Finite Group Databasebeta

← #50306694

Subgroups — #50306694

Order 38336.

268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 268 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#34062761C211yesmaximal, characteristic, complemented
2#34062760C211yesmaximal, characteristic, complemented
3#34062743C211yesmaximal, characteristic, complemented
4#34062742C212yesmaximal, complemented
5#34062739C212yesmaximal, complemented
6#34062736C212yesmaximal, complemented
7#34062735C211yesmaximal, characteristic, complemented
8C2×#23751063C211yesmaximal, characteristic, complemented
9D8×D599C212yesmaximal, complemented
10#34062723C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C599C211yesmaximal, characteristic, complemented
12#23751079C2212yescomplemented
13#23751078—21no—
14#23751078C2211yescharacteristic
15#23751078C2211yescharacteristic, complemented
16#23751077—21no—
17#23751077C2212yescomplemented
18C2×D2396—21no—
19C2×D2396C2211yescharacteristic, complemented
20C2×C22⋊D599—22no—
21D4×D599—21no—
22D4×D599—22no—
23D4×D599C2212yescomplemented
24D4×D599C2212yescomplemented
25#23751068C2211yescharacteristic, complemented
26#23751067C2212yescomplemented
27#23751066C2211yescharacteristic, complemented
28#23751065C2211yescharacteristic, complemented
29D4792C2212yescomplemented
30#23751063C2211yescharacteristic, complemented
31#23751063C2212yescomplemented
32#23751063C2212yescomplemented
33#23751061C2212yescomplemented
34C2×C599⋊C8C2211yescharacteristic, complemented
35C8×D599C2212yescomplemented
36#41×C599C2211yescharacteristic, complemented
37C2×D4×C599C2211yescharacteristic, complemented
38SD16×C599C2212yescomplemented
39D8×C599C2212yescomplemented
40M16×C599C2211yescharacteristic, complemented
41C22×D599—21no—
42C22×D599—22no—
43C22×D599—22no—
44Dic1198D411yescharacteristic
45Dic1198C2311yescharacteristic
46D2396—22no—
47D2396—21no—
48D2396D411yescharacteristic
49D2396C2312yes—
50D2396C2311yescharacteristic
51C22⋊D599—21no—
52C22⋊D599—22no—
53C22⋊D599—22no—
54C22⋊D599—22no—
55C22⋊D599D412yes—
56C2×Dic599—22no—
57C4×D599—21no—
58C4×D599—22no—
59C4×D599C2312yes—
60C599⋊C8C2311yescharacteristic
61C599⋊C8C2311yescharacteristic
62C23×C599—21no—
63Q8×C599C2311yescharacteristic
64D4×C599—21no—
65D4×C599—21no—
66D4×C599C2311yescharacteristic
67D4×C599C2312yes—
68C2×C4×C599—21no—
69C2×C4×C599C2311yescharacteristic
70C8×C599C2312yes—
71C22×C599—21no—
72C22×C599—22no—
73C22×C599—81no—
74C22×C599C2×D411yescharacteristic
75C2×D599—21no—
76C2×D599—22no—
77C2×D599—82no—
78C2×D599—82no—
79C2×D599—81no—
80C2×D599C2×D412yes—
81C4×C599—21no—
82C4×C599C2×D411yescharacteristic
83C4×C599C2411yescharacteristic
84Dic599—21no—
85Dic599C2×D412yes—
86C2×C599—21no—
87C2×C599—41no—
88C2×C599—42no—
89C2×C599C22×D411yescharacteristic
90D599—22no—
91D599—41no—
92D599—42no—
93C599#57611yescharacteristic, complemented, Sylow
94#576—5991nomaximal, Sylow
95H(5,𝔽2)—5991no—
96H(5,𝔽2)—5991no—
97AGL(1,ℤ/8)—5992no—
98AGL(1,ℤ/8)—5992no—
99AGL(1,ℤ/8)—5991no—
100AGL(1,ℤ/8)D59911yescharacteristic, complemented
101#135—5991no—
102#135—5992no—
