Finite Group Databasebeta

← #16829944

Subgroups — #16829944

Order 3712.

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×#11745270C214yesmaximal, complemented
2#14271713C211yesmaximal, characteristic, complemented
3C2×#11745236C211yesmaximal, characteristic, complemented
4#14271552C214yesmaximal, complemented
5#14271540C212yesmaximal, complemented
6#14271536C212yesmaximal, complemented
7C4×M16×C29C211yesmaximal, characteristic, complemented
8C2×#90805C2212yes—
9C22×D116—22no—
10C22×D116C2212yes—
11C2×M16×C29C2212yes—
12C2×C42×C29C2211yescharacteristic
13#11745292—22no—
14#11745270—216no—
15C2×D232C2218yescomplemented
16C2×#90773C2218yescomplemented
17#11745237C2212yescomplemented
18#11745236—22no—
19#11745236C2212yes—
20#11745236C2212yes—
21#11745236C2211yescharacteristic, complemented
22C4×D116—22no—
23#11745231C2211yescharacteristic, complemented
24C29×#97C2212yescomplemented
25C4×C8×C29C2212yescomplemented
26C23×D29—22no—
27C22×C4×C29D412yes—
28C22×C4×C29C2311yescharacteristic
29C2×C22⋊D29—22no—
30#90805—28no—
31C2×D116—28no—
32C2×D116—22no—
33C2×D116—24no—
34C2×D116—24no—
35C2×D116—22no—
36C2×D116—48no—
37C2×D116C2314yes—
38C2×D116C2312yes—
39C2×C4×D29—22no—
40C2×Dic58C2312yes—
41M16×C29D418yescomplemented
42C2×C8×C29C2314yes—
43C42×C29D412yes—
44C42×C29C2311yescharacteristic
45C42×C29C2311yescharacteristic
46#90781—24no—
47C4⋊Dic29—22no—
48D232—216no—
49#90773—216no—
50C23×C29C2×D411yescharacteristic
51C22×D29—22no—
52C22×D29—24no—
53C22×D29—48no—
54C22×D29—44no—
55C2×C4×C29—24no—
56C2×C4×C29C2×D412yes—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D414yes—
59C2×C4×C29C2×D412yes—
60C2×C4×C29C2411yescharacteristic
61C22⋊D29—44no—
62C2×Dic29—22no—
63D116—28no—
64D116—24no—
65D116—48no—
66D116—44no—
67D116—44no—
68D116—48no—
69C4×D29—44no—
70Dic58—24no—
71C8×C29C2×D418yescomplemented
72#3151—291nomaximal, Sylow
73C22×C29—22no—
74C22×C29#12712yes—
75C22×C29C22×D411yescharacteristic
76C2×D29—42no—
77C2×D29—44no—
78C2×D29—48no—
79C2×D29—44no—
80C2×D29—88no—
81C4×C29—22no—
82C4×C29#12712yes—
83C4×C29AGL(1,ℤ/8)14yescomplemented
84C4×C29C22×D412yes—
85Dic29—42no—
86C2×AGL(1,ℤ/8)—294no—
87#532—291no—
88C2×#127—291no—
89#496—294no—
90#493—292no—
91#492—292no—
92C4×M16D2911yescharacteristic, complemented
93C2×C29—22no—
94C2×C29C2×#12711yescharacteristic
95C2×C29C2×AGL(1,ℤ/8)12yes—
96D29—82no—
97D29—84no—
98C2×#41—292no—
99C22×D4—292no—
100C22×D4—582no—
101AGL(1,ℤ/8)—5816no—
102C2×SD16—298no—
103C2×D8—298no—
104C2×M16C2×D2912yes—
105C4⋊Q8—291no—
106#127—292no—
107#127—292no—
108#127—291no—
109#127—582no—
110#124—292no—
111#121—582no—
112C4×D4—582no—
113C2×C42C2×D2911yescharacteristic
114#97C2×D2912yescomplemented
115C4×C8C2×D2912yescomplemented
116C29#315111yescharacteristic, complemented, Sylow
117C24—582no—
118#41—588no—
119C2×Q8—292no—
120C2×D4—292no—
121C2×D4—294no—
122C2×D4—582no—
123C2×D4—588no—
124C2×D4—582no—
125C2×D4—584no—
126C2×D4—584no—
127C2×D4—582no—
128C2×D4—1168no—
129C22×C4—582no—
130C22×C4D11612yes—
131C22×C4C22×D2911yescharacteristic
132SD16—5816no—
133D8—5816no—
134M16D11618yescomplemented
135C2×C8C22×D2914yes—
136C4⋊C4—582no—
137C22⋊C4—584no—
138C42D11612yes—
139C42C22×D2911yescharacteristic
140C42C22×D2911yescharacteristic
141C23—582no—
142C23—584no—
143C23—1168no—
144C23—1164no—
145C23C2×D11611yescharacteristic
146Q8—584no—
147D4—584no—
148D4—588no—
149D4—1168no—
150D4—1164no—
151D4—1164no—
152D4—1168no—
153D4—1164no—
154C2×C4—24no—
155C2×C4—582no—
156C2×C4—1164no—
157C2×C4C2×D11612yes—
158C2×C4C2×D11614yes—
159C2×C4C2×D11611yescharacteristic
160C2×C4C2×D11612yes—
161C2×C4C23×D2911yescharacteristic
162C8C2×D11618yescomplemented
163C22—22no—
164C22—1168no—
165C22—1164no—
166C22—1162no—
167C22—1164no—
168C22—2328no—
169C22#1174523612yes—
170C22C22×D11611yescharacteristic
171C4—22no—
172C4—1162no—
173C4#1174523612yes—
174C4#1174527014yescomplemented
175C4C22×D11612yes—
176C2—22no—
177C2—2324no—
178C2—2322no—
179C2C2×#1174523611yescharacteristic
180C2C2×#1174527012yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC4×M16×C29C2
socleC22×C29C22×D4
hypercenterC4×M16D29
hypocenterC29#3151
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#11745270C2semidirect
2. #14271713C2semidirect
3. C2×#11745236C2semidirect
4. #14271552C2semidirect
5. #14271540C2semidirect
6. #14271536C2semidirect
7. C4×M16×C29C2semidirect
15. C2×D232C22semidirect
16. C2×#90773C22semidirect
17. #11745237C22semidirect
21. #11745236C22semidirect
23. #11745231C22semidirect
24. C29×#97C22semidirect
25. C4×C8×C29C22semidirect
41. M16×C29D4semidirect
71. C8×C29C2×D4semidirect
83. C4×C29AGL(1,ℤ/8)semidirect
92. C4×M16D29semidirect
114. #97C2×D29semidirect
115. C4×C8C2×D29semidirect
116. C29#3151semidirect
134. M16D116semidirect
162. C8C2×D116semidirect
174. C4#11745270semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
#142717132
C2×#117452362
#142715522
#142715402
#142715362
C4×M16×C292
#315129