Finite Group Databasebeta

← #28389167

Subgroups — #28389167

Order 14464.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#20299154C211yesmaximal, characteristic
2#20298550C212yesmaximal
3#20298340C211yesmaximal, characteristic, complemented
4#20298339C212yesmaximal, complemented
5#330×C113C211yesmaximal, characteristic, complemented
6C2×#14268630—22no—
7#16813621C412yes—
8#16813614C2211yescharacteristic
9#16813600—22no—
10#16813587—22no—
11#16813580C412yes—
12C42×D113C2211yescharacteristic
13#16813533C2212yes—
14C8×Dic113—22no—
15#125×C113C2211yescharacteristic
16#97×C113C2212yes—
17C2×Dic226—22no—
18C2×C4×D113C2×C411yescharacteristic
19C2×C4×D113D412yes—
20#14268630—28no—
21C2×#11744751—22no—
22C4⋊Dic113C2×C412yes—
23#14268626—22no—
24#14268626—22no—
25#14268624—22no—
26C4×Dic113—22no—
27C4×Dic113C2×C411yescharacteristic
28C4×Dic113D412yes—
29C2×C8×C113—22no—
30C4⋊C4×C113—22no—
31C4⋊C4×C113C2×C412yes—
32C42×C113C2311yescharacteristic
33C22×D113C22⋊C411yescharacteristic
34C2×C4×C113—22no—
35C2×C4×C113C22×C411yescharacteristic
36C2×C4×C113C2×D412yes—
37C2×Dic113—22no—
38C2×Dic113C22⋊C411yescharacteristic
39C2×Dic113C22⋊C412yes—
40C4×D113—22no—
41C4×D113—24no—
42Dic226—44no—
43C8×C113—24no—
44#11744751—24no—
45C22×C113C2×C22⋊C411yescharacteristic
46C2×D113—21no—
47C2×D113—22no—
48C4×C113—21no—
49C4×C113—22no—
50C4×C113—42no—
51Dic113—42no—
52Dic113#10112yes—
53Dic113#10414yes—
54C2×C113C2×#10111yescharacteristic
55C2×C113C2×#10412yes—
56D113—41no—
57#1526—1131nomaximal, Sylow
58C113#152611yescharacteristic, complemented, Sylow
59#533—1131no—
60C4×M16—1132no—
61#330—1131no—
62#330—1132no—
63#330D11311yescharacteristic, complemented
64C2×M16—2262no—
65C4⋊Q8—1132no—
66#125—1131no—
67#125C2×D11311yescharacteristic
68C22⋊Q8—2262no—
69C4×Q8—2262no—
70#117—1132no—
71C2×C42—1131no—
72#97—1132no—
73#97C2×D11312yes—
74C4×C8—2262no—
75C2×Q8—2262no—
76C22×C4—1131no—
77C22×C4—1132no—
78M16—2268no—
79C2×C8—22no—
80C2×C8—2262no—
81C4⋊C4—22no—
82C4⋊C4—1132no—
83C4⋊C4—2262no—
84C4⋊C4—2262no—
85C4⋊C4C4×D11312yes—
86C22⋊C4—2262no—
87C42—1131no—
88C42—1132no—
89C42—2262no—
90C42C22×D11311yescharacteristic
91C23—1131no—
92Q8—4524no—
93C2×C4—22no—
94C2×C4—1131no—
95C2×C4—1132no—
96C2×C4—2264no—
97C2×C4—2262no—
98C2×C4—2262no—
99C2×C4C2×C4×D11311yescharacteristic
100C2×C4D4×D11312yes—
101C8—24no—
102C8—2264no—
103C22—2261no—
104C22—2262no—
105C22C22⋊C4×D11311yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—1132no—
110C4—1134no—
111C4—4522no—
112C2—4521no—
113C2#101×D11311yescharacteristic
114C2#104×D11312yes—
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#330×C113C2
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C22⋊C4
cosocleC42×C113C23
hypercenter#330D113
hypocenterC113#1526
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #20298340C2semidirect
4. #20298339C2semidirect
5. #330×C113C2semidirect
58. C113#1526semidirect
63. #330D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202991542
#202985502
#202983402
#202983392
#330×C1132
#1526113