Finite Group Databasebeta

← #21447942

Subgroups — #21447942

Order 7808.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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#16840179C211yesmaximal, characteristic
3#16840037C211yesmaximal, characteristic
4#16839591C211yesmaximal, characteristic, complemented
5#16839578C211yesmaximal, characteristic, complemented
6#16839577C211yesmaximal, characteristic, complemented
7C61×#473C211yesmaximal, characteristic
8#14519807—21no—
9C2×Dic244C2211yescharacteristic
10#14519723—21no—
11#14519723—21no—
12#14519717—21no—
13#14519717C2211yescharacteristic
14C2×#11758185—21no—
15C2×#11758185C2211yescharacteristic
16#14519713C2211yescharacteristic
17#14519695—21no—
18#137×C61—21no—
19C2×Q16×C61C2211yescharacteristic
20#131×C61C2211yescharacteristic
21#108×C61C2211yescharacteristic
22#101×C61—21no—
23#41×C61D411yescharacteristic
24C2×Q8×C61—21no—
25C2×Dic122—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28Q16×C61—41no—
29SD16×C61—41no—
30M16×C61—21no—
31M16×C61—21no—
32M16×C61D411yescharacteristic
33C2×C8×C61—21no—
34C2×C8×C61C2311yescharacteristic
35#11758202—41no—
36#11758200—41no—
37#11758194—21no—
38Dic244—21no—
39Dic244—21no—
40#11758185—21no—
41#11758185D411yescharacteristic
42#11758185D411yescharacteristic
43Q8×C61—41no—
44Q8×C61—41no—
45Q8×C61D811yescharacteristic
46D4×C61—21no—
47D4×C61D811yescharacteristic
48C2×C4×C61—21no—
49C2×C4×C61—41no—
50C2×C4×C61C2×D411yescharacteristic
51C2×Dic61—41no—
52Dic122—41no—
53Dic122—41no—
54C8×C61—21no—
55C8×C61—41no—
56C8×C61C2×D411yescharacteristic
57C8×C61#4111yescharacteristic
58#92418—41no—
59C22×C61—21no—
60C22×C61#13511yescharacteristic
61C4×C61—21no—
62C4×C61—81no—
63C4×C61#12111yescharacteristic
64C4×C61C2×D811yescharacteristic
65Dic61—81no—
66#2222—611nomaximal, Sylow
67C2×C61—21no—
68C2×C61—41no—
69C2×C61#46611yescharacteristic
70C2×Q32—611no—
71#504—611no—
72#473—611no—
73#473D6111yescharacteristic
74#368—611no—
75#362—611no—
76#362—611no—
77C61#222211yescharacteristic, complemented, Sylow
78#137—21no—
79#137—1221no—
80C2×Q16—611no—
81C2×Q16C2×D6111yescharacteristic
82#131C2×D6111yescharacteristic
83Q32—1221no—
84Q32—1221no—
85M32—611no—
86M32—1221no—
87C2×C16—611no—
88C2×C16—1221no—
89#108—611no—
90#108C2×D6111yescharacteristic
91#101—21no—
92#101—1221no—
93#41C22⋊D6111yescharacteristic
94C2×Q8—21no—
95C2×Q8—1221no—
96Q16—21no—
97Q16—21no—
98Q16—41no—
99Q16—1221no—
100Q16—1221no—
101Q16—2441no—
102SD16—41no—
103SD16—2441no—
104M16—21no—
105M16—21no—
106M16—1221no—
107M16C22⋊D6111yescharacteristic
108C2×C8—21no—
109C2×C8C22×D6111yescharacteristic
110C16—611no—
111C16—611no—
112C16—1221no—
113Q8—41no—
114Q8—41no—
115Q8—2441no—
116Q8—2441no—
117Q8#1175819911yescharacteristic
118D4—21no—
119D4#1175819911yescharacteristic
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—2441no—
123C2×C4C2×C22⋊D6111yescharacteristic
124C8—21no—
125C8—41no—
126C8—2441no—
127C8D4×D6111yescharacteristic
128C8#1175822411yescharacteristic
129C22—21no—
130C22#1451979711yescharacteristic
131C4—21no—
132C4—81no—
133C4—4881no—
134C4#1451974911yescharacteristic
135C4C2×#1175819911yescharacteristic
136C2—21no—
137C2—41no—
138C2#1683999611yescharacteristic
subgroupG/H
centerC2#16839996
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#473C2
socleC2×C61#466
hypercenter#473D61
hypocenterC61#2222
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
1. C2×#14519723C2semidirect
4. #16839591C2semidirect
5. #16839578C2semidirect
6. #16839577C2semidirect
77. C61#2222semidirect