Finite Group Databasebeta

← #15683849

Subgroups — #15683849

Order 2944.

656 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#10625079C214yesmaximal, complemented
2#13092967C211yesmaximal, characteristic, complemented
3C2×#10625045C211yesmaximal, characteristic, complemented
4#13092806C214yesmaximal, complemented
5#13092794C212yesmaximal, complemented
6#13092790C212yesmaximal, complemented
7C4×M16×C23C211yesmaximal, characteristic, complemented
8C2×#67288C2212yes—
9C22×D92—22no—
10C22×D92C2212yes—
11C2×M16×C23C2212yes—
12C2×C42×C23C2211yescharacteristic
13#10625101—22no—
14#10625079—216no—
15C2×D184C2218yescomplemented
16C2×#67263C2218yescomplemented
17#10625046C2212yescomplemented
18#10625045—22no—
19#10625045C2212yes—
20#10625045C2212yes—
21#10625045C2211yescharacteristic, complemented
22C4×D92—22no—
23#10625040C2211yescharacteristic, complemented
24C23×#97C2212yescomplemented
25C4×C8×C23C2212yescomplemented
26C23×D23—22no—
27C22×C4×C23D412yes—
28C22×C4×C23C2311yescharacteristic
29C2×C22⋊D23—22no—
30#67288—28no—
31C2×D92—28no—
32C2×D92—22no—
33C2×D92—22no—
34C2×D92—24no—
35C2×D92—24no—
36C2×D92—48no—
37C2×D92C2314yes—
38C2×D92C2312yes—
39C2×C4×D23—22no—
40C2×Dic46C2312yes—
41M16×C23D418yescomplemented
42C2×C8×C23C2314yes—
43C42×C23D412yes—
44C42×C23C2311yescharacteristic
45C42×C23C2311yescharacteristic
46(C2×D23)⋊C4—24no—
47C4⋊Dic23—22no—
48D184—216no—
49#67263—216no—
50C23×C23C2×D411yescharacteristic
51C22×D23—22no—
52C22×D23—24no—
53C22×D23—48no—
54C22×D23—44no—
55C2×C4×C23—24no—
56C2×C4×C23C2×D412yes—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D414yes—
59C2×C4×C23C2×D412yes—
60C2×C4×C23C2411yescharacteristic
61C22⋊D23—44no—
62C2×Dic23—22no—
63D92—28no—
64D92—24no—
65D92—48no—
66D92—44no—
67D92—44no—
68D92—48no—
69C4×D23—44no—
70Dic46—24no—
71C8×C23C2×D418yescomplemented
72#3151—231nomaximal, Sylow
73C22×C23—22no—
74C22×C23#12712yes—
75C22×C23C22×D411yescharacteristic
76C2×D23—42no—
77C2×D23—44no—
78C2×D23—48no—
79C2×D23—44no—
80C2×D23—88no—
81C4×C23—22no—
82C4×C23#12712yes—
83C4×C23AGL(1,ℤ/8)14yescomplemented
84C4×C23C22×D412yes—
85Dic23—42no—
86C2×AGL(1,ℤ/8)—234no—
87#532—231no—
88C2×#127—231no—
89#496—234no—
90#493—232no—
91#492—232no—
92C4×M16D2311yescharacteristic, complemented
93C2×C23—22no—
94C2×C23C2×#12711yescharacteristic
95C2×C23C2×AGL(1,ℤ/8)12yes—
96D23—82no—
97D23—84no—
98C2×#41—232no—
99C22×D4—232no—
100C22×D4—462no—
101AGL(1,ℤ/8)—4616no—
102C2×SD16—238no—
103C2×D8—238no—
104C2×M16C2×D2312yes—
105C4⋊Q8—231no—
106#127—232no—
107#127—232no—
108#127—231no—
109#127—462no—
110#124—232no—
111#121—462no—
112C4×D4—462no—
113C2×C42C2×D2311yescharacteristic
114#97C2×D2312yescomplemented
115C4×C8C2×D2312yescomplemented
116C23#315111yescharacteristic, complemented, Sylow
117C24—462no—
118#41—468no—
119C2×Q8—232no—
120C2×D4—232no—
121C2×D4—234no—
122C2×D4—462no—
123C2×D4—468no—
124C2×D4—462no—
125C2×D4—464no—
126C2×D4—464no—
127C2×D4—462no—
128C2×D4—928no—
129C22×C4—462no—
130C22×C4D9212yes—
131C22×C4C22×D2311yescharacteristic
132SD16—4616no—
133D8—4616no—
134M16D9218yescomplemented
135C2×C8C22×D2314yes—
136C4⋊C4—462no—
137C22⋊C4—464no—
138C42D9212yes—
139C42C22×D2311yescharacteristic
140C42C22×D2311yescharacteristic
141C23—462no—
142C23—464no—
143C23—928no—
144C23—924no—
145C23C2×D9211yescharacteristic
146Q8—464no—
147D4—464no—
148D4—468no—
149D4—928no—
150D4—924no—
151D4—924no—
152D4—928no—
153D4—924no—
154C2×C4—24no—
155C2×C4—462no—
156C2×C4—924no—
157C2×C4C2×D9212yes—
158C2×C4C2×D9211yescharacteristic
159C2×C4C2×D9214yes—
160C2×C4C2×D9212yes—
161C2×C4C23×D2311yescharacteristic
162C8C2×D9218yescomplemented
163C22—22no—
164C22—928no—
165C22—924no—
166C22—922no—
167C22—924no—
168C22—1848no—
169C22#1062504512yes—
170C22C22×D9211yescharacteristic
171C4—22no—
172C4—922no—
173C4#1062504512yes—
174C4#1062507914yescomplemented
175C4C22×D9212yes—
176C2—22no—
177C2—1844no—
178C2—1842no—
179C2C2×#1062504511yescharacteristic
180C2C2×#1062507912yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC4×M16×C23C2
socleC22×C23C22×D4
hypercenterC4×M16D23
hypocenterC23#3151
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#10625079C2semidirect
2. #13092967C2semidirect
3. C2×#10625045C2semidirect
4. #13092806C2semidirect
5. #13092794C2semidirect
6. #13092790C2semidirect
7. C4×M16×C23C2semidirect
15. C2×D184C22semidirect
16. C2×#67263C22semidirect
17. #10625046C22semidirect
21. #10625045C22semidirect
23. #10625040C22semidirect
24. C23×#97C22semidirect
25. C4×C8×C23C22semidirect
41. M16×C23D4semidirect
71. C8×C23C2×D4semidirect
83. C4×C23AGL(1,ℤ/8)semidirect
92. C4×M16D23semidirect
114. #97C2×D23semidirect
115. C4×C8C2×D23semidirect
116. C23#3151semidirect
134. M16D92semidirect
162. C8C2×D92semidirect
174. C4#10625079semidirect

Maximal subgroups

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

subgroupindex
C2×#106250792
#130929672
C2×#106250452
#130928062
#130927942
#130927902
C4×M16×C232
#315123