Finite Group Databasebeta

← #21447993

Subgroups — #21447993

Order 7808.

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

normal subgroups only

This group has 120 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#16840162C211yesmaximal, characteristic, complemented
2#16839879C211yesmaximal, characteristic
3#16839585C211yesmaximal, characteristic, complemented
4#16839584C211yesmaximal, characteristic, complemented
5#16839582C211yesmaximal, characteristic, complemented
6#16839572C211yesmaximal, characteristic
7C61×#360C211yesmaximal, characteristic
8#14519784—21no—
9#14519768—21no—
10#14519717C2211yescharacteristic
11#14519713C2211yescharacteristic
12#14519710—21no—
13#14519709C2211yescharacteristic
14#14519704—21no—
15C8×Dic61C2211yescharacteristic
16#135×C61C2211yescharacteristic
17M32×C61C2211yescharacteristic
18#106×C61C2211yescharacteristic
19#41×C61—21no—
20Q16×C61Q811yescharacteristic
21SD16×C61—21no—
22D8×C61Q811yescharacteristic
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—21no—
25C4⋊Dic61—21no—
26C4⋊Dic61—41no—
27#11758196—41no—
28C4×Dic61D411yescharacteristic
29#11758194—21no—
30#11758194—41no—
31C2×#92418—41no—
32C2×#92418D411yescharacteristic
33C16×C61—21no—
34#11758185—21no—
35Q8×C61—21no—
36D4×C61—21no—
37D4×C61—41no—
38C2×C4×C61—41no—
39C2×C4×C61—41no—
40C2×C4×C61C2×D411yescharacteristic
41C2×Dic61—21no—
42C2×Dic61—41no—
43C8×C61C2×Q811yescharacteristic
44C8×C61#4111yescharacteristic
45#92418—41no—
46#92418SD1611yescharacteristic
47#92418SD1611yescharacteristic
48C22×C61—41no—
49C22×C61AGL(1,ℤ/8)11yescharacteristic
50C4×C61—41no—
51C4×C61—81no—
52C4×C61C22⋊Q811yescharacteristic
53C4×C61C2×SD1611yescharacteristic
54Dic61—41no—
55Dic61—81no—
56#2231—611nomaximal, Sylow
57C2×C61—21no—
58C2×C61—81no—
59C2×C61#47611yescharacteristic
60#499—611no—
61#443—611no—
62#365—611no—
63#365—611no—
64#364—611no—
65#360—611no—
66#360D6111yescharacteristic
67C61#223111yescharacteristic, complemented, Sylow
68#135C2×D6111yescharacteristic
69#131—1221no—
70#125—1221no—
71M32—611no—
72M32C2×D6111yescharacteristic
73#108—611no—
74#107—1221no—
75#106—611no—
76#106C2×D6111yescharacteristic
77#104—1221no—
78C4×C8—611no—
79#41—21no—
80Q16Dic12211yescharacteristic
81SD16—21no—
82D8Dic12211yescharacteristic
83M16—1221no—
84M16—2441no—
85C2×C8—611no—
86C2×C8—2441no—
87C2×C8C22×D6111yescharacteristic
88C4⋊C4—21no—
89C4⋊C4—1221no—
90C4⋊C4—2441no—
91C4⋊C4—2441no—
92C42—611no—
93C16—21no—
94C16—1221no—
95Q8—21no—
96D4—21no—
97D4—41no—
98C2×C4—41no—
99C2×C4—41no—
100C2×C4—1221no—
101C2×C4—2441no—
102C2×C4D4×D6111yescharacteristic
103C8—611no—
104C8—611no—
105C8—2441no—
106C8C2×Dic12211yescharacteristic
107C8#1175822411yescharacteristic
108C22—41no—
109C22#1451980111yescharacteristic
110C4—41no—
111C4—81no—
112C4—4881no—
113C4—2441no—
114C4#1451975411yescharacteristic
115C4SD16×D6111yescharacteristic
116C2—21no—
117C2—81no—
118C2#1684005011yescharacteristic
subgroupG/H
centerC2#16840050
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#360C2
socleC2×C61#476
hypercenter#360D61
hypocenterC61#2231
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
1. #16840162C2semidirect
3. #16839585C2semidirect
4. #16839584C2semidirect
5. #16839582C2semidirect
67. C61#2231semidirect