103C2×D8—5991no—
104C2×D8—5992no—
105#131—5991no—
106#41—5991no—
107#41—5992no—
108#41—5992no—
109#41—5991no—
110#41—11981no—
111#41—11981no—
112#41C2×D59911yescharacteristic, complemented
113C2×D4—5992no—
114C2×D4—5992no—
115C2×D4—5991no—
116C2×D4—11981no—
117C2×D4—11982no—
118C2×D4—11981no—
119C2×D4—11982no—
120C2×D4C2×D59911yescharacteristic, complemented
121Q16—5991no—
122SD16—5991no—
123SD16—5991no—
124SD16—5992no—
125SD16C2×D59912yescomplemented
126D8—5992no—
127D8—5991no—
128D8—5992no—
129D8—5992no—
130D8C2×D59912yescomplemented
131M16—5992no—
132M16C2×D59911yescharacteristic, complemented
133C2×C8—5991no—
134C2×C8—5992no—
135C23—21no—
136C23—11982no—
137C23—11982no—
138C23—11981no—
139Q8—5991no—
140Q8—5991no—
141Q8C22×D59911yescharacteristic
142D4—21no—
143D4—21no—
144D4—5992no—
145D4—5991no—
146D4—5992no—
147D4—5991no—
148D4—11982no—
149D4—11982no—
150D4—11982no—
151D4—11982no—
152D4—11981no—
153D4—11981no—
154D4C22×D59912yes—
155D4C22×D59911yescharacteristic
156C2×C4—21no—
157C2×C4—5992no—
158C2×C4—11982no—
159C2×C4—11982no—
160C2×C4—11981no—
161C2×C4C22×D59911yescharacteristic
162C8—5991no—
163C8—5991no—
164C8C22×D59912yes—
165C22—21no—
166C22—22no—
167C22—81no—
168C22—5992no—
169C22—11982no—
170C22—11981no—
171C22—47921no—
172C22—47922no—
173C22—47922no—
174C22D4×D59911yescharacteristic
175C4—21no—
176C4—5992no—
177C4—11981no—
178C4D4×D59911yescharacteristic
179C4C23×D59911yescharacteristic
180C2—21no—
181C2—42no—
182C2—41no—
183C2—23962no—
184C2—23961no—
185C2—11982no—
186C2C2×D4×D59911yescharacteristic
subgroupG/H
centerC2C2×D4×D599
commutator, cosocleC4×C599C24
FrattiniC4C23×D599
FittingAGL(1,ℤ/8)×C599C2
socleC2×C599C22×D4
hypercenterAGL(1,ℤ/8)D599
hypocenterC599#576
LCSG ▷ C4×C599 ▷ C2×C599 ▷ C599
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #34062761C2semidirect
2. #34062760C2semidirect
3. #34062743C2semidirect
4. #34062742C2semidirect
5. #34062739C2semidirect
6. #34062736C2semidirect
7. #34062735C2semidirect
8. C2×#23751063C2semidirect
9. D8×D599C2semidirect
10. #34062723C2semidirect
11. AGL(1,ℤ/8)×C599C2semidirect
12. #23751079C22semidirect
15. #23751078C22semidirect
17. #23751077C22semidirect
19. C2×D2396C22semidirect
23. D4×D599C22semidirect
24. D4×D599C22semidirect
25. #23751068C22semidirect
26. #23751067C22semidirect
27. #23751066C22semidirect
28. #23751065C22semidirect
29. D4792C22semidirect
30. #23751063C22semidirect
31. #23751063C22semidirect
32. #23751063C22semidirect
33. #23751061C22semidirect
34. C2×C599⋊C8C22semidirect
35. C8×D599C22semidirect
36. #41×C599C22semidirect
37. C2×D4×C599C22semidirect
38. SD16×C599C22semidirect
39. D8×C599C22semidirect
40. M16×C599C22semidirect
93. C599#576semidirect
100. AGL(1,ℤ/8)D599semidirect
112. #41C2×D599semidirect
120. C2×D4C2×D599semidirect
125. SD16C2×D599semidirect
130. D8C2×D599semidirect
132. M16C2×D599semidirect

Maximal subgroups

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

subgroupindex
#340627612
#340627602
#340627432
#340627422
#340627392
#340627362
#340627352
C2×#237510632
D8×D5992
#340627232
AGL(1,ℤ/8)×C5992
#576599