Finite Group Databasebeta

← #21447890

Subgroups — #21447890

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#16840197C211yesmaximal, characteristic
2#16840147C211yesmaximal, characteristic, complemented
3#16839879C211yesmaximal, characteristic, complemented
4#16839582C211yesmaximal, characteristic, complemented
5#16839578C211yesmaximal, characteristic, complemented
6#16839576C211yesmaximal, characteristic, complemented
7C61×#510C211yesmaximal, characteristic, complemented
8C2×#11758201—21no—
9C2×D488C2211yescharacteristic
10#14519784—21no—
11#14519766—21no—
12#14519720—21no—
13#14519718—21no—
14#14519717C2211yescharacteristic
15#14519713C2211yescharacteristic
16#14519704—21no—
17C8×Dic61C2211yescharacteristic
18#135×C61C2211yescharacteristic
19C2×Q16×C61C2211yescharacteristic
20Q32×C61—21no—
21SD32×C61—21no—
22M32×C61C2211yescharacteristic
23#41×C61—21no—
24C2×Q8×C61—21no—
25C2×D244—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28Q16×C61D411yescharacteristic
29SD16×C61—21no—
30D8×C61D411yescharacteristic
31C2×C8×C61C2311yescharacteristic
32#11758201—41no—
33#11758201—41no—
34#11758198—42no—
35C4×Dic61D411yescharacteristic
36#11758194—21no—
37#11758194—41no—
38C2×#92418—41no—
39C2×#92418D411yescharacteristic
40D488—21no—
41D488—21no—
42C16×C61—21no—
43#11758185—21no—
44C22×D61—41no—
45Q8×C61—21no—
46Q8×C61—41no—
47Q8×C61—41no—
48D4×C61—21no—
49D4×C61—41no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61C2×D411yescharacteristic
53C2×Dic61—21no—
54D244—41no—
55D244—41no—
56C8×C61C2×D411yescharacteristic
57C8×C61#4111yescharacteristic
58#92418—41no—
59#92418D811yescharacteristic
60#92418D811yescharacteristic
61C22×C61—41no—
62C22×C61AGL(1,ℤ/8)11yescharacteristic
63C2×D61—82no—
64C2×D61—81no—
65C4×C61—41no—
66C4×C61—81no—
67C4×C61#12111yescharacteristic
68C4×C61C2×D811yescharacteristic
69Dic61—41no—
70#2212—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61—81no—
73C2×C61#45911yescharacteristic
74D61—161no—
75#510D6111yescharacteristic, complemented
76#509—611no—
77#495—611no—
78#443—611no—
79#364—611no—
80#362—611no—
81#361—611no—
82C61#221211yescharacteristic, complemented, Sylow
83#135C2×D6111yescharacteristic
84C2×Q16C2×D6111yescharacteristic
85C2×SD16—1221no—
86C2×D8—611no—
87#131—1221no—
88#124—1221no—
89Q32—21no—
90SD32—21no—
91SD32—1221no—
92D16—1221no—
93M32—611no—
94M32C2×D6111yescharacteristic
95#108—611no—
96#104—1221no—
97C4×C8—611no—
98#41—21no—
99C2×Q8—21no—
100C2×D4—1221no—
101Q16—21no—
102Q16—21no—
103Q16C22⋊D6111yescharacteristic
104SD16—21no—
105SD16—2441no—
106SD16—2441no—
107D8—1221no—
108D8—1221no—
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—2441no—
120Q8—21no—
121Q8—41no—
122Q8—41no—
123D4—21no—
124D4—41no—
125D4—2441no—
126D4—2441no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—1221no—
130C2×C4D4×D6111yescharacteristic
131C8—611no—
132C8—611no—
133C8—2441no—
134C8#1175822411yescharacteristic
135C8C2×C22⋊D6111yescharacteristic
136C22—41no—
137C22—4882no—
138C22—4881no—
139C22#1451980111yescharacteristic
140C4—41no—
141C4—81no—
142C4—2441no—
143C4#1451974911yescharacteristic
144C4D8×D6111yescharacteristic
145C2—21no—
146C2—81no—
147C2—9761no—
148C2#1683995511yescharacteristic
subgroupG/H
centerC2#16839955
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#510C2
socleC2×C61#459
hypercenter#510D61
hypocenterC61#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #16840147C2semidirect
3. #16839879C2semidirect
4. #16839582C2semidirect
5. #16839578C2semidirect
6. #16839576C2semidirect
7. C61×#510C2semidirect
75. #510D61semidirect
82. C61#2212semidirect