Finite Group Databasebeta

← #23758069

Subgroups — #23758069

Order 10048.

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×#14578953C211yesmaximal, characteristic, complemented
2#41×D157C211yesmaximal, characteristic, complemented
3#19097804C211yesmaximal, characteristic, complemented
4#19097801C211yesmaximal, characteristic, complemented
5#19097800C212yesmaximal, complemented
6#19097797C211yesmaximal, characteristic, complemented
7#19097795C212yesmaximal, complemented
8#19097792C212yesmaximal, complemented
9#19097790C212yesmaximal, complemented
10M16×D157C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C157C211yesmaximal, characteristic, complemented
12#14578955C2211yescharacteristic, complemented
13#14578954—21no—
14#14578954C2211yescharacteristic
15#14578953—21no—
16#14578953—21no—
17#14578953—21no—
18#14578953C2212yes—
19#14578953C2211yescharacteristic, complemented
20#14578953C2212yescomplemented
21C2×Dic314C2211yescharacteristic, complemented
22Q8×D157C2211yescharacteristic, complemented
23C2×C22⋊D157—21no—
24D4×D157—21no—
25D4×D157C2211yescharacteristic, complemented
26C22×Dic157—21no—
27C2×C4×D157—21no—
28C2×C4×D157C2211yescharacteristic
29Dic628C2212yescomplemented
30#14578944C2212yescomplemented
31#14578943C2212yescomplemented
32#14578942C2212yescomplemented
33#14578942C2212yescomplemented
34#14578939C2212yescomplemented
35#14578938C2211yescharacteristic, complemented
36#14578937C2212yescomplemented
37C8×D157C2212yescomplemented
38#41×C157C2211yescharacteristic
39C2×D4×C157C2211yescharacteristic, complemented
40SD16×C157C2212yescomplemented
41D8×C157C2212yescomplemented
42M16×C157C2211yescharacteristic, complemented
43C22×D157—21no—
44C22×D157D411yescharacteristic
45Dic314—21no—
46Dic314—21no—
47Dic314C2312yes—
48Dic314C2311yescharacteristic
49D628—21no—
50D628C2311yescharacteristic
51C22⋊D157—21no—
52C22⋊D157—21no—
53C22⋊D157—22no—
54C22⋊D157—22no—
55C22⋊D157—21no—
56C2×Dic157—21no—
57C2×Dic157—21no—
58C2×Dic157—22no—
59C2×Dic157—22no—
60C2×Dic157D411yescharacteristic
61C4×D157—21no—
62C4×D157—21no—
63C4×D157—21no—
64C4×D157D411yescharacteristic
65C4×D157D411yescharacteristic
66C4×D157C2311yescharacteristic
67C4×D157C2311yescharacteristic
68#11929434C2312yes—
69C23×C157—21no—
70Q8×C157C2311yescharacteristic
71D4×C157—21no—
72D4×C157—21no—
73D4×C157C2311yescharacteristic
74D4×C157C2312yes—
75C2×C4×C157—21no—
76C2×C4×C157C2311yescharacteristic
77C8×C157C2312yes—
78C22×C157—21no—
79C22×C157—22no—
80C22×C157—42no—
81C22×C157C2×D411yescharacteristic
82C2×D157—21no—
83C2×D157—41no—
84C2×D157—42no—
85C2×D157C2×D411yescharacteristic
86C2×D157C2×D411yescharacteristic
87C4×C157—21no—
88C4×C157C2×D411yescharacteristic
89C4×C157C2411yescharacteristic
90Dic157—21no—
91Dic157—22no—
92Dic157C2×D411yescharacteristic
93Dic157C2×D411yescharacteristic
94C2×C157—21no—
95C2×C157—41no—
96C2×C157—42no—
97C2×C157C22×D411yescharacteristic
98D157—21no—
99D157—21no—
100D157—41no—
101C157#57511yescharacteristic, complemented, Sylow
102#575—1571nomaximal, Sylow
