Finite Group Databasebeta

← #37560232

Subgroups — #37560232

Order 23872.

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#26045839C211yesmaximal, characteristic, complemented
2#26045837C211yesmaximal, characteristic, complemented
3#26045825C211yesmaximal, characteristic, complemented
4#26045821C212yesmaximal, complemented
5#26045816C212yesmaximal, complemented
6#26045812C211yesmaximal, characteristic, complemented
7#26045811C212yesmaximal, complemented
8C2×#20238598C211yesmaximal, characteristic, complemented
9SD16×D373C212yesmaximal, complemented
10#26045800C211yesmaximal, characteristic, complemented
11AGL(1,ℤ/8)×C373C211yesmaximal, characteristic, complemented
12#20238610—21no—
13#20238610C2211yescharacteristic
14#20238610C2211yescharacteristic
15#20238609—21no—
16#20238609—22no—
17#20238609C2212yes—
18#20238609C2212yescomplemented
19C2×Dic746—21no—
20C2×Dic746C2211yescharacteristic, complemented
21Q8×D373C2212yescomplemented
22C2×C22⋊D373—22no—
23D4×D373—21no—
24D4×D373C2212yes—
25Dic1492C2212yescomplemented
26#20238600C2211yescharacteristic, complemented
27#20238599C2212yescomplemented
28#20238598C2212yescomplemented
29#20238598C2212yescomplemented
30#20238598C2211yescharacteristic, complemented
31#20238597C2211yescharacteristic, complemented
32#20238595C2211yescharacteristic, complemented
33#20238593C2212yescomplemented
34C2×#15688412C2211yescharacteristic, complemented
35C8×D373C2212yescomplemented
36#41×C373C2211yescharacteristic, complemented
37C2×D4×C373C2211yescharacteristic
38SD16×C373C2212yescomplemented
39D8×C373C2212yescomplemented
40M16×C373C2211yescharacteristic, complemented
41C22×D373—22no—
42Dic746—21no—
43Dic746—22no—
44Dic746D411yescharacteristic
45Dic746C2312yes—
46Dic746C2311yescharacteristic
47D1492D411yescharacteristic
48D1492C2311yescharacteristic
49C22⋊D373—21no—
50C22⋊D373—22no—
51C22⋊D373—22no—
52C22⋊D373—22no—
53C22⋊D373D412yes—
54C2×Dic373—21no—
55C2×Dic373—22no—
56C2×Dic373—22no—
57C4×D373—22no—
58C4×D373—21no—
59C4×D373C2312yes—
60#15688412C2311yescharacteristic
61#15688412C2311yescharacteristic
62C23×C373—21no—
63Q8×C373C2311yescharacteristic
64D4×C373—21no—
65D4×C373—21no—
66D4×C373C2311yescharacteristic
67D4×C373C2312yes—
68C2×C4×C373—21no—
69C2×C4×C373C2311yescharacteristic
70C8×C373C2312yes—
71C22×C373—21no—
72C22×C373—22no—
73C22×C373—81no—
74C22×C373C2×D411yescharacteristic
75C2×D373—21no—
76C2×D373—82no—
77C2×D373C2×D412yes—
78C4×C373—21no—
79C4×C373C2×D411yescharacteristic
80C4×C373C2411yescharacteristic
81Dic373—21no—
82Dic373—22no—
83Dic373C2×D412yes—
84C2×C373—21no—
85C2×C373—42no—
86C2×C373—41no—
87C2×C373C22×D411yescharacteristic
88D373—22no—
89D373—41no—
90C373#57711yescharacteristic, complemented, Sylow
91#577—3731nomaximal, Sylow
922−1+4—3731no—
93H(5,𝔽2)—3731no—
94#137—3732no—
95#137—3731no—
96AGL(1,ℤ/8)—3732no—
97AGL(1,ℤ/8)D37311yescharacteristic, complemented
98#135—3731no—
99#135—3732no—
