Finite Group Databasebeta

← #34092503

Subgroups — #34092503

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#23755754C211yesmaximal, characteristic, complemented
3#23755740C212yesmaximal, complemented
4#23755736C211yesmaximal, characteristic, complemented
5#23755735C212yesmaximal, complemented
6#23755731C212yesmaximal, complemented
7#23755728C211yesmaximal, characteristic, complemented
8C2×#19097302C211yesmaximal, characteristic, complemented
9SD16×D311C212yesmaximal, complemented
10#23755716C211yesmaximal, characteristic, complemented
11#137×C311C211yesmaximal, characteristic, complemented
12#19097316—21no—
13#19097316C2212yes—
14#19097316C2212yescomplemented
15#19097315—21no—
16#19097315—22no—
17#19097315C2211yescharacteristic
18#19097315C2211yescharacteristic, complemented
19Q8×D311—21no—
20Q8×D311C2212yescomplemented
21C2×D1244—21no—
22C2×D1244C2211yescharacteristic
23D4×D311—22no—
24D4×D311C2212yes—
25#19097305C2211yescharacteristic, complemented
26#19097304C2212yescomplemented
27#19097303C2211yescharacteristic, complemented
28#19097302C2212yescomplemented
29#19097302C2212yescomplemented
30#19097302C2211yescharacteristic, complemented
31D2488C2212yescomplemented
32#19097300C2211yescharacteristic, complemented
33#19097298C2212yescomplemented
34C2×C311⋊C8C2211yescharacteristic, complemented
35C8×D311C2212yescomplemented
36#41×C311C2211yescharacteristic
37C2×Q8×C311C2211yescharacteristic, complemented
38Q16×C311C2212yescomplemented
39SD16×C311C2212yescomplemented
40M16×C311C2211yescharacteristic, complemented
41C22×D311—21no—
42C22×D311—22no—
43Dic622—22no—
44Dic622D411yescharacteristic
45Dic622C2311yescharacteristic
46D1244—22no—
47D1244—22no—
48D1244—21no—
49D1244D411yescharacteristic
50D1244C2311yescharacteristic
51D1244C2312yes—
52C22⋊D311—21no—
53C22⋊D311—22no—
54C22⋊D311D412yes—
55C4×D311—22no—
56C4×D311—21no—
57C4×D311—22no—
58C4×D311—22no—
59C4×D311C2312yes—
60C311⋊C8C2311yescharacteristic
61C311⋊C8C2311yescharacteristic
62Q8×C311—21no—
63Q8×C311C2312yes—
64Q8×C311C2311yescharacteristic
65D4×C311—21no—
66D4×C311C2311yescharacteristic
67C2×C4×C311—21no—
68C2×C4×C311—21no—
69C2×C4×C311C2311yescharacteristic
70C8×C311C2312yes—
71C22×C311—21no—
72C22×C311C2×D411yescharacteristic
73C2×D311—21no—
74C2×D311—22no—
75C2×D311—82no—
76C2×D311—81no—
77C2×D311C2×D412yes—
78C4×C311—21no—
79C4×C311—22no—
80C4×C311C2×D411yescharacteristic
81C4×C311C2411yescharacteristic
82Dic311—21no—
83Dic311C2×D412yes—
84C2×C311—21no—
85C2×C311—41no—
86C2×C311C22×D411yescharacteristic
87D311—22no—
88D311—41no—
89D311—42no—
90C311#57711yescharacteristic, complemented, Sylow
91#577—3111nomaximal, Sylow
922−1+4—3111no—
93H(5,𝔽2)—3111no—
94#137—3112no—
95#137D31111yescharacteristic, complemented
96AGL(1,ℤ/8)—3112no—
97AGL(1,ℤ/8)—3111no—
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—6222no—
108#41—6221no—
109#41—6221no—
110#41C2×D31111yescharacteristic
111C2×Q8—3112no—
112C2×Q8—6221no—
113C2×Q8C2×D31111yescharacteristic, complemented
114C2×D4—3112no—
115C2×D4—3111no—
116C2×D4—6221no—
117C2×D4—6222no—
118Q16—3111no—
119Q16C2×D31112yescomplemented
120SD16—3112no—
121SD16—3112no—
122SD16—3111no—
123SD16—3111no—
124SD16—3112no—
125SD16C2×D31112yescomplemented
126D8—3111no—
127D8—3112no—
128M16—3112no—
129M16C2×D31111yescharacteristic, complemented
130C2×C8—3111no—
131C2×C8—3112no—
132C23—6222no—
133C23—6221no—
134Q8—21no—
135Q8—3111no—
136Q8—3111no—
137Q8—6222no—
138Q8C22×D31112yes—
139Q8C22×D31111yescharacteristic
140D4—21no—
141D4—3112no—
142D4—3111no—
143D4—3111no—
144D4—3112no—
145D4—6222no—
146D4—6222no—
147D4—6222no—
148D4—6221no—
149D4—6221no—
150D4C22×D31111yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—3112no—
154C2×C4—6222no—
155C2×C4—6222no—
156C2×C4—6222no—
157C2×C4—6221no—
158C2×C4C22×D31111yescharacteristic
159C8—3111no—
160C8—3111no—
161C8C22×D31112yes—
162C22—21no—
163C22—3112no—
164C22—6221no—
165C22—6222no—
166C22—24881no—
167C22—24882no—
168C22D4×D31111yescharacteristic
169C4—21no—
170C4—22no—
171C4—3112no—
172C4—6221no—
173C4D4×D31111yescharacteristic
174C4C23×D31111yescharacteristic
175C2—21no—
176C2—41no—
177C2—6222no—
178C2—12442no—
179C2—12441no—
180C2C2×D4×D31111yescharacteristic
subgroupG/H
centerC2C2×D4×D311
commutator, cosocleC4×C311C24
FrattiniC4C23×D311
Fitting#137×C311C2
socleC2×C311C22×D4
hypercenter#137D311
hypocenterC311#577
LCSG ▷ C4×C311 ▷ C2×C311 ▷ C311
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #23755756C2semidirect
2. #23755754C2semidirect
3. #23755740C2semidirect
4. #23755736C2semidirect
5. #23755735C2semidirect
6. #23755731C2semidirect
7. #23755728C2semidirect
8. C2×#19097302C2semidirect
9. SD16×D311C2semidirect
10. #23755716C2semidirect
11. #137×C311C2semidirect
14. #19097316C22semidirect
18. #19097315C22semidirect
20. Q8×D311C22semidirect
25. #19097305C22semidirect
26. #19097304C22semidirect
27. #19097303C22semidirect
28. #19097302C22semidirect
29. #19097302C22semidirect
30. #19097302C22semidirect
31. D2488C22semidirect
32. #19097300C22semidirect
33. #19097298C22semidirect
34. C2×C311⋊C8C22semidirect
35. C8×D311C22semidirect
37. C2×Q8×C311C22semidirect
38. Q16×C311C22semidirect
39. SD16×C311C22semidirect
40. M16×C311C22semidirect
90. C311#577semidirect
95. #137D311semidirect
113. C2×Q8C2×D311semidirect
119. Q16C2×D311semidirect
125. SD16C2×D311semidirect
129. M16C2×D311semidirect

Maximal subgroups

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

subgroupindex
#237557562
#237557542
#237557402
#237557362
#237557352
#237557312
#237557282
C2×#190973022
SD16×D3112
#237557162
#137×C3112
#577311