C211yesmaximal, characteristic
7C61×#358C211yesmaximal, characteristic, complemented
8C2×C8×D61C2211yescharacteristic
9#14519753—21no—
10#14519735—21no—
11C2×#11758185C2211yescharacteristic
12#14519711C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519708—21no—
15#14519701—21no—
16C2×Q16×C61C2211yescharacteristic
17C2×C16×C61C2211yescharacteristic
18#107×C61C2211yescharacteristic
19C2×Q8×C61—21no—
20C2×C4×D61D411yescharacteristic
21Q16×C61—21no—
22Q16×C61—21no—
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25#11758198—41no—
26#11758198—41no—
27C4⋊Dic61—21no—
28C4⋊Dic61—21no—
29#11758196—41no—
30C4×Dic61—41no—
31C2×#92418D411yescharacteristic
32C8×D61—21no—
33C8×D61—21no—
34C16×C61—21no—
35#11758185—21no—
36C22×D61D811yescharacteristic
37Q8×C61—41no—
38Q8×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61C2×D411yescharacteristic
42C2×Dic61—41no—
43C2×Dic61—41no—
44C2×Dic61D811yescharacteristic
45C4×D61—21no—
46C4×D61—21no—
47C8×C61#4111yescharacteristic
48C8×C61#4111yescharacteristic
49#92418—21no—
50C22×C61C2×D811yescharacteristic
51C2×D61—21no—
52C2×D61—21no—
53C2×D61—21no—
54C4×C61—81no—
55C4×C61—81no—
56C4×C61#12311yescharacteristic
57C4×C61#13711yescharacteristic
58Dic61—21no—
59Dic61—81no—
60Dic61—81no—
61#2237—611nomaximal, Sylow
62C2×C61#48011yescharacteristic
63C2×C61#50811yescharacteristic
64C2×C61#51011yescharacteristic
65D61—41no—
66#467—611no—
67#427—611no—
68#367—611no—
69#366—611no—
70#358—611no—
71#358D6111yescharacteristic, complemented
72C22⋊C16—611no—
73C61#223711yescharacteristic, complemented, Sylow
74C2×Q16C2×D6111yescharacteristic
75C22×C8—611no—
76C22⋊Q8—1221no—
77#117—1221no—
78C2×C16—611no—
79C2×C16C2×D6111yescharacteristic
80#107—611no—
81#107—611no—
82#107C2×D6111yescharacteristic
83#106—1221no—
84#103—1221no—
85C2×Q8—21no—
86C22×C4—611no—
87Q16—21no—
88Q16—21no—
89C2×C8—611no—
90C2×C8—1221no—
91C2×C8—1221no—
92C2×C8C22×D6111yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—1221no—
95C4⋊C4—1221no—
96C4⋊C4—2441no—
97C22⋊C4—2441no—
98C22⋊C4—2441no—
99C42—2441no—
100C16—21no—
101C16—1221no—
102C23—611no—
103Q8—41no—
104Q8—41no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—611no—
108C2×C4—1221no—
109C2×C4—1221no—
110C2×C4—2441no—
111C2×C4—2441no—
112C2×C4D4×D6111yescharacteristic
113C8—1221no—
114C8#1175822211yescharacteristic
115C8#1175822411yescharacteristic
116C22—1221no—
117C22—1221no—
118C22—1221no—
119C22D8×D6111yescharacteristic
120C4—81no—
121C4—81no—
122C4—1221no—
123C4—4881no—
124C4—4881no—
125C4#1451975911yescharacteristic
126C4#1451980611yescharacteristic
127C2—2441no—
128C2#1684007411yescharacteristic
129C2#1684019311yescharacteristic
130C2#1684020411yescharacteristic
subgroupG/H
centerC22D8×D61
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#358C2
socleC22×C61C2×D8
hypercenter#358D61
hypocenterC61#2237
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
3. #16839590C2semidirect
4. #16839587C2semidirect
5. #16839566C2semidirect
7. C61×#358C2semidirect
71. #358D61semidirect
73. C61#2237semidirect