Finite Group Databasebeta

← #28392269

Subgroups — #28392269

Order 14464.

230 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 73 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#20298582C212yesmaximal
2#20298397C214yesmaximal, complemented
3#536×C113C211yesmaximal, characteristic
4C2×#14268631—22no—
5#16813541C2214yes—
6#16813539—22no—
7C2×#41×C113C2211yescharacteristic
8C22×Q8×C113C411yescharacteristic
9C4⋊Q8×C113C2212yes—
10#124×C113C412yes—
11#123×C113—22no—
12C22⋊Q8×C113—22no—
13#117×C113C411yescharacteristic
14#14268631—24no—
15#14268631—42no—
16C2×#11744751—42no—
17#41×C113—42no—
18C2×Q8×C113—21no—
19C2×Q8×C113—42no—
20C2×Q8×C113C2×C412yes—
21C2×Q8×C113C2311yescharacteristic
22C2×D4×C113C2×C411yescharacteristic
23C2×D4×C113D412yes—
24C22×C4×C113—21no—
25C22×C4×C113C2×C411yescharacteristic
26C22×C4×C113D412yes—
27C4⋊C4×C113—21no—
28C4⋊C4×C113—24no—
29C22⋊C4×C113—21no—
30C22⋊C4×C113—24no—
31C42×C113C2×C412yes—
32C23×C113C22⋊C412yes—
33C23×C113C22⋊C411yescharacteristic
34Q8×C113—41no—
35Q8×C113—42no—
36Q8×C113—42no—
37D4×C113—41no—
38D4×C113—42no—
39C2×C4×C113—22no—
40C2×C4×C113—22no—
41C2×C4×C113—22no—
42C2×C4×C113—22no—
43C2×C4×C113—22no—
44C2×C4×C113—42no—
45C2×C4×C113C22⋊C411yescharacteristic
46C2×C4×C113C22×C411yescharacteristic
47C2×C4×C113C2×D412yes—
48#11744751—44no—
49C22×C113—21no—
50C22×C113—22no—
51C22×C113—42no—
52C22×C113—41no—
53C22×C113C2×C22⋊C411yescharacteristic
54C4×C113—22no—
55C4×C113—21no—
56C4×C113—42no—
57C4×C113—42no—
58C4×C113#9912yes—
59C2×C113—21no—
60C2×C113—41no—
61C2×C113—42no—
62C2×C113C2×#9911yescharacteristic
63#2135—1131nomaximal, Sylow
64C113#213511yescharacteristic, complemented, Sylow
65#536D11311yescharacteristic
66#413—1132no—
67#356—1134no—
68C2×#41C2×D11311yescharacteristic
69C22×Q8Dic11311yescharacteristic
70C2×M16—2262no—
71C4⋊Q8C2×D11312yes—
72#124Dic11312yes—
73#123—22no—
74C22⋊Q8—22no—
75#117Dic11311yescharacteristic
76#101—1134no—
77#100—2262no—
78#41—42no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8C2×Dic11312yes—
82C2×Q8C22×D11311yescharacteristic
83C2×D4C2×Dic11311yescharacteristic
84C2×D4C22⋊D11312yes—
85C22×C4—21no—
86C22×C4C2×Dic11311yescharacteristic
87C22×C4C22⋊D11312yes—
88M16—4522no—
89M16—2264no—
90C2×C8—4522no—
91C4⋊C4—21no—
92C4⋊C4—24no—
93C22⋊C4—21no—
94C22⋊C4—24no—
95C42C2×Dic11312yes—
96C23C22⋊Dic11312yes—
97C23C22⋊Dic11311yescharacteristic
98Q8—41no—
99Q8—42no—
100Q8—42no—
101D4—41no—
102D4—42no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—22no—
106C2×C4—22no—
107C2×C4—22no—
108C2×C4—42no—
109C2×C4C22⋊Dic11311yescharacteristic
110C2×C4C22×Dic11311yescharacteristic
111C2×C4C2×C22⋊D11312yes—
112C8—4524no—
113C22—21no—
114C22—22no—
115C22—42no—
116C22—41no—
117C22C2×C22⋊Dic11311yescharacteristic
118C4—22no—
119C4—21no—
120C4—42no—
121C4—42no—
122C4#1681353712yes—
123C2—21no—
124C2—41no—
125C2—42no—
126C2C2×#1681353711yescharacteristic
subgroupG/H
centerC2C2×#16813537
commutatorC2×C4×C113C22×C4
FrattiniC2×Q8C22×D113
Fitting#536×C113C2
socleC2×C113C2×#99
prime radicalC2×#41×C113C22
cosocleC2×Q8×C113C23
hypercenter#536D113
hypocenterC113#2135
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #20298397C2semidirect
64. C113#2135semidirect

Maximal subgroups

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

subgroupindex
#202985822
#202983972
#536×C1132
#2135113