Finite Group Databasebeta

← #21448040

Subgroups — #21448040

Order 7808.

124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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#16840021C211yesmaximal, characteristic
2#16839809C211yesmaximal, characteristic
3#16839584C211yesmaximal, characteristic, complemented
4#16839579C211yesmaximal, characteristic, complemented
5#16839577C211yesmaximal, characteristic, complemented
6#16839543C211yesmaximal, characteristic
7C61×#365C211yesmaximal, characteristic, complemented
8C2×Dic244C2211yescharacteristic
9C2×#11758189C2211yescharacteristic
10M16×D61—21no—
11#14519757—21no—
12#14519717C2211yescharacteristic
13#14519713C2211yescharacteristic
14#14519712—21no—
15#14519700—21no—
16M32×C61C2211yescharacteristic
17#108×C61C2211yescharacteristic
18#106×C61C2211yescharacteristic
19C2×C4×D61D411yescharacteristic
20C2×Dic122—21no—
21M16×C61—21no—
22C2×C8×C61C2311yescharacteristic
23C4⋊C4×C61—21no—
24#11758198—41no—
25C4⋊Dic61—41no—
26#11758194—21no—
27C2×#92418D411yescharacteristic
28Dic244—21no—
29Dic244—21no—
30#11758189—21no—
31#11758189—21no—
32#11758189—41no—
33C8×D61—41no—
34C16×C61—21no—
35#11758185—21no—
36C22×D61SD1611yescharacteristic
37C2×C4×C61—41no—
38C2×C4×C61C2×D411yescharacteristic
39C2×Dic61—41no—
40C2×Dic61SD1611yescharacteristic
41C4×D61—21no—
42C4×D61—21no—
43Dic122—41no—
44Dic122—41no—
45C8×C61—41no—
46C8×C61#4111yescharacteristic
47C8×C61#4111yescharacteristic
48#92418—21no—
49#92418—41no—
50C22×C61C2×SD1611yescharacteristic
51C2×D61—21no—
52C2×D61—41no—
53C4×C61—81no—
54C4×C61#12311yescharacteristic
55C4×C61AGL(1,ℤ/8)11yescharacteristic
56Dic61—21no—
57Dic61—81no—
58#2239—611nomaximal, Sylow
59C2×C61—21no—
60C2×C61#48111yescharacteristic
61D61—41no—
62#470—611no—
63#430—611no—
64#365—611no—
65#365D6111yescharacteristic, complemented
66#362—611no—
67#362—611no—
68#349—611no—
69C61#223911yescharacteristic, complemented, Sylow
70C2×Q16—611no—
71C2×M16—611no—
72C2×M16—1221no—
73C22⋊Q8—1221no—
74M32—611no—
75M32C2×D6111yescharacteristic
76#108—611no—
77#108—1221no—
78#108C2×D6111yescharacteristic
79#106C2×D6111yescharacteristic
80#103—1221no—
81C2×Q8—1221no—
82C22×C4—611no—
83Q16—1221no—
84Q16—1221no—
85M16—21no—
86M16—1221no—
87M16—1221no—
88M16—1221no—
89M16—2441no—
90C2×C8—611no—
91C2×C8—2441no—
92C2×C8C22×D6111yescharacteristic
93C4⋊C4—21no—
94C4⋊C4—2441no—
95C22⋊C4—2441no—
96C16—21no—
97C16—1221no—
98C23—611no—
99Q8—2441no—
100Q8—2441no—
101C2×C4—41no—
102C2×C4—611no—
103C2×C4—1221no—
104C2×C4—1221no—
105C2×C4—2441no—
106C2×C4D4×D6111yescharacteristic
107C8—41no—
108C8—1221no—
109C8—2441no—
110C8#1175822211yescharacteristic
111C8#1175822611yescharacteristic
112C22—1221no—
113C22—2441no—
114C22SD16×D6111yescharacteristic
115C4—81no—
116C4—1221no—
117C4—4881no—
118C4#1451976211yescharacteristic
119C4#1451980411yescharacteristic
120C2—21no—
121C2—2441no—
122C2#1684008211yescharacteristic
subgroupG/H
centerC2#16840082
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#365C2
socleC2×C61#481
hypercenter#365D61
hypocenterC61#2239
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #365

Complements

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

NH ≅ G/Ntype
3. #16839584C2semidirect
4. #16839579C2semidirect
5. #16839577C2semidirect
7. C61×#365C2semidirect
65. #365D61semidirect
69. C61#2239semidirect