Finite Group Databasebeta

← #34094962

Subgroups — #34094962

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#23756542C211yesmaximal, characteristic, complemented
3#23756530C211yesmaximal, characteristic, complemented
4#23756526C212yesmaximal, complemented
5#23756521C212yesmaximal, complemented
6#23756517C211yesmaximal, characteristic, complemented
7#23756516C212yesmaximal, complemented
8C2×#19097549C211yesmaximal, characteristic, complemented
9SD16×D313C212yesmaximal, complemented
10#23756505C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C313C211yesmaximal, characteristic, complemented
12#19097561—21no—
13#19097561C2211yescharacteristic
14#19097561C2211yescharacteristic
15#19097560—21no—
16#19097560—22no—
17#19097560C2212yes—
18#19097560C2212yescomplemented
19C2×Dic626—21no—
20C2×Dic626C2211yescharacteristic, complemented
21Q8×D313C2212yescomplemented
22C2×C22⋊D313—22no—
23D4×D313—21no—
24D4×D313C2212yes—
25Dic1252C2212yescomplemented
26#19097551C2211yescharacteristic, complemented
27#19097550C2212yescomplemented
28#19097549C2212yescomplemented
29#19097549C2212yescomplemented
30#19097549C2211yescharacteristic, complemented
31#19097548C2211yescharacteristic, complemented
32#19097546C2211yescharacteristic, complemented
33#19097544C2212yescomplemented
34C2×#14578809C2211yescharacteristic, complemented
35C8×D313C2212yescomplemented
36#41×C313C2211yescharacteristic, complemented
37C2×D4×C313C2211yescharacteristic
38SD16×C313C2212yescomplemented
39D8×C313C2212yescomplemented
40M16×C313C2211yescharacteristic, complemented
41C22×D313—22no—
42Dic626—21no—
43Dic626—22no—
44Dic626D411yescharacteristic
45Dic626C2312yes—
46Dic626C2311yescharacteristic
47D1252D411yescharacteristic
48D1252C2311yescharacteristic
49C22⋊D313—21no—
50C22⋊D313—22no—
51C22⋊D313—22no—
52C22⋊D313—22no—
53C22⋊D313D412yes—
54C2×Dic313—21no—
55C2×Dic313—22no—
56C2×Dic313—22no—
57C4×D313—22no—
58C4×D313—21no—
59C4×D313C2312yes—
60#14578809C2311yescharacteristic
61#14578809C2311yescharacteristic
62C23×C313—21no—
63Q8×C313C2311yescharacteristic
64D4×C313—21no—
65D4×C313—21no—
66D4×C313C2311yescharacteristic
67D4×C313C2312yes—
68C2×C4×C313—21no—
69C2×C4×C313C2311yescharacteristic
70C8×C313C2312yes—
71C22×C313—21no—
72C22×C313—22no—
73C22×C313—81no—
74C22×C313C2×D411yescharacteristic
75C2×D313—21no—
76C2×D313—82no—
77C2×D313C2×D412yes—
78C4×C313—21no—
79C4×C313C2×D411yescharacteristic
80C4×C313C2411yescharacteristic
81Dic313—21no—
82Dic313—22no—
83Dic313C2×D412yes—
84C2×C313—21no—
85C2×C313—42no—
86C2×C313—41no—
87C2×C313C22×D411yescharacteristic
88D313—22no—
89D313—41no—
90C313#57711yescharacteristic, complemented, Sylow
91#577—3131nomaximal, Sylow
922−1+4—3131no—
93H(5,𝔽2)—3131no—
94#137—3132no—
95#137—3131no—
96AGL(1,ℤ/8)—3132no—
97AGL(1,ℤ/8)D31311yescharacteristic, complemented
98#135—3131no—
99#135—3132no—
100C2×SD16—3131no—
101C2×SD16—3132no—
102#131—3131no—
103#41—3131no—
104#41—3132no—
105#41—3132no—
106#41—3131no—
107#41—6261no—
108#41—6262no—
109#41—6261no—
110#41C2×D31311yescharacteristic, complemented
111C2×Q8—3132no—
112C2×Q8—3131no—
113C2×Q8—6261no—
114C2×D4—3132no—
115C2×D4—6261no—
116C2×D4—6262no—
117C2×D4C2×D31311yescharacteristic
118Q16—3131no—
119Q16—3132no—
120SD16—3131no—
121SD16—3132no—
122SD16—3132no—
123SD16—3131no—
124SD16—3132no—
125SD16C2×D31312yescomplemented
126D8—3131no—
127D8C2×D31312yescomplemented
128M16—3132no—
129M16C2×D31311yescharacteristic, complemented
130C2×C8—3131no—
131C2×C8—3132no—
132C23—21no—
133C23—6262no—
134Q8—3131no—
135Q8—3132no—
136Q8—3131no—
137Q8—6262no—
138Q8—6261no—
139Q8C22×D31311yescharacteristic
140D4—21no—
141D4—21no—
142D4—3132no—
143D4—3131no—
144D4—3131no—
145D4—6262no—
146D4—6262no—
147D4—6262no—
148D4—6261no—
149D4C22×D31311yescharacteristic
150D4C22×D31312yes—
151C2×C4—21no—
152C2×C4—3132no—
153C2×C4—6262no—
154C2×C4—6262no—
155C2×C4—6262no—
156C2×C4—6261no—
157C2×C4—6261no—
158C2×C4C22×D31311yescharacteristic
159C8—3131no—
160C8—3131no—
161C8C22×D31312yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—3132no—
166C22—6261no—
167C22—25042no—
168C22D4×D31311yescharacteristic
169C4—21no—
170C4—3132no—
171C4—6261no—
172C4—6262no—
173C4D4×D31311yescharacteristic
174C4C23×D31311yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—6262no—
179C2—12521no—
180C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC2C2×D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
FittingAGL(1,ℤ/8)×C313C2
socleC2×C313C22×D4
hypercenterAGL(1,ℤ/8)D313
hypocenterC313#577
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #23756544C2semidirect
2. #23756542C2semidirect
3. #23756530C2semidirect
4. #23756526C2semidirect
5. #23756521C2semidirect
6. #23756517C2semidirect
7. #23756516C2semidirect
8. C2×#19097549C2semidirect
9. SD16×D313C2semidirect
10. #23756505C2semidirect
11. AGL(1,ℤ/8)×C313C2semidirect
18. #19097560C22semidirect
20. C2×Dic626C22semidirect
21. Q8×D313C22semidirect
25. Dic1252C22semidirect
26. #19097551C22semidirect
27. #19097550C22semidirect
28. #19097549C22semidirect
29. #19097549C22semidirect
30. #19097549C22semidirect
31. #19097548C22semidirect
32. #19097546C22semidirect
33. #19097544C22semidirect
34. C2×#14578809C22semidirect
35. C8×D313C22semidirect
36. #41×C313C22semidirect
38. SD16×C313C22semidirect
39. D8×C313C22semidirect
40. M16×C313C22semidirect
90. C313#577semidirect
97. AGL(1,ℤ/8)D313semidirect
110. #41C2×D313semidirect
125. SD16C2×D313semidirect
127. D8C2×D313semidirect
129. M16C2×D313semidirect

Maximal subgroups

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

subgroupindex
#237565442
#237565422
#237565302
#237565262
#237565212
#237565172
#237565162
C2×#190975492
SD16×D3132
#237565052
AGL(1,ℤ/8)×C3132
#577313