Finite Group Databasebeta

← #34094948

Subgroups — #34094948

Order 20032.

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

normal subgroups only

This group has 262 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
1C2×#19097560C211yesmaximal, characteristic, complemented
2#41×D313C211yesmaximal, characteristic, complemented
3#23756530C211yesmaximal, characteristic, complemented
4#23756527C211yesmaximal, characteristic, complemented
5#23756526C212yesmaximal, complemented
6#23756523C211yesmaximal, characteristic, complemented
7#23756521C212yesmaximal, complemented
8#23756518C212yesmaximal, complemented
9#23756516C212yesmaximal, complemented
10M16×D313C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C313C211yesmaximal, characteristic, complemented
12#19097562C2211yescharacteristic, complemented
13#19097561—21no—
14#19097561C2211yescharacteristic
15#19097560—21no—
16#19097560—21no—
17#19097560—21no—
18#19097560C2212yes—
19#19097560C2211yescharacteristic, complemented
20#19097560C2212yescomplemented
21C2×Dic626C2211yescharacteristic, complemented
22Q8×D313C2211yescharacteristic, complemented
23C2×C22⋊D313—21no—
24D4×D313—21no—
25D4×D313C2211yescharacteristic, complemented
26C22×Dic313—21no—
27C2×C4×D313—21no—
28C2×C4×D313C2211yescharacteristic
29Dic1252C2212yescomplemented
30#19097551C2212yescomplemented
31#19097550C2212yescomplemented
32#19097549C2212yescomplemented
33#19097549C2212yescomplemented
34#19097546C2212yescomplemented
35#19097545C2211yescharacteristic, complemented
36#19097544C2212yescomplemented
37C8×D313C2212yescomplemented
38#41×C313C2211yescharacteristic
39C2×D4×C313C2211yescharacteristic, complemented
40SD16×C313C2212yescomplemented
41D8×C313C2212yescomplemented
42M16×C313C2211yescharacteristic, complemented
43C22×D313—21no—
44C22×D313D411yescharacteristic
45Dic626—21no—
46Dic626—21no—
47Dic626C2311yescharacteristic
48Dic626C2312yes—
49D1252—21no—
50D1252C2311yescharacteristic
51C22⋊D313—21no—
52C22⋊D313—21no—
53C22⋊D313—22no—
54C22⋊D313—22no—
55C22⋊D313—21no—
56C2×Dic313—21no—
57C2×Dic313—21no—
58C2×Dic313—22no—
59C2×Dic313—22no—
60C2×Dic313D411yescharacteristic
61C4×D313—21no—
62C4×D313—21no—
63C4×D313—21no—
64C4×D313D411yescharacteristic
65C4×D313D411yescharacteristic
66C4×D313C2311yescharacteristic
67C4×D313C2311yescharacteristic
68#14578809C2312yes—
69C23×C313—21no—
70Q8×C313C2311yescharacteristic
71D4×C313—21no—
72D4×C313—21no—
73D4×C313C2311yescharacteristic
74D4×C313C2312yes—
75C2×C4×C313—21no—
76C2×C4×C313C2311yescharacteristic
77C8×C313C2312yes—
78C22×C313—21no—
79C22×C313—22no—
80C22×C313—42no—
81C22×C313C2×D411yescharacteristic
82C2×D313—21no—
83C2×D313—41no—
84C2×D313—42no—
85C2×D313C2×D411yescharacteristic
86C2×D313C2×D411yescharacteristic
87C4×C313—21no—
88C4×C313C2×D411yescharacteristic
89C4×C313C2411yescharacteristic
90Dic313—21no—
91Dic313—22no—
92Dic313C2×D411yescharacteristic
93Dic313C2×D411yescharacteristic
94C2×C313—21no—
95C2×C313—41no—
96C2×C313—42no—
97C2×C313C22×D411yescharacteristic
98D313—21no—
99D313—21no—
100D313—41no—
101C313#57511yescharacteristic, complemented, Sylow
