Finite Group Databasebeta

← #28391121

Subgroups — #28391121

Order 14464.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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#20299162C211yesmaximal, characteristic
2#20298582C211yesmaximal, characteristic, complemented
3C2×#16813538C212yesmaximal, complemented
4#20298370C212yesmaximal, complemented
5#568×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic
7C2×#14268631C2212yes—
8#16813618—21no—
9#16813611—21no—
10#16813596—22no—
11#16813590C414yes—
12#16813581C2211yescharacteristic
13#16813541—21no—
14#16813539—21no—
15#16813538—24no—
16C2×#41×C113C2211yescharacteristic
17#131×C113—24no—
18C2×M16×C113—22no—
19C2×M16×C113C2212yes—
20C23×D113C2×C412yes—
21C2×D452—21no—
22C2×D452—21no—
23C2×D452—22no—
24C2×D452—22no—
25C2×C22⋊D113—24no—
26#14268631—22no—
27#14268631—22no—
28C2×#11744751—22no—
29C4⋊Dic113—21no—
30C22⋊Dic113C2×C412yes—
31#14268624—24no—
32C4×Dic113—21no—
33#41×C113—22no—
34#41×C113—22no—
35C2×Q8×C113D411yescharacteristic
36C2×D4×C113C2×C412yes—
37C2×D4×C113D411yescharacteristic
38C22×C4×C113D412yes—
39C22×C4×C113C2311yescharacteristic
40M16×C113—24no—
41M16×C113—22no—
42M16×C113D414yescomplemented
43C2×C8×C113—24no—
44C2×C8×C113—22no—
45C23×C113C22⋊C412yes—
46C23×C113C22×C411yescharacteristic
47C22×D113—22no—
48C22×D113—24no—
49C22×D113—82no—
50Q8×C113—22no—
51D4×C113—24no—
52D4×C113—22no—
53C2×C4×C113—22no—
54C2×C4×C113—22no—
55C2×C4×C113C22⋊C412yes—
56C2×C4×C113C2×D412yes—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113#4112yes—
60C22⋊D113—84no—
61C2×Dic113—22no—
62D452—41no—
63D452—42no—
64D452—41no—
65C8×C113—24no—
66#11744751—42no—
67C22×C113—22no—
68C22×C113—41no—
69C22×C113—42no—
70C22×C113C2×C22⋊C411yescharacteristic
71C22×C113C4×D412yes—
72C2×D113—44no—
73C2×D113—42no—
74C2×D113—84no—
75C4×C113—22no—
76C4×C113#12011yescharacteristic
77C4×C113#12112yes—
78C4×C113#12311yescharacteristic
79Dic113—42no—
80C2×C113—21no—
81C2×C113—22no—
82C2×C113—42no—
83C2×C113#38611yescharacteristic
84D113—82no—
85#1914—1131nomaximal, Sylow
86C113#191411yescharacteristic, complemented, Sylow
87#568D11311yescharacteristic, complemented
88#535—1131no—
89#413—1131no—
90C2×#100—1132no—
91#344—1132no—
92C2×#41C2×D11311yescharacteristic
93C22×D4—1131no—
94#131—24no—
95C2×M16—22no—
96C2×M16—1132no—
97C2×M16C2×D11312yes—
98#127—2261no—
99#124—2261no—
100#121—2262no—
101#120—1134no—
102#117—1131no—
103#101—2261no—
104#100—2261no—
105#100—2264no—
106C24—1132no—
107#41—22no—
108#41—22no—
109C2×Q8D45211yescharacteristic
110C2×D4—2264no—
111C2×D4—2262no—
112C2×D4—2261no—
113C2×D4—2261no—
114C2×D4—2262no—
115C2×D4C4×D11312yes—
116C2×D4D45211yescharacteristic
117C22×C4C22⋊D11312yes—
118C22×C4C22×D11311yescharacteristic
119M16—24no—
120M16—22no—
121M16—2262no—
122M16—2262no—
123M16C22⋊D11314yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—2262no—
127C4⋊C4—2261no—
128C22⋊C4—1132no—
129C22⋊C4—2264no—
130C42—2261no—
131C23—9042no—
132C23—2264no—
133C23—2262no—
134C23#1426862412yes—
135C23C2×C4×D11311yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—9044no—
140D4—4521no—
141D4—4522no—
142D4—4521no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—2262no—
146C2×C4#1426862412yes—
147C2×C4C2×C22⋊D11312yes—
148C2×C4C2×C22⋊D11311yescharacteristic
149C2×C4C2×D45211yescharacteristic
150C2×C4#1426864712yes—
151C8—24no—
152C8—4522no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—9044no—
157C22—4524no—
158C22—4522no—
159C22C2×#1426862411yescharacteristic
160C22C4×C22⋊D11312yes—
161C4—22no—
162C4—4522no—
163C4#1681359111yescharacteristic
164C4#1681359612yes—
165C4#1681360511yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—9042no—
170C2#2029847711yescharacteristic
subgroupG/H
centerC2#20298477
commutatorC23×C113C22×C4
FrattiniC22×C4C22×D113
Fitting#568×C113C2
socleC2×C113#386
prime radical#20299162C2
cosocleC22×C4×C113C23
hypercenter#568D113
hypocenterC113#1914
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #20298582C2semidirect
3. C2×#16813538C2semidirect
4. #20298370C2semidirect
5. #568×C113C2semidirect
42. M16×C113D4semidirect
86. C113#1914semidirect
87. #568D113semidirect
123. M16C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991622
#202985822
C2×#168135382
#202983702
#568×C1132
#1914113