Finite Group Databasebeta

← #15685190

Subgroups — #15685190

Order 2944.

460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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#13093223C214yesmaximal, complemented
2#13092677C214yesmaximal, complemented
3#13092599C212yesmaximal, complemented
4#13092584C212yesmaximal, complemented
5#13092535C212yesmaximal, complemented
6C23×#492C211yesmaximal, characteristic, complemented
7#10625158C2212yes—
8#10625155C2212yescomplemented
9C2×SD16×C23C2214yescomplemented
10C23×C4⋊Q8C2211yescharacteristic, complemented
11C23×#127C2211yescharacteristic
12#10625113C2214yescomplemented
13#10625103C2214yes—
14#10625087—24no—
15#10625086—24no—
16#10625085—24no—
17SD16×D23—24no—
18#10625075C2212yes—
19#10625072C2214yescomplemented
20C4×C8×C23C2211yescharacteristic, complemented
21#10625018C2212yescomplemented
22#10625015C2212yescomplemented
23#10625001C2212yescomplemented
24#10624987C2214yescomplemented
25C2×Q8×C23C2312yes—
26C2×D4×C23—41no—
27C2×D4×C23C2312yes—
28C2×C22⋊D23—42no—
29#67292—24no—
30Q8×D23—24no—
31#67290—24no—
32D4×D23—24no—
33#67288—42no—
34#67288C2314yes—
35SD16×C23—24no—
36SD16×C23—24no—
37C2×C8×C23C2312yes—
38C4⋊C4×C23—41no—
39C42×C23C2311yescharacteristic
40#67275—24no—
41#67274—24no—
42#67273—24no—
43#67272—24no—
44#67267C2314yes—
45Dic92D412yescomplemented
46D184D412yescomplemented
47#67263D414yescomplemented
48#67262—24no—
49C8×D23—24no—
50C23×C23—22no—
51C22×D23—42no—
52Q8×C23—24no—
53D4×C23—24no—
54D4×C23—82no—
55C2×C4×C23—21no—
56C2×C4×C23—22no—
57C2×C4×C23C2411yescharacteristic
58C22⋊D23—24no—
59C22⋊D23—44no—
60C2×Dic23—42no—
61D92—42no—
62D92C2×D414yes—
63C4×D23—24no—
64C4×D23—44no—
65Dic46—42no—
66Dic46C2×D414yes—
67C8×C23C2×D412yes—
68C8×C23C2×D412yes—
69C23⋊C8—24no—
70#3291—231nomaximal, Sylow
71C22×C23—42no—
72C22×C23—82no—
73C22×C23H(5,𝔽2)11yescharacteristic
74C2×D23—24no—
75C2×D23—162no—
76C4×C23—22no—
77C4×C23—42no—
78C4×C23C22×D412yes—
79Dic23—24no—
80#577—234no—
81#492D2311yescharacteristic, complemented
82#471—234no—
83#456—232no—
84#453—232no—
85#443—232no—
86C2×C23—21no—
87C2×C23—82no—
88C2×C23D4211yescharacteristic
89D23—44no—
902−1+4—232no—
91H(5,𝔽2)—232no—
92#137—234no—
93#137—464no—
94AGL(1,ℤ/8)—234no—
95AGL(1,ℤ/8)—464no—
96#135—232no—
97#135—464no—
98C2×SD16—464no—
99C2×SD16C2×D2314yescomplemented
100#131—234no—
101C4⋊Q8C2×D2311yescharacteristic, complemented
102#127C2×D2311yescharacteristic
103#108—232no—
104#104—234no—
105#101—232no—
106#100—232no—
107C4×C8C2×D2311yescharacteristic, complemented
108C23#329111yescharacteristic, complemented, Sylow
109#41—234no—
110#41—464no—
111#41—464no—
112#41—922no—
113C2×Q8—464no—
114C2×Q8C22×D2312yes—
115C2×D4—41no—
116C2×D4—464no—
117C2×D4—922no—
118C2×D4C22×D2312yes—
119Q16—232no—
120Q16—464no—
121SD16—24no—
122SD16—24no—
123SD16—234no—
124SD16—464no—
125SD16—464no—
126D8—232no—
127D8—464no—
128M16—234no—
129M16—464no—
130C2×C8—464no—
131C2×C8C22×D2312yes—
132C4⋊C4—41no—
133C42C22×D2311yescharacteristic
134C23—22no—
135C23—922no—
136Q8—24no—
137Q8—234no—
138Q8—922no—
139D4—24no—
140D4—82no—
141D4—234no—
142D4—464no—
143D4—922no—
144D4—924no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—464no—
148C2×C4—924no—
149C2×C4—922no—
150C2×C4C23×D2311yescharacteristic
151C8—464no—
152C8D4×D2312yes—
153C8D4×D2312yes—
154C22—42no—
155C22—82no—
156C22—464no—
157C22—3682no—
158C22#1062515511yescharacteristic
159C4—22no—
160C4—42no—
161C4—464no—
162C4C2×D4×D2312yes—
163C2—21no—
164C2—82no—
165C2—924no—
166C2#1309305211yescharacteristic
subgroupG/H
centerC2#13093052
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#492C2
socleC2×C23D42
hypercenter#492D23
hypocenterC23#3291
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #13093223C2semidirect
2. #13092677C2semidirect
3. #13092599C2semidirect
4. #13092584C2semidirect
5. #13092535C2semidirect
6. C23×#492C2semidirect
8. #10625155C22semidirect
9. C2×SD16×C23C22semidirect
10. C23×C4⋊Q8C22semidirect
12. #10625113C22semidirect
19. #10625072C22semidirect
20. C4×C8×C23C22semidirect
21. #10625018C22semidirect
22. #10625015C22semidirect
23. #10625001C22semidirect
24. #10624987C22semidirect
45. Dic92D4semidirect
46. D184D4semidirect
47. #67263D4semidirect
81. #492D23semidirect
99. C2×SD16C2×D23semidirect
101. C4⋊Q8C2×D23semidirect
107. C4×C8C2×D23semidirect
108. C23#3291semidirect

Maximal subgroups

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

subgroupindex
#130932232
#130926772
#130925992
#130925842
#130925352
C23×#4922
#329123