Finite Group Databasebeta

← #20261534

Subgroups — #20261534

Order 6208.

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

normal subgroups only

This group has 262 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
1C2×#13095512C211yesmaximal, characteristic, complemented
2#41×D97C211yesmaximal, characteristic, complemented
3#15690842C212yesmaximal, complemented
4#15690841C211yesmaximal, characteristic, complemented
5#15690838C211yesmaximal, characteristic, complemented
6#15690837C212yesmaximal, complemented
7#15690835C211yesmaximal, characteristic, complemented
8#15690833C212yesmaximal, complemented
9#15690831C212yesmaximal, complemented
10M16×D97C211yesmaximal, characteristic, complemented
11#137×C97C211yesmaximal, characteristic, complemented
12#13095512—21no—
13#13095512—21no—
14#13095512C2212yes—
15#13095512C2212yescomplemented
16#13095512C2211yescharacteristic, complemented
17#13095511—21no—
18#13095511C2211yescharacteristic
19#13095510—21no—
20#13095510C2211yescharacteristic, complemented
21Q8×D97C2211yescharacteristic, complemented
22C2×D388—21no—
23C2×D388C2211yescharacteristic, complemented
24D4×D97—21no—
25D4×D97C2211yescharacteristic, complemented
26C2×C4×D97—21no—
27C2×C4×D97—21no—
28C2×C4×D97C2211yescharacteristic
29#13095501C2212yescomplemented
30#13095500C2212yescomplemented
31#13095498C2212yescomplemented
32#13095498C2212yescomplemented
33D776C2212yescomplemented
34#13095496C2212yescomplemented
35#13095495C2211yescharacteristic, complemented
36#13095494C2212yescomplemented
37C8×D97C2212yescomplemented
38#41×C97C2211yescharacteristic
39C2×Q8×C97C2211yescharacteristic, complemented
40Q16×C97C2212yescomplemented
41SD16×C97C2212yescomplemented
42M16×C97C2211yescharacteristic, complemented
43C22×D97—21no—
44C22×D97—21no—
45C22×D97D411yescharacteristic
46Q8×C97—21no—
47Q8×C97C2312yes—
48Q8×C97C2311yescharacteristic
49D4×C97—21no—
50D4×C97C2311yescharacteristic
51C2×C4×C97—21no—
52C2×C4×C97—21no—
53C2×C4×C97C2311yescharacteristic
54C22⋊D97—21no—
55C22⋊D97—21no—
56C22⋊D97—21no—
57C2×Dic97—21no—
58C2×Dic97D411yescharacteristic
59D388—21no—
60D388—22no—
61D388—22no—
62D388—21no—
63D388C2312yes—
64D388C2311yescharacteristic
65C4×D97—21no—
66C4×D97—21no—
67C4×D97—21no—
68C4×D97—22no—
69C4×D97—22no—
70C4×D97D411yescharacteristic
71C4×D97D411yescharacteristic
72C4×D97C2311yescharacteristic
73C4×D97C2311yescharacteristic
74Dic194—21no—
75Dic194C2311yescharacteristic
76C8×C97C2312yes—
77#11715895C2312yes—
78C22×C97—21no—
79C22×C97C2×D411yescharacteristic
80C2×D97—22no—
81C2×D97—21no—
82C2×D97—41no—
83C2×D97—42no—
84C2×D97—42no—
85C2×D97C2×D411yescharacteristic
86C2×D97C2×D411yescharacteristic
87C4×C97—21no—
88C4×C97—22no—
89C4×C97C2×D411yescharacteristic
90C4×C97C2411yescharacteristic
91Dic97—21no—
92Dic97C2×D411yescharacteristic
93Dic97C2×D411yescharacteristic
94C2×C97—21no—
95C2×C97—41no—
96C2×C97C22×D411yescharacteristic
97D97—21no—
98D97—21no—
99D97—42no—
100D97—41no—
