Finite Group Databasebeta

← #34094958

Subgroups — #34094958

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#23756545C211yesmaximal, characteristic, complemented
2#23756542C211yesmaximal, characteristic, complemented
3#23756528C211yesmaximal, characteristic, complemented
4#23756526C212yesmaximal, complemented
5#23756524C212yesmaximal, complemented
6#23756523C211yesmaximal, characteristic, complemented
7#23756519C211yesmaximal, characteristic, complemented
8#23756518C212yesmaximal, complemented
9SD16×D313C212yesmaximal, complemented
10#23756503C211yesmaximal, characteristic, complemented
11C2×SD16×C313C211yesmaximal, characteristic, complemented
12#19097562—21no—
13#19097562C2212yescomplemented
14#19097561—22no—
15#19097561C2211yescharacteristic
16#19097561C2211yescharacteristic
17#19097561C2211yescharacteristic, complemented
18#19097560—21no—
19#19097560C2212yes—
20Q8×D313—21no—
21Q8×D313C2212yescomplemented
22C2×C22⋊D313—22no—
23D4×D313—21no—
24D4×D313C2212yes—
25Dic1252C2211yescharacteristic, complemented
26#19097551C2212yescomplemented
27#19097550C2211yescharacteristic, complemented
28#19097550C2211yescharacteristic, complemented
29#19097549C2212yescomplemented
30#19097548C2212yescomplemented
31D2504C2211yescharacteristic, complemented
32#19097546C2212yescomplemented
33#19097545C2211yescharacteristic, complemented
34#19097544C2212yescomplemented
35C8×D313C2212yescomplemented
36C2×Q8×C313C2211yescharacteristic, complemented
37C2×D4×C313C2211yescharacteristic
38SD16×C313C2212yescomplemented
39SD16×C313C2212yescomplemented
40C2×C8×C313C2211yescharacteristic, complemented
41C22×D313—22no—
42Dic626—22no—
43Dic626D411yescharacteristic
44Dic626C2311yescharacteristic
45Dic626C2311yescharacteristic
46D1252—22no—
47D1252D411yescharacteristic
48D1252C2311yescharacteristic
49D1252C2311yescharacteristic
50C22⋊D313—21no—
51C22⋊D313—21no—
52C22⋊D313—22no—
53C22⋊D313—22no—
54C22⋊D313D412yes—
55C2×Dic313—22no—
56C4×D313—22no—
57C4×D313—21no—
58C4×D313—21no—
59C4×D313—22no—
60C4×D313C2312yes—
61#14578809C2312yes—
62C23×C313—21no—
63Q8×C313—21no—
64Q8×C313C2312yes—
65D4×C313—21no—
66D4×C313C2312yes—
67C2×C4×C313—21no—
68C2×C4×C313C2311yescharacteristic
69C8×C313C2311yescharacteristic
70C8×C313C2311yescharacteristic
71C22×C313—22no—
72C22×C313—81no—
73C22×C313C2×D411yescharacteristic
74C2×D313—21no—
75C2×D313—21no—
76C2×D313—82no—
77C2×D313C2×D412yes—
78C4×C313—22no—
79C4×C313C2×D411yescharacteristic
80C4×C313C2411yescharacteristic
81Dic313—21no—
82Dic313—21no—
83Dic313C2×D412yes—
84C2×C313—21no—
85C2×C313—42no—
86C2×C313C22×D411yescharacteristic
87D313—22no—
88D313—41no—
89D313—41no—
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#135—3131no—
100C2×SD16—3132no—
101C2×SD16D31311yescharacteristic, complemented
102#131—3131no—
103#41—3131no—
104#41—3132no—
105#41—3132no—
106#41—3131no—
107#41—3131no—
108#41—6262no—
109#41—6261no—
110#41—6261no—
111C2×Q8—3132no—
112C2×Q8—6261no—
113C2×Q8C2×D31311yescharacteristic, complemented
114C2×D4—3132no—
115C2×D4—6261no—
116C2×D4—6262no—
117C2×D4C2×D31311yescharacteristic
118Q16—3132no—
119Q16—3131no—
120SD16—3132no—
121SD16—3132no—
122SD16—3131no—
123SD16—3131no—
124SD16C2×D31312yescomplemented
125SD16C2×D31312yescomplemented
126D8—3132no—
127D8—3131no—
128M16—3131no—
129M16—3132no—
130C2×C8—3132no—
131C2×C8C2×D31311yescharacteristic, complemented
132C23—21no—
133C23—6262no—
134Q8—21no—
135Q8—3131no—
136Q8—3131no—
137Q8—3131no—
138Q8—6262no—
139Q8C22×D31312yes—
140D4—21no—
141D4—3132no—
142D4—3131no—
143D4—3131no—
144D4—3131no—
145D4—6262no—
146D4—6262no—
147D4—6262no—
148D4—6261no—
149D4—6261no—
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—3132no—
160C8C22×D31311yescharacteristic
161C8C22×D31311yescharacteristic
162C22—22no—
163C22—81no—
164C22—3132no—
165C22—6261no—
166C22—6261no—
167C22—25042no—
168C22D4×D31311yescharacteristic
169C4—22no—
170C4—3132no—
171C4—6261no—
172C4—6261no—
173C4D4×D31311yescharacteristic
174C4C23×D31311yescharacteristic
175C2—21no—
176C2—42no—
177C2—6262no—
178C2—12521no—
179C2—12521no—
180C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC2C2×D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
FittingC2×SD16×C313C2
socleC2×C313C22×D4
hypercenterC2×SD16D313
hypocenterC313#577
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #23756545C2semidirect
2. #23756542C2semidirect
3. #23756528C2semidirect
4. #23756526C2semidirect
5. #23756524C2semidirect
6. #23756523C2semidirect
7. #23756519C2semidirect
8. #23756518C2semidirect
9. SD16×D313C2semidirect
10. #23756503C2semidirect
11. C2×SD16×C313C2semidirect
13. #19097562C22semidirect
17. #19097561C22semidirect
21. Q8×D313C22semidirect
25. Dic1252C22semidirect
26. #19097551C22semidirect
27. #19097550C22semidirect
28. #19097550C22semidirect
29. #19097549C22semidirect
30. #19097548C22semidirect
31. D2504C22semidirect
32. #19097546C22semidirect
33. #19097545C22semidirect
34. #19097544C22semidirect
35. C8×D313C22semidirect
36. C2×Q8×C313C22semidirect
38. SD16×C313C22semidirect
39. SD16×C313C22semidirect
40. C2×C8×C313C22semidirect
90. C313#577semidirect
101. C2×SD16D313semidirect
113. C2×Q8C2×D313semidirect
124. SD16C2×D313semidirect
125. SD16C2×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
#237565452
#237565422
#237565282
#237565262
#237565242
#237565232
#237565192
#237565182
SD16×D3132
#237565032
C2×SD16×C3132
#577313