Finite Group Databasebeta

← #21447889

Subgroups — #21447889

Order 7808.

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

normal subgroups only

This group has 154 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
1#16840205C211yesmaximal, characteristic, complemented
2#16840200C211yesmaximal, characteristic
3#16840146C211yesmaximal, characteristic, complemented
4#16839880C211yesmaximal, characteristic, complemented
5#16839579C211yesmaximal, characteristic, complemented
6#16839576C211yesmaximal, characteristic, complemented
7C61×#364C211yesmaximal, characteristic, complemented
8#14519799C2211yescharacteristic
9C2×Dic244C2211yescharacteristic
10C2×#11758190—21no—
11C2×D488C2211yescharacteristic
12#14519783—21no—
13#14519765—21no—
14Dic488—21no—
15#14519722—21no—
16#14519722—21no—
17D976—21no—
18#14519713C2211yescharacteristic
19#14519705—21no—
20M32×C61C2211yescharacteristic
21M32×C61C2211yescharacteristic
22C4×C8×C61C2211yescharacteristic
23#11758222—21no—
24C2×D244—21no—
25C2×Dic122—21no—
26C2×C8×C61D411yescharacteristic
27C2×C8×C61C2311yescharacteristic
28C42×C61D411yescharacteristic
29#11758198—42no—
30#11758194—21no—
31Dic244—21no—
32Dic244—21no—
33Dic244D411yescharacteristic
34D488—21no—
35D488—21no—
36D488D411yescharacteristic
37#11758190—21no—
38#11758190—41no—
39#11758190—41no—
40#11758189—41no—
41C8×D61—41no—
42C16×C61—21no—
43C16×C61—21no—
44C22×D61—41no—
45C2×C4×C61—21no—
46C2×C4×C61C2×D411yescharacteristic
47C22⋊D61—41no—
48C2×Dic61—41no—
49D244—21no—
50D244—41no—
51D244—41no—
52C4×D61—41no—
53Dic122—21no—
54Dic122—41no—
55Dic122—41no—
56C8×C61D811yescharacteristic
57C8×C61D811yescharacteristic
58C8×C61C2×D411yescharacteristic
59C8×C61#4111yescharacteristic
60#92418—41no—
61C22×C61AGL(1,ℤ/8)11yescharacteristic
62C2×D61—41no—
63C2×D61—82no—
64C2×D61—81no—
65C4×C61—41no—
66C4×C61#12111yescharacteristic
67C4×C61C2×D811yescharacteristic
68Dic61—41no—
69Dic61—81no—
70#2212—611nomaximal, Sylow
71C2×C61—21no—
72C2×C61#45911yescharacteristic
73D61—81no—
74D61—161no—
75#510—611no—
76#509—611no—
77#495—611no—
78#443—611no—
79#364D6111yescharacteristic, complemented
80#362—611no—
81#361—611no—
82C61#221211yescharacteristic, complemented, Sylow
83#135—611no—
84C2×Q16—611no—
85C2×SD16—1221no—
86C2×D8—611no—
87#131—1221no—
88#124—1221no—
89Q32—1221no—
90SD32—1221no—
91SD32—1221no—
92D16—1221no—
93M32C2×D6111yescharacteristic
94M32C2×D6111yescharacteristic
95#108—611no—
96#104—1221no—
97C4×C8C2×D6111yescharacteristic
98#41—1221no—
99C2×Q8—1221no—
100C2×D4—1221no—
101Q16—611no—
102Q16—1221no—
103Q16—1221no—
104SD16—1221no—
105SD16—2441no—
106SD16—2441no—
107D8—611no—
108D8—1221no—
109D8—1221no—
110M16—1221no—
111M16—2441no—
112C2×C8—2441no—
113C2×C8D24411yescharacteristic
114C2×C8C22×D6111yescharacteristic
115C22⋊C4—2442no—
116C42D24411yescharacteristic
117C16—21no—
118C16—21no—
119C23—2441no—
120Q8—1221no—
121Q8—2441no—
122Q8—2441no—
123D4—1221no—
124D4—2441no—
125D4—2441no—
126D4—2441no—
127C2×C4—21no—
128C2×C4—2441no—
129C2×C4—2441no—
130C2×C4C2×D24411yescharacteristic
131C8—2441no—
132C8D48811yescharacteristic
133C8D48811yescharacteristic
134C8D4×D6111yescharacteristic
135C8#1175822611yescharacteristic
136C22—4882no—
137C22—4881no—
138C22—2441no—
139C22#1451980511yescharacteristic
140C4—41no—
141C4—4881no—
142C4—2441no—
143C4#1451975211yescharacteristic
144C4C2×D48811yescharacteristic
145C2—21no—
146C2—9761no—
147C2—4881no—
148C2#1683995811yescharacteristic
subgroupG/H
centerC2#16839958
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#364C2
socleC2×C61#459
hypercenter#364D61
hypocenterC61#2212
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #364

Complements

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

NH ≅ G/Ntype
1. #16840205C2semidirect
3. #16840146C2semidirect
4. #16839880C2semidirect
5. #16839579C2semidirect
6. #16839576C2semidirect
7. C61×#364C2semidirect
79. #364D61semidirect
82. C61#2212semidirect