103C2×#41—1571no—
104C2×#41—1571no—
105#137—1571no—
106#137—1572no—
107#137—1571no—
108AGL(1,ℤ/8)—1571no—
109AGL(1,ℤ/8)—1572no—
110AGL(1,ℤ/8)D15711yescharacteristic, complemented
111#135—1572no—
112#135—1572no—
113C2×M16—1571no—
114#41—3141no—
115#41—3141no—
116#41—3141no—
117#41—3141no—
118#41—1571no—
119#41—1572no—
120#41—1572no—
121#41—1571no—
122#41—1571no—
123#41C2×D15711yescharacteristic
124C2×Q8—1571no—
125C2×Q8—1571no—
126C2×D4—3141no—
127C2×D4—3141no—
128C2×D4—1571no—
129C2×D4C2×D15711yescharacteristic, complemented
130C22×C4—3141no—
131C22×C4—3141no—
132C22×C4—1571no—
133Q16—1572no—
134Q16—1572no—
135SD16—1572no—
136SD16—1572no—
137SD16—1572no—
138SD16C2×D15712yescomplemented
139D8—1572no—
140D8C2×D15712yescomplemented
141M16—1571no—
142M16—1572no—
143M16C2×D15711yescharacteristic, complemented
144C2×C8—1572no—
145C23—21no—
146C23—3141no—
147C23—1571no—
148Q8—3141no—
149Q8—3141no—
150Q8—1571no—
151Q8—1572no—
152Q8C22×D15711yescharacteristic
153D4—21no—
154D4—21no—
155D4—3141no—
156D4—3141no—
157D4—3142no—
158D4—3142no—
159D4—3141no—
160D4—3141no—
161D4—1571no—
162D4C22×D15712yes—
163D4C22×D15711yescharacteristic
164C2×C4—21no—
165C2×C4—3141no—
166C2×C4—3141no—
167C2×C4—3141no—
168C2×C4—3141no—
169C2×C4—3142no—
170C2×C4—3142no—
171C2×C4—3141no—
172C2×C4—1571no—
173C2×C4—1571no—
174C2×C4—1571no—
175C2×C4—1571no—
176C2×C4—1571no—
177C2×C4C22×D15711yescharacteristic
178C8—1572no—
179C8C22×D15712yes—
180C22—21no—
181C22—22no—
182C22—42no—
183C22—3141no—
184C22—6281no—
185C22—6282no—
186C22—1571no—
187C22—1571no—
188C22D4×D15711yescharacteristic
189C4—21no—
190C4—3141no—
191C4—3142no—
192C4—1571no—
193C4—1571no—
194C4D4×D15711yescharacteristic
195C4C23×D15711yescharacteristic
196C2—21no—
197C2—42no—
198C2—41no—
199C2—3141no—
200C2—3141no—
201C2—6281no—
202C2C2×D4×D15711yescharacteristic
subgroupG/H
centerC2C2×D4×D157
commutator, cosocleC4×C157C24
FrattiniC4C23×D157
FittingAGL(1,ℤ/8)×C157C2
socleC2×C157C22×D4
hypercenterAGL(1,ℤ/8)D157
hypocenterC157#575
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#14578953C2semidirect
2. #41×D157C2semidirect
3. #19097804C2semidirect
4. #19097801C2semidirect
5. #19097800C2semidirect
6. #19097797C2semidirect
7. #19097795C2semidirect
8. #19097792C2semidirect
9. #19097790C2semidirect
10. M16×D157C2semidirect
11. AGL(1,ℤ/8)×C157C2semidirect
12. #14578955C22semidirect
19. #14578953C22semidirect
20. #14578953C22semidirect
21. C2×Dic314C22semidirect
22. Q8×D157C22semidirect
25. D4×D157C22semidirect
29. Dic628C22semidirect
30. #14578944C22semidirect
31. #14578943C22semidirect
32. #14578942C22semidirect
33. #14578942C22semidirect
34. #14578939C22semidirect
35. #14578938C22semidirect
36. #14578937C22semidirect
37. C8×D157C22semidirect
39. C2×D4×C157C22semidirect
40. SD16×C157C22semidirect
41. D8×C157C22semidirect
42. M16×C157C22semidirect
101. C157#575semidirect
110. AGL(1,ℤ/8)D157semidirect
129. C2×D4C2×D157semidirect
138. SD16C2×D157semidirect
140. D8C2×D157semidirect
143. M16C2×D157semidirect