Finite Group Databasebeta

← C4×#14519848 #21461637

Subgroups — C4×#14519848 #21461637

Order 7808.

228 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14519848C212yesmaximal
2C4×#11758213C212yesmaximal
3#16840638C212yesmaximal
4C4×C8×D61C211yesmaximal, characteristic
5C2×#11758213C2214yes—
6#14519848C418yesdirect product factor
7#14519832—22no—
8C4×#92420—22no—
9C2×C8×D61C2211yescharacteristic
10C2×C8×D61C2211yescharacteristic
11C42×D61C2211yescharacteristic
12C4×#92418C411yescharacteristic
13C8×Dic61C411yescharacteristic
14C8×Dic61C411yescharacteristic
15C4×C8×C61C411yescharacteristic
16C2×C4×D61Q811yescharacteristic
17C2×C4×D61Q811yescharacteristic
18C2×C4×D61C2311yescharacteristic
19C2×#92420—24no—
20#11758213—24no—
21#11758213C2×C418yes—
22C2×C8×C61C2×C411yescharacteristic
23C2×C8×C61C2×C411yescharacteristic
24C42×C61C2×C411yescharacteristic
25C4×Dic61C2×C411yescharacteristic
26C4×Dic61D411yescharacteristic
27C4×Dic61D411yescharacteristic
28C2×#92418C2×C411yescharacteristic
29C2×#92418C2×C411yescharacteristic
30C8×D61—22no—
31C8×D61C2×C414yes—
32C22×D61C2×Q811yescharacteristic
33C2×C4×C61C4⋊C411yescharacteristic
34C2×C4×C61C4⋊C411yescharacteristic
35C2×C4×C61C22×C411yescharacteristic
36C2×Dic61C4⋊C411yescharacteristic
37C2×Dic61C4⋊C411yescharacteristic
38C2×Dic61C2×D411yescharacteristic
39C4×D61—22no—
40C4×D61—22no—
41C4×D61C22×C412yes—
42C4×D61#4112yes—
43#92420—28no—
44C8×C61—21no—
45C8×C61C4212yes—
46#92418—21no—
47#92418C4212yes—
48C22×C61C2×C4⋊C411yescharacteristic
49C2×D61—21no—
50C2×D61—21no—
51C2×D61C4×Q812yes—
52C4×C61—21no—
53C4×C61#10812yescomplemented
54C4×C61C2×C4211yescharacteristic
55C4×C61#11711yescharacteristic
56Dic61—21no—
57Dic61#10812yescomplemented
58Dic61C4×D412yes—
59C4×#108—611nomaximal, Sylow
60C2×C61C4×C4⋊C411yescharacteristic
61C2×C61C2×#10811yescharacteristic
62C2×C61C2×#10811yescharacteristic
63D61—22no—
64C2×#108—612no—
65C4×M16—612no—
66C2×C4×C8—611no—
67#341—612no—
68C61C4×#10811yescharacteristic, complemented, Sylow
69C2×M16—614no—
70C22×C8—611no—
71C22×C8—611no—
72C2×C42—611no—
73#108—618no—
74#97—1222no—
75C4×C8—611no—
76C4×C8—611no—
77C4×C8—611no—
78C4×C8—1222no—
79C4×C8#692311yescharacteristic
80C22×C4—611no—
81C22×C4—611no—
82C22×C4—611no—
83M16—618no—
84M16—1224no—
85C2×C8—611no—
86C2×C8—614no—
87C2×C8—611no—
88C2×C8—1222no—
89C2×C8—1224no—
90C2×C8C2×#692311yescharacteristic
91C2×C8C2×#692311yescharacteristic
92C42—611no—
93C42—611no—
94C42—611no—
95C42C2×#692311yescharacteristic
96C23—611no—
97C2×C4—611no—
98C2×C4—611no—
99C2×C4—612no—
100C2×C4—612no—
101C2×C4—611no—
102C2×C4—1222no—
103C2×C4—1222no—
104C2×C4C4⋊#692311yescharacteristic
105C2×C4C4⋊#692311yescharacteristic
106C2×C4C22×#692311yescharacteristic
107C8—21no—
108C8—612no—
109C8—1228no—
110C8—1221no—
111C8C4×#692312yes—
112C22—612no—
113C22—1221no—
114C22—1221no—
115C22C2×C4⋊#692311yescharacteristic
116C4—21no—
117C4—612no—
118C4—612no—
119C4—1221no—
120C4#1451984812yesdirect product factor
121C4C2×C4×#692311yescharacteristic
122C4#1451985611yescharacteristic
123C2—1222no—
124C2C4×C4⋊#692311yescharacteristic
125C2D61⋊#10811yescharacteristic
126C2C2×#1451984811yescharacteristic
subgroupG/H
centerC2×C4C4⋊#6923
commutatorC4×C61C2×C42
FrattiniC2×C4C22×#6923
FittingC4×C8×C61C4
socleC22×C61C2×C4⋊C4
hypercenterC4×C8#6923
hypocenterC61C4×#108
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
6. #14519848C4direct (N × H)
53. C4×C61#108semidirect
57. Dic61#108semidirect
68. C61C4×#108semidirect
120. C4#14519848direct (N × H)