Finite Group Databasebeta

← #28406878

Subgroups — #28406878

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#20299509C214yesmaximal, complemented
3#20299174C211yesmaximal, characteristic
4D113⋊M16—22no—
5#16813683C2214yes—
6#16813682—22no—
7C2×#14268647C2211yescharacteristic
8C22×Dic226C411yescharacteristic
9#16813622C2212yes—
10#16813610C412yes—
11#16813606—22no—
12#16813602—22no—
13#117×C113C411yescharacteristic
14#14268657—42no—
15#14268656—24no—
16#14268655—42no—
17#14268647—42no—
18C2×Dic226—21no—
19C2×Dic226—42no—
20C2×Dic226C2×C412yes—
21C2×Dic226C2311yescharacteristic
22C2×D452C2×C411yescharacteristic
23C2×C22⋊D113D412yes—
24C22×Dic113—21no—
25C2×C4×D113D412yes—
26C4⋊Dic113—24no—
27#14268624—24no—
28C22×C4×C113C2×C411yescharacteristic
29C4⋊C4×C113—21no—
30C22⋊C4×C113—21no—
31C42×C113C2×C412yes—
32C23×C113C22⋊C411yescharacteristic
33C22×D113C22⋊C412yes—
34C2×C4×C113—22no—
35C2×C4×C113—22no—
36C2×C4×C113C22⋊C411yescharacteristic
37C2×C4×C113C22×C411yescharacteristic
38C22⋊D113—42no—
39C2×Dic113—22no—
40C2×Dic113—42no—
41C2×Dic113C2×D412yes—
42D452—41no—
43C4×D113—22no—
44C4×D113—22no—
45Dic226—41no—
46Dic226—42no—
47Dic226—42no—
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—1131no—
70C2×M16—2262no—
71C4⋊Q8—1132no—
72#124—1132no—
73#123—2262no—
74C22⋊Q8—2262no—
75#117#9067311yescharacteristic
76#101—1134no—
77#100—2262no—
78#41—4522no—
79C2×Q8—1131no—
80C2×Q8—1132no—
81C2×Q8—4522no—
82C2×Q8—2261no—
83C2×D4—1132no—
84C2×D4—1131no—
85C22×C4—1132no—
86C22×C4—2261no—
87C22×C4C2×#9067311yescharacteristic
88M16—4522no—
89M16—2264no—
90C2×C8—4522no—
91C4⋊C4—21no—
92C4⋊C4—2264no—
93C22⋊C4—21no—
94C22⋊C4—2264no—
95C42C2×#9067312yes—
96C23—1132no—
97C23C22⋊#9067311yescharacteristic
98Q8—4522no—
99Q8—4521no—
100Q8—4522no—
101D4—4521no—
102D4—4522no—
103C2×C4—22no—
104C2×C4—22no—
105C2×C4—1132no—
106C2×C4—4522no—
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#1681368112yes—
123C2—21no—
124C2—41no—
125C2—4522no—
126C2C2×#1681368111yescharacteristic
subgroupG/H
centerC2C2×#16813681
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#117×C113C4
socleC2×C113C2×#99
prime radicalC2×#14268647C22
cosocleC2×Dic226C23
hypercenter#117#90673
hypocenterC113#2135
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #20299509C2semidirect
64. C113#2135semidirect

Maximal subgroups

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

subgroupindex
#202995842
#202995092
#202991742
#2135113