Finite Group Databasebeta

← #20268598

Subgroups — #20268598

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#15693068C211yesmaximal, characteristic, complemented
2#15693067C211yesmaximal, characteristic, complemented
3#15693053C212yesmaximal, complemented
4#15693051C211yesmaximal, characteristic, complemented
5#15693046C211yesmaximal, characteristic, complemented
6#15693045C212yesmaximal, complemented
7#15693042C212yesmaximal, complemented
8C2×#13110094C211yesmaximal, characteristic, complemented
9SD16×D103C212yesmaximal, complemented
10#15693027C211yesmaximal, characteristic, complemented
11#135×C103C211yesmaximal, characteristic, complemented
12#13110106C2212yes—
13#13110105—21no—
14#13110105—21no—
15#13110105C2211yescharacteristic
16#13110104—22no—
17#13110104C2212yescomplemented
18C2×Dic206—21no—
19C2×Dic206C2211yescharacteristic, complemented
20Q8×D103C2212yescomplemented
21C2×D412—21no—
22C2×D412C2211yescharacteristic
23D4×D103—22no—
24D4×D103C2212yes—
25#13110095C2212yescomplemented
26#13110094C2212yescomplemented
27#13110094C2212yescomplemented
28#13110093C2212yescomplemented
29#13110092C2212yescomplemented
30#13110090C2212yescomplemented
31#13110089C2211yescharacteristic, complemented
32#13110088C2212yescomplemented
33C8×D103C2212yescomplemented
34#41×C103C2211yescharacteristic
35#41×C103C2211yescharacteristic, complemented
36Q16×C103C2211yescharacteristic, complemented
37SD16×C103C2211yescharacteristic, complemented
38SD16×C103C2211yescharacteristic, complemented
39D8×C103C2211yescharacteristic, complemented
40C2×C8×C103C2211yescharacteristic, complemented
41C22×D103—21no—
42C22×D103—22no—
43Q8×C103C2311yescharacteristic
44Q8×C103C2311yescharacteristic
45D4×C103—21no—
46D4×C103—21no—
47D4×C103C2311yescharacteristic
48D4×C103C2311yescharacteristic
49C2×C4×C103—21no—
50C2×C4×C103—21no—
51C2×C4×C103C2311yescharacteristic
52C22⋊D103—22no—
53C22⋊D103—22no—
54C22⋊D103D412yes—
55C2×Dic103—21no—
56C2×Dic103—22no—
57D412—22no—
58D412—21no—
59D412D411yescharacteristic
60D412C2312yes—
61C4×D103—22no—
62C4×D103—22no—
63C4×D103C2312yes—
64Dic206—21no—
65Dic206—22no—
66Dic206D411yescharacteristic
67Dic206C2312yes—
68C8×C103C2311yescharacteristic
69C8×C103C2311yescharacteristic
70C103⋊C8C2312yes—
71C22×C103—21no—
72C22×C103—21no—
73C22×C103C2×D411yescharacteristic
74C2×D103—22no—
75C2×D103—82no—
76C2×D103—81no—
77C2×D103C2×D412yes—
78C4×C103—21no—
79C4×C103—21no—
80C4×C103C2×D411yescharacteristic
81C4×C103C2411yescharacteristic
82Dic103—22no—
83Dic103C2×D412yes—
84C2×C103—21no—
85C2×C103—41no—
86C2×C103—41no—
87C2×C103C22×D411yescharacteristic
88D103—22no—
89D103—42no—
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#135D10311yescharacteristic, complemented
100C2×SD16—1032no—
101C2×SD16—1031no—
102#131—1031no—
103#41—1031no—
104#41—1032no—
105#41—1032no—
106#41—2061no—
107#41—2061no—
108#41—2062no—
109#41C2×D10311yescharacteristic
110#41C2×D10311yescharacteristic, complemented
111C2×Q8—1032no—
112C2×Q8—1031no—
113C2×Q8—2061no—
114C2×D4—1032no—
115C2×D4—1031no—
116C2×D4—2061no—
117C2×D4—2062no—
118Q16—1032no—
119Q16C2×D10311yescharacteristic, complemented
120SD16—1032no—
121SD16—1032no—
122SD16—1032no—
123SD16—1032no—
124SD16C2×D10311yescharacteristic, complemented
125SD16C2×D10311yescharacteristic, complemented
126D8—1032no—
127D8C2×D10311yescharacteristic, complemented
128M16—1031no—
129M16—1032no—
130C2×C8—1032no—
131C2×C8C2×D10311yescharacteristic, complemented
132C23—2062no—
133C23—2061no—
134Q8—1031no—
135Q8—1032no—
136Q8—2062no—
137Q8—2061no—
138Q8C22×D10311yescharacteristic
139Q8C22×D10311yescharacteristic
140D4—21no—
141D4—21no—
142D4—1032no—
143D4—1031no—
144D4—1032no—
145D4—2062no—
146D4—2062no—
147D4—2062no—
148D4—2061no—
149D4C22×D10311yescharacteristic
150D4C22×D10311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—1032no—
154C2×C4—2062no—
155C2×C4—2062no—
156C2×C4—2062no—
157C2×C4—2061no—
158C2×C4C22×D10311yescharacteristic
159C8—1032no—
160C8C22×D10311yescharacteristic
161C8C22×D10311yescharacteristic
162C22—21no—
163C22—21no—
164C22—8241no—
165C22—8242no—
166C22—1032no—
167C22—2062no—
168C22D4×D10311yescharacteristic
169C4—21no—
170C4—21no—
171C4—1032no—
172C4—2062no—
173C4D4×D10311yescharacteristic
174C4C23×D10311yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—4122no—
179C2—2062no—
180C2C2×D4×D10311yescharacteristic
subgroupG/H
centerC2C2×D4×D103
commutatorC4×C103C24
FrattiniC4C23×D103
Fitting#135×C103C2
socleC2×C103C22×D4
hypercenter#135D103
hypocenterC103#577
LCSG ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #15693068C2semidirect
2. #15693067C2semidirect
3. #15693053C2semidirect
4. #15693051C2semidirect
5. #15693046C2semidirect
6. #15693045C2semidirect
7. #15693042C2semidirect
8. C2×#13110094C2semidirect
9. SD16×D103C2semidirect
10. #15693027C2semidirect
11. #135×C103C2semidirect
17. #13110104C22semidirect
19. C2×Dic206C22semidirect
20. Q8×D103C22semidirect
25. #13110095C22semidirect
26. #13110094C22semidirect
27. #13110094C22semidirect
28. #13110093C22semidirect
29. #13110092C22semidirect
30. #13110090C22semidirect
31. #13110089C22semidirect
32. #13110088C22semidirect
33. C8×D103C22semidirect
35. #41×C103C22semidirect
36. Q16×C103C22semidirect
37. SD16×C103C22semidirect
38. SD16×C103C22semidirect
39. D8×C103C22semidirect
40. C2×C8×C103C22semidirect
90. C103#577semidirect
99. #135D103semidirect
110. #41C2×D103semidirect
119. Q16C2×D103semidirect
124. SD16C2×D103semidirect
125. SD16C2×D103semidirect
127. D8C2×D103semidirect
131. C2×C8C2×D103semidirect