Finite Group Databasebeta

← #20268597

Subgroups — #20268597

Order 6592.

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#15693069C211yesmaximal, characteristic, complemented
2#15693066C211yesmaximal, characteristic, complemented
3#15693052C211yesmaximal, characteristic, complemented
4#15693050C212yesmaximal, complemented
5#15693048C212yesmaximal, complemented
6#15693047C211yesmaximal, characteristic, complemented
7#15693043C211yesmaximal, characteristic, complemented
8#15693042C212yesmaximal, complemented
9SD16×D103C212yesmaximal, complemented
10#15693027C211yesmaximal, characteristic, complemented
11C2×SD16×C103C211yesmaximal, characteristic, complemented
12#13110106—21no—
13#13110106C2212yescomplemented
14#13110105—22no—
15#13110105C2211yescharacteristic
16#13110105C2211yescharacteristic
17#13110105C2211yescharacteristic, complemented
18#13110104—21no—
19#13110104C2212yes—
20Q8×D103—21no—
21Q8×D103C2212yescomplemented
22C2×C22⋊D103—22no—
23D4×D103—21no—
24D4×D103C2212yes—
25Dic412C2211yescharacteristic, complemented
26#13110095C2212yescomplemented
27#13110094C2211yescharacteristic, complemented
28#13110094C2211yescharacteristic, complemented
29#13110093C2212yescomplemented
30#13110092C2212yescomplemented
31D824C2211yescharacteristic, complemented
32#13110090C2212yescomplemented
33#13110089C2211yescharacteristic, complemented
34#13110088C2212yescomplemented
35C8×D103C2212yescomplemented
36C2×Q8×C103C2211yescharacteristic, complemented
37C2×D4×C103C2211yescharacteristic
38SD16×C103C2212yescomplemented
39SD16×C103C2212yescomplemented
40C2×C8×C103C2211yescharacteristic, complemented
41C23×C103—21no—
42C22×D103—22no—
43Q8×C103—21no—
44Q8×C103C2312yes—
45D4×C103—21no—
46D4×C103C2312yes—
47C2×C4×C103—21no—
48C2×C4×C103C2311yescharacteristic
49C22⋊D103—21no—
50C22⋊D103—21no—
51C22⋊D103—22no—
52C22⋊D103—22no—
53C22⋊D103D412yes—
54C2×Dic103—22no—
55D412—22no—
56D412D411yescharacteristic
57D412C2311yescharacteristic
58D412C2311yescharacteristic
59C4×D103—22no—
60C4×D103—21no—
61C4×D103—21no—
62C4×D103—22no—
63C4×D103C2312yes—
64Dic206—22no—
65Dic206D411yescharacteristic
66Dic206C2311yescharacteristic
67Dic206C2311yescharacteristic
68C8×C103C2311yescharacteristic
69C8×C103C2311yescharacteristic
70C103⋊C8C2312yes—
71C22×C103—22no—
72C22×C103—81no—
73C22×C103C2×D411yescharacteristic
74C2×D103—21no—
75C2×D103—21no—
76C2×D103—82no—
77C2×D103C2×D412yes—
78C4×C103—22no—
79C4×C103C2×D411yescharacteristic
80C4×C103C2411yescharacteristic
81Dic103—21no—
82Dic103—21no—
83Dic103C2×D412yes—
84C2×C103—21no—
85C2×C103—42no—
86C2×C103C22×D411yescharacteristic
87D103—22no—
88D103—41no—
89D103—41no—
90C103#57711yescharacteristic, complemented, Sylow
91#577—1031nomaximal, Sylow
922−1+4—1031no—
93H(5,𝔽2)—1031no—
94#137—1031no—
95#137—1032no—
96AGL(1,ℤ/8)—1031no—
97AGL(1,ℤ/8)—1032no—
98#135—1032no—
99#135—1031no—
100C2×SD16—1032no—
101C2×SD16D10311yescharacteristic, complemented
102#131—1031no—
103#41—1031no—
104#41—1032no—
105#41—1032no—
106#41—1031no—
107#41—1031no—
108#41—2062no—
109#41—2061no—
110#41—2061no—
111C2×Q8—1032no—
112C2×Q8—2061no—
113C2×Q8C2×D10311yescharacteristic, complemented
114C2×D4—1032no—
115C2×D4—2061no—
116C2×D4—2062no—
117C2×D4C2×D10311yescharacteristic
118Q16—1032no—
119Q16—1031no—
120SD16—1032no—
121SD16—1032no—
122SD16—1031no—
123SD16—1031no—
124SD16C2×D10312yescomplemented
125SD16C2×D10312yescomplemented
126D8—1032no—
127D8—1031no—
128M16—1031no—
129M16—1032no—
130C2×C8—1032no—
131C2×C8C2×D10311yescharacteristic, complemented
132C23—21no—
133C23—2062no—
134Q8—21no—
135Q8—1031no—
136Q8—1031no—
137Q8—1031no—
138Q8—2062no—
139Q8C22×D10312yes—
140D4—21no—
141D4—1032no—
142D4—1031no—
143D4—1031no—
144D4—1031no—
145D4—2062no—
146D4—2062no—
147D4—2062no—
148D4—2061no—
149D4—2061no—
150D4C22×D10312yes—
151C2×C4—21no—
152C2×C4—1032no—
153C2×C4—2062no—
154C2×C4—2062no—
155C2×C4—2062no—
156C2×C4—2061no—
157C2×C4—2061no—
158C2×C4C22×D10311yescharacteristic
159C8—1032no—
160C8C22×D10311yescharacteristic
161C8C22×D10311yescharacteristic
162C22—22no—
163C22—81no—
164C22—8242no—
165C22—1032no—
166C22—2061no—
167C22—2061no—
168C22D4×D10311yescharacteristic
169C4—22no—
170C4—1032no—
171C4—2061no—
172C4—2061no—
173C4D4×D10311yescharacteristic
174C4C23×D10311yescharacteristic
175C2—21no—
176C2—42no—
177C2—4121no—
178C2—4121no—
179C2—2062no—
180C2C2×D4×D10311yescharacteristic
subgroupG/H
centerC2C2×D4×D103
commutatorC4×C103C24
FrattiniC4C23×D103
FittingC2×SD16×C103C2
socleC2×C103C22×D4
hypercenterC2×SD16D103
hypocenterC103#577
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #15693069C2semidirect
2. #15693066C2semidirect
3. #15693052C2semidirect
4. #15693050C2semidirect
5. #15693048C2semidirect
6. #15693047C2semidirect
7. #15693043C2semidirect
8. #15693042C2semidirect
9. SD16×D103C2semidirect
10. #15693027C2semidirect
11. C2×SD16×C103C2semidirect
13. #13110106C22semidirect
17. #13110105C22semidirect
21. Q8×D103C22semidirect
25. Dic412C22semidirect
26. #13110095C22semidirect
27. #13110094C22semidirect
28. #13110094C22semidirect
29. #13110093C22semidirect
30. #13110092C22semidirect
31. D824C22semidirect
32. #13110090C22semidirect
33. #13110089C22semidirect
34. #13110088C22semidirect
35. C8×D103C22semidirect
36. C2×Q8×C103C22semidirect
38. SD16×C103C22semidirect
39. SD16×C103C22semidirect
40. C2×C8×C103C22semidirect
90. C103#577semidirect
101. C2×SD16D103semidirect
113. C2×Q8C2×D103semidirect
124. SD16C2×D103semidirect
125. SD16C2×D103semidirect
131. C2×C8C2×D103semidirect