Finite Group Databasebeta

← #23758079

Subgroups — #23758079

Order 10048.

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#19097819C211yesmaximal, characteristic, complemented
2#19097816C211yesmaximal, characteristic, complemented
3#19097802C211yesmaximal, characteristic, complemented
4#19097800C212yesmaximal, complemented
5#19097798C212yesmaximal, complemented
6#19097797C211yesmaximal, characteristic, complemented
7#19097793C211yesmaximal, characteristic, complemented
8#19097792C212yesmaximal, complemented
9SD16×D157C212yesmaximal, complemented
10#19097777C211yesmaximal, characteristic, complemented
11C2×SD16×C157C211yesmaximal, characteristic, complemented
12#14578955—21no—
13#14578955C2212yescomplemented
14#14578954—22no—
15#14578954C2211yescharacteristic
16#14578954C2211yescharacteristic
17#14578954C2211yescharacteristic, complemented
18#14578953—21no—
19#14578953C2212yes—
20Q8×D157—21no—
21Q8×D157C2212yescomplemented
22C2×C22⋊D157—22no—
23D4×D157—21no—
24D4×D157C2212yes—
25Dic628C2211yescharacteristic, complemented
26#14578944C2212yescomplemented
27#14578943C2211yescharacteristic, complemented
28#14578943C2211yescharacteristic, complemented
29#14578942C2212yescomplemented
30#14578941C2212yescomplemented
31D1256C2211yescharacteristic, complemented
32#14578939C2212yescomplemented
33#14578938C2211yescharacteristic, complemented
34#14578937C2212yescomplemented
35C8×D157C2212yescomplemented
36C2×Q8×C157C2211yescharacteristic, complemented
37C2×D4×C157C2211yescharacteristic
38SD16×C157C2212yescomplemented
39SD16×C157C2212yescomplemented
40C2×C8×C157C2211yescharacteristic, complemented
41C22×D157—22no—
42Dic314—22no—
43Dic314D411yescharacteristic
44Dic314C2311yescharacteristic
45Dic314C2311yescharacteristic
46D628—22no—
47D628D411yescharacteristic
48D628C2311yescharacteristic
49D628C2311yescharacteristic
50C22⋊D157—21no—
51C22⋊D157—21no—
52C22⋊D157—22no—
53C22⋊D157—22no—
54C22⋊D157D412yes—
55C2×Dic157—22no—
56C4×D157—22no—
57C4×D157—21no—
58C4×D157—21no—
59C4×D157—22no—
60C4×D157C2312yes—
61#11929434C2312yes—
62C23×C157—21no—
63Q8×C157—21no—
64Q8×C157C2312yes—
65D4×C157—21no—
66D4×C157C2312yes—
67C2×C4×C157—21no—
68C2×C4×C157C2311yescharacteristic
69C8×C157C2311yescharacteristic
70C8×C157C2311yescharacteristic
71C22×C157—22no—
72C22×C157—81no—
73C22×C157C2×D411yescharacteristic
74C2×D157—21no—
75C2×D157—21no—
76C2×D157—82no—
77C2×D157C2×D412yes—
78C4×C157—22no—
79C4×C157C2×D411yescharacteristic
80C4×C157C2411yescharacteristic
81Dic157—21no—
82Dic157—21no—
83Dic157C2×D412yes—
84C2×C157—21no—
85C2×C157—42no—
86C2×C157C22×D411yescharacteristic
87D157—22no—
88D157—41no—
89D157—41no—
90C157#57711yescharacteristic, complemented, Sylow
91#577—1571nomaximal, Sylow
922−1+4—1571no—
93H(5,𝔽2)—1571no—
94#137—1571no—
95#137—1572no—
96AGL(1,ℤ/8)—1571no—
97AGL(1,ℤ/8)—1572no—
98#135—1572no—
99#135—1571no—
100C2×SD16—1572no—
101C2×SD16D15711yescharacteristic, complemented
102#131—1571no—
103#41—3142no—
104#41—3141no—
105#41—3141no—
106#41—1572no—
107#41—1572no—
108#41—1571no—
109#41—1571no—
110#41—1571no—
111C2×Q8—3141no—
112C2×Q8—1572no—
113C2×Q8C2×D15711yescharacteristic, complemented
114C2×D4—3141no—
115C2×D4—3142no—
116C2×D4—1572no—
117C2×D4C2×D15711yescharacteristic
118Q16—1572no—
119Q16—1571no—
120SD16—1572no—
121SD16—1572no—
122SD16—1571no—
123SD16—1571no—
124SD16C2×D15712yescomplemented
125SD16C2×D15712yescomplemented
126D8—1572no—
127D8—1571no—
128M16—1571no—
129M16—1572no—
130C2×C8—1572no—
131C2×C8C2×D15711yescharacteristic, complemented
132C23—21no—
133C23—3142no—
134Q8—21no—
135Q8—3142no—
136Q8—1571no—
137Q8—1571no—
138Q8—1571no—
139Q8C22×D15712yes—
140D4—21no—
141D4—3142no—
142D4—3142no—
143D4—3141no—
144D4—3141no—
145D4—3142no—
146D4—1572no—
147D4—1571no—
148D4—1571no—
149D4—1571no—
150D4C22×D15712yes—
151C2×C4—21no—
152C2×C4—3142no—
153C2×C4—3142no—
154C2×C4—3142no—
155C2×C4—3141no—
156C2×C4—3141no—
157C2×C4—1572no—
158C2×C4C22×D15711yescharacteristic
159C8—1572no—
160C8C22×D15711yescharacteristic
161C8C22×D15711yescharacteristic
162C22—22no—
163C22—81no—
164C22—3141no—
165C22—3141no—
166C22—1572no—
167C22—12562no—
168C22D4×D15711yescharacteristic
169C4—22no—
170C4—3141no—
171C4—3141no—
172C4—1572no—
173C4D4×D15711yescharacteristic
174C4C23×D15711yescharacteristic
175C2—21no—
176C2—42no—
177C2—3142no—
178C2—6281no—
179C2—6281no—
180C2C2×D4×D15711yescharacteristic
subgroupG/H
centerC2C2×D4×D157
commutator, cosocleC4×C157C24
FrattiniC4C23×D157
FittingC2×SD16×C157C2
socleC2×C157C22×D4
hypercenterC2×SD16D157
hypocenterC157#577
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #19097819C2semidirect
2. #19097816C2semidirect
3. #19097802C2semidirect
4. #19097800C2semidirect
5. #19097798C2semidirect
6. #19097797C2semidirect
7. #19097793C2semidirect
8. #19097792C2semidirect
9. SD16×D157C2semidirect
10. #19097777C2semidirect
11. C2×SD16×C157C2semidirect
13. #14578955C22semidirect
17. #14578954C22semidirect
21. Q8×D157C22semidirect
25. Dic628C22semidirect
26. #14578944C22semidirect
27. #14578943C22semidirect
28. #14578943C22semidirect
29. #14578942C22semidirect
30. #14578941C22semidirect
31. D1256C22semidirect
32. #14578939C22semidirect
33. #14578938C22semidirect
34. #14578937C22semidirect
35. C8×D157C22semidirect
36. C2×Q8×C157C22semidirect
38. SD16×C157C22semidirect
39. SD16×C157C22semidirect
40. C2×C8×C157C22semidirect
90. C157#577semidirect
101. C2×SD16D157semidirect
113. C2×Q8C2×D157semidirect
124. SD16C2×D157semidirect
125. SD16C2×D157semidirect
131. C2×C8C2×D157semidirect