Finite Group Databasebeta

← #21447688

Subgroups — #21447688

Order 7808.

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

normal subgroups only

This group has 148 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
1C2×#14519723C211yesmaximal, characteristic
2C4×Dic244C211yesmaximal, characteristic
3#16839589C211yesmaximal, characteristic
4#16839566C211yesmaximal, characteristic
5#16839565C211yesmaximal, characteristic
6#16839538C211yesmaximal, characteristic
7C4×Q16×C61C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C4×Dic122—21no—
10#14519723C414yescomplemented
11C2×#11758185C2211yescharacteristic
12C2×#11758185C2211yescharacteristic
13#14519711C2211yescharacteristic
14#14519702—21no—
15C2×Q16×C61C2211yescharacteristic
16C4×Q8×C61—21no—
17#107×C61C2211yescharacteristic
18#103×C61—21no—
19C4×C8×C61C2211yescharacteristic
20C2×Q8×C61—21no—
21C2×Dic122—21no—
22Q16×C61—21no—
23Q16×C61C2×C412yes—
24C2×C8×C61D411yescharacteristic
25C2×C8×C61C2311yescharacteristic
26C4⋊C4×C61—21no—
27C4⋊C4×C61—41no—
28C42×C61—41no—
29C42×C61D411yescharacteristic
30C4⋊Dic61—21no—
31#11758196—41no—
32C4×Dic61—41no—
33Dic244—21no—
34Dic244C2×C412yes—
35#11758185—21no—
36#11758185C2×C412yes—
37Q8×C61—22no—
38Q8×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61—41no—
41C2×C4×C61D811yescharacteristic
42C2×C4×C61D811yescharacteristic
43C2×C4×C61C2×D411yescharacteristic
44C2×Dic61—41no—
45C2×Dic61—41no—
46Dic122—22no—
47Dic122—41no—
48C8×C61—21no—
49C8×C61C22×C411yescharacteristic
50C8×C61#4111yescharacteristic
51C22×C61C2×D811yescharacteristic
52C4×C61—21no—
53C4×C61—21no—
54C4×C61—42no—
55C4×C61—81no—
56C4×C61C4×D411yescharacteristic
57C4×C61#13511yescharacteristic
58Dic61—42no—
59Dic61—81no—
60#2176—611nomaximal, Sylow
61C2×C61C4×D811yescharacteristic
62C2×C61#51011yescharacteristic
63C2×C61#51011yescharacteristic
64C2×Q32—611no—
65C4×Q16—611no—
66C4×Q16D6111yescharacteristic
67#367—611no—
68#358—611no—
69#358—611no—
70#346—611no—
71C61#217611yescharacteristic, complemented, Sylow
72C2×Q16—611no—
73C2×Q16C2×D6111yescharacteristic
74C4×Q8—21no—
75C4×Q8—1221no—
76Q32—614no—
77C2×C16—611no—
78C2×C16—611no—
79#107—611no—
80#107C2×D6111yescharacteristic
81#103—21no—
82#103—1221no—
83C4×C8C2×D6111yescharacteristic
84C2×Q8—21no—
85C2×Q8—1221no—
86Q16—21no—
87Q16—612no—
88Q16—1221no—
89Q16C4×D6112yes—
90C2×C8C22⋊D6111yescharacteristic
91C2×C8C22×D6111yescharacteristic
92C4⋊C4—21no—
93C4⋊C4—41no—
94C4⋊C4—1221no—
95C4⋊C4—2441no—
96C42—41no—
97C42—2441no—
98C42C22⋊D6111yescharacteristic
99C16—612no—
100C16—1221no—
101Q8—22no—
102Q8—41no—
103Q8—1222no—
104Q8—2441no—
105C2×C4—41no—
106C2×C4—41no—
107C2×C4—2441no—
108C2×C4—2441no—
109C2×C4#1175819911yescharacteristic
110C2×C4#1175819911yescharacteristic
111C2×C4C2×C22⋊D6111yescharacteristic
112C8—21no—
113C8C2×C4×D6111yescharacteristic
114C8#1175822211yescharacteristic
115C22C2×#1175819911yescharacteristic
116C4—21no—
117C4—21no—
118C4—42no—
119C4—81no—
120C4—4881no—
121C4—2442no—
122C4C4×C22⋊D6111yescharacteristic
123C4#1451979711yescharacteristic
124C2C4×#1175819911yescharacteristic
125C2#1684020211yescharacteristic
126C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC8×C61C22×C4
FrattiniC2×C8C22×D61
FittingC4×Q16×C61C2
socleC22×C61C2×D8
hypercenterC4×Q16D61
hypocenterC61#2176
LCSG ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
10. #14519723C4semidirect
71. C61#2176semidirect