102#575—3131nomaximal, Sylow
103C2×#41—3131no—
104C2×#41—3131no—
105#137—3131no—
106#137—3132no—
107#137—3131no—
108AGL(1,ℤ/8)—3131no—
109AGL(1,ℤ/8)—3132no—
110AGL(1,ℤ/8)D31311yescharacteristic, complemented
111#135—3132no—
112#135—3132no—
113C2×M16—3131no—
114#41—3131no—
115#41—3132no—
116#41—3131no—
117#41—3132no—
118#41—3131no—
119#41—6261no—
120#41—6261no—
121#41—6261no—
122#41—6261no—
123#41C2×D31311yescharacteristic
124C2×Q8—3131no—
125C2×Q8—3131no—
126C2×D4—3131no—
127C2×D4—6261no—
128C2×D4—6261no—
129C2×D4C2×D31311yescharacteristic, complemented
130C22×C4—3131no—
131C22×C4—6261no—
132C22×C4—6261no—
133Q16—3132no—
134Q16—3132no—
135SD16—3132no—
136SD16—3132no—
137SD16—3132no—
138SD16C2×D31312yescomplemented
139D8—3132no—
140D8C2×D31312yescomplemented
141M16—3131no—
142M16—3132no—
143M16C2×D31311yescharacteristic, complemented
144C2×C8—3132no—
145C23—21no—
146C23—3131no—
147C23—6261no—
148Q8—3131no—
149Q8—3132no—
150Q8—6261no—
151Q8—6261no—
152Q8C22×D31311yescharacteristic
153D4—21no—
154D4—21no—
155D4—3131no—
156D4—6261no—
157D4—6261no—
158D4—6261no—
159D4—6262no—
160D4—6262no—
161D4—6261no—
162D4C22×D31312yes—
163D4C22×D31311yescharacteristic
164C2×C4—21no—
165C2×C4—3131no—
166C2×C4—3131no—
167C2×C4—3131no—
168C2×C4—3131no—
169C2×C4—3131no—
170C2×C4—6261no—
171C2×C4—6261no—
172C2×C4—6261no—
173C2×C4—6262no—
174C2×C4—6262no—
175C2×C4—6261no—
176C2×C4—6261no—
177C2×C4C22×D31311yescharacteristic
178C8—3132no—
179C8C22×D31312yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—3131no—
184C22—3131no—
185C22—6261no—
186C22—12521no—
187C22—12522no—
188C22D4×D31311yescharacteristic
189C4—21no—
190C4—3131no—
191C4—3131no—
192C4—6261no—
193C4—6262no—
194C4D4×D31311yescharacteristic
195C4C23×D31311yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—6261no—
200C2—6261no—
201C2—12521no—
202C2C2×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#575
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. C2×#19097560C2semidirect
2. #41×D313C2semidirect
3. #23756530C2semidirect
4. #23756527C2semidirect
5. #23756526C2semidirect
6. #23756523C2semidirect
7. #23756521C2semidirect
8. #23756518C2semidirect
9. #23756516C2semidirect
10. M16×D313C2semidirect
11. AGL(1,ℤ/8)×C313C2semidirect
12. #19097562C22semidirect
19. #19097560C22semidirect
20. #19097560C22semidirect
21. C2×Dic626C22semidirect
22. Q8×D313C22semidirect
25. D4×D313C22semidirect
29. Dic1252C22semidirect
30. #19097551C22semidirect
31. #19097550C22semidirect
32. #19097549C22semidirect
33. #19097549C22semidirect
34. #19097546C22semidirect
35. #19097545C22semidirect
36. #19097544C22semidirect
37. C8×D313C22semidirect
39. C2×D4×C313C22semidirect
40. SD16×C313C22semidirect
41. D8×C313C22semidirect
42. M16×C313C22semidirect
101. C313#575semidirect
110. AGL(1,ℤ/8)D313semidirect
129. C2×D4C2×D313semidirect
138. SD16C2×D313semidirect
140. D8C2×D313semidirect
143. M16C2×D313semidirect

Maximal subgroups

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

subgroupindex
C2×#190975602
#41×D3132
#237565302
#237565272
#237565262
#237565232
#237565212
#237565182
#237565162
M16×D3132
AGL(1,ℤ/8)×C3132
#575313