Finite Group Databasebeta

← #21447886

Subgroups — #21447886

Order 7808.

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

normal subgroups only

This group has 154 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#16840202C211yesmaximal, characteristic, complemented
2#16840145C211yesmaximal, characteristic, complemented
3#16839879C211yesmaximal, characteristic, complemented
4#16839582C211yesmaximal, characteristic, complemented
5#16839579C211yesmaximal, characteristic, complemented
6#16839575C211yesmaximal, characteristic, complemented
7C61×#509C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×#11758200—21no—
10#14519784—21no—
11#14519764—21no—
12#14519723—21no—
13#14519721—21no—
14#14519717C2211yescharacteristic
15#14519713C2211yescharacteristic
16#14519704—21no—
17C8×Dic61C2211yescharacteristic
18#135×C61C2211yescharacteristic
19C2×D8×C61C2211yescharacteristic
20SD32×C61—21no—
21D16×C61—21no—
22M32×C61C2211yescharacteristic
23#41×C61—21no—
24C2×D4×C61—21no—
25C2×Dic122—21no—
26Q16×C61D411yescharacteristic
27SD16×C61—21no—
28D8×C61—21no—
29D8×C61—21no—
30D8×C61D411yescharacteristic
31C2×C8×C61C2311yescharacteristic
32C22⋊Dic61—42no—
33#11758200—41no—
34#11758200—41no—
35C4×Dic61D411yescharacteristic
36#11758194—21no—
37#11758194—41no—
38C2×#92418—41no—
39C2×#92418D411yescharacteristic
40Dic244—21no—
41Dic244—21no—
42C16×C61—21no—
43#11758185—21no—
44C23×C61—41no—
45Q8×C61—21no—
46D4×C61—21no—
47D4×C61—41no—
48D4×C61—41no—
49D4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61C2×D411yescharacteristic
52C2×Dic61—21no—
53C2×Dic61—41no—
54Dic122—41no—
55Dic122—41no—
56C8×C61C2×D411yescharacteristic
57C8×C61#4111yescharacteristic
58#92418—41no—
59#92418D811yescharacteristic
60#92418D811yescharacteristic
61C22×C61—41no—
62C22×C61—82no—
63C22×C61—81no—
64C22×C61AGL(1,ℤ/8)11yescharacteristic
65C4×C61—41no—
66C4×C61#12111yescharacteristic
67C4×C61C2×D811yescharacteristic
68Dic61—41no—
69Dic61—81no—
70#2212—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61—81no—
73C2×C61—161no—
74C2×C61#45911yescharacteristic
75#510—611no—
76#509D6111yescharacteristic
77#495—611no—
78#443—611no—
79#364—611no—
80#362—611no—
81#361—611no—
82C61#221211yescharacteristic, complemented, Sylow
83#135C2×D6111yescharacteristic
84C2×Q16—611no—
85C2×SD16—1221no—
86C2×D8C2×D6111yescharacteristic
87#131—1221no—
88#124—1221no—
89Q32—1221no—
90SD32—21no—
91SD32—1221no—
92D16—21no—
93M32—611no—
94M32C2×D6111yescharacteristic
95#108—611no—
96#104—1221no—
97C4×C8—611no—
98#41—21no—
99C2×Q8—1221no—
100C2×D4—21no—
101Q16—1221no—
102Q16—1221no—
103Q16C22⋊D6111yescharacteristic
104SD16—21no—
105SD16—2441no—
106SD16—2441no—
107D8—21no—
108D8—21no—
109D8C22⋊D6111yescharacteristic
110M16—1221no—
111M16—2441no—
112C2×C8—611no—
113C2×C8—2441no—
114C2×C8C22×D6111yescharacteristic
115C22⋊C4—2442no—
116C42—611no—
117C16—21no—
118C16—1221no—
119C23—41no—
120Q8—21no—
121Q8—2441no—
122Q8—2441no—
123D4—21no—
124D4—41no—
125D4—41no—
126D4—41no—
127C2×C4—41no—
128C2×C4—1221no—
129C2×C4—2441no—
130C2×C4D4×D6111yescharacteristic
131C8—611no—
132C8—611no—
133C8—2441no—
134C8#1175822411yescharacteristic
135C8C2×C22⋊D6111yescharacteristic
136C22—41no—
137C22—82no—
138C22—81no—
139C22#1451980111yescharacteristic
140C4—41no—
141C4—4881no—
142C4—2441no—
143C4#1451974911yescharacteristic
144C4D8×D6111yescharacteristic
145C2—21no—
146C2—81no—
147C2—161no—
148C2#1683995511yescharacteristic
subgroupG/H
centerC2#16839955
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#509C2
socleC2×C61#459
hypercenter#509D61
hypocenterC61#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #509

Complements

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

NH ≅ G/Ntype
1. #16840202C2semidirect
2. #16840145C2semidirect
3. #16839879C2semidirect
4. #16839582C2semidirect
5. #16839579C2semidirect
6. #16839575C2semidirect
82. C61#2212semidirect