Finite Group Databasebeta

← #34094961

Subgroups — #34094961

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#23756543C211yesmaximal, characteristic, complemented
3#23756529C212yesmaximal, complemented
4#23756525C211yesmaximal, characteristic, complemented
5#23756524C212yesmaximal, complemented
6#23756520C212yesmaximal, complemented
7#23756517C211yesmaximal, characteristic, complemented
8C2×#19097548C211yesmaximal, characteristic, complemented
9SD16×D313C212yesmaximal, complemented
10#23756505C211yesmaximal, characteristic, complemented
11#137×C313C211yesmaximal, characteristic, complemented
12#19097562—21no—
13#19097562C2212yes—
14#19097562C2212yescomplemented
15#19097561—21no—
16#19097561—22no—
17#19097561C2211yescharacteristic
18#19097561C2211yescharacteristic, complemented
19Q8×D313—21no—
20Q8×D313C2212yescomplemented
21C2×D1252—21no—
22C2×D1252C2211yescharacteristic
23D4×D313—22no—
24D4×D313C2212yes—
25#19097551C2211yescharacteristic, complemented
26#19097550C2212yescomplemented
27#19097549C2211yescharacteristic, complemented
28#19097548C2212yescomplemented
29#19097548C2212yescomplemented
30#19097548C2211yescharacteristic, complemented
31D2504C2212yescomplemented
32#19097546C2211yescharacteristic, complemented
33#19097544C2212yescomplemented
34C2×#14578809C2211yescharacteristic, complemented
35C8×D313C2212yescomplemented
36#41×C313C2211yescharacteristic
37C2×Q8×C313C2211yescharacteristic, complemented
38Q16×C313C2212yescomplemented
39SD16×C313C2212yescomplemented
40M16×C313C2211yescharacteristic, complemented
41C22×D313—21no—
42C22×D313—22no—
43Dic626—22no—
44Dic626D411yescharacteristic
45Dic626C2311yescharacteristic
46D1252—22no—
47D1252—22no—
48D1252—21no—
49D1252D411yescharacteristic
50D1252C2311yescharacteristic
51D1252C2312yes—
52C22⋊D313—21no—
53C22⋊D313—22no—
54C22⋊D313D412yes—
55C4×D313—22no—
56C4×D313—21no—
57C4×D313—22no—
58C4×D313—22no—
59C4×D313C2312yes—
60#14578809C2311yescharacteristic
61#14578809C2311yescharacteristic
62Q8×C313—21no—
63Q8×C313C2312yes—
64Q8×C313C2311yescharacteristic
65D4×C313—21no—
66D4×C313C2311yescharacteristic
67C2×C4×C313—21no—
68C2×C4×C313—21no—
69C2×C4×C313C2311yescharacteristic
70C8×C313C2312yes—
71C22×C313—21no—
72C22×C313C2×D411yescharacteristic
73C2×D313—21no—
74C2×D313—22no—
75C2×D313—82no—
76C2×D313—81no—
77C2×D313C2×D412yes—
78C4×C313—21no—
79C4×C313—22no—
80C4×C313C2×D411yescharacteristic
81C4×C313C2411yescharacteristic
82Dic313—21no—
83Dic313C2×D412yes—
84C2×C313—21no—
85C2×C313—41no—
86C2×C313C22×D411yescharacteristic
87D313—22no—
88D313—41no—
89D313—42no—
90C313#57711yescharacteristic, complemented, Sylow
91#577—3131nomaximal, Sylow
922−1+4—3131no—
93H(5,𝔽2)—3131no—
94#137—3132no—
95#137D31311yescharacteristic, complemented
96AGL(1,ℤ/8)—3132no—
97AGL(1,ℤ/8)—3131no—
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—6262no—
108#41—6261no—
109#41—6261no—
110#41C2×D31311yescharacteristic
111C2×Q8—3132no—
112C2×Q8—6261no—
113C2×Q8C2×D31311yescharacteristic, complemented
114C2×D4—3132no—
115C2×D4—3131no—
116C2×D4—6261no—
117C2×D4—6262no—
118Q16—3131no—
119Q16C2×D31312yescomplemented
120SD16—3132no—
121SD16—3132no—
122SD16—3131no—
123SD16—3131no—
124SD16—3132no—
125SD16C2×D31312yescomplemented
126D8—3131no—
127D8—3132no—
128M16—3132no—
129M16C2×D31311yescharacteristic, complemented
130C2×C8—3131no—
131C2×C8—3132no—
132C23—6262no—
133C23—6261no—
134Q8—21no—
135Q8—3131no—
136Q8—3131no—
137Q8—6262no—
138Q8C22×D31312yes—
139Q8C22×D31311yescharacteristic
140D4—21no—
141D4—3132no—
142D4—3131no—
143D4—3131no—
144D4—3132no—
145D4—6262no—
146D4—6262no—
147D4—6262no—
148D4—6261no—
149D4—6261no—
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—3131no—
160C8—3131no—
161C8C22×D31312yes—
162C22—21no—
163C22—3132no—
164C22—6261no—
165C22—6262no—
166C22—25041no—
167C22—25042no—
168C22D4×D31311yescharacteristic
169C4—21no—
170C4—22no—
171C4—3132no—
172C4—6261no—
173C4D4×D31311yescharacteristic
174C4C23×D31311yescharacteristic
175C2—21no—
176C2—41no—
177C2—6262no—
178C2—12522no—
179C2—12521no—
180C2C2×D4×D31311yescharacteristic
subgroupG/H
centerC2C2×D4×D313
commutator, cosocleC4×C313C24
FrattiniC4C23×D313
Fitting#137×C313C2
socleC2×C313C22×D4
hypercenter#137D313
hypocenterC313#577
LCSG ▷ C4×C313 ▷ C2×C313 ▷ C313
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #23756545C2semidirect
2. #23756543C2semidirect
3. #23756529C2semidirect
4. #23756525C2semidirect
5. #23756524C2semidirect
6. #23756520C2semidirect
7. #23756517C2semidirect
8. C2×#19097548C2semidirect
9. SD16×D313C2semidirect
10. #23756505C2semidirect
11. #137×C313C2semidirect
14. #19097562C22semidirect
18. #19097561C22semidirect
20. Q8×D313C22semidirect
25. #19097551C22semidirect
26. #19097550C22semidirect
27. #19097549C22semidirect
28. #19097548C22semidirect
29. #19097548C22semidirect
30. #19097548C22semidirect
31. D2504C22semidirect
32. #19097546C22semidirect
33. #19097544C22semidirect
34. C2×#14578809C22semidirect
35. C8×D313C22semidirect
37. C2×Q8×C313C22semidirect
38. Q16×C313C22semidirect
39. SD16×C313C22semidirect
40. M16×C313C22semidirect
90. C313#577semidirect
95. #137D313semidirect
113. C2×Q8C2×D313semidirect
119. Q16C2×D313semidirect
125. SD16C2×D313semidirect
129. M16C2×D313semidirect

Maximal subgroups

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

subgroupindex
#237565452
#237565432
#237565292
#237565252
#237565242
#237565202
#237565172
C2×#190975482
SD16×D3132
#237565052
#137×C3132
#577313