Finite Group Databasebeta

← #50306696

Subgroups — #50306696

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#34062760C211yesmaximal, characteristic, complemented
3#34062746C211yesmaximal, characteristic, complemented
4#34062744C212yesmaximal, complemented
5#34062742C212yesmaximal, complemented
6#34062741C211yesmaximal, characteristic, complemented
7#34062737C211yesmaximal, characteristic, complemented
8#34062736C212yesmaximal, complemented
9SD16×D599C212yesmaximal, complemented
10#34062721C211yesmaximal, characteristic, complemented
11C2×SD16×C599C211yesmaximal, characteristic, complemented
12#23751079—21no—
13#23751079C2212yescomplemented
14#23751078—22no—
15#23751078C2211yescharacteristic
16#23751078C2211yescharacteristic
17#23751078C2211yescharacteristic, complemented
18#23751077—21no—
19#23751077C2212yes—
20Q8×D599—21no—
21Q8×D599C2212yescomplemented
22C2×C22⋊D599—22no—
23D4×D599—21no—
24D4×D599C2212yes—
25Dic2396C2211yescharacteristic, complemented
26#23751068C2212yescomplemented
27#23751067C2211yescharacteristic, complemented
28#23751067C2211yescharacteristic, complemented
29#23751066C2212yescomplemented
30#23751065C2212yescomplemented
31D4792C2211yescharacteristic, complemented
32#23751063C2212yescomplemented
33#23751062C2211yescharacteristic, complemented
34#23751061C2212yescomplemented
35C8×D599C2212yescomplemented
36C2×Q8×C599C2211yescharacteristic, complemented
37C2×D4×C599C2211yescharacteristic
38SD16×C599C2212yescomplemented
39SD16×C599C2212yescomplemented
40C2×C8×C599C2211yescharacteristic, complemented
41C22×D599—22no—
42Dic1198—22no—
43Dic1198D411yescharacteristic
44Dic1198C2311yescharacteristic
45Dic1198C2311yescharacteristic
46D2396—22no—
47D2396D411yescharacteristic
48D2396C2311yescharacteristic
49D2396C2311yescharacteristic
50C22⋊D599—21no—
51C22⋊D599—21no—
52C22⋊D599—22no—
53C22⋊D599—22no—
54C22⋊D599D412yes—
55C2×Dic599—22no—
56C4×D599—22no—
57C4×D599—21no—
58C4×D599—21no—
59C4×D599—22no—
60C4×D599C2312yes—
61C599⋊C8C2312yes—
62C23×C599—21no—
63Q8×C599—21no—
64Q8×C599C2312yes—
65D4×C599—21no—
66D4×C599C2312yes—
67C2×C4×C599—21no—
68C2×C4×C599C2311yescharacteristic
69C8×C599C2311yescharacteristic
70C8×C599C2311yescharacteristic
71C22×C599—22no—
72C22×C599—81no—
73C22×C599C2×D411yescharacteristic
74C2×D599—21no—
75C2×D599—21no—
76C2×D599—82no—
77C2×D599C2×D412yes—
78C4×C599—22no—
79C4×C599C2×D411yescharacteristic
80C4×C599C2411yescharacteristic
81Dic599—21no—
82Dic599—21no—
83Dic599C2×D412yes—
84C2×C599—21no—
85C2×C599—42no—
86C2×C599C22×D411yescharacteristic
87D599—22no—
88D599—41no—
89D599—41no—
90C599#57711yescharacteristic, complemented, Sylow
91#577—5991nomaximal, Sylow
922−1+4—5991no—
93H(5,𝔽2)—5991no—
94#137—5991no—
95#137—5992no—
96AGL(1,ℤ/8)—5991no—
97AGL(1,ℤ/8)—5992no—
98#135—5992no—
99#135—5991no—
100C2×SD16—5992no—
101C2×SD16D59911yescharacteristic, complemented
102#131—5991no—
103#41—5991no—
104#41—5992no—
105#41—5992no—
106#41—5991no—
107#41—5991no—
108#41—11982no—
109#41—11981no—
110#41—11981no—
111C2×Q8—5992no—
112C2×Q8—11981no—
113C2×Q8C2×D59911yescharacteristic, complemented
114C2×D4—5992no—
115C2×D4—11981no—
116C2×D4—11982no—
117C2×D4C2×D59911yescharacteristic
118Q16—5992no—
119Q16—5991no—
120SD16—5992no—
121SD16—5992no—
122SD16—5991no—
123SD16—5991no—
124SD16C2×D59912yescomplemented
125SD16C2×D59912yescomplemented
126D8—5992no—
127D8—5991no—
128M16—5991no—
129M16—5992no—
130C2×C8—5992no—
131C2×C8C2×D59911yescharacteristic, complemented
132C23—21no—
133C23—11982no—
134Q8—21no—
135Q8—5991no—
136Q8—5991no—
137Q8—5991no—
138Q8—11982no—
139Q8C22×D59912yes—
140D4—21no—
141D4—5992no—
142D4—5991no—
143D4—5991no—
144D4—5991no—
145D4—11982no—
146D4—11982no—
147D4—11982no—
148D4—11981no—
149D4—11981no—
150D4C22×D59912yes—
151C2×C4—21no—
152C2×C4—5992no—
153C2×C4—11982no—
154C2×C4—11982no—
155C2×C4—11982no—
156C2×C4—11981no—
157C2×C4—11981no—
158C2×C4C22×D59911yescharacteristic
159C8—5992no—
160C8C22×D59911yescharacteristic
161C8C22×D59911yescharacteristic
162C22—22no—
163C22—81no—
164C22—5992no—
165C22—11981no—
166C22—11981no—
167C22—47922no—
168C22D4×D59911yescharacteristic
169C4—22no—
170C4—5992no—
171C4—11981no—
172C4—11981no—
173C4D4×D59911yescharacteristic
174C4C23×D59911yescharacteristic
175C2—21no—
176C2—42no—
177C2—23961no—
178C2—23961no—
179C2—11982no—
180C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC2C2×D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
FittingC2×SD16×C599C2
socleC2×C599C22×D4
hypercenterC2×SD16D599
hypocenterC599#577
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #34062763C2semidirect
2. #34062760C2semidirect
3. #34062746C2semidirect
4. #34062744C2semidirect
5. #34062742C2semidirect
6. #34062741C2semidirect
7. #34062737C2semidirect
8. #34062736C2semidirect
9. SD16×D599C2semidirect
10. #34062721C2semidirect
11. C2×SD16×C599C2semidirect
13. #23751079C22semidirect
17. #23751078C22semidirect
21. Q8×D599C22semidirect
25. Dic2396C22semidirect
26. #23751068C22semidirect
27. #23751067C22semidirect
28. #23751067C22semidirect
29. #23751066C22semidirect
30. #23751065C22semidirect
31. D4792C22semidirect
32. #23751063C22semidirect
33. #23751062C22semidirect
34. #23751061C22semidirect
35. C8×D599C22semidirect
36. C2×Q8×C599C22semidirect
38. SD16×C599C22semidirect
39. SD16×C599C22semidirect
40. C2×C8×C599C22semidirect
90. C599#577semidirect
101. C2×SD16D599semidirect
113. C2×Q8C2×D599semidirect
124. SD16C2×D599semidirect
125. SD16C2×D599semidirect
131. C2×C8C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627632
#340627602
#340627462
#340627442
#340627422
#340627412
#340627372
#340627362
SD16×D5992
#340627212
C2×SD16×C5992
#577599