Finite Group Databasebeta

← #20261207

Subgroups — #20261207

Order 6208.

338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×D4×D97C211yesmaximal, characteristic
2C4×D388C211yesmaximal, characteristic, complemented
3D4×Dic97C211yesmaximal, characteristic, complemented
4#15690772C211yesmaximal, characteristic, complemented
5C4×C22⋊D97C212yesmaximal, complemented
6#15690770C212yesmaximal, complemented
7#15690768C211yesmaximal, characteristic, complemented
8#15690767C211yesmaximal, characteristic, complemented
9C2×#13095488C212yesmaximal, complemented
10C22⋊C4×D97C212yesmaximal, complemented
11C4×D4×C97C211yesmaximal, characteristic, complemented
12C23×D97C2212yes—
13C2×D388C2211yescharacteristic
14C2×C22⋊D97C2212yes—
15D4×D97C418yescomplemented
16C22×Dic97C2212yescomplemented
17C2×C4×D97C2211yescharacteristic
18C2×C4×D97C2212yescomplemented
19C2×C4×D97C2212yescomplemented
20C4⋊Dic97C2211yescharacteristic, complemented
21#13095490C2211yescharacteristic, complemented
22#13095490C2211yescharacteristic, complemented
23C22⋊Dic97C2212yescomplemented
24#13095488C2211yescharacteristic
25#13095488C2212yes—
26#13095488C2211yescharacteristic
27#13095488C2212yescomplemented
28#13095488C2212yescomplemented
29C4×Dic97C2211yescharacteristic, complemented
30C4×Dic97C2212yescomplemented
31C2×D4×C97C2211yescharacteristic
32C22×C4×C97C2212yescomplemented
33C4⋊C4×C97C2211yescharacteristic, complemented
34C22⋊C4×C97C2212yescomplemented
35C42×C97C2211yescharacteristic, complemented
36C23×C97C2312yes—
37C22×D97—42no—
38C22×D97—42no—
39C22×D97C2×C418yescomplemented
40C22×D97C2311yescharacteristic
41C22×D97C2312yes—
42D4×C97C2×C414yescomplemented
43C2×C4×C97—42no—
44C2×C4×C97C2311yescharacteristic
45C2×C4×C97C2311yescharacteristic
46C2×C4×C97C2312yes—
47C2×C4×C97C2311yescharacteristic
48C22⋊D97C2×C418yescomplemented
49C2×Dic97—42no—
50C2×Dic97C2311yescharacteristic
51C2×Dic97C2312yes—
52C2×Dic97C2311yescharacteristic
53C2×Dic97C2311yescharacteristic
54D388C2×C414yescomplemented
55C4×D97—42no—
56C4×D97—42no—
57C4×D97C2×C414yescomplemented
58C22×C97—22no—
59C22×C97—22no—
60C22×C97C22×C414yes—
61C22×C97C2411yescharacteristic
62C2×D97—22no—
63C2×D97—22no—
64C2×D97—21no—
65C2×D97—21no—
66C2×D97—48no—
67C2×D97C22×C412yes—
68C2×D97C22×C414yes—
69C4×C97—21no—
70C4×C97—22no—
71C4×C97—21no—
72C4×C97C22×C412yes—
73Dic97—21no—
74Dic97—22no—
75Dic97—21no—
76Dic97C22×C412yes—
77C2×C97—24no—
78C2×C97C23×C411yescharacteristic
79C2×C97H(5,𝔽2)11yescharacteristic
80C2×C97H(5,𝔽2)11yescharacteristic
81D97—22no—
82D97—24no—
83C97#51811yescharacteristic, complemented, Sylow
84#518—971nomaximal, Sylow
85C22×D4—971no—
86C4×D4—971no—
87C4×D4—972no—
88C4×D4—971no—
89C4×D4—972no—
