Finite Group Databasebeta

← #34092504

Subgroups — #34092504

Order 19904.

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#23755755C211yesmaximal, characteristic, complemented
2#23755753C211yesmaximal, characteristic, complemented
3#23755741C211yesmaximal, characteristic, complemented
4#23755737C212yesmaximal, complemented
5#23755732C212yesmaximal, complemented
6#23755728C211yesmaximal, characteristic, complemented
7#23755727C212yesmaximal, complemented
8C2×#19097303C211yesmaximal, characteristic, complemented
9SD16×D311C212yesmaximal, complemented
10#23755716C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C311C211yesmaximal, characteristic, complemented
12#19097315—21no—
13#19097315C2211yescharacteristic
14#19097315C2211yescharacteristic
15#19097314—21no—
16#19097314—22no—
17#19097314C2212yes—
18#19097314C2212yescomplemented
19C2×Dic622—21no—
20C2×Dic622C2211yescharacteristic, complemented
21Q8×D311C2212yescomplemented
22C2×C22⋊D311—22no—
23D4×D311—21no—
24D4×D311C2212yes—
25Dic1244C2212yescomplemented
26#19097305C2211yescharacteristic, complemented
27#19097304C2212yescomplemented
28#19097303C2212yescomplemented
29#19097303C2212yescomplemented
30#19097303C2211yescharacteristic, complemented
31#19097302C2211yescharacteristic, complemented
32#19097300C2211yescharacteristic, complemented
33#19097298C2212yescomplemented
34C2×C311⋊C8C2211yescharacteristic, complemented
35C8×D311C2212yescomplemented
36#41×C311C2211yescharacteristic, complemented
37C2×D4×C311C2211yescharacteristic
38SD16×C311C2212yescomplemented
39D8×C311C2212yescomplemented
40M16×C311C2211yescharacteristic, complemented
41C22×D311—22no—
42Dic622—21no—
43Dic622—22no—
44Dic622D411yescharacteristic
45Dic622C2312yes—
46Dic622C2311yescharacteristic
47D1244D411yescharacteristic
48D1244C2311yescharacteristic
49C22⋊D311—21no—
50C22⋊D311—22no—
51C22⋊D311—22no—
52C22⋊D311—22no—
53C22⋊D311D412yes—
54C2×Dic311—21no—
55C2×Dic311—22no—
56C2×Dic311—22no—
57C4×D311—22no—
58C4×D311—21no—
59C4×D311C2312yes—
60C311⋊C8C2311yescharacteristic
61C311⋊C8C2311yescharacteristic
62C23×C311—21no—
63Q8×C311C2311yescharacteristic
64D4×C311—21no—
65D4×C311—21no—
66D4×C311C2311yescharacteristic
67D4×C311C2312yes—
68C2×C4×C311—21no—
69C2×C4×C311C2311yescharacteristic
70C8×C311C2312yes—
71C22×C311—21no—
72C22×C311—22no—
73C22×C311—81no—
74C22×C311C2×D411yescharacteristic
75C2×D311—21no—
76C2×D311—82no—
77C2×D311C2×D412yes—
78C4×C311—21no—
79C4×C311C2×D411yescharacteristic
80C4×C311C2411yescharacteristic
81Dic311—21no—
82Dic311—22no—
83Dic311C2×D412yes—
84C2×C311—21no—
85C2×C311—42no—
86C2×C311—41no—
87C2×C311C22×D411yescharacteristic
88D311—22no—
89D311—41no—
90C311#57711yescharacteristic, complemented, Sylow
91#577—3111nomaximal, Sylow
922−1+4—3111no—
93H(5,𝔽2)—3111no—
94#137—3112no—
95#137—3111no—
96AGL(1,ℤ/8)—3112no—
97AGL(1,ℤ/8)D31111yescharacteristic, complemented
