Finite Group Databasebeta

← #20261544

Subgroups — #20261544

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#15690856C211yesmaximal, characteristic, complemented
3#15690842C212yesmaximal, complemented
4#15690838C211yesmaximal, characteristic, complemented
5#15690837C212yesmaximal, complemented
6#15690833C212yesmaximal, complemented
7#15690830C211yesmaximal, characteristic, complemented
8C2×#13095498C211yesmaximal, characteristic, complemented
9SD16×D97C212yesmaximal, complemented
10#15690818C211yesmaximal, characteristic, complemented
11#137×C97C211yesmaximal, characteristic, complemented
12#13095512—21no—
13#13095512C2212yes—
14#13095512C2212yescomplemented
15#13095511—22no—
16#13095511—21no—
17#13095511C2211yescharacteristic
18#13095511C2211yescharacteristic, complemented
19Q8×D97—21no—
20Q8×D97C2212yescomplemented
21C2×D388—21no—
22C2×D388C2211yescharacteristic
23D4×D97—22no—
24D4×D97C2212yes—
25#13095501C2211yescharacteristic, complemented
26#13095500C2212yescomplemented
27#13095499C2211yescharacteristic, complemented
28#13095498C2212yescomplemented
29#13095498C2212yescomplemented
30#13095498C2211yescharacteristic, complemented
31D776C2212yescomplemented
32#13095496C2211yescharacteristic, complemented
33#13095494C2212yescomplemented
34C2×#11715895C2211yescharacteristic, complemented
35C8×D97C2212yescomplemented
36#41×C97C2211yescharacteristic
37C2×Q8×C97C2211yescharacteristic, complemented
38Q16×C97C2212yescomplemented
39SD16×C97C2212yescomplemented
40M16×C97C2211yescharacteristic, complemented
41C22×D97—21no—
42C22×D97—22no—
43Q8×C97—21no—
44Q8×C97C2312yes—
45Q8×C97C2311yescharacteristic
46D4×C97—21no—
47D4×C97C2311yescharacteristic
48C2×C4×C97—21no—
49C2×C4×C97—21no—
50C2×C4×C97C2311yescharacteristic
51C22⋊D97—21no—
52C22⋊D97—22no—
53C22⋊D97D412yes—
54D388—22no—
55D388—22no—
56D388—21no—
57D388D411yescharacteristic
58D388C2311yescharacteristic
59D388C2312yes—
60C4×D97—22no—
61C4×D97—21no—
62C4×D97—22no—
63C4×D97—22no—
64C4×D97C2312yes—
65Dic194—22no—
66Dic194D411yescharacteristic
67Dic194C2311yescharacteristic
68C8×C97C2312yes—
69#11715895C2311yescharacteristic
70#11715895C2311yescharacteristic
71C22×C97—21no—
72C22×C97C2×D411yescharacteristic
73C2×D97—21no—
74C2×D97—22no—
75C2×D97—82no—
76C2×D97—81no—
77C2×D97C2×D412yes—
78C4×C97—22no—
79C4×C97—21no—
80C4×C97C2×D411yescharacteristic
81C4×C97C2411yescharacteristic
82Dic97—21no—
83Dic97C2×D412yes—
84C2×C97—21no—
85C2×C97—41no—
86C2×C97C22×D411yescharacteristic
87D97—22no—
88D97—41no—
89D97—42no—
90C97#57711yescharacteristic, complemented, Sylow
91#577—971nomaximal, Sylow
922−1+4—971no—
93H(5,𝔽2)—971no—
94#137—972no—
95#137D9711yescharacteristic, complemented
96AGL(1,ℤ/8)—972no—
97AGL(1,ℤ/8)—971no—
98#135—971no—
99#135—972no—
100C2×SD16—971no—
101C2×SD16—972no—
102#131—971no—
103#41—971no—
104#41—972no—
105#41—972no—
106#41—971no—
107#41—1942no—
108#41—1941no—
109#41—1941no—
110#41C2×D9711yescharacteristic
111C2×Q8—972no—
112C2×Q8—1941no—
113C2×Q8C2×D9711yescharacteristic, complemented
114C2×D4—972no—
115C2×D4—971no—
116C2×D4—1941no—
117C2×D4—1942no—
118Q16—971no—
119Q16C2×D9712yescomplemented
120SD16—972no—
121SD16—972no—
122SD16—971no—
123SD16—971no—
124SD16—972no—
125SD16C2×D9712yescomplemented
126D8—971no—
127D8—972no—
128M16—972no—
129M16C2×D9711yescharacteristic, complemented
130C2×C8—971no—
131C2×C8—972no—
132C23—1942no—
133C23—1941no—
134Q8—21no—
135Q8—971no—
136Q8—971no—
137Q8—1942no—
138Q8C22×D9712yes—
139Q8C22×D9711yescharacteristic
140D4—21no—
141D4—972no—
142D4—971no—
143D4—971no—
144D4—972no—
145D4—1942no—
146D4—1942no—
147D4—1942no—
148D4—1941no—
149D4—1941no—
150D4C22×D9711yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—972no—
154C2×C4—1942no—
155C2×C4—1942no—
156C2×C4—1942no—
157C2×C4—1941no—
158C2×C4C22×D9711yescharacteristic
159C8—971no—
160C8—971no—
161C8C22×D9712yes—
162C22—21no—
163C22—7761no—
164C22—7762no—
165C22—972no—
166C22—1941no—
167C22—1942no—
168C22D4×D9711yescharacteristic
169C4—21no—
170C4—22no—
171C4—972no—
172C4—1941no—
173C4D4×D9711yescharacteristic
174C4C23×D9711yescharacteristic
175C2—21no—
176C2—41no—
177C2—3882no—
178C2—3881no—
179C2—1942no—
180C2C2×D4×D9711yescharacteristic
subgroupG/H
centerC2C2×D4×D97
commutatorC4×C97C24
FrattiniC4C23×D97
Fitting#137×C97C2
socleC2×C97C22×D4
hypercenter#137D97
hypocenterC97#577
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #15690858C2semidirect
2. #15690856C2semidirect
3. #15690842C2semidirect
4. #15690838C2semidirect
5. #15690837C2semidirect
6. #15690833C2semidirect
7. #15690830C2semidirect
8. C2×#13095498C2semidirect
9. SD16×D97C2semidirect
10. #15690818C2semidirect
11. #137×C97C2semidirect
14. #13095512C22semidirect
18. #13095511C22semidirect
20. Q8×D97C22semidirect
25. #13095501C22semidirect
26. #13095500C22semidirect
27. #13095499C22semidirect
28. #13095498C22semidirect
29. #13095498C22semidirect
30. #13095498C22semidirect
31. D776C22semidirect
32. #13095496C22semidirect
33. #13095494C22semidirect
34. C2×#11715895C22semidirect
35. C8×D97C22semidirect
37. C2×Q8×C97C22semidirect
38. Q16×C97C22semidirect
39. SD16×C97C22semidirect
40. M16×C97C22semidirect
90. C97#577semidirect
95. #137D97semidirect
113. C2×Q8C2×D97semidirect
119. Q16C2×D97semidirect
125. SD16C2×D97semidirect
129. M16C2×D97semidirect