Finite Group Databasebeta

← #13093223

Subgroups — #13093223

Order 1472.

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#10625158C211yesmaximal, characteristic, complemented
2#10625155C211yesmaximal, characteristic, complemented
3C2×SD16×C23C211yesmaximal, characteristic, complemented
4#10625113C211yesmaximal, characteristic, complemented
5#10625103C211yesmaximal, characteristic, complemented
6#10625087C212yesmaximal, complemented
7#10625086C212yesmaximal, complemented
8#10625085C212yesmaximal, complemented
9SD16×D23C212yesmaximal, complemented
10#10625075C211yesmaximal, characteristic, complemented
11#10625072C211yesmaximal, characteristic, complemented
12C2×Q8×C23C2211yescharacteristic, complemented
13C2×D4×C23C2211yescharacteristic
14C2×C22⋊D23—22no—
15#67292—21no—
16#67292C2212yescomplemented
17Q8×D23—21no—
18Q8×D23C2212yescomplemented
19#67290—21no—
20#67290C2212yes—
21D4×D23—21no—
22D4×D23C2212yes—
23#67288—22no—
24#67288C2211yescharacteristic
25#67288C2211yescharacteristic
26#67288C2211yescharacteristic, complemented
27SD16×C23C2212yescomplemented
28SD16×C23C2212yescomplemented
29C2×C8×C23C2211yescharacteristic, complemented
30#67275C2212yescomplemented
31#67274C2212yescomplemented
32#67273C2212yescomplemented
33#67272C2212yescomplemented
34#67267C2211yescharacteristic, complemented
35Dic92C2211yescharacteristic, complemented
36D184C2211yescharacteristic, complemented
37#67263C2211yescharacteristic, complemented
38#67263C2211yescharacteristic, complemented
39#67262C2212yescomplemented
40C8×D23C2212yescomplemented
41C23×C23—21no—
42C22×D23—22no—
43Q8×C23—21no—
44Q8×C23C2312yes—
45D4×C23—21no—
46D4×C23C2312yes—
47C2×C4×C23—21no—
48C2×C4×C23C2311yescharacteristic
49C22⋊D23—21no—
50C22⋊D23—21no—
51C22⋊D23—22no—
52C22⋊D23—22no—
53C22⋊D23D412yes—
54C2×Dic23—22no—
55D92—22no—
56D92D411yescharacteristic
57D92C2311yescharacteristic
58D92C2311yescharacteristic
59C4×D23—22no—
60C4×D23—21no—
61C4×D23—21no—
62C4×D23—22no—
63C4×D23C2312yes—
64Dic46—22no—
65Dic46D411yescharacteristic
66Dic46C2311yescharacteristic
67Dic46C2311yescharacteristic
68C8×C23C2311yescharacteristic
69C8×C23C2311yescharacteristic
70C23⋊C8C2312yes—
71C22×C23—22no—
72C22×C23—81no—
73C22×C23C2×D411yescharacteristic
74C2×D23—21no—
75C2×D23—21no—
76C2×D23—82no—
77C2×D23C2×D412yes—
78C4×C23—22no—
79C4×C23C2×D411yescharacteristic
80C4×C23C2411yescharacteristic
81Dic23—21no—
82Dic23—21no—
83Dic23C2×D412yes—
84#577—231nomaximal, Sylow
85C2×C23—21no—
86C2×C23—42no—
87C2×C23C22×D411yescharacteristic
88D23—22no—
89D23—41no—
90D23—41no—
912−1+4—231no—
92H(5,𝔽2)—231no—
93#137—231no—
94#137—232no—
95AGL(1,ℤ/8)—231no—
96AGL(1,ℤ/8)—232no—
97#135—232no—
98#135—231no—
99C2×SD16—232no—
100C2×SD16D2311yescharacteristic, complemented
101#131—231no—
102C23#57711yescharacteristic, complemented, Sylow
103#41—231no—
104#41—232no—
105#41—232no—
106#41—231no—
107#41—231no—
108#41—462no—
109#41—461no—
110#41—461no—
111C2×Q8—232no—
112C2×Q8—461no—
113C2×Q8C2×D2311yescharacteristic, complemented
114C2×D4—232no—
115C2×D4—461no—
116C2×D4—462no—
117C2×D4C2×D2311yescharacteristic
118Q16—232no—
119Q16—231no—
120SD16—232no—
121SD16—232no—
122SD16—231no—
123SD16—231no—
124SD16C2×D2312yescomplemented
125SD16C2×D2312yescomplemented
126D8—232no—
127D8—231no—
128M16—231no—
129M16—232no—
130C2×C8—232no—
131C2×C8C2×D2311yescharacteristic, complemented
132C23—21no—
133C23—462no—
134Q8—21no—
135Q8—231no—
136Q8—231no—
137Q8—231no—
138Q8—462no—
139Q8C22×D2312yes—
140D4—21no—
141D4—232no—
142D4—231no—
143D4—231no—
144D4—231no—
145D4—462no—
146D4—462no—
147D4—462no—
148D4—461no—
149D4—461no—
150D4C22×D2312yes—
151C2×C4—21no—
152C2×C4—232no—
153C2×C4—462no—
154C2×C4—462no—
155C2×C4—462no—
156C2×C4—461no—
157C2×C4—461no—
158C2×C4C22×D2311yescharacteristic
159C8—232no—
160C8C22×D2311yescharacteristic
161C8C22×D2311yescharacteristic
162C22—22no—
163C22—81no—
164C22—232no—
165C22—461no—
166C22—461no—
167C22—1842no—
168C22D4×D2311yescharacteristic
169C4—22no—
170C4—232no—
171C4—461no—
172C4—461no—
173C4D4×D2311yescharacteristic
174C4C23×D2311yescharacteristic
175C2—21no—
176C2—42no—
177C2—462no—
178C2—921no—
179C2—921no—
180C2C2×D4×D2311yescharacteristic
subgroupG/H
centerC2C2×D4×D23
commutator, cosocleC4×C23C24
FrattiniC4C23×D23
FittingC2×SD16×C23C2
socleC2×C23C22×D4
hypercenterC2×SD16D23
hypocenterC23#577
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #10625158C2semidirect
2. #10625155C2semidirect
3. C2×SD16×C23C2semidirect
4. #10625113C2semidirect
5. #10625103C2semidirect
6. #10625087C2semidirect
7. #10625086C2semidirect
8. #10625085C2semidirect
9. SD16×D23C2semidirect
10. #10625075C2semidirect
11. #10625072C2semidirect
12. C2×Q8×C23C22semidirect
16. #67292C22semidirect
18. Q8×D23C22semidirect
26. #67288C22semidirect
27. SD16×C23C22semidirect
28. SD16×C23C22semidirect
29. C2×C8×C23C22semidirect
30. #67275C22semidirect
31. #67274C22semidirect
32. #67273C22semidirect
33. #67272C22semidirect
34. #67267C22semidirect
35. Dic92C22semidirect
36. D184C22semidirect
37. #67263C22semidirect
38. #67263C22semidirect
39. #67262C22semidirect
40. C8×D23C22semidirect
100. C2×SD16D23semidirect
102. C23#577semidirect
113. C2×Q8C2×D23semidirect
124. SD16C2×D23semidirect
125. SD16C2×D23semidirect
131. C2×C8C2×D23semidirect

Maximal subgroups

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

subgroupindex
#106251582
#106251552
C2×SD16×C232
#106251132
#106251032
#106250872
#106250862
#106250852
SD16×D232
#106250752
#106250722
#57723