98#135—3111no—
99#135—3112no—
100C2×SD16—3111no—
101C2×SD16—3112no—
102#131—3111no—
103#41—3111no—
104#41—3112no—
105#41—3112no—
106#41—3111no—
107#41—6221no—
108#41—6222no—
109#41—6221no—
110#41C2×D31111yescharacteristic, complemented
111C2×Q8—3112no—
112C2×Q8—3111no—
113C2×Q8—6221no—
114C2×D4—3112no—
115C2×D4—6221no—
116C2×D4—6222no—
117C2×D4C2×D31111yescharacteristic
118Q16—3111no—
119Q16—3112no—
120SD16—3111no—
121SD16—3112no—
122SD16—3112no—
123SD16—3111no—
124SD16—3112no—
125SD16C2×D31112yescomplemented
126D8—3111no—
127D8C2×D31112yescomplemented
128M16—3112no—
129M16C2×D31111yescharacteristic, complemented
130C2×C8—3111no—
131C2×C8—3112no—
132C23—21no—
133C23—6222no—
134Q8—3111no—
135Q8—3112no—
136Q8—3111no—
137Q8—6222no—
138Q8—6221no—
139Q8C22×D31111yescharacteristic
140D4—21no—
141D4—21no—
142D4—3112no—
143D4—3111no—
144D4—3111no—
145D4—6222no—
146D4—6222no—
147D4—6222no—
148D4—6221no—
149D4C22×D31111yescharacteristic
150D4C22×D31112yes—
151C2×C4—21no—
152C2×C4—3112no—
153C2×C4—6222no—
154C2×C4—6222no—
155C2×C4—6222no—
156C2×C4—6221no—
157C2×C4—6221no—
158C2×C4C22×D31111yescharacteristic
159C8—3111no—
160C8—3111no—
161C8C22×D31112yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—3112no—
166C22—6221no—
167C22—24882no—
168C22D4×D31111yescharacteristic
169C4—21no—
170C4—3112no—
171C4—6221no—
172C4—6222no—
173C4D4×D31111yescharacteristic
174C4C23×D31111yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—6222no—
179C2—12441no—
180C2C2×D4×D31111yescharacteristic
subgroupG/H
centerC2C2×D4×D311
commutator, cosocleC4×C311C24
FrattiniC4C23×D311
FittingAGL(1,ℤ/8)×C311C2
socleC2×C311C22×D4
hypercenterAGL(1,ℤ/8)D311
hypocenterC311#577
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #23755755C2semidirect
2. #23755753C2semidirect
3. #23755741C2semidirect
4. #23755737C2semidirect
5. #23755732C2semidirect
6. #23755728C2semidirect
7. #23755727C2semidirect
8. C2×#19097303C2semidirect
9. SD16×D311C2semidirect
10. #23755716C2semidirect
11. AGL(1,ℤ/8)×C311C2semidirect
18. #19097314C22semidirect
20. C2×Dic622C22semidirect
21. Q8×D311C22semidirect
25. Dic1244C22semidirect
26. #19097305C22semidirect
27. #19097304C22semidirect
28. #19097303C22semidirect
29. #19097303C22semidirect
30. #19097303C22semidirect
31. #19097302C22semidirect
32. #19097300C22semidirect
33. #19097298C22semidirect
34. C2×C311⋊C8C22semidirect
35. C8×D311C22semidirect
36. #41×C311C22semidirect
38. SD16×C311C22semidirect
39. D8×C311C22semidirect
40. M16×C311C22semidirect
90. C311#577semidirect
97. AGL(1,ℤ/8)D311semidirect
110. #41C2×D311semidirect
125. SD16C2×D311semidirect
127. D8C2×D311semidirect
129. M16C2×D311semidirect

Maximal subgroups

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

subgroupindex
#237557552
#237557532
#237557412
#237557372
#237557322
#237557282
#237557272
C2×#190973032
SD16×D3112
#237557162
AGL(1,ℤ/8)×C3112
#577311