Finite Group Databasebeta

← #21447898

Subgroups — #21447898

Order 7808.

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

normal subgroups only

This group has 150 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
2#16840140C211yesmaximal, characteristic, complemented
3#16839879C211yesmaximal, characteristic
4#16839582C211yesmaximal, characteristic, complemented
5#16839579C211yesmaximal, characteristic, complemented
6#16839578C211yesmaximal, characteristic, complemented
7C61×#510C211yesmaximal, characteristic
8C2×Dic244C2211yescharacteristic
9C2×#11758202—21no—
10#14519784—21no—
11#14519775—21no—
12#14519723—21no—
13#14519721—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×Dic122—21no—
26Q16×C61—21no—
27Q16×C61—21no—
28Q16×C61D411yescharacteristic
29SD16×C61—21no—
30D8×C61D411yescharacteristic
31C2×C8×C61C2311yescharacteristic
32#11758202—41no—
33#11758202—41no—
34#11758196—42no—
35C4×Dic61D411yescharacteristic
36#11758194—21no—
37#11758194—41no—
38C2×#92418—41no—
39C2×#92418D411yescharacteristic
40Dic244—21no—
41Dic244—21no—
42C16×C61—21no—
43#11758185—21no—
44Q8×C61—21no—
45Q8×C61—41no—
46Q8×C61—41no—
47D4×C61—21no—
48D4×C61—41no—
49C2×C4×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×C61AGL(1,ℤ/8)11yescharacteristic
63C4×C61—41no—
64C4×C61—81no—
65C4×C61#12111yescharacteristic
66C4×C61C2×D811yescharacteristic
67Dic61—22no—
68Dic61—81no—
69#2214—611nomaximal, Sylow
70C2×C61—21no—
71C2×C61—81no—
72C2×C61#45911yescharacteristic
73#510—611no—
74#510D6111yescharacteristic
75#494—611no—
76#443—611no—
77#364—611no—
78#362—611no—
79#362—611no—
80C61#221411yescharacteristic, complemented, Sylow
81#135C2×D6111yescharacteristic
82C2×Q16—611no—
83C2×Q16—1221no—
84C2×Q16C2×D6111yescharacteristic
85#131—1221no—
86C4⋊Q8—1221no—
87Q32—21no—
88Q32—1221no—
89SD32—21no—
90SD32—1221no—
91M32—611no—
92M32C2×D6111yescharacteristic
93#108—611no—
94#104—1221no—
95C4×C8—611no—
96#41—21no—
97C2×Q8—21no—
98C2×Q8—1221no—
99Q16—21no—
100Q16—21no—
101Q16—1221no—
102Q16—1221no—
103Q16—2441no—
104Q16—2441no—
105Q16C22⋊D6111yescharacteristic
106SD16—21no—
107D8C22⋊D6111yescharacteristic
108M16—1221no—
109M16—2441no—
110C2×C8—611no—
111C2×C8—2441no—
112C2×C8C22×D6111yescharacteristic
113C4⋊C4—2442no—
114C42—611no—
115C16—21no—
116C16—1221no—
117Q8—21no—
118Q8—41no—
119Q8—41no—
120Q8—2441no—
121Q8—2441no—
122D4—21no—
123D4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—1221no—
127C2×C4—2441no—
128C2×C4D4×D6111yescharacteristic
129C8—611no—
130C8—611no—
131C8—2441no—
132C8#1175822411yescharacteristic
133C8C2×C22⋊D6111yescharacteristic
134C22—41no—
135C22#1451980111yescharacteristic
136C4—41no—
137C4—81no—
138C4—1222no—
139C4—4881no—
140C4#1451974911yescharacteristic
141C4D8×D6111yescharacteristic
142C2—21no—
143C2—81no—
144C2#1683995511yescharacteristic
subgroupG/H
centerC2#16839955
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#510C2
socleC2×C61#459
hypercenter#510D61
hypocenterC61#2214
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. #16840140C2semidirect
4. #16839582C2semidirect
5. #16839579C2semidirect
6. #16839578C2semidirect
80. C61#2214semidirect