Finite Group Databasebeta

← #34092500

Subgroups — #34092500

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#23755756C211yesmaximal, characteristic, complemented
2#23755753C211yesmaximal, characteristic, complemented
3#23755739C211yesmaximal, characteristic, complemented
4#23755737C212yesmaximal, complemented
5#23755735C212yesmaximal, complemented
6#23755734C211yesmaximal, characteristic, complemented
7#23755730C211yesmaximal, characteristic, complemented
8#23755729C212yesmaximal, complemented
9SD16×D311C212yesmaximal, complemented
10#23755714C211yesmaximal, characteristic, complemented
11C2×SD16×C311C211yesmaximal, characteristic, complemented
12#19097316—21no—
13#19097316C2212yescomplemented
14#19097315—22no—
15#19097315C2211yescharacteristic
16#19097315C2211yescharacteristic
17#19097315C2211yescharacteristic, complemented
18#19097314—21no—
19#19097314C2212yes—
20Q8×D311—21no—
21Q8×D311C2212yescomplemented
22C2×C22⋊D311—22no—
23D4×D311—21no—
24D4×D311C2212yes—
25Dic1244C2211yescharacteristic, complemented
26#19097305C2212yescomplemented
27#19097304C2211yescharacteristic, complemented
28#19097304C2211yescharacteristic, complemented
29#19097303C2212yescomplemented
30#19097302C2212yescomplemented
31D2488C2211yescharacteristic, complemented
32#19097300C2212yescomplemented
33#19097299C2211yescharacteristic, complemented
34#19097298C2212yescomplemented
35C8×D311C2212yescomplemented
36C2×Q8×C311C2211yescharacteristic, complemented
37C2×D4×C311C2211yescharacteristic
38SD16×C311C2212yescomplemented
39SD16×C311C2212yescomplemented
40C2×C8×C311C2211yescharacteristic, complemented
41C22×D311—22no—
42Dic622—22no—
43Dic622D411yescharacteristic
44Dic622C2311yescharacteristic
45Dic622C2311yescharacteristic
46D1244—22no—
47D1244D411yescharacteristic
48D1244C2311yescharacteristic
49D1244C2311yescharacteristic
50C22⋊D311—21no—
51C22⋊D311—21no—
52C22⋊D311—22no—
53C22⋊D311—22no—
54C22⋊D311D412yes—
55C2×Dic311—22no—
56C4×D311—22no—
57C4×D311—21no—
58C4×D311—21no—
59C4×D311—22no—
60C4×D311C2312yes—
61C311⋊C8C2312yes—
62C23×C311—21no—
63Q8×C311—21no—
64Q8×C311C2312yes—
65D4×C311—21no—
66D4×C311C2312yes—
67C2×C4×C311—21no—
68C2×C4×C311C2311yescharacteristic
69C8×C311C2311yescharacteristic
70C8×C311C2311yescharacteristic
71C22×C311—22no—
72C22×C311—81no—
73C22×C311C2×D411yescharacteristic
74C2×D311—21no—
75C2×D311—21no—
76C2×D311—82no—
77C2×D311C2×D412yes—
78C4×C311—22no—
79C4×C311C2×D411yescharacteristic
80C4×C311C2411yescharacteristic
81Dic311—21no—
82Dic311—21no—
83Dic311C2×D412yes—
84C2×C311—21no—
85C2×C311—42no—
86C2×C311C22×D411yescharacteristic
87D311—22no—
88D311—41no—
89D311—41no—
90C311#57711yescharacteristic, complemented, Sylow
91#577—3111nomaximal, Sylow
922−1+4—3111no—
93H(5,𝔽2)—3111no—
94#137—3111no—
95#137—3112no—
96AGL(1,ℤ/8)—3111no—
97AGL(1,ℤ/8)—3112no—
98#135—3112no—
99#135—3111no—
100C2×SD16—3112no—
101C2×SD16D31111yescharacteristic, complemented
102#131—3111no—
103#41—3111no—
104#41—3112no—
105#41—3112no—
106#41—3111no—
107#41—3111no—
108#41—6222no—
109#41—6221no—
110#41—6221no—
111C2×Q8—3112no—
112C2×Q8—6221no—
113C2×Q8C2×D31111yescharacteristic, complemented
114C2×D4—3112no—
115C2×D4—6221no—
116C2×D4—6222no—
117C2×D4C2×D31111yescharacteristic
118Q16—3112no—
119Q16—3111no—
120SD16—3112no—
121SD16—3112no—
122SD16—3111no—
123SD16—3111no—
124SD16C2×D31112yescomplemented
125SD16C2×D31112yescomplemented
126D8—3112no—
127D8—3111no—
128M16—3111no—
129M16—3112no—
130C2×C8—3112no—
131C2×C8C2×D31111yescharacteristic, complemented
132C23—21no—
133C23—6222no—
134Q8—21no—
135Q8—3111no—
136Q8—3111no—
137Q8—3111no—
138Q8—6222no—
139Q8C22×D31112yes—
140D4—21no—
141D4—3112no—
142D4—3111no—
143D4—3111no—
144D4—3111no—
145D4—6222no—
146D4—6222no—
147D4—6222no—
148D4—6221no—
149D4—6221no—
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—3112no—
160C8C22×D31111yescharacteristic
161C8C22×D31111yescharacteristic
162C22—22no—
163C22—81no—
164C22—3112no—
165C22—6221no—
166C22—6221no—
167C22—24882no—
168C22D4×D31111yescharacteristic
169C4—22no—
170C4—3112no—
171C4—6221no—
172C4—6221no—
173C4D4×D31111yescharacteristic
174C4C23×D31111yescharacteristic
175C2—21no—
176C2—42no—
177C2—6222no—
178C2—12441no—
179C2—12441no—
180C2C2×D4×D31111yescharacteristic
subgroupG/H
centerC2C2×D4×D311
commutator, cosocleC4×C311C24
FrattiniC4C23×D311
FittingC2×SD16×C311C2
socleC2×C311C22×D4
hypercenterC2×SD16D311
hypocenterC311#577
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #23755756C2semidirect
2. #23755753C2semidirect
3. #23755739C2semidirect
4. #23755737C2semidirect
5. #23755735C2semidirect
6. #23755734C2semidirect
7. #23755730C2semidirect
8. #23755729C2semidirect
9. SD16×D311C2semidirect
10. #23755714C2semidirect
11. C2×SD16×C311C2semidirect
13. #19097316C22semidirect
17. #19097315C22semidirect
21. Q8×D311C22semidirect
25. Dic1244C22semidirect
26. #19097305C22semidirect
27. #19097304C22semidirect
28. #19097304C22semidirect
29. #19097303C22semidirect
30. #19097302C22semidirect
31. D2488C22semidirect
32. #19097300C22semidirect
33. #19097299C22semidirect
34. #19097298C22semidirect
35. C8×D311C22semidirect
36. C2×Q8×C311C22semidirect
38. SD16×C311C22semidirect
39. SD16×C311C22semidirect
40. C2×C8×C311C22semidirect
90. C311#577semidirect
101. C2×SD16D311semidirect
113. C2×Q8C2×D311semidirect
124. SD16C2×D311semidirect
125. SD16C2×D311semidirect
131. C2×C8C2×D311semidirect

Maximal subgroups

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

subgroupindex
#237557562
#237557532
#237557392
#237557372
#237557352
#237557342
#237557302
#237557292
SD16×D3112
#237557142
C2×SD16×C3112
#577311