Finite Group Databasebeta

← #20261539

Subgroups — #20261539

Order 6208.

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

normal subgroups only

This group has 268 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#15690856C211yesmaximal, characteristic, complemented
2#15690855C211yesmaximal, characteristic, complemented
3#15690838C211yesmaximal, characteristic, complemented
4#15690837C212yesmaximal, complemented
5#15690834C212yesmaximal, complemented
6#15690831C212yesmaximal, complemented
7#15690830C211yesmaximal, characteristic, complemented
8C2×#13095496C211yesmaximal, characteristic, complemented
9D8×D97C212yesmaximal, complemented
10#15690818C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C97C211yesmaximal, characteristic, complemented
12#13095512C2212yescomplemented
13#13095511—21no—
14#13095511C2211yescharacteristic
15#13095511C2211yescharacteristic, complemented
16#13095510—21no—
17#13095510C2212yescomplemented
18C2×D388—21no—
19C2×D388C2211yescharacteristic, complemented
20C2×C22⋊D97—22no—
21D4×D97—22no—
22D4×D97—21no—
23D4×D97C2212yescomplemented
24D4×D97C2212yescomplemented
25#13095501C2211yescharacteristic, complemented
26#13095500C2212yescomplemented
27#13095499C2211yescharacteristic, complemented
28#13095498C2211yescharacteristic, complemented
29D776C2212yescomplemented
30#13095496C2211yescharacteristic, complemented
31#13095496C2212yescomplemented
32#13095496C2212yescomplemented
33#13095494C2212yescomplemented
34C2×#11715895C2211yescharacteristic, complemented
35C8×D97C2212yescomplemented
36#41×C97C2211yescharacteristic, complemented
37C2×D4×C97C2211yescharacteristic, complemented
38SD16×C97C2212yescomplemented
39D8×C97C2212yescomplemented
40M16×C97C2211yescharacteristic, complemented
41C23×C97—21no—
42C22×D97—21no—
43C22×D97—22no—
44C22×D97—22no—
45Q8×C97C2311yescharacteristic
46D4×C97—21no—
47D4×C97—21no—
48D4×C97C2311yescharacteristic
49D4×C97C2312yes—
50C2×C4×C97—21no—
51C2×C4×C97C2311yescharacteristic
52C22⋊D97—21no—
53C22⋊D97—22no—
54C22⋊D97—22no—
55C22⋊D97—22no—
56C22⋊D97D412yes—
57C2×Dic97—22no—
58D388—22no—
59D388—21no—
60D388D411yescharacteristic
61D388C2312yes—
62D388C2311yescharacteristic
63C4×D97—21no—
64C4×D97—22no—
65C4×D97C2312yes—
66Dic194D411yescharacteristic
67Dic194C2311yescharacteristic
68C8×C97C2312yes—
69#11715895C2311yescharacteristic
70#11715895C2311yescharacteristic
71C22×C97—22no—
72C22×C97—21no—
73C22×C97—81no—
74C22×C97C2×D411yescharacteristic
75C2×D97—22no—
76C2×D97—21no—
77C2×D97—82no—
78C2×D97—82no—
79C2×D97—81no—
80C2×D97C2×D412yes—
81C4×C97—21no—
82C4×C97C2×D411yescharacteristic
83C4×C97C2411yescharacteristic
84Dic97—21no—
85Dic97C2×D412yes—
86C2×C97—21no—
87C2×C97—41no—
88C2×C97—42no—
89C2×C97C22×D411yescharacteristic
90D97—22no—
91D97—42no—
92D97—41no—
93C97#57611yescharacteristic, complemented, Sylow
94#576—971nomaximal, Sylow
95H(5,𝔽2)—971no—
96H(5,𝔽2)—971no—
