Finite Group Databasebeta

← #28399484

Subgroups — #28399484

Order 14464.

458 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 217 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#20299365C212yesmaximal, complemented
2#20298720C214yesmaximal, complemented
3#20298715C214yesmaximal, complemented
4#20298647C211yesmaximal, characteristic, complemented
5C2×#16813549C212yesmaximal, complemented
6M16×Dic113C211yesmaximal, characteristic, complemented
7#575×C113C211yesmaximal, characteristic
8#16813629—24no—
9#16813629C2218yescomplemented
10C2×#14268631—24no—
11C2×#14268631C2212yes—
12C2×#14268631C2211yescharacteristic
13C2×C4×Dic113C2211yescharacteristic
14#16813558C2214yescomplemented
15#16813549C2214yescomplemented
16#16813549C2214yescomplemented
17#16813532C2212yescomplemented
18C8×Dic113C2212yescomplemented
19C2×#41×C113C2212yes—
20#137×C113C414yescomplemented
21AGL(1,ℤ/8)×C113C414yescomplemented
22#135×C113C2214yes—
23C2×M16×C113C2211yescharacteristic
24C22×Dic113—21no—
25#14268631—22no—
26#14268631—28no—
27#14268631D414yes—
28#14268631C2314yes—
29C2×#11744751—22no—
30C2×#11744751—28no—
31C2×#11744751C2312yes—
32C4×Dic113—21no—
33C4×Dic113C2311yescharacteristic
34C4×Dic113C2311yescharacteristic
35#41×C113—22no—
36#41×C113—22no—
37#41×C113C2×C414yes—
38#41×C113C2314yes—
39C2×Q8×C113C2×C412yes—
40C2×D4×C113—22no—
41C2×D4×C113C2×C412yes—
42C22×C4×C113—22no—
43C22×C4×C113C2311yescharacteristic
44Q16×C113C2×C414yescomplemented
45SD16×C113C2×C418yescomplemented
46D8×C113C2×C414yescomplemented
47M16×C113C2×C414yes—
48C2×C8×C113C2312yes—
49C23×C113—22no—
50C23×C113#4111yescharacteristic
51Q8×C113—22no—
52Q8×C113C22×C414yes—
53D4×C113—24no—
54D4×C113—24no—
55D4×C113—22no—
56D4×C113C22×C414yes—
57C2×C4×C113—22no—
58C2×C4×C113—24no—
59C2×C4×C113—24no—
60C2×C4×C113C22×C412yes—
61C2×C4×C113C2×D412yes—
62C2×C4×C113#4111yescharacteristic
63C2×C4×C113C2411yescharacteristic
64C2×Dic113—21no—
65C2×Dic113—21no—
66C2×Dic113—42no—
67C8×C113C22×C414yes—
68#11744751—24no—
69#11744751C2×D414yes—
70C22×C113—24no—
71C22×C113—41no—
72C22×C113—82no—
73C22×C113C4×D412yes—
74C22×C113C2×#4111yescharacteristic
75C4×C113—24no—
76C4×C113C4×D412yes—
77C4×C113C23×C411yescharacteristic
78C4×C113C22×D411yescharacteristic
79Dic113—22no—
80Dic113—41no—
81C2×C113—21no—
82C2×C113—22no—
83C2×C113—44no—
84C2×C113C2×C4×D411yescharacteristic
85#2956—1131nomaximal, Sylow
86C113#295611yescharacteristic, complemented, Sylow
87#575D11311yescharacteristic
88#568—1132no—
89#444—1134no—
90#443—1134no—
91#430—1131no—
92C2×#104—1132no—
93C4×M16—1131no—
94C2×#41C2×D11312yes—
95#137Dic11314yescomplemented
96AGL(1,ℤ/8)Dic11314yescomplemented
97#135C2×D11314yes—
98#131—1138no—
99#131—2264no—
100C2×M16—1131no—
101C2×M16—1132no—
102C2×M16—2264no—
103C2×M16C2×D11311yescharacteristic
104C2×C42—1131no—
105#108—1134no—
106#104—1134no—
107#104—1134no—
108#97—1132no—
109C4×C8—1132no—
110#41—22no—
111#41—22no—
112#41C2×Dic11314yes—
113#41C22×D11314yes—
114C2×Q8C2×Dic11312yes—
115C2×D4—22no—
116C2×D4C2×Dic11312yes—
117C22×C4—22no—
118C22×C4—2261no—
119C22×C4C22×D11311yescharacteristic
120Q16C2×Dic11314yescomplemented
121SD16C2×Dic11318yescomplemented
122D8C2×Dic11314yescomplemented
123M16—1134no—
124M16—1134no—
125M16—2268no—
126M16—2262no—
127M16C2×Dic11314yes—
128C2×C8—1132no—
129C2×C8—2268no—
130C2×C8—2262no—
131C2×C8C22×D11312yes—
132C42—1131no—
133C42—1131no—
134C42—2261no—
135C23—22no—
136C23#1426864611yescharacteristic
137Q8—22no—
138Q8C22×Dic11314yes—
139D4—24no—
140D4—24no—
141D4—22no—
142D4C22×Dic11314yes—
143C2×C4—22no—
144C2×C4—24no—
145C2×C4—24no—
146C2×C4—4522no—
147C2×C4—2261no—
148C2×C4—2261no—
149C2×C4C22×Dic11312yes—
150C2×C4D4×D11312yes—
151C2×C4#1426864611yescharacteristic
152C2×C4C23×D11311yescharacteristic
153C8—1134no—
154C8—2264no—
155C8C22×Dic11314yes—
156C22—24no—
157C22—41no—
158C22—82no—
159C22D4×Dic11312yes—
160C22C2×#1426864611yescharacteristic
161C4—24no—
162C4—4521no—
163C4—2262no—
164C4D4×Dic11312yes—
165C4C23×Dic11311yescharacteristic
166C4C2×D4×D11311yescharacteristic
167C2—21no—
168C2—22no—
169C2—44no—
170C2C2×D4×Dic11311yescharacteristic
subgroupG/H
centerC4C2×D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
Fitting, prime radical#575×C113C2
socleC2×C113C2×C4×D4
cosocleC2×C4×C113C24
hypercenter#575D113
hypocenterC113#2956
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #20299365C2semidirect
2. #20298720C2semidirect
3. #20298715C2semidirect
4. #20298647C2semidirect
5. C2×#16813549C2semidirect
6. M16×Dic113C2semidirect
9. #16813629C22semidirect
14. #16813558C22semidirect
15. #16813549C22semidirect
16. #16813549C22semidirect
17. #16813532C22semidirect
18. C8×Dic113C22semidirect
20. #137×C113C4semidirect
21. AGL(1,ℤ/8)×C113C4semidirect
44. Q16×C113C2×C4semidirect
45. SD16×C113C2×C4semidirect
46. D8×C113C2×C4semidirect
86. C113#2956semidirect
95. #137Dic113semidirect
96. AGL(1,ℤ/8)Dic113semidirect
120. Q16C2×Dic113semidirect
121. SD16C2×Dic113semidirect
122. D8C2×Dic113semidirect

Maximal subgroups

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

subgroupindex
#202993652
#202987202
#202987152
#202986472
C2×#168135492
M16×Dic1132
#575×C1132
#2956113