Finite Group Databasebeta

← #34094959

Subgroups — #34094959

Order 20032.

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#23756544C211yesmaximal, characteristic, complemented
2#23756543C211yesmaximal, characteristic, complemented
3#23756529C212yesmaximal, complemented
4#23756527C211yesmaximal, characteristic, complemented
5#23756522C211yesmaximal, characteristic, complemented
6#23756521C212yesmaximal, complemented
7#23756518C212yesmaximal, complemented
8C2×#19097550C211yesmaximal, characteristic, complemented
9SD16×D313C212yesmaximal, complemented
10#23756503C211yesmaximal, characteristic, complemented
11#135×C313C211yesmaximal, characteristic, complemented
12#19097562C2212yes—
13#19097561—21no—
14#19097561—21no—
15#19097561C2211yescharacteristic
16#19097560—22no—
17#19097560C2212yescomplemented
18C2×Dic626—21no—
19C2×Dic626C2211yescharacteristic, complemented
20Q8×D313C2212yescomplemented
21C2×D1252—21no—
22C2×D1252C2211yescharacteristic
23D4×D313—22no—
24D4×D313C2212yes—
25#19097551C2212yescomplemented
26#19097550C2212yescomplemented
27#19097550C2212yescomplemented
28#19097549C2212yescomplemented
29#19097548C2212yescomplemented
30#19097546C2212yescomplemented
31#19097545C2211yescharacteristic, complemented
32#19097544C2212yescomplemented
33C8×D313C2212yescomplemented
34#41×C313C2211yescharacteristic
35#41×C313C2211yescharacteristic, complemented
36Q16×C313C2211yescharacteristic, complemented
37SD16×C313C2211yescharacteristic, complemented
38SD16×C313C2211yescharacteristic, complemented
39D8×C313C2211yescharacteristic, complemented
40C2×C8×C313C2211yescharacteristic, complemented
41C22×D313—21no—
42C22×D313—22no—
43Dic626—21no—
44Dic626—22no—
45Dic626D411yescharacteristic
46Dic626C2312yes—
47D1252—22no—
48D1252—21no—
49D1252D411yescharacteristic
50D1252C2312yes—
51C22⋊D313—22no—
52C22⋊D313—22no—
53C22⋊D313D412yes—
54C2×Dic313—21no—
55C2×Dic313—22no—
56C4×D313—22no—
57C4×D313—22no—
58C4×D313C2312yes—
59#14578809C2312yes—
60Q8×C313C2311yescharacteristic
61Q8×C313C2311yescharacteristic
62D4×C313—21no—
63D4×C313—21no—
64D4×C313C2311yescharacteristic
65D4×C313C2311yescharacteristic
66C2×C4×C313—21no—
67C2×C4×C313—21no—
68C2×C4×C313C2311yescharacteristic
69C8×C313C2311yescharacteristic
70C8×C313C2311yescharacteristic
71C22×C313—21no—
72C22×C313—21no—
73C22×C313C2×D411yescharacteristic
74C2×D313—22no—
75C2×D313—82no—
76C2×D313—81no—
77C2×D313C2×D412yes—
78C4×C313—21no—
79C4×C313—21no—
80C4×C313C2×D411yescharacteristic
81C4×C313C2411yescharacteristic
82Dic313—22no—
83Dic313C2×D412yes—
84C2×C313—21no—
85C2×C313—41no—
86C2×C313—41no—
87C2×C313C22×D411yescharacteristic
88D313—22no—
89D313—42no—
90C313#57711yescharacteristic, complemented, Sylow
91#577—3131nomaximal, Sylow
922−1+4—3131no—
93H(5,𝔽2)—3131no—
94#137—3131no—
95#137—3132no—
96AGL(1,ℤ/8)—3131no—
97AGL(1,ℤ/8)—3132no—
98#135—3132no—
99#135D31311yescharacteristic, complemented
100C2×SD16—3132no—
101C2×SD16—3131no—
