Finite Group Databasebeta

← #21447861

Subgroups — #21447861

Order 7808.

166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#14519720C212yesmaximal
2C4×D488C211yesmaximal, characteristic
3C4⋊#11758185C211yesmaximal, characteristic, complemented
4#16839566C212yesmaximal, complemented
5C61×#494C211yesmaximal, characteristic, complemented
6C2×D488C2211yescharacteristic
7C4×D244—21no—
8#14519720—24no—
9C2×#11758185C2212yes—
10#14519711C2211yescharacteristic
11#14519699—21no—
12C2×Q16×C61—21no—
13C2×Q16×C61C2212yes—
14C4⋊Q8×C61—21no—
15C4×C8×C61C2211yescharacteristic
16C2×Q8×C61—22no—
17C2×D244—21no—
18C2×C4×D61—41no—
19Q16×C61—22no—
20Q16×C61—22no—
21Q16×C61—42no—
22C2×C8×C61D411yescharacteristic
23C2×C8×C61C2311yescharacteristic
24C4⋊C4×C61—41no—
25C4⋊C4×C61—41no—
26C42×C61D411yescharacteristic
27#11758198—41no—
28C4⋊Dic61—21no—
29D488—21no—
30D488D412yes—
31#11758185—22no—
32C22×D61—41no—
33Q8×C61—42no—
34Q8×C61—42no—
35C2×C4×C61—42no—
36C2×C4×C61D811yescharacteristic
37C2×C4×C61D811yescharacteristic
38C2×C4×C61C2×D411yescharacteristic
39C2×Dic61—41no—
40D244—22no—
41D244—41no—
42C4×D61—82no—
43C8×C61—21no—
44C8×C61C2×D411yescharacteristic
45C8×C61#4111yescharacteristic
46C22×C61C2×D811yescharacteristic
47C2×D61—42no—
48C2×D61—81no—
49C2×D61—81no—
50C4×C61—21no—
51C4×C61—82no—
52C4×C61SD3212yescomplemented
53C4×C61#12111yescharacteristic
54C4×C61AGL(1,ℤ/8)11yescharacteristic
55Dic61—81no—
56#2208—611nomaximal, Sylow
57C2×C61#45911yescharacteristic
58C2×C61C2×SD3211yescharacteristic
59C2×C61#51011yescharacteristic
60D61—82no—
61C2×SD32—612no—
62#494D6111yescharacteristic, complemented
63C4×D8—611no—
64C4⋊C16—611no—
65#358—612no—
66C61#220811yescharacteristic, complemented, Sylow
67C2×Q16—21no—
68C2×Q16C2×D6112yes—
69C2×D8—611no—
70C4⋊Q8—21no—
71C4×D4—1221no—
72SD32—1224no—
73C2×C16—612no—
74#107—611no—
75#102—1221no—
76C4×C8C2×D6111yescharacteristic
77C2×Q8—22no—
78C2×D4—1221no—
79C22×C4—2441no—
80Q16—22no—
81Q16—22no—
82Q16—42no—
83D8—612no—
84D8—1221no—
85C2×C8C22⋊D6111yescharacteristic
86C2×C8C22×D6111yescharacteristic
87C4⋊C4—41no—
88C4⋊C4—41no—
89C4⋊C4—1221no—
90C22⋊C4—2441no—
91C42C22⋊D6111yescharacteristic
92C16—1222no—
93C23—2441no—
94Q8—42no—
95Q8—42no—
96D4—1222no—
97D4—2441no—
98C2×C4—42no—
99C2×C4—4882no—
100C2×C4—2441no—
101C2×C4#1175819911yescharacteristic
102C2×C4#1175819911yescharacteristic
103C2×C4C2×C22⋊D6111yescharacteristic
104C8—21no—
105C8D4×D6111yescharacteristic
106C8#1175822411yescharacteristic
107C22—4881no—
108C22—4881no—
109C22—2442no—
110C22C2×#1175819911yescharacteristic
111C4—21no—
112C4—82no—
113C4—4881no—
114C4#1451972012yescomplemented
115C4#1451974811yescharacteristic
116C4#1451980311yescharacteristic
117C2—4882no—
118C2#1683995411yescharacteristic
119C2C2×#1451972011yescharacteristic
120C2#1684020311yescharacteristic
subgroupG/H
centerC22C2×#11758199
commutatorC2×C8×C61C23
FrattiniC2×C8C22×D61
FittingC61×#494C2
socleC22×C61C2×D8
hypercenter#494D61
hypocenterC61#2208
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. C4⋊#11758185C2semidirect
4. #16839566C2semidirect
5. C61×#494C2semidirect
52. C4×C61SD32semidirect
62. #494D61semidirect
66. C61#2208semidirect
114. C4#14519720semidirect