Finite Group Databasebeta

← C4×#14556661 #22625748

Subgroups — C4×#14556661 #22625748

Order 9344.

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×#14556661C212yesmaximal
2C4×#11924038C212yesmaximal
3#17989463C212yesmaximal
4C4×C8×D73C211yesmaximal, characteristic
5C2×#11924038C2214yes—
6#14556661C418yesdirect product factor
7#14556646—22no—
8C4×#10596833—22no—
9C2×C8×D73C2211yescharacteristic
10C2×C8×D73C2211yescharacteristic
11C42×D73C2211yescharacteristic
12C4×#10596831C411yescharacteristic
13C8×Dic73C411yescharacteristic
14C8×Dic73C411yescharacteristic
15C4×C8×C73C411yescharacteristic
16#11924038—24no—
17#11924038C2×C418yes—
18C2×#10596833—24no—
19C2×C4×D73Q811yescharacteristic
20C2×C4×D73Q811yescharacteristic
21C2×C4×D73C2311yescharacteristic
22C2×#10596831C2×C411yescharacteristic
23C2×#10596831C2×C411yescharacteristic
24C8×D73—22no—
25C8×D73C2×C414yes—
26C4×Dic73C2×C411yescharacteristic
27C4×Dic73D411yescharacteristic
28C4×Dic73D411yescharacteristic
29C2×C8×C73C2×C411yescharacteristic
30C2×C8×C73C2×C411yescharacteristic
31C42×C73C2×C411yescharacteristic
32C22×D73C2×Q811yescharacteristic
33C2×C4×C73C4⋊C411yescharacteristic
34C2×C4×C73C4⋊C411yescharacteristic
35C2×C4×C73C22×C411yescharacteristic
36C2×Dic73C4⋊C411yescharacteristic
37C2×Dic73C4⋊C411yescharacteristic
38C2×Dic73C2×D411yescharacteristic
39C4×D73—22no—
40C4×D73—22no—
41C4×D73C22×C412yes—
42C4×D73#4112yes—
43#10596833—28no—
44C8×C73—21no—
45C8×C73C4212yes—
46#10596831—21no—
47#10596831C4212yes—
48C22×C73C2×C4⋊C411yescharacteristic
49C2×D73—21no—
50C2×D73—21no—
51C2×D73C4×Q812yes—
52C4×C73—21no—
53C4×C73#10812yescomplemented
54C4×C73C2×C4211yescharacteristic
55C4×C73#11711yescharacteristic
56Dic73—21no—
57Dic73#10812yescomplemented
58Dic73C4×D412yes—
59C2×C73C4×C4⋊C411yescharacteristic
60C2×C73C2×#10811yescharacteristic
61C2×C73C2×#10811yescharacteristic
62D73—22no—
63C4×#108—731nomaximal, Sylow
64C73C4×#10811yescharacteristic, complemented, Sylow
65C2×#108—732no—
66C4×M16—732no—
67C2×C4×C8—731no—
68#341—732no—
69C2×M16—734no—
70C22×C8—731no—
71C22×C8—731no—
72C2×C42—731no—
73#108—738no—
74#97—1462no—
75C4×C8—731no—
76C4×C8—731no—
77C4×C8—731no—
78C4×C8—1462no—
79C4×C8#6440811yescharacteristic
80C22×C4—731no—
81C22×C4—731no—
82C22×C4—731no—
83M16—738no—
84M16—1464no—
85C2×C8—731no—
86C2×C8—734no—
87C2×C8—731no—
88C2×C8—1462no—
89C2×C8—1464no—
90C2×C8C2×#6440811yescharacteristic
91C2×C8C2×#6440811yescharacteristic
92C42—731no—
93C42—731no—
94C42—731no—
95C42C2×#6440811yescharacteristic
96C23—731no—
97C2×C4—731no—
98C2×C4—731no—
99C2×C4—732no—
100C2×C4—732no—
101C2×C4—731no—
102C2×C4—1462no—
103C2×C4—1462no—
104C2×C4C4⋊#6440811yescharacteristic
105C2×C4C4⋊#6440811yescharacteristic
106C2×C4C22×#6440811yescharacteristic
107C8—21no—
108C8—732no—
109C8—1468no—
110C8—1461no—
111C8C4×#6440812yes—
112C22—732no—
113C22—1461no—
114C22—1461no—
115C22C2×C4⋊#6440811yescharacteristic
116C4—21no—
117C4—732no—
118C4—732no—
119C4—1461no—
120C4#1455666112yesdirect product factor
121C4C2×C4×#6440811yescharacteristic
122C4#1455667011yescharacteristic
123C2—1462no—
124C2C4×C4⋊#6440811yescharacteristic
125C2C2×#1455666111yescharacteristic
126C2D73⋊#10811yescharacteristic
subgroupG/H
centerC2×C4C4⋊#64408
commutatorC4×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC4×C8×C73C4
socleC22×C73C2×C4⋊C4
hypercenterC4×C8#64408
hypocenterC73C4×#108
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
6. #14556661C4direct (N × H)
53. C4×C73#108semidirect
57. Dic73#108semidirect
64. C73C4×#108semidirect
120. C4#14556661direct (N × H)