101C97#57511yescharacteristic, complemented, Sylow
102#575—971nomaximal, Sylow
103C2×#41—971no—
104C2×#41—971no—
105#137—971no—
106#137—972no—
107#137D9711yescharacteristic, complemented
108AGL(1,ℤ/8)—971no—
109AGL(1,ℤ/8)—972no—
110AGL(1,ℤ/8)—971no—
111#135—972no—
112#135—972no—
113C2×M16—971no—
114#41—972no—
115#41—971no—
116#41—972no—
117#41—971no—
118#41—971no—
119#41—1941no—
120#41—1941no—
121#41—1941no—
122#41—1941no—
123#41C2×D9711yescharacteristic
124C2×Q8—971no—
125C2×Q8C2×D9711yescharacteristic, complemented
126C2×D4—971no—
127C2×D4—971no—
128C2×D4—1941no—
129C2×D4—1941no—
130C22×C4—971no—
131C22×C4—1941no—
132C22×C4—1941no—
133Q16—972no—
134Q16C2×D9712yescomplemented
135SD16—972no—
136SD16—972no—
137SD16—972no—
138SD16C2×D9712yescomplemented
139D8—972no—
140D8—972no—
141M16—971no—
142M16—972no—
143M16C2×D9711yescharacteristic, complemented
144C2×C8—972no—
145C23—971no—
146C23—1941no—
147C23—1941no—
148Q8—21no—
149Q8—971no—
150Q8—1941no—
151Q8C22×D9711yescharacteristic
152Q8C22×D9712yes—
153D4—21no—
154D4—972no—
155D4—971no—
156D4—1941no—
157D4—1942no—
158D4—1942no—
159D4—1941no—
160D4—1941no—
161D4—1941no—
162D4—1941no—
163D4C22×D9711yescharacteristic
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—971no—
167C2×C4—971no—
168C2×C4—971no—
169C2×C4—971no—
170C2×C4—971no—
171C2×C4—1941no—
172C2×C4—1942no—
173C2×C4—1942no—
174C2×C4—1941no—
175C2×C4—1941no—
176C2×C4—1941no—
177C2×C4C22×D9711yescharacteristic
178C8—972no—
179C8C22×D9712yes—
180C22—21no—
181C22—971no—
182C22—971no—
183C22—3882no—
184C22—3881no—
185C22—3882no—
186C22—1942no—
187C22—1941no—
188C22D4×D9711yescharacteristic
189C4—21no—
190C4—22no—
191C4—971no—
192C4—971no—
193C4—1941no—
194C4D4×D9711yescharacteristic
195C4C23×D9711yescharacteristic
196C2—21no—
197C2—41no—
198C2—3882no—
199C2—3881no—
200C2—1941no—
201C2—1941no—
202C2C2×D4×D9711yescharacteristic
subgroupG/H
centerC2C2×D4×D97
commutatorC4×C97C24
FrattiniC4C23×D97
Fitting#137×C97C2
socleC2×C97C22×D4
hypercenter#137D97
hypocenterC97#575
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. C2×#13095512C2semidirect
2. #41×D97C2semidirect
3. #15690842C2semidirect
4. #15690841C2semidirect
5. #15690838C2semidirect
6. #15690837C2semidirect
7. #15690835C2semidirect
8. #15690833C2semidirect
9. #15690831C2semidirect
10. M16×D97C2semidirect
11. #137×C97C2semidirect
15. #13095512C22semidirect
16. #13095512C22semidirect
20. #13095510C22semidirect
21. Q8×D97C22semidirect
23. C2×D388C22semidirect
25. D4×D97C22semidirect
29. #13095501C22semidirect
30. #13095500C22semidirect
31. #13095498C22semidirect
32. #13095498C22semidirect
33. D776C22semidirect
34. #13095496C22semidirect
35. #13095495C22semidirect
36. #13095494C22semidirect
37. C8×D97C22semidirect
39. C2×Q8×C97C22semidirect
40. Q16×C97C22semidirect
41. SD16×C97C22semidirect
42. M16×C97C22semidirect
101. C97#575semidirect
107. #137D97semidirect
125. C2×Q8C2×D97semidirect
134. Q16C2×D97semidirect
138. SD16C2×D97semidirect
143. M16C2×D97semidirect