Finite Group Databasebeta

← #34094956

Subgroups — #34094956

Order 20032.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 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#23756543C211yesmaximal, characteristic, complemented
2#23756542C211yesmaximal, characteristic, complemented
3#23756525C211yesmaximal, characteristic, complemented
4#23756524C212yesmaximal, complemented
5#23756521C212yesmaximal, complemented
6#23756518C212yesmaximal, complemented
7#23756517C211yesmaximal, characteristic, complemented
8C2×#19097546C211yesmaximal, characteristic, complemented
9D8×D313C212yesmaximal, complemented
10#23756505C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C313C211yesmaximal, characteristic, complemented
12#19097562C2212yescomplemented
13#19097561—21no—
14#19097561C2211yescharacteristic
15#19097561C2211yescharacteristic, complemented
16#19097560—21no—
17#19097560C2212yescomplemented
18C2×D1252—21no—
19C2×D1252C2211yescharacteristic, complemented
20C2×C22⋊D313—22no—
21D4×D313—21no—
22D4×D313—22no—
23D4×D313C2212yescomplemented
24D4×D313C2212yescomplemented
25#19097551C2211yescharacteristic, complemented
26#19097550C2212yescomplemented
27#19097549C2211yescharacteristic, complemented
28#19097548C2211yescharacteristic, complemented
29D2504C2212yescomplemented
30#19097546C2211yescharacteristic, complemented
31#19097546C2212yescomplemented
32#19097546C2212yescomplemented
33#19097544C2212yescomplemented
34C2×#14578809C2211yescharacteristic, complemented
35C8×D313C2212yescomplemented
36#41×C313C2211yescharacteristic, complemented
37C2×D4×C313C2211yescharacteristic, complemented
38SD16×C313C2212yescomplemented
39D8×C313C2212yescomplemented
40M16×C313C2211yescharacteristic, complemented
41C22×D313—21no—
42C22×D313—22no—
43C22×D313—22no—
44Dic626D411yescharacteristic
45Dic626C2311yescharacteristic
46D1252—22no—
47D1252—21no—
48D1252D411yescharacteristic
49D1252C2312yes—
50D1252C2311yescharacteristic
51C22⋊D313—21no—
52C22⋊D313—22no—
53C22⋊D313—22no—
54C22⋊D313—22no—
55C22⋊D313D412yes—
56C2×Dic313—22no—
57C4×D313—21no—
58C4×D313—22no—
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—22no—
77C2×D313—82no—
78C2×D313—82no—
79C2×D313—81no—
80C2×D313C2×D412yes—
81C4×C313—21no—
82C4×C313C2×D411yescharacteristic
83C4×C313C2411yescharacteristic
84Dic313—21no—
85Dic313C2×D412yes—
86C2×C313—21no—
87C2×C313—41no—
88C2×C313—42no—
89C2×C313C22×D411yescharacteristic
90D313—22no—
91D313—41no—
92D313—42no—
93C313#57611yescharacteristic, complemented, Sylow
94#576—3131nomaximal, Sylow
95H(5,𝔽2)—3131no—
96H(5,𝔽2)—3131no—
97AGL(1,ℤ/8)—3132no—
98AGL(1,ℤ/8)—3132no—
99AGL(1,ℤ/8)—3131no—
100AGL(1,ℤ/8)D31311yescharacteristic, complemented
101#135—3131no—
102#135—3132no—
103C2×D8—3131no—
104C2×D8—3132no—
105#131—3131no—
106#41—3131no—
107#41—3132no—
108#41—3132no—
109#41—3131no—
110#41—6261no—
111#41—6261no—
112#41C2×D31311yescharacteristic, complemented
113C2×D4—3132no—
114C2×D4—3132no—
115C2×D4—3131no—
116C2×D4—6261no—
117C2×D4—6262no—
118C2×D4—6261no—
119C2×D4—6262no—
120C2×D4C2×D31311yescharacteristic, complemented
121Q16—3131no—
122SD16—3131no—
123SD16—3131no—
124SD16—3132no—
125SD16C2×D31312yescomplemented
126D8—3132no—
127D8—3131no—
128D8—3132no—
129D8—3132no—
130D8C2×D31312yescomplemented
131M16—3132no—
132M16C2×D31311yescharacteristic, complemented
133C2×C8—3131no—
134C2×C8—3132no—
135C23—21no—
136C23—6262no—
137C23—6262no—
138C23—6261no—
139Q8—3131no—
140Q8—3131no—
141Q8C22×D31311yescharacteristic
142D4—21no—
143D4—21no—
144D4—3132no—
145D4—3131no—
146D4—3132no—
147D4—3131no—
148D4—6262no—
149D4—6262no—
150D4—6262no—
151D4—6262no—
152D4—6261no—
153D4—6261no—
154D4C22×D31312yes—
155D4C22×D31311yescharacteristic
156C2×C4—21no—
157C2×C4—3132no—
158C2×C4—6262no—
159C2×C4—6262no—
160C2×C4—6261no—
161C2×C4C22×D31311yescharacteristic
162C8—3131no—
163C8—3131no—
164C8C22×D31312yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—3132no—
169C22—6262no—
170C22—6261no—
171C22—25041no—
172C22—25042no—
173C22—25042no—
174C22D4×D31311yescharacteristic
175C4—21no—
176C4—3132no—
177C4—6261no—
178C4D4×D31311yescharacteristic
179C4C23×D31311yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—6262no—
184C2—12522no—
185C2—12521no—
186C2C2×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#576
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. #23756543C2semidirect
2. #23756542C2semidirect
3. #23756525C2semidirect
4. #23756524C2semidirect
5. #23756521C2semidirect
6. #23756518C2semidirect
7. #23756517C2semidirect
8. C2×#19097546C2semidirect
9. D8×D313C2semidirect
10. #23756505C2semidirect
11. AGL(1,ℤ/8)×C313C2semidirect
12. #19097562C22semidirect
15. #19097561C22semidirect
17. #19097560C22semidirect
19. C2×D1252C22semidirect
23. D4×D313C22semidirect
24. D4×D313C22semidirect
25. #19097551C22semidirect
26. #19097550C22semidirect
27. #19097549C22semidirect
28. #19097548C22semidirect
29. D2504C22semidirect
30. #19097546C22semidirect
31. #19097546C22semidirect
32. #19097546C22semidirect
33. #19097544C22semidirect
34. C2×#14578809C22semidirect
35. C8×D313C22semidirect
36. #41×C313C22semidirect
37. C2×D4×C313C22semidirect
38. SD16×C313C22semidirect
39. D8×C313C22semidirect
40. M16×C313C22semidirect
93. C313#576semidirect
100. AGL(1,ℤ/8)D313semidirect
112. #41C2×D313semidirect
120. C2×D4C2×D313semidirect
125. SD16C2×D313semidirect
130. D8C2×D313semidirect
132. M16C2×D313semidirect

Maximal subgroups

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

subgroupindex
#237565432
#237565422
#237565252
#237565242
#237565212
#237565182
#237565172
C2×#190975462
D8×D3132
#237565052
AGL(1,ℤ/8)×C3132
#576313