Finite Group Databasebeta

← #28406875

Subgroups — #28406875

Order 14464.

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

normal subgroups only

This group has 262 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, complemented
2#20299507C214yesmaximal, complemented
3#20299167C211yesmaximal, characteristic
4D113⋊M16—22no—
5#16813683C2214yescomplemented
6#16813682—22no—
7C2×#14268647C2211yescharacteristic
8C22×D452C411yescharacteristic
9#16813619C412yes—
10#16813610C2212yes—
11#16813597—22no—
12#16813592—22no—
13#117×C113C411yescharacteristic
14#14268657—42no—
15#14268656—24no—
16#14268655—42no—
17C23×D113—21no—
18#14268647—42no—
19C2×Dic226C2311yescharacteristic
20C2×D452—21no—
21C2×D452—24no—
22C2×D452—42no—
23C2×D452C2×C412yes—
24C2×D452C2×C411yescharacteristic
25C2×C22⋊D113D412yes—
26C2×C4×D113D412yes—
27#14268624—24no—
28C22×C4×C113C2×C411yescharacteristic
29C4⋊C4×C113—21no—
30C22⋊C4×C113—21no—
31C42×C113C2×C412yes—
32C23×C113C22⋊C411yescharacteristic
33C22×D113—22no—
34C22×D113—42no—
35C22×D113—82no—
36C22×D113C22⋊C412yes—
37C2×C4×C113—22no—
38C2×C4×C113—22no—
39C2×C4×C113C22⋊C411yescharacteristic
40C2×C4×C113C22×C411yescharacteristic
41C22⋊D113—42no—
42C2×Dic113C2×D412yes—
43D452—41no—
44D452—42no—
45D452—42no—
46D452—84no—
47C4×D113—22no—
48C4×D113—22no—
49Dic226—41no—
50#11744753—44no—
51C22×C113—21no—
52C22×C113—41no—
53C22×C113C2×C22⋊C411yescharacteristic
54C2×D113—22no—
55C2×D113—42no—
56C2×D113—44no—
57C2×D113—42no—
58C2×D113—84no—
59C4×C113—21no—
60C4×C113—42no—
61C4×C113#9912yes—
62Dic113—22no—
63C2×C113—21no—
64C2×C113—41no—
65C2×C113C2×#9911yescharacteristic
66D113—42no—
67D113—82no—
68#2134—1131nomaximal, Sylow
69C113#213411yescharacteristic, complemented, Sylow
70#535—1131no—
71#413—1132no—
72#355—1134no—
73C2×#41—1131no—
74C22×D4—1131no—
75C2×M16—2262no—
76#127—1132no—
77#124—1132no—
78#121—2262no—
79#120—2262no—
80#117#9067311yescharacteristic
81#101—1134no—
82#100—2262no—
83C24—2261no—
84#41—4522no—
85C2×Q8—1131no—
86C2×D4—1132no—
87C2×D4—1131no—
88C2×D4—1132no—
89C2×D4—4522no—
90C2×D4—2264no—
91C2×D4—2261no—
92C22×C4—1132no—
93C22×C4C2×#9067311yescharacteristic
94M16—4522no—
95M16—2264no—
96C2×C8—4522no—
97C4⋊C4—21no—
98C22⋊C4—21no—
99C22⋊C4—2264no—
100C42C2×#9067312yes—
101C23—1132no—
102C23—9042no—
103C23—4522no—
104C23—2262no—
105C23C22⋊#9067311yescharacteristic
106Q8—4521no—
107D4—9044no—
108D4—4522no—
109D4—4521no—
110D4—4522no—
111D4—4522no—
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—1132no—
115C2×C4—2262no—
116C2×C4—2262no—
117C2×C4C22⋊#9067311yescharacteristic
118C2×C4C22×#9067311yescharacteristic
119C8—4524no—
120C22—21no—
121C22—41no—
122C22—9044no—
123C22—4524no—
124C22—4522no—
125C22—4522no—
126C22—2262no—
127C22C2×C22⋊#9067311yescharacteristic
128C4—21no—
129C4—42no—
130C4—2262no—
131C4#1681368112yes—
132C2—21no—
133C2—41no—
134C2—9042no—
135C2—4522no—
136C2C2×#1681368111yescharacteristic
subgroupG/H
centerC2C2×#16813681
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#117×C113C4
socleC2×C113C2×#99
prime radical#20299167C2
cosocleC2×Dic226C23
hypercenter#117#90673
hypocenterC113#2134
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
1. #20299584C2semidirect
2. #20299507C2semidirect
5. #16813683C22semidirect
69. C113#2134semidirect

Maximal subgroups

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

subgroupindex
#202995842
#202995072
#202991672
#2134113