90C4×D4—971no—
91C4×D4D9711yescharacteristic, complemented
92#117—971no—
93#117—971no—
94C2×C22⋊C4—972no—
95C2×C22⋊C4—972no—
96C24—972no—
97C2×D4—972no—
98C2×D4—978no—
99C2×D4—971no—
100C2×D4C2×D9711yescharacteristic
101C22×C4—971no—
102C22×C4—972no—
103C22×C4—972no—
104C22×C4—972no—
105C22×C4C2×D9712yescomplemented
106C4⋊C4—971no—
107C4⋊C4—971no—
108C4⋊C4—971no—
109C4⋊C4C2×D9711yescharacteristic, complemented
110C22⋊C4—972no—
111C22⋊C4—972no—
112C22⋊C4—971no—
113C22⋊C4—971no—
114C22⋊C4—972no—
115C22⋊C4—972no—
116C22⋊C4C2×D9712yescomplemented
117C42—972no—
118C42—971no—
119C42C2×D9711yescharacteristic, complemented
120C23—978no—
121C23—971no—
122C23—972no—
123C23—3882no—
124C23—3882no—
125C23C22×D9712yes—
126D4—978no—
127D4—974no—
128D4C4×D9714yescomplemented
129C2×C4—42no—
130C2×C4—971no—
131C2×C4—974no—
132C2×C4—971no—
133C2×C4—972no—
134C2×C4—971no—
135C2×C4—3882no—
136C2×C4—3882no—
137C2×C4—3882no—
138C2×C4C22×D9712yes—
139C2×C4C22×D9711yescharacteristic
140C2×C4C22×D9711yescharacteristic
141C2×C4C22×D9711yescharacteristic
142C22—22no—
143C22—22no—
144C22—972no—
145C22—974no—
146C22—3888no—
147C22—1942no—
148C22—1941no—
149C22—1942no—
150C22—1941no—
151C22C2×C4×D9714yes—
152C22C23×D9711yescharacteristic
153C4—21no—
154C4—22no—
155C4—21no—
156C4—972no—
157C4—1941no—
158C4—1942no—
159C4—1941no—
160C4C2×C4×D9712yes—
161C2—24no—
162C2—1942no—
163C2—1944no—
164C2C22×C4×D9711yescharacteristic
165C2#1569085511yescharacteristic
166C2#1569085611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D97
commutatorC2×C97C23×C4
FittingC4×D4×C97C2
socleC22×C97C24
hypercenterC4×D4D97
hypocenterC97#518
LCSG ▷ C2×C97 ▷ C97
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D388C2semidirect
3. D4×Dic97C2semidirect
4. #15690772C2semidirect
5. C4×C22⋊D97C2semidirect
6. #15690770C2semidirect
7. #15690768C2semidirect
8. #15690767C2semidirect
9. C2×#13095488C2semidirect
10. C22⋊C4×D97C2semidirect
11. C4×D4×C97C2semidirect
15. D4×D97C4semidirect
16. C22×Dic97C22semidirect
18. C2×C4×D97C22semidirect
19. C2×C4×D97C22semidirect
20. C4⋊Dic97C22semidirect
21. #13095490C22semidirect
22. #13095490C22semidirect
23. C22⋊Dic97C22semidirect
27. #13095488C22semidirect
28. #13095488C22semidirect
29. C4×Dic97C22semidirect
30. C4×Dic97C22semidirect
32. C22×C4×C97C22semidirect
33. C4⋊C4×C97C22semidirect
34. C22⋊C4×C97C22semidirect
35. C42×C97C22semidirect
39. C22×D97C2×C4semidirect
42. D4×C97C2×C4semidirect
48. C22⋊D97C2×C4semidirect
54. D388C2×C4semidirect
57. C4×D97C2×C4semidirect
83. C97#518semidirect
91. C4×D4D97semidirect
105. C22×C4C2×D97semidirect
109. C4⋊C4C2×D97semidirect
116. C22⋊C4C2×D97semidirect
119. C42C2×D97semidirect
128. D4C4×D97semidirect