100C2×SD16—3731no—
101C2×SD16—3732no—
102#131—3731no—
103#41—3731no—
104#41—3732no—
105#41—3732no—
106#41—3731no—
107#41—7461no—
108#41—7462no—
109#41—7461no—
110#41C2×D37311yescharacteristic, complemented
111C2×Q8—3732no—
112C2×Q8—3731no—
113C2×Q8—7461no—
114C2×D4—3732no—
115C2×D4—7461no—
116C2×D4—7462no—
117C2×D4C2×D37311yescharacteristic
118Q16—3731no—
119Q16—3732no—
120SD16—3731no—
121SD16—3732no—
122SD16—3732no—
123SD16—3731no—
124SD16—3732no—
125SD16C2×D37312yescomplemented
126D8—3731no—
127D8C2×D37312yescomplemented
128M16—3732no—
129M16C2×D37311yescharacteristic, complemented
130C2×C8—3731no—
131C2×C8—3732no—
132C23—21no—
133C23—7462no—
134Q8—3731no—
135Q8—3732no—
136Q8—3731no—
137Q8—7462no—
138Q8—7461no—
139Q8C22×D37311yescharacteristic
140D4—21no—
141D4—21no—
142D4—3732no—
143D4—3731no—
144D4—3731no—
145D4—7462no—
146D4—7462no—
147D4—7462no—
148D4—7461no—
149D4C22×D37311yescharacteristic
150D4C22×D37312yes—
151C2×C4—21no—
152C2×C4—3732no—
153C2×C4—7462no—
154C2×C4—7462no—
155C2×C4—7462no—
156C2×C4—7461no—
157C2×C4—7461no—
158C2×C4C22×D37311yescharacteristic
159C8—3731no—
160C8—3731no—
161C8C22×D37312yes—
162C22—21no—
163C22—22no—
164C22—81no—
165C22—3732no—
166C22—29842no—
167C22—7461no—
168C22D4×D37311yescharacteristic
169C4—21no—
170C4—3732no—
171C4—7461no—
172C4—7462no—
173C4D4×D37311yescharacteristic
174C4C23×D37311yescharacteristic
175C2—21no—
176C2—42no—
177C2—41no—
178C2—14921no—
179C2—7462no—
180C2C2×D4×D37311yescharacteristic
subgroupG/H
centerC2C2×D4×D373
commutator, cosocleC4×C373C24
FrattiniC4C23×D373
FittingAGL(1,ℤ/8)×C373C2
socleC2×C373C22×D4
hypercenterAGL(1,ℤ/8)D373
hypocenterC373#577
LCSG ▷ C4×C373 ▷ C2×C373 ▷ C373
UCSC1 ◁ C2 ◁ C2×C4 ◁ AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. #26045839C2semidirect
2. #26045837C2semidirect
3. #26045825C2semidirect
4. #26045821C2semidirect
5. #26045816C2semidirect
6. #26045812C2semidirect
7. #26045811C2semidirect
8. C2×#20238598C2semidirect
9. SD16×D373C2semidirect
10. #26045800C2semidirect
11. AGL(1,ℤ/8)×C373C2semidirect
18. #20238609C22semidirect
20. C2×Dic746C22semidirect
21. Q8×D373C22semidirect
25. Dic1492C22semidirect
26. #20238600C22semidirect
27. #20238599C22semidirect
28. #20238598C22semidirect
29. #20238598C22semidirect
30. #20238598C22semidirect
31. #20238597C22semidirect
32. #20238595C22semidirect
33. #20238593C22semidirect
34. C2×#15688412C22semidirect
35. C8×D373C22semidirect
36. #41×C373C22semidirect
38. SD16×C373C22semidirect
39. D8×C373C22semidirect
40. M16×C373C22semidirect
90. C373#577semidirect
97. AGL(1,ℤ/8)D373semidirect
110. #41C2×D373semidirect
125. SD16C2×D373semidirect
127. D8C2×D373semidirect
129. M16C2×D373semidirect

Maximal subgroups

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

subgroupindex
#260458392
#260458372
#260458252
#260458212
#260458162
#260458122
#260458112
C2×#202385982
SD16×D3732
#260458002
AGL(1,ℤ/8)×C3732
#577373