Finite Group Databasebeta

← #21447943

Subgroups — #21447943

Order 7808.

140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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, complemented
2#16840180C211yesmaximal, characteristic
3#16840038C211yesmaximal, characteristic
4#16840034C211yesmaximal, characteristic
5#16839591C211yesmaximal, characteristic, complemented
6#16839579C211yesmaximal, characteristic, complemented
7C61×#362C211yesmaximal, characteristic, complemented
8#14519810—21no—
9#14519808—21no—
10C2×Dic244C2211yescharacteristic
11#14519783C2211yescharacteristic
12#14519723—21no—
13#14519723—21no—
14#14519716—21no—
15C2×#11758185C2211yescharacteristic
16C16×D61—21no—
17#14519713C2211yescharacteristic
18#14519696—21no—
19#14519695—21no—
20C2×Q16×C61C2211yescharacteristic
21M32×C61C2211yescharacteristic
22#108×C61C2211yescharacteristic
23C2×Q8×C61—21no—
24#11758222D411yescharacteristic
25C2×Dic122—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28M16×C61—21no—
29C2×C8×C61C2311yescharacteristic
30#11758202—41no—
31#11758201—41no—
32#11758194—21no—
33#11758194D411yescharacteristic
34Dic244—21no—
35Dic244—21no—
36Dic244—41no—
37#11758190—41no—
38#11758189—21no—
39C8×D61—21no—
40C16×C61—21no—
41#11758185D411yescharacteristic
42#11758185D411yescharacteristic
43Q8×C61—41no—
44Q8×C61—41no—
45C2×C4×C61—41no—
46C2×C4×C61C2×D411yescharacteristic
47C22⋊D61—21no—
48C2×Dic61—41no—
49D244D811yescharacteristic
50C4×D61—21no—
51Dic122—41no—
52Dic122—41no—
53Dic122D811yescharacteristic
54C8×C61—41no—
55C8×C61C2×D411yescharacteristic
56C8×C61#4111yescharacteristic
57#92418—21no—
58#92418—41no—
59C22×C61#13511yescharacteristic
60C2×D61—21no—
61C4×C61—81no—
62C4×C61#12111yescharacteristic
63C4×C61C2×D811yescharacteristic
64Dic61—21no—
65Dic61—81no—
66#2222—611nomaximal, Sylow
67C2×C61—21no—
68C2×C61#46611yescharacteristic
69D61—41no—
70C2×Q32—611no—
71#504—611no—
72#473—611no—
73#473—611no—
74#368—611no—
75#362—611no—
76#362D6111yescharacteristic, complemented
77C61#222211yescharacteristic, complemented, Sylow
78#137—1221no—
79#137—1221no—
80C2×Q16—611no—
81C2×Q16C2×D6111yescharacteristic
82#131—611no—
83Q32—1221no—
84Q32—1221no—
85M32—1221no—
86M32C2×D6111yescharacteristic
87C2×C16—611no—
88C2×C16—1221no—
89#108—611no—
90#108C2×D6111yescharacteristic
91#101—1221no—
92#101—1221no—
93#41—611no—
94C2×Q8—21no—
95C2×Q8—1221no—
96Q16—21no—
97Q16—21no—
98Q16—1221no—
99Q16—1221no—
100Q16—2441no—
101Q16—2441no—
102SD16—2441no—
103SD16—2441no—
104M16—21no—
105M16—611no—
106M16—1221no—
107M16—1221no—
108C2×C8—1221no—
109C2×C8C22×D6111yescharacteristic
110C16—21no—
111C16—611no—
112C16—611no—
113Q8—41no—
114Q8—41no—
115Q8—611no—
116Q8—2441no—
117Q8—2441no—
118D4—611no—
119D4—1221no—
120C2×C4—41no—
121C2×C4—1221no—
122C2×C4—2441no—
123C2×C4D4×D6111yescharacteristic
124C8—41no—
125C8—1221no—
126C8—2441no—
127C8#1175822211yescharacteristic
128C8D4×D6111yescharacteristic
129C22—1221no—
130C22#1451979811yescharacteristic
131C4—81no—
132C4—1221no—
133C4—4881no—
134C4#1451975011yescharacteristic
135C4D8×D6111yescharacteristic
136C2—21no—
137C2—2441no—
138C2#1683999711yescharacteristic
subgroupG/H
centerC2#16839997
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#362C2
socleC2×C61#466
hypercenter#362D61
hypocenterC61#2222
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
1. C2×#14519723C2semidirect
5. #16839591C2semidirect
6. #16839579C2semidirect
7. C61×#362C2semidirect
76. #362D61semidirect
77. C61#2222semidirect