97AGL(1,ℤ/8)—972no—
98AGL(1,ℤ/8)—972no—
99AGL(1,ℤ/8)—971no—
100AGL(1,ℤ/8)D9711yescharacteristic, complemented
101#135—971no—
102#135—972no—
103C2×D8—971no—
104C2×D8—972no—
105#131—971no—
106#41—971no—
107#41—972no—
108#41—972no—
109#41—971no—
110#41—1941no—
111#41—1941no—
112#41C2×D9711yescharacteristic, complemented
113C2×D4—972no—
114C2×D4—972no—
115C2×D4—971no—
116C2×D4—1941no—
117C2×D4—1942no—
118C2×D4—1941no—
119C2×D4—1942no—
120C2×D4C2×D9711yescharacteristic, complemented
121Q16—971no—
122SD16—971no—
123SD16—971no—
124SD16—972no—
125SD16C2×D9712yescomplemented
126D8—972no—
127D8—971no—
128D8—972no—
129D8—972no—
130D8C2×D9712yescomplemented
131M16—972no—
132M16C2×D9711yescharacteristic, complemented
133C2×C8—971no—
134C2×C8—972no—
135C23—21no—
136C23—1942no—
137C23—1942no—
138C23—1941no—
139Q8—971no—
140Q8—971no—
141Q8C22×D9711yescharacteristic
142D4—21no—
143D4—21no—
144D4—972no—
145D4—971no—
146D4—972no—
147D4—971no—
148D4—1942no—
149D4—1942no—
150D4—1942no—
151D4—1942no—
152D4—1941no—
153D4—1941no—
154D4C22×D9712yes—
155D4C22×D9711yescharacteristic
156C2×C4—21no—
157C2×C4—972no—
158C2×C4—1942no—
159C2×C4—1942no—
160C2×C4—1941no—
161C2×C4C22×D9711yescharacteristic
162C8—971no—
163C8—971no—
164C8C22×D9712yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—7761no—
169C22—7762no—
170C22—7762no—
171C22—972no—
172C22—1942no—
173C22—1941no—
174C22D4×D9711yescharacteristic
175C4—21no—
176C4—972no—
177C4—1941no—
178C4D4×D9711yescharacteristic
179C4C23×D9711yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—3882no—
184C2—3881no—
185C2—1942no—
186C2C2×D4×D9711yescharacteristic
subgroupG/H
centerC2C2×D4×D97
commutatorC4×C97C24
FrattiniC4C23×D97
FittingAGL(1,ℤ/8)×C97C2
socleC2×C97C22×D4
hypercenterAGL(1,ℤ/8)D97
hypocenterC97#576
LCSG ▷ C4×C97 ▷ C2×C97 ▷ C97
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #15690856C2semidirect
2. #15690855C2semidirect
3. #15690838C2semidirect
4. #15690837C2semidirect
5. #15690834C2semidirect
6. #15690831C2semidirect
7. #15690830C2semidirect
8. C2×#13095496C2semidirect
9. D8×D97C2semidirect
10. #15690818C2semidirect
11. AGL(1,ℤ/8)×C97C2semidirect
12. #13095512C22semidirect
15. #13095511C22semidirect
17. #13095510C22semidirect
19. C2×D388C22semidirect
23. D4×D97C22semidirect
24. D4×D97C22semidirect
25. #13095501C22semidirect
26. #13095500C22semidirect
27. #13095499C22semidirect
28. #13095498C22semidirect
29. D776C22semidirect
30. #13095496C22semidirect
31. #13095496C22semidirect
32. #13095496C22semidirect
33. #13095494C22semidirect
34. C2×#11715895C22semidirect
35. C8×D97C22semidirect
36. #41×C97C22semidirect
37. C2×D4×C97C22semidirect
38. SD16×C97C22semidirect
39. D8×C97C22semidirect
40. M16×C97C22semidirect
93. C97#576semidirect
100. AGL(1,ℤ/8)D97semidirect
112. #41C2×D97semidirect
120. C2×D4C2×D97semidirect
125. SD16C2×D97semidirect
130. D8C2×D97semidirect
132. M16C2×D97semidirect