Finite Group Databasebeta

← #21447897

Subgroups — #21447897

Order 7808.

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

normal subgroups only

This group has 150 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#16840203C212yesmaximal
2#16839880C211yesmaximal, characteristic
3#16839583C211yesmaximal, characteristic, complemented
4#16839578C212yesmaximal, complemented
5C61×#494C211yesmaximal, characteristic, complemented
6#14519799C2211yescharacteristic
7#14519783—21no—
8#14519723—22no—
9#14519720—22no—
10#14519717C2212yes—
11#14519713C2211yescharacteristic
12#14519705—21no—
13C2×Q16×C61—21no—
14C2×Q16×C61C2212yes—
15C4⋊Q8×C61—21no—
16C4×C8×C61C2211yescharacteristic
17C2×Q8×C61—22no—
18#11758222—21no—
19Q16×C61—22no—
20Q16×C61—22no—
21Q16×C61—41no—
22Q16×C61—41no—
23C2×C8×C61D411yescharacteristic
24C2×C8×C61C2311yescharacteristic
25C4⋊C4×C61—42no—
26C42×C61D411yescharacteristic
27#11758194—21no—
28Dic244D411yescharacteristic
29D488D411yescharacteristic
30#11758190—21no—
31#11758189—41no—
32C8×D61—41no—
33#11758185—22no—
34Q8×C61—42no—
35Q8×C61—42no—
36C2×C4×C61—21no—
37C2×C4×C61—42no—
38C2×C4×C61C2×D411yescharacteristic
39C22⋊D61—41no—
40D244—21no—
41C4×D61—41no—
42Dic122—21no—
43C8×C61D811yescharacteristic
44C8×C61D811yescharacteristic
45C8×C61C2×D411yescharacteristic
46C8×C61#4111yescharacteristic
47#92418—41no—
48C22×C61AGL(1,ℤ/8)11yescharacteristic
49C2×D61—41no—
50C4×C61—22no—
51C4×C61—82no—
52C4×C61#12111yescharacteristic
53C4×C61C2×D811yescharacteristic
54Dic61—41no—
55#2214—611nomaximal, Sylow
56C2×C61—21no—
57C2×C61#45911yescharacteristic
58D61—81no—
59#510—612no—
60#494D6111yescharacteristic, complemented
61#443—611no—
62#364—611no—
63#362—612no—
64C61#221411yescharacteristic, complemented, Sylow
65#135—611no—
66C2×Q16—21no—
67C2×Q16C2×D6112yes—
68#131—1221no—
69C4⋊Q8—21no—
70Q32—1222no—
71SD32—1222no—
72M32—612no—
73#108—611no—
74#104—1221no—
75C4×C8C2×D6111yescharacteristic
76#41—1221no—
77C2×Q8—22no—
78Q16—22no—
79Q16—22no—
80Q16—41no—
81Q16—41no—
82Q16—611no—
83SD16—1221no—
84D8—611no—
85M16—1221no—
86M16—2441no—
87C2×C8—2441no—
88C2×C8C22⋊D6111yescharacteristic
89C2×C8C22×D6111yescharacteristic
90C4⋊C4—42no—
91C42C22⋊D6111yescharacteristic
92C16—1222no—
93Q8—42no—
94Q8—42no—
95Q8—1221no—
96D4—1221no—
97D4—2441no—
98C2×C4—21no—
99C2×C4—42no—
100C2×C4—2441no—
101C2×C4C2×C22⋊D6111yescharacteristic
102C8—2441no—
103C8#1175819911yescharacteristic
104C8#1175819911yescharacteristic
105C8D4×D6111yescharacteristic
106C8#1175822411yescharacteristic
107C22—2441no—
108C22#1451980311yescharacteristic
109C4—22no—
110C4—82no—
111C4—2441no—
112C4#1451974811yescharacteristic
113C4C2×#1175819911yescharacteristic
114C2—21no—
115C2—4881no—
116C2#1683995411yescharacteristic
subgroupG/H
centerC2#16839954
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#494C2
socleC2×C61#459
hypercenter#494D61
hypocenterC61#2214
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #16839583C2semidirect
4. #16839578C2semidirect
5. C61×#494C2semidirect
60. #494D61semidirect
64. C61#2214semidirect