Finite Group Databasebeta

← #50306699

Subgroups — #50306699

Order 38336.

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#34062763C211yesmaximal, characteristic, complemented
2#34062761C211yesmaximal, characteristic, complemented
3#34062747C212yesmaximal, complemented
4#34062743C211yesmaximal, characteristic, complemented
5#34062742C212yesmaximal, complemented
6#34062738C212yesmaximal, complemented
7#34062735C211yesmaximal, characteristic, complemented
8C2×#23751065C211yesmaximal, characteristic, complemented
9SD16×D599C212yesmaximal, complemented
10#34062723C211yesmaximal, characteristic, complemented
11#137×C599C211yesmaximal, characteristic, complemented
12#23751079—21no—
13#23751079C2212yes—
14#23751079C2212yescomplemented
15#23751078—21no—
16#23751078—22no—
17#23751078C2211yescharacteristic
18#23751078C2211yescharacteristic, complemented
19Q8×D599—21no—
20Q8×D599C2212yescomplemented
21C2×D2396—21no—
22C2×D2396C2211yescharacteristic
23D4×D599—22no—
24D4×D599C2212yes—
25#23751068C2211yescharacteristic, complemented
26#23751067C2212yescomplemented
27#23751066C2211yescharacteristic, complemented
28#23751065C2212yescomplemented
29#23751065C2212yescomplemented
30#23751065C2211yescharacteristic, complemented
31D4792C2212yescomplemented
32#23751063C2211yescharacteristic, complemented
33#23751061C2212yescomplemented
34C2×C599⋊C8C2211yescharacteristic, complemented
35C8×D599C2212yescomplemented
36#41×C599C2211yescharacteristic
37C2×Q8×C599C2211yescharacteristic, complemented
38Q16×C599C2212yescomplemented
39SD16×C599C2212yescomplemented
40M16×C599C2211yescharacteristic, complemented
41C22×D599—21no—
42C22×D599—22no—
43Dic1198—22no—
44Dic1198D411yescharacteristic
45Dic1198C2311yescharacteristic
46D2396—22no—
47D2396—22no—
48D2396—21no—
49D2396D411yescharacteristic
50D2396C2311yescharacteristic
51D2396C2312yes—
52C22⋊D599—21no—
53C22⋊D599—22no—
54C22⋊D599D412yes—
55C4×D599—22no—
56C4×D599—21no—
57C4×D599—22no—
58C4×D599—22no—
59C4×D599C2312yes—
60C599⋊C8C2311yescharacteristic
61C599⋊C8C2311yescharacteristic
62Q8×C599—21no—
63Q8×C599C2312yes—
64Q8×C599C2311yescharacteristic
65D4×C599—21no—
66D4×C599C2311yescharacteristic
67C2×C4×C599—21no—
68C2×C4×C599—21no—
69C2×C4×C599C2311yescharacteristic
70C8×C599C2312yes—
71C22×C599—21no—
72C22×C599C2×D411yescharacteristic
73C2×D599—21no—
74C2×D599—22no—
75C2×D599—82no—
76C2×D599—81no—
77C2×D599C2×D412yes—
78C4×C599—21no—
79C4×C599—22no—
80C4×C599C2×D411yescharacteristic
81C4×C599C2411yescharacteristic
82Dic599—21no—
83Dic599C2×D412yes—
84C2×C599—21no—
85C2×C599—41no—
86C2×C599C22×D411yescharacteristic
87D599—22no—
88D599—41no—
89D599—42no—
90C599#57711yescharacteristic, complemented, Sylow
91#577—5991nomaximal, Sylow
922−1+4—5991no—
93H(5,𝔽2)—5991no—
94#137—5992no—
95#137D59911yescharacteristic, complemented
96AGL(1,ℤ/8)—5992no—
97AGL(1,ℤ/8)—5991no—
98#135—5991no—
99#135—5992no—
100C2×SD16—5991no—
101C2×SD16—5992no—
102#131—5991no—
103#41—5991no—
104#41—5992no—
105#41—5992no—
106#41—5991no—
107#41—11982no—
108#41—11981no—
109#41—11981no—
110#41C2×D59911yescharacteristic
111C2×Q8—5992no—
112C2×Q8—11981no—
113C2×Q8C2×D59911yescharacteristic, complemented
114C2×D4—5992no—
115C2×D4—5991no—
116C2×D4—11981no—
117C2×D4—11982no—
118Q16—5991no—
119Q16C2×D59912yescomplemented
120SD16—5992no—
121SD16—5992no—
122SD16—5991no—
123SD16—5991no—
124SD16—5992no—
125SD16C2×D59912yescomplemented
126D8—5991no—
127D8—5992no—
128M16—5992no—
129M16C2×D59911yescharacteristic, complemented
130C2×C8—5991no—
131C2×C8—5992no—
132C23—11982no—
133C23—11981no—
134Q8—21no—
135Q8—5991no—
136Q8—5991no—
137Q8—11982no—
138Q8C22×D59912yes—
139Q8C22×D59911yescharacteristic
140D4—21no—
141D4—5992no—
142D4—5991no—
143D4—5991no—
144D4—5992no—
145D4—11982no—
146D4—11982no—
147D4—11982no—
148D4—11981no—
149D4—11981no—
150D4C22×D59911yescharacteristic
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—5992no—
154C2×C4—11982no—
155C2×C4—11982no—
156C2×C4—11982no—
157C2×C4—11981no—
158C2×C4C22×D59911yescharacteristic
159C8—5991no—
160C8—5991no—
161C8C22×D59912yes—
162C22—21no—
163C22—5992no—
164C22—11981no—
165C22—11982no—
166C22—47921no—
167C22—47922no—
168C22D4×D59911yescharacteristic
169C4—21no—
170C4—22no—
171C4—5992no—
172C4—11981no—
173C4D4×D59911yescharacteristic
174C4C23×D59911yescharacteristic
175C2—21no—
176C2—41no—
177C2—23962no—
178C2—23961no—
179C2—11982no—
180C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC2C2×D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
Fitting#137×C599C2
socleC2×C599C22×D4
hypercenter#137D599
hypocenterC599#577
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ #137

Complements

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

NH ≅ G/Ntype
1. #34062763C2semidirect
2. #34062761C2semidirect
3. #34062747C2semidirect
4. #34062743C2semidirect
5. #34062742C2semidirect
6. #34062738C2semidirect
7. #34062735C2semidirect
8. C2×#23751065C2semidirect
9. SD16×D599C2semidirect
10. #34062723C2semidirect
11. #137×C599C2semidirect
14. #23751079C22semidirect
18. #23751078C22semidirect
20. Q8×D599C22semidirect
25. #23751068C22semidirect
26. #23751067C22semidirect
27. #23751066C22semidirect
28. #23751065C22semidirect
29. #23751065C22semidirect
30. #23751065C22semidirect
31. D4792C22semidirect
32. #23751063C22semidirect
33. #23751061C22semidirect
34. C2×C599⋊C8C22semidirect
35. C8×D599C22semidirect
37. C2×Q8×C599C22semidirect
38. Q16×C599C22semidirect
39. SD16×C599C22semidirect
40. M16×C599C22semidirect
90. C599#577semidirect
95. #137D599semidirect
113. C2×Q8C2×D599semidirect
119. Q16C2×D599semidirect
125. SD16C2×D599semidirect
129. M16C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627632
#340627612
#340627472
#340627432
#340627422
#340627382
#340627352
C2×#237510652
SD16×D5992
#340627232
#137×C5992
#577599