102#131—3131no—
103#41—3131no—
104#41—3132no—
105#41—3132no—
106#41—6261no—
107#41—6261no—
108#41—6262no—
109#41C2×D31311yescharacteristic
110#41C2×D31311yescharacteristic, complemented
111C2×Q8—3132no—
112C2×Q8—3131no—
113C2×Q8—6261no—
114C2×D4—3132no—
115C2×D4—3131no—
116C2×D4—6261no—
117C2×D4—6262no—
118Q16—3132no—
119Q16C2×D31311yescharacteristic, complemented
120SD16—3132no—
121SD16—3132no—
122SD16—3132no—
123SD16—3132no—
124SD16C2×D31311yescharacteristic, complemented
125SD16C2×D31311yescharacteristic, complemented
126D8—3132no—
127D8C2×D31311yescharacteristic, complemented
128M16—3131no—
129M16—3132no—
130C2×C8—3132no—
131C2×C8C2×D31311yescharacteristic, complemented
132C23—6262no—
133C23—6261no—
134Q8—3131no—
135Q8—3132no—
136Q8—6262no—
137Q8—6261no—
138Q8C22×D31311yescharacteristic
139Q8C22×D31311yescharacteristic
140D4—21no—
141D4—21no—
142D4—3132no—
143D4—3131no—
144D4—3132no—
145D4—6262no—
146D4—6262no—
147D4—6262no—
148D4—6261no—
149D4C22×D31311yescharacteristic
150D4C22×D31311yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3132no—
154C2×C4—6262no—
155C2×C4—6262no—
156C2×C4—6262no—
157C2×C4—6261no—
158C2×C4C22×D31311yescharacteristic
159C8—3132no—
160C8C22×D31311yescharacteristic
161C8C22×D31311yescharacteristic
162C22—21no—
163C22—21no—
164C22—3132no—
165C22—6262no—
166C22—25041no—
167C22—25042no—
168C22D4×D31311yescharacteristic
169C4—21no—
170C4—21no—
171C4—3132no—
172C4—6262no—
173C4D4×D31311yescharacteristic
174C4C23×D31311yescharacteristic
175C2—21no—
176C2—41no—
177C2—41no—
178C2—6262no—
179C2—12522no—
180C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC2C2×D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
Fitting#135×C313C2
socleC2×C313C22×D4
hypercenter#135D313
hypocenterC313#577
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #23756544C2semidirect
2. #23756543C2semidirect
3. #23756529C2semidirect
4. #23756527C2semidirect
5. #23756522C2semidirect
6. #23756521C2semidirect
7. #23756518C2semidirect
8. C2×#19097550C2semidirect
9. SD16×D313C2semidirect
10. #23756503C2semidirect
11. #135×C313C2semidirect
17. #19097560C22semidirect
19. C2×Dic626C22semidirect
20. Q8×D313C22semidirect
25. #19097551C22semidirect
26. #19097550C22semidirect
27. #19097550C22semidirect
28. #19097549C22semidirect
29. #19097548C22semidirect
30. #19097546C22semidirect
31. #19097545C22semidirect
32. #19097544C22semidirect
33. C8×D313C22semidirect
35. #41×C313C22semidirect
36. Q16×C313C22semidirect
37. SD16×C313C22semidirect
38. SD16×C313C22semidirect
39. D8×C313C22semidirect
40. C2×C8×C313C22semidirect
90. C313#577semidirect
99. #135D313semidirect
110. #41C2×D313semidirect
119. Q16C2×D313semidirect
124. SD16C2×D313semidirect
125. SD16C2×D313semidirect
127. D8C2×D313semidirect
131. C2×C8C2×D313semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237565442
#237565432
#237565292
#237565272
#237565222
#237565212
#237565182
C2×#190975502
SD16×D3132
#237565032
#135×C3132
#577313