Finite Group Databasebeta

← #13093214

Subgroups — #13093214

Order 1472.

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

normal subgroups only

This group has 262 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#41×D23C212yesmaximal, complemented
2C23×#135C211yesmaximal, characteristic, complemented
3#10625121C212yesmaximal, complemented
4#10625089C212yesmaximal, complemented
5#10625086C212yesmaximal, complemented
6#10625085C212yesmaximal, complemented
7#10625082C212yesmaximal, complemented
8#10625075C211yesmaximal, characteristic, complemented
9C2×#67262C211yesmaximal, characteristic, complemented
10#41×C23C2212yescomplemented
11#67292C2212yes—
12Q8×D23C2212yescomplemented
13#67290—22no—
14#67290C2212yes—
15D4×D23—22no—
16D4×D23C2212yescomplemented
17#67288—22no—
18#67288C2212yescomplemented
19C2×C4×D23—22no—
20C2×C4×D23C2211yescharacteristic
21Q16×C23C2211yescharacteristic, complemented
22SD16×C23C2212yescomplemented
23D8×C23C2211yescharacteristic, complemented
24C2×C8×C23C2211yescharacteristic, complemented
25#67275C2212yescomplemented
26#67274C2212yescomplemented
27#67273C2212yescomplemented
28#67272C2212yescomplemented
29C2×C23⋊C8C2211yescharacteristic, complemented
30Dic92C2211yescharacteristic, complemented
31D184C2211yescharacteristic, complemented
32#67263C2212yescomplemented
33#67262C2212yescomplemented
34#67262C2212yescomplemented
35C22×D23—22no—
36C22×D23D411yescharacteristic
37Q8×C23C2312yes—
38D4×C23—22no—
39D4×C23C2312yes—
40C2×C4×C23—22no—
41C2×C4×C23C2311yescharacteristic
42C22⋊D23—22no—
43C22⋊D23—22no—
44C22⋊D23—22no—
45C2×Dic23—22no—
46C2×Dic23D411yescharacteristic
47D92—22no—
48D92C2312yes—
49C4×D23—22no—
50C4×D23—22no—
51C4×D23—22no—
52C4×D23D412yes—
53C4×D23C2312yes—
54Dic46—22no—
55Dic46C2312yes—
56C8×C23C2311yescharacteristic
57C8×C23C2311yescharacteristic
58C23⋊C8C2312yes—
59C22×C23—22no—
60C22×C23C2×D411yescharacteristic
61C2×D23—22no—
62C2×D23—41no—
63C2×D23—44no—
64C2×D23C2×D412yes—
65C4×C23—22no—
66C4×C23C2×D411yescharacteristic
67C4×C23C2411yescharacteristic
68Dic23—22no—
69Dic23C2×D412yes—
70#575—231nomaximal, Sylow
71C2×C23—21no—
72C2×C23—42no—
73C2×C23C22×D411yescharacteristic
74D23—22no—
75D23—42no—
76C2×#41—232no—
77#137—232no—
78#137—232no—
79AGL(1,ℤ/8)—232no—
80AGL(1,ℤ/8)—232no—
81#135—232no—
82#135—231no—
83#135D2311yescharacteristic, complemented
84C2×M16—231no—
85C23#57511yescharacteristic, complemented, Sylow
86#41—232no—
87#41—232no—
88#41—232no—
89#41—462no—
90#41—462no—
91#41C2×D2312yescomplemented
92C2×Q8—232no—
93C2×D4—232no—
94C2×D4—462no—
95C22×C4—231no—
96C22×C4—462no—
97Q16—232no—
98Q16—231no—
99Q16C2×D2311yescharacteristic, complemented
100SD16—232no—
101SD16—232no—
102SD16—232no—
103SD16C2×D2312yescomplemented
104D8—232no—
105D8—231no—
106D8C2×D2311yescharacteristic, complemented
107M16—232no—
108M16—232no—
109C2×C8—231no—
110C2×C8C2×D2311yescharacteristic, complemented
111C23—231no—
112C23—462no—
113Q8—232no—
114Q8—462no—
115Q8C22×D2312yes—
116D4—22no—
117D4—232no—
118D4—462no—
119D4—462no—
120D4—462no—
121D4—462no—
122D4C22×D2312yes—
123C2×C4—22no—
124C2×C4—231no—
125C2×C4—232no—
126C2×C4—232no—
127C2×C4—462no—
128C2×C4—462no—
129C2×C4—462no—
130C2×C4—462no—
131C2×C4C22×D2311yescharacteristic
132C8—232no—
133C8C22×D2311yescharacteristic
134C8C22×D2311yescharacteristic
135C22—22no—
136C22—232no—
137C22—462no—
138C22—921no—
139C22—924no—
140C22D4×D2311yescharacteristic
141C4—22no—
142C4—232no—
143C4—462no—
144C4D4×D2311yescharacteristic
145C4C23×D2311yescharacteristic
146C2—21no—
147C2—42no—
148C2—462no—
149C2—922no—
150C2C2×D4×D2311yescharacteristic
subgroupG/H
centerC4D4×D23
commutator, cosocleC4×C23C24
FrattiniC4C23×D23
FittingC23×#135C2
socleC2×C23C22×D4
hypercenter#135D23
hypocenterC23#575
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

Complements

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

NH ≅ G/Ntype
1. #41×D23C2semidirect
2. C23×#135C2semidirect
3. #10625121C2semidirect
4. #10625089C2semidirect
5. #10625086C2semidirect
6. #10625085C2semidirect
7. #10625082C2semidirect
8. #10625075C2semidirect
9. C2×#67262C2semidirect
10. #41×C23C22semidirect
12. Q8×D23C22semidirect
16. D4×D23C22semidirect
18. #67288C22semidirect
21. Q16×C23C22semidirect
22. SD16×C23C22semidirect
23. D8×C23C22semidirect
24. C2×C8×C23C22semidirect
25. #67275C22semidirect
26. #67274C22semidirect
27. #67273C22semidirect
28. #67272C22semidirect
29. C2×C23⋊C8C22semidirect
30. Dic92C22semidirect
31. D184C22semidirect
32. #67263C22semidirect
33. #67262C22semidirect
34. #67262C22semidirect
83. #135D23semidirect
85. C23#575semidirect
91. #41C2×D23semidirect
99. Q16C2×D23semidirect
103. SD16C2×D23semidirect
106. D8C2×D23semidirect
110. C2×C8C2×D23semidirect

Maximal subgroups

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

subgroupindex
#41×D232
C23×#1352
#106251212
#106250892
#106250862
#106250852
#106250822
#106250752
C2×#672622
#57523