Finite Group Databasebeta

← #28406876

Subgroups — #28406876

Order 14464.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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#20299584C212yesmaximal
2#20299508C214yesmaximal, complemented
3#20299172C211yesmaximal, characteristic
4D113⋊M16—22no—
5#16813683C2214yes—
6#16813682—22no—
7C2×#14268647C2211yescharacteristic
8#16813620C2212yes—
9#16813611C412yes—
10#16813605—22no—
11#16813598—22no—
12#16813581C411yescharacteristic
13C22×Q8×C113C411yescharacteristic
14#14268657—42no—
15#14268656—24no—
16#14268655—42no—
17#14268647—42no—
18C2×Dic226C2311yescharacteristic
19C2×D452C2×C411yescharacteristic
20C2×C22⋊D113D412yes—
21C2×C4×D113D412yes—
22C4⋊Dic113—21no—
23#14268626—24no—
24C22⋊Dic113—21no—
25#14268624—24no—
26C4×Dic113C2×C412yes—
27C2×Q8×C113—21no—
28C2×Q8×C113—42no—
29C2×Q8×C113C2×C412yes—
30C22×C4×C113—21no—
31C22×C4×C113C2×C411yescharacteristic
32C23×C113C22⋊C411yescharacteristic
33C22×D113C22⋊C412yes—
34Q8×C113—42no—
35Q8×C113—42no—
36C2×C4×C113—22no—
37C2×C4×C113—22no—
38C2×C4×C113—42no—
39C2×C4×C113C22⋊C411yescharacteristic
40C2×C4×C113C22×C411yescharacteristic
41C22⋊D113—42no—
42C2×Dic113—22no—
43C2×Dic113C2×D412yes—
44D452—41no—
45C4×D113—22no—
46C4×D113—22no—
47Dic226—41no—
48#11744753—44no—
49C22×C113—21no—
50C22×C113—41no—
51C22×C113C2×C22⋊C411yescharacteristic
52C2×D113—22no—
53C2×D113—42no—
54C4×C113—21no—
55C4×C113—42no—
56C4×C113#9912yes—
57Dic113—22no—
58Dic113—42no—
59C2×C113—21no—
60C2×C113—41no—
61C2×C113C2×#9911yescharacteristic
62D113—42no—
63#2135—1131nomaximal, Sylow
64C113#213511yescharacteristic, complemented, Sylow
65#536—1131no—
66#413—1132no—
67#356—1134no—
68C2×#41—1131no—
69C22×Q8#9067311yescharacteristic
70C2×M16—2262no—
71C4⋊Q8—1132no—
72#124—1132no—
73#123—2262no—
74C22⋊Q8—2262no—
75#117—1131no—
76#101—1134no—
77#100—2262no—
78#41—4522no—
79C2×Q8—21no—
80C2×Q8—42no—
81C2×Q8—1131no—
82C2×Q8C2×#9067312yes—
83C2×D4—1132no—
84C2×D4—1131no—
85C22×C4—21no—
86C22×C4—1132no—
87C22×C4C2×#9067311yescharacteristic
88M16—4522no—
89M16—2264no—
90C2×C8—4522no—
91C4⋊C4—2264no—
92C4⋊C4—2261no—
93C22⋊C4—2264no—
94C22⋊C4—2261no—
95C42—1132no—
96C23—1132no—
97C23C22⋊#9067311yescharacteristic
98Q8—42no—
99Q8—42no—
100Q8—4521no—
101D4—4521no—
102D4—4522no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—42no—
106C2×C4—1132no—
107C2×C4—2262no—
108C2×C4—2262no—
109C2×C4—2262no—
110C2×C4C22⋊#9067311yescharacteristic
111C2×C4C22×#9067311yescharacteristic
112C8—4524no—
113C22—21no—
114C22—41no—
115C22—4522no—
116C22—2262no—
117C22C2×C22⋊#9067311yescharacteristic
118C4—21no—
119C4—42no—
120C4—4522no—
121C4—2262no—
122C4#1681368012yes—
123C2—21no—
124C2—41no—
125C2—4522no—
126C2C2×#1681368011yescharacteristic
subgroupG/H
centerC2C2×#16813680
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22×Q8×C113C4
socleC2×C113C2×#99
prime radicalC2×#14268647C22
cosocleC2×Dic226C23
hypercenterC22×Q8#90673
hypocenterC113#2135
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #20299508C2semidirect
64. C113#2135semidirect

Maximal subgroups

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

subgroupindex
#202995842
#202995082
#202991722
#2135113