Finite Group Databasebeta

← #28406877

Subgroups — #28406877

Order 14464.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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#20299585C212yesmaximal
2#20299509C212yesmaximal, complemented
3#20299508C212yesmaximal, complemented
4#20299168C211yesmaximal, characteristic
5C2×#14268656—22no—
6#16813683C2214yes—
7#16813682—22no—
8C2×#14268646C2211yescharacteristic
9C2×Q8×D113C411yescharacteristic
10#16813622C2211yescharacteristic
11#16813620C2211yescharacteristic
12#16813609C411yescharacteristic
13#16813604—22no—
14#16813599—22no—
15#16813579C411yescharacteristic
16#124×C113C411yescharacteristic
17#14268656—24no—
18#14268656—42no—
19C2×#11744753—42no—
20#14268646—42no—
21C2×Dic226—21no—
22C2×Dic226C2×C411yescharacteristic
23C2×Dic226C2311yescharacteristic
24Q8×D113—42no—
25C2×C22⋊D113D412yes—
26C22×Dic113D412yes—
27C2×C4×D113—21no—
28C2×C4×D113C2×C411yescharacteristic
29C4⋊Dic113—22no—
30#14268626—21no—
31#14268626—22no—
32C22⋊Dic113—22no—
33#14268624—21no—
34C4×Dic113C2×C411yescharacteristic
35C2×Q8×C113C2×C411yescharacteristic
36C2×D4×C113C2×C411yescharacteristic
37C22⋊C4×C113—22no—
38C42×C113C2×C411yescharacteristic
39C23×C113C22⋊C412yes—
40C22×D113C22⋊C411yescharacteristic
41Q8×C113—41no—
42D4×C113—41no—
43C2×C4×C113—21no—
44C2×C4×C113—21no—
45C2×C4×C113C22×C411yescharacteristic
46C22⋊D113—42no—
47C2×Dic113—22no—
48C2×Dic113—22no—
49C2×Dic113—21no—
50C2×Dic113—21no—
51C2×Dic113C22⋊C411yescharacteristic
52C2×Dic113C2×D412yes—
53C4×D113—22no—
54C4×D113—42no—
55Dic226—41no—
56Dic226—42no—
57Dic226—41no—
58#11744753—44no—
59C22×C113—22no—
60C22×C113—42no—
61C22×C113C2×C22⋊C411yescharacteristic
62C2×D113—21no—
63C2×D113—41no—
64C4×C113—21no—
65C4×C113—41no—
66C4×C113—41no—
67Dic113—22no—
68Dic113—41no—
69Dic113—41no—
70Dic113#9912yes—
71C2×C113—21no—
72C2×C113—42no—
73C2×C113C2×#9911yescharacteristic
74D113—41no—
75#2135—1131nomaximal, Sylow
76C113#213511yescharacteristic, complemented, Sylow
77#536—1131no—
78#413—1132no—
79#356—1132no—
80#356—1132no—
81C2×#41—1131no—
82C22×Q8—1131no—
83C2×M16—2262no—
84C4⋊Q8—1131no—
85C4⋊Q8—1131no—
86#124—1131no—
87#124#9067311yescharacteristic
88#123—2262no—
89C22⋊Q8—2262no—
90#117—1131no—
91#101—1134no—
92#100—2262no—
93#41—4522no—
94C2×Q8—1131no—
95C2×Q8—1131no—
96C2×Q8—4522no—
97C2×Q8—2261no—
98C2×Q8C2×#9067311yescharacteristic
99C2×D4—1132no—
100C2×D4C2×#9067311yescharacteristic
101C22×C4—1132no—
102C22×C4—1131no—
103C22×C4—2261no—
104M16—4522no—
105M16—2264no—
106C2×C8—4522no—
107C4⋊C4—2261no—
108C4⋊C4—2262no—
109C4⋊C4—2262no—
110C22⋊C4—22no—
111C22⋊C4—2261no—
112C22⋊C4—2262no—
113C42—1131no—
114C42C2×#9067311yescharacteristic
115C23—1131no—
116C23C22⋊#9067312yes—
117Q8—41no—
118Q8—4521no—
119Q8—4521no—
120Q8—4522no—
121D4—41no—
122D4—4522no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—1131no—
126C2×C4—1132no—
127C2×C4—4522no—
128C2×C4—2262no—
129C2×C4—2262no—
130C2×C4—2262no—
131C2×C4—2261no—
132C2×C4—2261no—
133C2×C4C22×#9067311yescharacteristic
134C8—4524no—
135C22—22no—
136C22—42no—
137C22—4521no—
138C22—2261no—
139C22C2×C22⋊#9067311yescharacteristic
140C4—21no—
141C4—41no—
142C4—41no—
143C4—1132no—
144C4—4521no—
145C4—4521no—
146C4—2262no—
147C2—21no—
148C2—42no—
149C2—4521no—
150C2D113⋊#9911yescharacteristic
subgroupG/H
centerC2D113⋊#99
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
Fitting#124×C113C4
socleC2×C113C2×#99
prime radicalC2×#14268646C22
cosocleC2×Dic226C23
hypercenter#124#90673
hypocenterC113#2135
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #20299509C2semidirect
3. #20299508C2semidirect
76. C113#2135semidirect

Maximal subgroups

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

subgroupindex
#202995852
#202995092
#202995082
#202991682
#2135113