Finite Group Databasebeta

← #20261541

Subgroups — #20261541

Order 6208.

258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 99 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#15690858C211yesmaximal, characteristic, complemented
2#15690855C211yesmaximal, characteristic, complemented
3#15690841C211yesmaximal, characteristic, complemented
4#15690839C212yesmaximal, complemented
5#15690837C212yesmaximal, complemented
6#15690836C211yesmaximal, characteristic, complemented
7#15690832C211yesmaximal, characteristic, complemented
8#15690831C212yesmaximal, complemented
9SD16×D97C212yesmaximal, complemented
10#15690816C211yesmaximal, characteristic, complemented
11C2×SD16×C97C211yesmaximal, characteristic, complemented
12#13095512—21no—
13#13095512C2212yescomplemented
14#13095511—22no—
15#13095511C2211yescharacteristic
16#13095511C2211yescharacteristic
17#13095511C2211yescharacteristic, complemented
18#13095510—21no—
19#13095510C2212yes—
20Q8×D97—21no—
21Q8×D97C2212yescomplemented
22C2×C22⋊D97—22no—
23D4×D97—21no—
24D4×D97C2212yes—
25Dic388C2211yescharacteristic, complemented
26#13095501C2212yescomplemented
27#13095500C2211yescharacteristic, complemented
28#13095500C2211yescharacteristic, complemented
29#13095499C2212yescomplemented
30#13095498C2212yescomplemented
31D776C2211yescharacteristic, complemented
32#13095496C2212yescomplemented
33#13095495C2211yescharacteristic, complemented
34#13095494C2212yescomplemented
35C8×D97C2212yescomplemented
36C2×Q8×C97C2211yescharacteristic, complemented
37C2×D4×C97C2211yescharacteristic
38SD16×C97C2212yescomplemented
39SD16×C97C2212yescomplemented
40C2×C8×C97C2211yescharacteristic, complemented
41C23×C97—21no—
42C22×D97—22no—
43Q8×C97—21no—
44Q8×C97C2312yes—
45D4×C97—21no—
46D4×C97C2312yes—
47C2×C4×C97—21no—
48C2×C4×C97C2311yescharacteristic
49C22⋊D97—21no—
50C22⋊D97—21no—
51C22⋊D97—22no—
52C22⋊D97—22no—
53C22⋊D97D412yes—
54C2×Dic97—22no—
55D388—22no—
56D388D411yescharacteristic
57D388C2311yescharacteristic
58D388C2311yescharacteristic
59C4×D97—22no—
60C4×D97—21no—
61C4×D97—21no—
62C4×D97—22no—
63C4×D97C2312yes—
64Dic194—22no—
65Dic194D411yescharacteristic
66Dic194C2311yescharacteristic
67Dic194C2311yescharacteristic
68C8×C97C2311yescharacteristic
69C8×C97C2311yescharacteristic
70#11715895C2312yes—
71C22×C97—22no—
72C22×C97—81no—
73C22×C97C2×D411yescharacteristic
74C2×D97—21no—
75C2×D97—21no—
76C2×D97—82no—
77C2×D97C2×D412yes—
78C4×C97—22no—
79C4×C97C2×D411yescharacteristic
80C4×C97C2411yescharacteristic
81Dic97—21no—
82Dic97—21no—
83Dic97C2×D412yes—
84C2×C97—21no—
85C2×C97—42no—
86C2×C97C22×D411yescharacteristic
87D97—22no—
88D97—41no—
89D97—41no—
90C97#57711yescharacteristic, complemented, Sylow
91#577—971nomaximal, Sylow
922−1+4—971no—
93H(5,𝔽2)—971no—
94#137—971no—
95#137—972no—
96AGL(1,ℤ/8)—971no—
97AGL(1,ℤ/8)—972no—
98#135—972no—
99#135—971no—
100C2×SD16—972no—
101C2×SD16D9711yescharacteristic, complemented
102#131—971no—
103#41—971no—
104#41—972no—
105#41—972no—
106#41—971no—
107#41—971no—
108#41—1942no—
109#41—1941no—
110#41—1941no—
111C2×Q8—972no—
112C2×Q8—1941no—
113C2×Q8C2×D9711yescharacteristic, complemented
114C2×D4—972no—
115C2×D4—1941no—
116C2×D4—1942no—
117C2×D4C2×D9711yescharacteristic
118Q16—972no—
119Q16—971no—
120SD16—972no—
121SD16—972no—
122SD16—971no—
123SD16—971no—
124SD16C2×D9712yescomplemented
125SD16C2×D9712yescomplemented
126D8—972no—
127D8—971no—
128M16—971no—
129M16—972no—
130C2×C8—972no—
131C2×C8C2×D9711yescharacteristic, complemented
132C23—21no—
133C23—1942no—
134Q8—21no—
135Q8—971no—
136Q8—971no—
137Q8—971no—
138Q8—1942no—
139Q8C22×D9712yes—
140D4—21no—
141D4—972no—
142D4—971no—
143D4—971no—
144D4—971no—
145D4—1942no—
146D4—1942no—
147D4—1942no—
148D4—1941no—
149D4—1941no—
150D4C22×D9712yes—
151C2×C4—21no—
152C2×C4—972no—
153C2×C4—1942no—
154C2×C4—1942no—
155C2×C4—1942no—
156C2×C4—1941no—
157C2×C4—1941no—
158C2×C4C22×D9711yescharacteristic
159C8—972no—
160C8C22×D9711yescharacteristic
161C8C22×D9711yescharacteristic
162C22—22no—
163C22—81no—
164C22—7762no—
165C22—972no—
166C22—1941no—
167C22—1941no—
168C22D4×D9711yescharacteristic
169C4—22no—
170C4—972no—
171C4—1941no—
172C4—1941no—
173C4D4×D9711yescharacteristic
174C4C23×D9711yescharacteristic
175C2—21no—
176C2—42no—
177C2—3881no—
178C2—3881no—
179C2—1942no—
180C2C2×D4×D9711yescharacteristic
subgroupG/H
centerC2C2×D4×D97
commutatorC4×C97C24
FrattiniC4C23×D97
FittingC2×SD16×C97C2
socleC2×C97C22×D4
hypercenterC2×SD16D97
hypocenterC97#577
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #15690858C2semidirect
2. #15690855C2semidirect
3. #15690841C2semidirect
4. #15690839C2semidirect
5. #15690837C2semidirect
6. #15690836C2semidirect
7. #15690832C2semidirect
8. #15690831C2semidirect
9. SD16×D97C2semidirect
10. #15690816C2semidirect
11. C2×SD16×C97C2semidirect
13. #13095512C22semidirect
17. #13095511C22semidirect
21. Q8×D97C22semidirect
25. Dic388C22semidirect
26. #13095501C22semidirect
27. #13095500C22semidirect
28. #13095500C22semidirect
29. #13095499C22semidirect
30. #13095498C22semidirect
31. D776C22semidirect
32. #13095496C22semidirect
33. #13095495C22semidirect
34. #13095494C22semidirect
35. C8×D97C22semidirect
36. C2×Q8×C97C22semidirect
38. SD16×C97C22semidirect
39. SD16×C97C22semidirect
40. C2×C8×C97C22semidirect
90. C97#577semidirect
101. C2×SD16D97semidirect
113. C2×Q8C2×D97semidirect
124. SD16C2×D97semidirect
125. SD16C2×D97semidirect
131. C2×C8C2×D97semidirect